Analytica: Soft Propositional Reasoning for Robust and Scalable LLM-Driven Analysis
Authors: Junyan Cheng
Kyle Richardson
Peter Chin
Venue: ICLR 2026 Poster (2026)
Keywords: Large Languege Models
LLM Agent
Reasoning
Forecast
Primary area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

Abstract: Large language model (LLM) agents are increasingly tasked with complex real-world analysis (e.g., in financial forecasting, scientific discovery), yet their reasoning suffers from stochastic instability and lacks a verifiable, compositional structure. To address this, we introduce **Analytica**, a novel agent architecture built on the principle of **Soft Propositional Reasoning (SPR)**. SPR reframes complex analysis as a structured process of estimating the soft truth values of different outcome propositions, allowing us to formally model and minimize the estimation error in terms of its bias and variance.
Analytica operationalizes this through a parallel, divide-and-conquer framework that systematically reduces both sources of error. To reduce bias, problems are first decomposed into a tree of subpropositions, and tool-equipped LLM *grounder agents* are employed —including a novel Jupyter Notebook agent for data-driven analysis—that help to validate and score facts. To reduce variance, Analytica recursively synthesizes these grounded leaves using robust linear models that average out stochastic noise with superior efficiency, scalability, and enable interactive "what-if" scenario analysis.
Our theoretical and empirical results on economic, financial, and political forecasting tasks show that Analytica improves 15.84\% accuracy on average over diverse base models, achieving 71.06\% accuracy with the lowest variance of 6.02\% when working with a Deep Research grounder. Our Jupyter Notebook grounder shows strong cost-effectiveness that achieves a close 70.11\% accuracy with 90.35\% less cost and 52.85\% less time. Analytica also exhibits highly noise-resilient and stable performance growth as the analysis depth increases, with a near-linear time complexity, as well as good adaptivity to open-weight LLMs and scientific domains.

Published as a conference paper at ICLR 2026
ANALYTICA: SOFT PROPOSITIONAL REASONING FOR ROBUST AND SCALABLE LLM- ANALYSIS
Junyan Cheng Dartmouth College je. th@darrroouutttt edu
Kyle Richardson
Peter Chin Dartmouth College
Allen Institute for Al kylerêal Sereraalleniiooog
ABSTRACT
Large language model (LLM) agents are increasingly tasked with complex real- world analysis (e-g. financial forecasting, scientific discovery). yet their reason- ing suffers from stochastic instability and lacks a verifiable, compositional struc- ture. To address this, we introduce Analytica, novel agent architecture built the principle of Soft Propositional Reasoning (SPR). SPR reframes complex analysis as a structured process of estimating the soft truth values of different out- come propositions, allowing error in terms of its bias and variance. Analytica operationalizes this through a parallel, divide-and-cooques framework that systematically reduces both sources of error. To reduce bias, problems are first decomposed into a tree of subproposi- tions, and tool-equipped LLM grounder agents are employed -including novel Jupyter Notebook agent for data-driven analysis- help to validate and score facts. To reduce variance, Analytica recursively synthesizes these grounded leaves using robust linear models that average out stochastic noise with superior effi- ciency, scalability, and enable interactive "what-if" scenario analysis. Our theo- retical and empirical results on economic, financial, and political forecasting tasks show that Analytica improves 15.84% accuracy on average over diverse base mod- els, achieving 71.06% accuracy with the lowest variance of 6.02% when working with Deep Research grounder. Our Jupyter Notebook grounder shows strong cost-effectiveness that achieves close 70. 11% accuracy with 90.35% less cost and 52.85% less time. Analytica also exhibits highly noise-resilient and stable performance growth the analysis depth increases, with near-lineat time com- plexity, as well as good adaptivity to open-weight LLMs and scientific domains.
formally model and minimize the estimation
INTRODUCTION
Capable LLM agents require foresight: the ability to form, update, and act probabilistic forecasts of future states. For example, effectively answering open open-ended questions in domains like experi- mental science financial forecasting (e.g., What the best way improve the performance of my model on task Y? or What is the best strategy to invest in SNVDDA this year? in Fig. involves pre- dicting the future state of the world via complex information gathering, case analysis, and explicit uncertainty estimation. While considerable progress has been made recently through the develop- ment of new large reasoning models (Jaech et al. 2024 Guo et al., 2025 Comanici al.) 2025) and deep research architectures (Xu & Peng 2025; OpenAl 2025) that explicitly encourage deep analysis through test-time scaling, such approaches fundamentally rely on free-form text reasoning, which often lacks the precision and reliability needed for decision making in many critical areas.
In this paper, we investigate an alternative framework called Soft Propositional Reasoning (SPR) that reframes complex LLM--riven analysis as a structured process of assigning a soft truth value or degree of belief (Huber et al.) 2009) to different possible outcomes. For example, answering the query in Fig. I can be done through deep case analysis on specific outcomes such as Long SNVDA and hold for the year is the best and by decomposing this root hypothesis into testable sub- propositions that be grounded and experimentation) and scored for correctness. Key to our approach is that the degrees of belief (e.g., 0.7 for hypothesis in Fig. [T are computed compositionally from such evidence, which aims
real-world data (e.g. via further information gathering

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Published as a conference paper at ICLR 2026
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Figure 1: Given complex query (e.g., forecasting SNVDA), Analytica selects the most plausible outcome by estimating the "soft truth value" of each provided competing proposition (Green box). The analysis process begins when an analyzer agent decomposes proposition into tree of sub- propositions (Orange box), terminating is a set of testable leaf nodes. Next, grounder agents, such as a Jupyter Notebook agent mimicking a human analyst, evaluate the leaves (Purple box) and assign soft scores that reflect the evidence for each leaf. Finally, synthesis stage recursively aggregates these scores up the tree (middle) to compute a final score for the root proposition.
to strike a balance between pure text-based reasoning and traditional relational and probabilistic approaches to Al (De Raedt et al., 2007 Richardson & Domingos 2006 Koller & Friedman 2009).
We investigate the SPR framework through a new LLM-agent architecture called Analytica that employs a highly parallel, three-stage divide-and-conquer strategy. As illustrated in Fig. D. a given hypothesis is first automatically decomposed into a tree of sub-hypotheses through an analysis stage, which, by design, terminates in a set of testable Icaf nodes or hypotheses. This is followed by grounding stage, in which tool-equipped L.LM agents validate and score the leaf hypotheses through further search and experimentation. For example, our most powerful grounder agents simulate hu- man analysts by working with the Jupyter notebook environments that facilitate web-based and data-driven analysis (e.g., via research APIs), generic code writing in Python (e.g., for running simulations), and report writing (e.g., using markdown blocks). The scores of leaf nodes are then recursively propagated up to the root through synthesis stage and aggregation function f. For example, our best synthesis strategy involves taking a linear combination of mroduu-poducedd con- fidences coupled with additional linear coefficients (as illustrated in the tree edges in Fig. D). which we show through first principles helps average out stochastic noise and minimize forecast variance.
We empirically test our approach on 736 real- world economies and financial forecasting challenges, which naturally take the form of true/false proposition prediction (e.g.. making yes/no long-short equity predictions in financial markets and future predictions in polymarkets) and have recently been shown to be promising testbed for evaluating the general forecasting and reasoning abilities of L.MMs (?Schoenegger & Park, 2023; Tan al. 2024, Zeng et al. 2025 Paleka al. [025 inter alia). Compared with several text- based reasoning baselines, including advanced variants of chain- of-thought (Wei et al., 2022 Yao et al. 2023; Besta et al.) 2024 Bi et al. 2025), as well as the deep research agent of [ our best variant of Analytica achieves an average 15.84% improvement in end-task prediction accuracy. Analytica with Jupyter Notebook agents in particular demonstrates strong cost-effectiveness, reaching the near-highest accuracy of 70. 10.11% 11% with 90.35% less budget and 52.85% less time. Furthermore, Analytica displays impressive scalability, handling exponential growth in analytical complexity (e.g., 54x more nodes) with only near-linear rise in computation time (12x), while the performance shows a stable improvement over the analysis depth, highlighting the high practicality and potential of our proposed framework. We also show how Analytica exhibits good adaptivity to smaller open-weight models as well as other domains such as scientific claim verification (Jansen al. 2025a). Our code and data are available at hotps: //github. com/ www/cheno/ca.cccc Junaanl analytica
RELATED WORK
Structured Reasoning in LLMs Our work takes inspiration from the large literature on modular
and decomposition-baased reasoning architectures (Andreas al. 2016 Khot et al.; 2021 2023
2

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Published as a conference paper at ICLR 2026
Talmor & Berant 2018 Zhou et al., 2022 inter alia), well as more recent variants of chain-
of-thought reasoning (Wei et al. 2022 Yao et al. 2023 Besta et al. 2024: Yang et al. 2024 Aytes et al. 2025) and deep research agents (OpenAl |025] Xu & Peng 2025 all of which aim to improve the robustness and scalability of neural reasoning through problem decomposition, test-time scaling (Snell et al. 2024) and tool use. As discussed above, however, much of this work operates mostly in a discrete text space, whereas Analytica focuses on reasoning in a soft propositional space and attempts to integrate model confidences more directly into the process of aggregating reasoning paths (see Cao et al. (2023) and quantifying an agent's 's degree of belief (see Chen et al. (2024))
LLM Agents for Real-world Analysis We also fo- cus on the growing body of work using LLM agents to tackle wide range of open-ended analysis tasks, such as societal dynamics (Cheng & Chin (024a), fi-
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(Li et al.) 2024). predictive markets (Halawi et al. 2024), general data analysis (Majumder et al., 2025
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Gottweis al. 2025: Jansen al.] 2025b)
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et al. 2025). among others. While our overall anal- ysis framework is domain agnostic, we focus on fore- casting problems in economics, finance, and politics due their high uncertainty, difficulty, and richness of data (Zou et al.
P_true of "Long NVDA year better short"
Figure 2:
An illustration of estimation vari- ance and bias. Analytica with a linear rule has lower bias (closer to the ground truth of 1) and variance. Hitting a better trade-off.
2022
Chen et al. [2023) Tan et al.
2024
Karger et al. 2024 Wildman et al. 2025)
Hybrid LLM Reasoning Finally, our approach re-
lates to many recent attempts to enhance the reasoning
power of LLMs with classical relational and probabilistic methods Olausson al. (2023); ); Pan et al.
2023 Li et al. 2025); | Cheng et al. (2023), often by integrating symbolic solvers into the reasoning
pipelime or using LLMs to produce symbolic representations. Rather than directly incorporating
plicit solvers into our reasoning pipeline, we instead follow other work in neuro-symbel ncuro-symbolic modeling on distilling model behavior classical models (e.g., tractable probabilistic models, PGMs) (Zhang
et al., 2024) Qiu et al., 2025) Feng et al.] [2025] Dohan et al., [022]] Cheng & Chin (024b). in our case, interpreting LLM and agent outputs as if-then structures that we reason over using soft and
noisy relaxations of both model beliefs and the logical operators used to combine beliefs.
3 SOFT PROPOSITIONAL REASONING
The objective soft proposition reasoning (SPR) is to accurately estimate the soft truth value of a complex proposition, Pirwe- A robust agent is one that minimizes the expected error of this estimate. To formalize this, we consider the Mean Squared Error (MSE) of the forecast, which is the expected squared difference between the estimate and the ground truth value:
MSE(ptrue) = E [Ptrue -Pr
[E[ptrue]
Pirue) + E [Perue - E E[ptreel)?
(I)
Bias
The expectation E|-] is taken over the randomness in the agent's 's reasoning process (e.g., model sampling stochasticity, variations in tool outputs). This total error can therefore be standardly de- composed into two distinct sources: bias and variance.
Accordingly, a robust analysis must systematically minimize both bias and variance. The compo- sitional nature of complex problems from SPR provides foundation to address this challenge, which assumes that the truthfulness of a complex proposition is recursively supported by a set of child propositions, e.g., the truth of "NVIDIA's revenue will beat consensus" is function of its underlying evidential drivers (e.g., "AI capex is rising"), as depicted in Fig. [ That is, Pp-Perue {(e, Ptrru...... Pe.. Pe..Preee)) The synthesis rule can be a flexible and arbitrary function f: [0, 1j" - [0, 1]. We develop the Analytica architecture based on SPR(S 4 where Bias is miti- gated by reducing the original complex query simple leaves which are relatively simple to process
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Ground. & Synthesis (Alg. 2) "Nios-free" lnver
Amalyticaapp): T Analyze(pp) synthesize roat) return T
Legend Ungrounded
00.
Grounded
Analysis Stage (Alg.
Boot node
Leaf node
Non-leaf
① Input proposition Po root node
Expand until reach limits
Grounders ground leaves parallel
Synthesize non-
Terminate until reaching root node
Updated
leaves recursively
Figure: 3: Illustration Analytica. First, in the Analysis Stage (Alg. [ a root proposition is recur- sively decomposed into tree of sub-propositions (Steps 1-2). This is followed by the Grounding and Synthesis Stages (Alg. 2 a bottom-up process where (Step 3) Grounder agents evaluate all leaf nodes parallel to assign soft truth values, and (Steps 4-5) Synthesizer recursively aggregates these grounded values the tree until final, robust estimate for the root is computed.
by the powerful Grounder agents; V Variance is reduced during synthesis, where an Analyzer and Synthesizer work in concert with robust linear synthesis rule average out the stochastic noise from many subproblems, ensuring stable error propagation. Fig. 2 shows that Analytica effectively decreases both variance (tighter distribution) and bias (mean closer the ground truth).
Comparison with CoT and its variants This results in a recursive, divide-and-conquer strategy for problem solving, which differs from existing structured reasoning methods that center around linear reasoning paths. In the standard Chain of- Thought (CoT) (Wei et al. (2022). the model generates a linear sequence of tokens = fro...., [n) to derive a final output. Advanced approaches like Tree-of- Tree-of-Thought Thoughts (ToT) (aao et al. 2023) and Graph-of- ofaph-of-Thoughts (GoT) Besta et al. (2024) search for an optimal path R" by maximizing heuristic L.L.-based valuation function V(R):
ÿ = fI, R*) where
R
arg max V(R).
Paths
where FLLM is the call to LLM generation, Forest-of- (FoT) (Bi et al. 2025 further extending this by aggregating results from multiple trees, i.e. ÿ = Aggr( (f (z, R;) ) which is conceptually related our synthesis mechanism. However, instead of aggregating different reasoning paths for the same problem, we aggregate results from different subproblems recursively, i..., y Aggr( ((0r JMM Here, ůc. denotes child subproblems C. that are generated via analyzers; their results are aggregated from solutions of their own children in the same fashion recursively, until reaching the leaves, which are solved by our grounder agents.
ANALYTICA
Based on the SPR framework, introduce Analytica, architecture for complex analysis and forecasting. An overview of the Analytica architecture is provided in $ [.11] Subsequently, we ex- plain how minimizes both estimation bias and variance in $ 4.2 Finally, discuss the robustness and efficiency of Analytica in 4.3 and $ 44.4 respectively.
4.1 OVERVIEW
Analytica employs divide-and-conquee strategy, operationalizes SPR through three core compo- nents: an Analyzer AA. which expands a proposition tree or single root proposition with new nodes or branches. Grounder Ag. which determines the soft truth values leaves and produces a report; and Synthesizer As. which combines reports and soft truth value from fully-grounded children to deduce the report and Ptrue. of their parent. Analytica consists two algorithms: Ana 1 yze (Alg- I and Synthesiz ized with the root proposition Po, then passes the root to Synthesize to ground the entire tree bottom-up. Details of each component are provided below:
(Alg. 2). Illustrated in Fig. 3 it calls Analyze to expand the tree initial-
Analyzer The analyzer agent Av, expands a proposition tree to an expanded tree T AA T T It begins with consisting only of root query proposition. The agent then
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Algorithm Analyze(po, AA. Imner T
Algorithm 2 Synthesize(p;; Ag, As)
Require: Proposition Po+ Analyzer LLM AA.
Require: Proposition node Pj T, Grounder
Max leaves Limazs Max steps Tmax
LLM Ag. Synthesizer LLM As
Ensure: Proposition tree 'T rooted Po
Ensure: Grounded pt with Ptrue and report
1: T < -InitializeTree((p))
1: if P; is a leaf then
2: for t 1...., Tmaz do
pi.report, Pi-Ptrue +- AG(p:)
3:
if CuumberOfLLeves(11)) 2 Lmaz then break
3: else
4:
4: for all pij E pi.children do in parallel
5: Pnew (T)
> Expand tree
5:
Pig asyne Synthesize(p.g) 6: pt.report, Ps.Ptrue +- cs(pl.children)
6: T + Updatet .P Pnew))
7:
return T
7:
return Pi
prompted to progressively deepen the analysis by adding independent child nodes to one multiple existing nodes, repeating until either a completion signal is reached or a predetermined maximum leaf count is exceeded.
Grounder The Grounder agent, Ag. grounds a leaf proposition Pleaf by estimating Ptrue with a report: Ac(Pteaf) + Pleaf- We study three variants of the Grounder: 1) Basic Search agent that relies on standard web search to gather evidence; 2) OpenAl Deep Research (OpenAl) 2025) that extensively searches the internet to compile report for the query; and 3) Jupyter Notebook, our most advanced hybrid Grounder that mimics professional data analysts by iteratively writing, executing, and debugging Python and markdown blocks in a Jupyter notebook environment with access to various search and financial APIs. Jupyter agents operate follows. Upon receiving input query, agents are instructed to repeatedly produce interleaved markdown cells for qualitative reasoning and Python cells for programmatic execution at each step. Similar ReACT (Yao al., 2022), these cells are executed by the Jupyter backend and outputs are returned to the agent, which then decides whether continue or to terminate the notebook. If an error arises, the agent must correct it before proceeding. Upon termination, the agent is prompted to compile the entire session into a final report and produce soft truth value (Ptrue). More details and examples found C.44
Synthesizer The Synthesizer agent, As. then grounds, scores, a non-leaf proposition based on the scores of its children ps-children (Pro, p..,.... Formally, As(ps, pt.children) > where contains the truth value Pi.Ptrue and report. We employ a Linear synthesis rule:
Pi-Ptrue Bo Σ Bi - Pij-Ptrucs
where |,3]| < 1, 1,
c, and Pi-Pirue E [0
which resembles factor-based models widely adopted in economics and political science (Fama & French 2015 Gregg & Banks 1965). The LLM is tasked with outputting coefficients Bj. and an intercept Bo in JSON format detailed in E.2 and $ D.8, where restricts the intercept from surpassing the impact of children. In $ B we show how the computation graphs produced by this process can be modeled semantics of synthesis (e.g., the assumptions made about the relationships hetween sub-claims) and
special type of linear Bayesian network, which gives insights into the
suggests other scoring strategies (e.g., using techniques from PGMs (Koller & Friedman 2009
To discover the characteristics of ideal synthesis, we study two alternative synthesis rules: a) Vanilla rule, which calls LLM directly output Ptrue with report; and b) a Simple logic strategy, which prompts the LLM to generate a logical formula that connects the soft truth val- ues of all children through fuzzy logical operators (Van Krieken al.) 2022 Grespan et al.) [002]): A AND B = A x B, A OR B A + B A x B, and NOT A = A, and an "assumption" variable, PA [0, account for external factors, e.g., P; Pa OR (NOT P:2 AND PA), where P.j denotes the j-th child of proposition (sec more examples in $D.
The locality inherent in the synthesis process, where each synthesizer accesses only specific node and its children, facilitates Analytica's efficient scenario analysis for addressing "what-iff" inquiries, which is highly useful in practice. After tree fully grounded, users can manually edit the truth value, statements, or reports of any node, add/remove nodes explore
Resynthesis
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Published as a conference paper at ICLR 2026
counterfactual (e.g.. "What if inflation does not slow down?"). Instead of reexecuting the entire Analytica process, the system triggers a fast recomputation, calling the synthesizer to update only the affected branches up to the root. This allows for rapid and interactive exploration of how varying assumptions affect the final outcome (see example in Fig. T6).
4.2 DERIVATION FROM FIRST PRINCIPLES
Analytica is designed so that most effort dedicated to verifying the leaves, and soft truth values of non-leaves are linearly composed from the children. The subsequent reasoning step, where soft truth values of non-leaves are linearly composed from the children, acts as a highly lightweight, "effectively free" mathematical wrapper that aggregates these grounded values. Under Eq. [ we can show that such strategy can be derived from first principles. We model the ground truth pi linear combination of its k leaves: p 3 Σ i,true For
of the root proposition analytical purposes, this expression is derived by algebraically expanding the nested linear equations from the root to the leaves. Each coefficient 8 represents the cumulative impact of a leaf the root, effectively forming beta path: the product of all local / coefficients along the unique path through the tree from root leaf 1g. Similarly, & is the aggregated intercept of all non- non-leaves. The estimated
Ptrue can be written as a similar linear composition of leaves: Ptrue = 1% + Σi= Bili,true- Each leaf estimate tier is random variable characterized by its own bias and variance. We now derive the bias and variance of the final root estimate Perue as function of its components.
Bias The bias of the root estimate is a weighted sum the biases of the individual leaf estimates:
Bias(Perue) = E[ptrue] po
Σ 3 (Elli,ruel
19t (,true)
B(Bias(4,true
The bias decreases in two ways. 1) Simplified leaves: as the analysis deepens, we hypothe- size that the leaf nodes will gradually approach simple atomic propositions whose truthfulness is easy to judge. This makes the weighted summation of the leaf biases smaller than the bias di- rectly evaluating the root. More formally, we note the root bias as Bias(root) and assume that when Bias(k = 5, Bioooo. where 0 < ó, < 1 for all leaves i, then: Bias(prrue) = E 355, use of powerful grounders helps to further reduce bias, as empirically supported by Table and Fig. 6 This forms the basis for the strategy of employing an Analyzer to achieve detailed break- down of the complex query proposition, combined with an emphasis on utilizing strong grounder agents to manage leaf propositions, such as our sophisticated Jupyter Notebook grounder.
Σ (BBias(l,,true))
= (rost)) 3,5,)) Bias(root). 2) The
Variance
The variance of the root estimate is function of the leaf variances and their covariance:
Var(ptrue) = Σ 3 Var(li,rue)) + Σ 8 Cov (y,
k=000 0
It is minimized by: 1) Granular decomposition, the leaf variances are suppressed by the squared weights (B13), which approach 0 as the leaf number grows; and 2) Ideal analysis, generating chil- dren with minimal covariance, where the analyzer is forced to uncover independent factors a top-down, fivide-anddconquue manner in Analytica. This theoretical insight aligns with our empir- ical findings, where the prediction accuracy grows with the size of the proposition tree (Fig. 4 and the low variance of our method (Table 2p. It also guides us highly value system scalability, which is crucial for not only practical application but also results in reduced estimation variance.
4.3 ROBUSTNESS OF ANALYTICA AND IDEAL SYNTHESIS
We now analyze the robustness of Analytica under the linear rule, and then generalize to the principles of ideal synthesis to delve deeper into the criteria necessary for achieving optimal per- formance. The synthesis rule is crucial as averages the variances of the leaves, and thus must be robust against noise in the leaf estimates to preserve the stability gains. This is fundamentally based on its mathematical structure. To analyze this, let a synthesis rule be a function P f(,,...., C.,) that maps child truth values {C₃} parent value P. We assume the grounder produces noisy

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Published as a conference paper at ICLR 2026
Basic
Analytica
Analytica"
Analytica"
Analytica'
Avg. time (s)
0.5
5.3 (1.0x)
16.4 (3.1x)
33.3 (6.3x)
63.5 (12.0x)
Nodes
19.9 (1.0x)
68.1 (3.4x)
359.5 (18.1x)
1075.3 (54.0x)
# Tokens
3.6K
58.6K
169.4K
929.0K
2.8M
Scalability of recursive Analytica. the recursion depth increases, the number of nodes and tokens grows exponentially, while the average computation time increases near-linearly.
Table I:
estimates C₁ Cj Ej. where ej is random error term. The rule's sensitivity to this input noise can be measured by its partial derivatives 0ʃ aC, The Linear rule demonstrates a superior stability:
Proposition (Constant Sensitivity of the Linear Rule), The Linear synthesis rule, P p= 30 Σj= B has a constant sensitivity to input noise given by the partial derivative: ac; 33 that ensures stable and bounded error propagation, independent of other inputs.
OP
The formal proof detailed in A.I. which identifies a set of conditions for an ideal synthesis rule: 1) Bounded Sensitivity: The function's 's partial derivatives with respect to its inputs should be bounded and preferably small, preventing any single input from having an outsized, unpredictable impact; 2) A Smoothing Property: The function should have a natural averaging effect that in- herently dampens or smooths noise from its inputs, rather than propagating it; and 3) Graceful Degradation: The function should be smooth and continuous, without sharp "tipping points" or cliffs where small perturbation can cause disproportionate volatility. The linear rule satisfies all three conditions, providing strong theoretical explanation for its superior empirical performance over others in terms of accuracy, stability (Table D and noise resistance (Fig.
4.4 EFFICIENCY AND SCALABILITY OF ANALYTICA
The theoretical benefits of scaling up the depth of the analysis, as discussed in 44.2 are attainable in practice only if the architecture is capable of efficiently supporting considerable number of leaves. Analytica allows unbounded scaling by recursively invoking itself at leaves with each leaf serving proposition that act where n indicates the depth of the recursion. Recursive invocation results in a tree-level locality, segment of the ultimately expanded tree, which
root for another Analytica analysis. We denote it Analytica",
where each instance of Analytica concentrates may exceed the limit for single Analyzer to produce. The locality of synthesizers, grounders, and Analytica itself facilitates massive parallelism. which shows near-linear time complexity with respect to the depth of the analysis, as shown in Table I and formally proved in A.2
5 EMPIRICAL VALIDATION
Accuracy Soft
Stability
Efficiency Cost
Accu.
Imp.
Hard
BS
Conf.
Var
Time
Random
48.
48.32
47.11
33.92
74.70
48.53
Basic Search
53.94
51.12
53.92
26.73
64.95
10.30
$0.02
0.54m
Tree of Thgt.
60.19
11.59
55.74
57.51
26.46
76.89
9.21
$0.28
6.55m
+ Graph of Thgt.
57.88
7.30
53.52
57.18
26.85
75.23
10.12
$0.18
4.72m
Forest of Thgt. 60.73
12.59
56.87
57.64
26.44
78.35
8.28
$0.55
10.32m
+ Analytica-V
63.18
17.13
56.56
59.37
26.33
85.44
10.89
$0.24
5,42m
Analytica-S
57.61
6.80
53.82
56.70
26.36
74.99
7.45
$0.23
5.38m
+ Annaltiic-LL
65.62
21.65
58.51
60.13
24.21
85.56
6.46
$0.26
5,49m
Table Performance, stability, and efficiency results across different Analytica setups and compar- isons with structured reasoning approaches. Bold/underline indicates best/second. "Imp." means improvement. 'V", 'S', and 'L' denote the vanilla, simple logic, and linear rules, respectively.

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Published as a conference paper at ICLR 2026
In this section, empirically validate the core theoretical claims of the Analytica framework pre- sented in $ through three key research questions (RQs). RQ1: Bias and Variance Reduction 5.5.2. We nypothesize that Analytica minimizes bias, while its linear synthesis minimizes variance ($ 4.2 We test this by comparing accuracy uplifts and stability metrics against baselines across forecasting tasks (Table : RQ2: Scalability and Robustness ($5..) We hypothesize that per-
formance improves with analysis depth while maintaining efficiency due to recursive parallelism ($ 4.4p. We examine this by tracking how accuracy scales as the number of nodes grows (Fig. We further hypothesize that the Linear rule provides stronger robustness to noise than the simple logic rule ($ 4$3. Prop. T. We test this via noise cnjse-injection stress experiment (Fig. 5) RQ3: Cost- Effectiveness ($ 5.4). We study the practical usefulness and trade-offs between reasoning capability and costs. We illustrate this via efficiency frontier plots (Fig. ( Additional results, including
domain-specific breakdowns and model ablations, are provided in D
Accu.
Imp.
Soft
Hard
BS
Conf.
Var
Cost
Time
Deep Research
63.04
57.22
59.31
26.24
82.57
9.28
$4.02
7.60m
+ Analytica-V
69.16
9.77
39.26
63.16
22.77
83.41
9.88
$12.70
33.07m
Analytica-S
66.30
5.17
58.79
63.71
24.15
76.34
7.27
$13.70
29.90m
+ Analytica-L
71.06
12.72
60.01
66.57
22.79
83.59
6.02
$14.10
30.01m
Jupyter NB
61.96
56.92
62.67
26.90
76.68
12.28
$0.07
2.61m
+ Analytica-V
68.89
11.18
61.57
67.40
21.67
80.75
12.90
$1.05
13.98m
Analytica-S
62.77
1.31
57.19
64.48
25.71
77.28
8.65
$1.25
13.81m
+ Analytica-L 70.11
13.15
60.25
68.01
22.89
81.10
7.28
$1.36
14.15m
Table 3: Ablation on the advanced grounders and comparison Deep Research.
5.1 EXPERIMENT SETUP
Dataset The agent is tasked with evaluating a collection of propositions related to potential out- comes of upcoming real-world event. A dataset comprised 736 unique events derived from the predictive and financial markets was compiled. Events were carefully filtered to ensure they were resolved after our model's knowledge cut-off. The Financial Market Tasks involve making year "long vs. short" prediction for an asset (like stocks, indices, commodities), necessitating high- level strategic thinking rather than short-term speculation. The Predictive Market Tasks directly use the options provided by the market, e.g., for "who will win the 2024 US presidential election?", the two options are Kamala Harris and Donald Trump For each task, the agent receives the event description, the current date, and the target proposition (e.g.. "The best strategy for $NVDA over the next year is to go long") for each option in the event. The agent must provide Ptrue for each given proposition that corresponds to the options in an event. For more information, refer to C.2
Baselines We structure our comparisons into two components. First, we evaluate the standalone base agents (Basic Search, Deep Research (OpenAl, 2025). Jupyter Notebook) that operate di- rectly on the root query. Second, we evaluate reasoning frameworks that use these same agents as subroutines (grounders). We compare Analytica with Thee/GGraph/Forest of Thoughts (Yao et al., 2023 Besta et al. 2024 Bi et al. 2025), which are implemented over Basic Search for fairness, as well against random baseline. Áll experiments use the o3-2025-04-16 6 model with knowledge cutoff of June 01, 2024. For ablation studies in other base models, see $ [D4] A low temperature of 0.1 was used following Cheng & Chin (2024a). The web search is powered by Exa.a3 We also set a limit of 10 leaves for Analytica. See C.I for further details.
Each option for an event is associated with a ground-truth dollar value, rep- resenting the utility of that choice (e.g., the return on one-dollar investment). We apply multiple performance metrics: Accuracy (Accu.) measures if the agent assigns the highest Ptrue to the option with the best utility, measuring the top-1 correctness. Hard and Soft scores evaluate the value of the highest-Pires option and the -eiggtee value across all options, respectively, to evaluate the practical return of agent decisions. For cross- cross-task comparability, Min-max normalization is applied to the hard and soft scores with respect to the values of options for every task. Brier Score (BS) quantifies the MSE of the predicted distribution across options. In addition, assess prediction
Evaluation Metries
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Published as a conference paper at ICLR 2026
Model
Number Nodes
Type Ratio
75.0
Oets Ressac 0eed
Deep Reeaact Sarplo
japyer Netbbok- (5mog
Netabokk romila)
Accuracy 195)
Accuracy
67.5
japyer Nertbok-
Andyliee (Hamal
03.0
Andykkell (UKcosee)
Ansydia (heaero)
Andyliad (Urceraln)
Asdrice (Tenasal
Bocie
6.5
Number of Nodes
Noise Ratio
Figure 4: Accuracy vs. number of nodes.
Figure 5: Robustness of different synthesis rules.
stability by performing runs of each task on a 100-task subset, then compute Confidence (Conf.) as the average highest Ptrue the agent produced, indicating its self-assessed certainty, and Variance (Var.) of the hard score. Lastly, we measure efficiency by API Cost and Wall-clock Time.
5.2 RQ1: ANALYTICA PERFORMANCE AND STABILITY
In Table we illustrate that Analytica substantially improves performance. We perform a Mc- Nemar's test to assess our findings in $ D.I In particular, on average, the linear rule improves 15.84% accuracy, achieving a highest confidence 83.41 with a variance of 6.59%. supports our bias- vlas-variance reduction framework discussed in [422 We ablate the grounders in Table 3 Analytica augments for all base grounders. Moreover, outperforms Deep Research with a Basic Search, which can also be enhanced by Analytica. Meanwhile, it confirms that grounder builds the founda- tion of lowering biases. Notably, our Jupyter Notebook (NB) grounder with Analytica-L shows an accuracy close to Deep Research (-1.34% worse) with 90.35% lower cost and 52.85% time saving. Conversely, the simple logic rule shows the lowest accuracy enhancement at 4.22%, corroborating theoretical results presented in 4.3 We extend our evaluation to the scientific domain by
Matter-of- benchmark (Jansen et al. 2025a in $ DJ5) and small open-weight models in $ D.4.4
5.3 RQ2: SCALABILITY AND ROBUSTNESS OF ANALYTICA
We study scalability by running Analytica with 10 to 100 leaf limits in the 100-task subset above. Once a tree reaches a leaf limit 10, we apply recursion explained in $ 4.4 to expand each leaf sequentially to ensure stopping around the target limit. Fig. shows a clear positive correlation between the number of nodes and the accuracy, strongly endorsing the scalability of our method. We further study the robustness of different synthesis rules with the same subset by injecting different types of noise into the grounder: normal noise Perue = Ptrue + UO, a) where a is the noise ratio, uncertain and reverse noise where Ptrue UO, 1) or Ptrue 1 Ptrue with probability o, respectively. Fig- 5 indicates that the simple logic rule is highly susceptible to noise, whereas the linear rule demonstrates high robustness as analyzed in Proposition [ In contrast, the vanilla rule is minimally affected as it mainly depends on textual reports rather than the estimated truth value.
5.4
RQ3: UNDERSTANDING THE PERFORMANCE VS. COST TRADE-OFF
Fig. 6 provides a comprehensive overview the performance-cost trade-offs. Overall, Analytica sits closely on the effective frontier with negligible overhead (analyze and synthesize). Most costs arise from invoking the leaf base agent. The plot of accuracy against monetary and time cost clearly illustrates that more powerful configurations occupy the high-performance, high-cost quadrant. The choice of Grounder is the single largest determinant of cost and performance, establishing distinct efficiency frontiers. Notably, Jupyter Notebook grounder demonstrates high cost-effectiveness.

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Published as a conference paper at ICLR 2026
Performance vs. Cost
Performance vs. Response Time
75
75
Leaders
Powerhouses
Leaders
Powerhouses
(Low Cost, High Pert.)
(High High
(Fast Resp., High
Resp., High Parf.)
Analviga- (DR)
Analy g (D
70
Analytcai Analytica (IN)
AnayicaV (DR)
70
Analyticasl (N)
Analytica- (JN]
Anwlytica (DR)
Analytica-L
Analy S Analyeea-5 (DR)
Analytica
Analytica-S (DR)
Accuracy (%)
jupiter Notebook
(BS))
S
Deeps Ressarch
Accuracy (%)
Analyticv (85)
Jupree Notabook
Ueep Research
Analytica's
Forest of Thoughts
Forest Thoughts
60
Tree Thoughts
60
Tee Thoughis
Graph Thoughts
Graph Thoughts
Snalytica-1155)
Analyfic (651
55
55
Agent Groups
Basic Search
Search
Basic Search
Jupyter Notebook
Deep Research
50
50
Other Baselines
Random
Random Baseline
Idealized Fronljer
Budget
Inefficient (High Cost, Low Perf.)
Budget
Inefficient
45
(Low Cost, Low Perf.)
45
Fast Resp Low Perf.)
(Slow Resp., Low Perf.)
10"
10?
10"
15
Average Per Queries (USD) Log Scale
Average Response Time Query [min)
Figure 6: Performance vs. cost trade-off analysis. The plots visualize accuracy against monetary
cost (left, log scale) and response time (right, linear scale) for all evaluated methods.
LIMITATION AND DISCUSSION
Analytica still omits some potential error sources in addition to the ones we discussed in 4.2
1) Assumption of Independence: Our framework performs best when the child propositions are independent. While our Analyzer agent presents an empirical solution, ensuring independence in principle and estimating the correlations for real-world propositions remains an open challenge. 2) Robust Synthesizer: Errors in estimated coefficients of the synthesizer can lead to potential errors, as shown in D.8 Producing reliable estimations for these coefficients can be crucial. 3) Hybrid Grounder: We currently apply the same grounder to all leaves; however, different propositions may have different properties and require grounders with different skill sets. It is possible to adap- tively select grounders with diverse capacities for different propositions to improve efficiency and accuracy, recently studied in model routing (Ong et al. 2025 Ding et al. 2025).
Analytica's practical value extends to complex, high-stakes, critical real-world domains, where decision-making and analysis require transparent reasoning and robustness, such as applications for economists, policymakers, scientists, and robots. More generally, Analytica can serve as a complex analysis backbone for autonomous systems by breaking down uncertain, poorly specified problems into calibrated, empirically testable soft propositions, thereby supporting downstream autonomous agents in performing interpretable, reliable reasoning in real-world conditions.
7 CONCLUSION
In this work, we introduce Soft Propositional Reasoning (SPR) for complex, real-world analysis, transitioning from heuristic reasoning in unstructured text to a principled, robust process within a soft propositional space. Our system, Analytica, leverages this framework and derived from first principles to achieve high accuracy across various forecasting tasks, significantly enhancing both accuracy and stability over strong baselines while consistently augmenting various grounders. architecture enables exceptional scalability through massive par-
The modular, allelism, providing unique capabilities for interactive scenario analysis with resynthesis. In addition, conduct comprehensive theoretical and empirical assessments examine the underlying princi- ples of robust LLM- analysis and forecasting, which establishes a strong and transparent basis for creating reliable L.M agents in high-stakes, real-world domains.
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Published as a conference paper at ICLR 2026
ETHICS STATEMENT
Our study is foundational research for the L.LM agentic forecast and analysis. We see no potential negative impact society.
REPRODUCIBILITY STATEMENT
We provide complete details of our experiment setup in $ 5.1 and $C.1 We also disclose details of
our dataset construction in C.2 and agent implementations in C.3 and $ C.4
USE OF LLMS STATEMENT
We primarily use LLMs polish the writing and check typos.
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Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Ad- vances in neural information processing systems, 36: 1809-118222 2023.
Yangyang Yu, Zhiyuan Yao, Haohang Li, Zhiyang Deng, Yuechen Jiang, Yupeng Cao, Zhi Chen, Jordan W. Suchow, Zhenyu Cui, Rong Liu, Zhaozhuo Xu, Denghui Zhang, Koduvayur Subbal- akshmi, GUOJUN XIONG, Yueru He, Jimin Huang, Dong Li, and Qianqian Xie. Fincon: A synthesized LLM multi-agent system with conceptual verbal reinforcement for enhanced finan- cial decision making. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL http:::t/
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Zhiyuan Zeng. Jiashuo Liu, Siyuan Chen, Tianci He, Yali Liao, Jinpeng Wang. Zaiyuan Wang, Yang Yang. Lingyue Yin, Mingren Yin, Zhenwei Zhu, Tianle Cai, Zehui Chen, Jiecao Chen, Yantao Du, Xiang Gao, Jiacheng Guo, Liang Hu, Jianpeng Jiao, Xiangsheng Li, Jingkai Liu, Shuang Ni, Zhoufutu Wen, Ge Zhang, Kaiyuan Zhang, Xin Zhou, Jose Blanchet, Xipeng Qiu, Mengdi Wang. and Wenhao Huang. Futurex: An advanced live benchmark for Ilm agents in future prediction, 2025. URL hetttp::/axxxv.oor//ttt.
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A THEORETICAL ANALYSIS
A.1 ROBUSTNESS OF THE SYNTHESIS RULE
In this section, we provide the formal proof for Proposition I and a further analysis of why the Linear synthesis rule is more robust to noise in its inputs than the Simple Logic rule. A robust rule should ensure that small errors in the estimation of child propositions do not lead to large, unpredictable errors in the parent proposition's 's estimate. We demonstrate that the Linear rule's structure inherently dampens noise, whereas the logical operators amplify it.
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Setup: Modeling Estimation Error Let C be the unknown "true" soft truth value for child proposition. The Grounder produces an estimate, Cj. which includes some random error, ej. We can model this as:
C = c t
We assume the errors are unbiased (Ele,] = 0) and have a variance of Var(e,) = o3. P I(C,,...., ,,C) be the true value of the parent, and P = -(Ci, ......... C..) be the final estimate based on the noisy inputs, A rule f is robust if the propagated error, P P. small. We can approximate the variance of the output estimate, Var(P). using the propagation of uncertainty formula (a first- order Taylor expansion):
Var P) ~0
The partial derivative, ac, measures the sensitivity of the output to an error in the input Cy. A smaller sensitivity indicates a more robust rule.
of
Analysis of the Simple Logic Rule The Simple Logic rule uses non-linear operators like AND (A B) and OR (A + B AB). Let's analyze the sensitivity for two-input function:
* For an AND gate, P C1 C2, the sensitivities are:
0P
OP
C2 and
Ci
00,
0C2
For an OR gate, P C1 + C2 - C1C₂, the sensitivities are:
0P
OP
0C1 = 1 - C2 and aC2 = 1-
The key issue is that the sensitivity to an error in one input depends on the value of the other inputs. For an AND gate, if C2 is high (e.g., 0.9), any error in C₁ is passed through with high impact. This creates a brittle system where high-confidence inputs can paradoxically increase the rule's sensitivity to noise from other inputs. This also leads to "tipping points"; a small error can cause a dramatic change the output (e.g., if one input to an AND gate flips from high to low, the output collapses).
Analysis of the Linear Rule For the Linear rule, P= P-Bo+ B,Cj, the sensitivity is constant for each input:
OP aC, = 33
The sensitivity error in Cj is simply its weight, 33. It does not depend the values of other inputs. Since the weights By are typically less than 1, the rule acts as weighted average that inherently dampens or smooths input noise. The error propagation is stable and predictable.
Fig. and visualized the gradient surfaces and sensitivity plots for linear and simple logic rules, respectively (see similar analysis in Van Krieken et al. (002)). ). The surface of the Simple Logic rule
curved. This lineariyyy is the source its unpredictable behavior. The surface of the Linear rule is a perfect plane, demonstrating its smooth and predictable nature. Small changes in the inputs lead to proportional changes in the output.
The sensitivity plot for the Simple Logic rule is ramp. The sensitivity to noise is very low when both inputs are near zero, but becomes very high when the inputs are near one. This visually confirms the "state-dependent sensitivity" mentioned in the proof-the rule's robustness changes depending on the data, making it brittle. The sensitivity plot for the Linear rule is perfectly flat plane. This is the most important takeaway. It shows that the rule's sensitivity noise is constant and bounded across the entire input space. It dampens errors predictably, regardless of whether the input propo- sitions considered likely unlikely to be true.
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Surface of Simple Logic Rule (AND)
Surface of Linear Rule
1.0
0.9
0.8
(d) aaianee
06
0.6
0.4
02
1.0
1.0
02
C
Value
1.0
C
Value
94
1.0
0.2
C₁ Value
Value
0.0
0.5
a. 0.0
Figure 7: Gradient surfaces of simple logic formula C₁ A C2 and a linear formula 0.1 0.1 C1 +
0.4 C2 respectively.
Sensitivity of Simple Logic Rule
Sensitivity of Linear Rule
Sa som Seddenn
0.62
0.59
0.60
1.0
0.8
057
0.58
0.8
0.5
0.56
0.4
0.55
02
0.0
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0.2
1.0
0.0
C
Value
Value
0.0
022
0.4
Value
0.0
0.2
0.4
Ct
Value
Figure 8: Noise sensitivities simple logic formula C1 C2 and a linear formula 0.1+0.4-C,
0.4 C2 respectively.
Principles for a Robust Synthesis Rule This analysis allows us to conclude with three general principles for designing a robust synthesis rule, f:
Conclusion:
The partial derivatives dt, should be bounded and preferably small. A rule where sensitivity can approach or exceed is prone to amplifying noise. The Linear rule's sensitivities are bounded by the learned weights, whereas the Logic rule's can be large.
Bounded Sensitivity:
2. Smoothing Property:
The function should have natural smoothing averaging effect. Weighted averages, like the Linear rule, are classic examples of noise-reducing functions.
3. Graceful Degradation: The function should be smooth, without sharp "cliffs" or discon- tinuities its derivatives. This ensures that small changes in inputs lead to proportionally small changes in the output, avoiding the "tipping point" behavior in logical gates.
The Linear rule satisfies all three principles, providing a strong theoretical reason for its superior empirical performance in noisy, real-world scenarios.
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A.2 EFFICIENCY AND SCALABILITY OF RECURSIVE ANALYTICA
In this section, we provide a formal analysis of the computational complexity and scalability of the recursive Analytica" framework. We demonstrate that while the total computation required grows exponentially with the recursion depth n, the wall-clock time can be managed to near-linear growth due to massive parallelism. Furthermore, we show that the recursive, divide-and-conquer approach provides a crucial benefit we term Context Locality, which makes scaling feasible within the finite context windows LLMs.
Setup
Let us define the parameters for our analysis:
The recursion depth of Analytica". Analytica' is the base case.
K: The average number of leaf nodes created by the Analyzer each decomposition step
(i.e., the branching factor, denoted as Lmaax in Algorithm [
M: The total number of final leaf nodes to be grounded. In an n-level recursive structure,
M Az K
To: The average time (latency) required to Ground single leaf proposition. This repre- sents the atomic unit of deep reasoning work.
P: The number of parallel workers available for executing Ground tasks concurrently.
Work Complexity (Total Computation) The work represents the total computational cost if the entire process final leaf nodes.
sequentially single processor. It is dominated by the grounding of all
(Exponential Work Complexity). The total work complexity W(n) of Analytica" is exponential in the recursion depth
Proposition
((n) OOK"OKKTT
Proof. At recursion depth n, the total number of final leaf nodes is approximately M S.".n each of these M leaves requires independent grounding process of average time To, the total sequential time (work) is the product of these two quantities.
Time Complexity (Parallel Execution) The time complexity (also known as span depth) measures the wall-clock time assuming parallel execution. The structure of Analytica allows all leaf nodes at the final level be grounded simultaneously.
Proposition (Parallel Time Complexity). With P parallel workers, the time complexity (n(n) of Analytica" is primarily determined by the parallel execution of the final grounding phase.
Tr(n) = (n K
To
Proof. The process has a sequential dependency through the n levels recursion (analysis and synthesis each level), contributing the O(n) term for overhead. The dominant term the final step, where all M = K leaves are grounded. With P workers, this phase takes [K"/P] batches of parallel executions, each taking time TG. For large n, the exponential term O K linear term O(n).
P dominates the
Interpretation This explains the empirical results. While the total work W(n) is exponential, the execution time (n) is divided by the number parallel workers P. For system with high parallelism (large P. e.g., 1000 in Table [D. the exponential growth is drastically mitigated, leading to the observed pear-linear time growth for moderate n. This demonstrates the immense scalability power unlocked by the framework's parallel design.
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The Benefit of Recursion: Context Locality Beyond parallelism, the recursive, divide-and- conquer nature of Analytica" is essential for its feasibility. A monolithic, non-recursive approach would be intractable due to the context limitations of LLMs.
Proposition 4 (Context Locality). The recursive structure of Analytica" maintains a small, bounded context size for each L.M call, whereas a monolithic approach would require a con- text size that grows exponentially with the problem complexity.
Proof. Consider monolithic agent trying solve the problem in one pass. would need to gener- ate the entire proposition tree with M K leaves. The size of this tree, which must be maintained in the LLM's context, would be O(K*). For even modest n and K, this would quickly exceed any modern LLM's context window.
In contrast, Analytica" exhibits context locality. Each call the Grounder operates on single leaf' proposition, task with constant context size, O(1). Each call to the Analyzer or Synthesizer op- erates on parent and its children, context size O(K), which is independent of the recursion depth n. The maximum context required at any point in the process remains small and bounded, regardless of the overall size of the problem.
Conclusion The power of the recursive Analytica" framework stems from two sources. First, its parallel architecture transforms an exponentially complex problem terms of work into a manage- able task in terms of time. Second, and more fundamentally, its recursive decomposition provides context locality, breaking an intractably large problem into vast number of small, independent sub-problems that fit within an LLM's finite context. This combination of parallelism and locality what endows Analytica with its profound scalability.
B FORMAL ANALYSIS OF THE ANALYTICA REASONING MODEL
To better understand the semantics of Analytica's 's underlying reasoning model and linear synthesis rule from Eq. [ in this section, we provide sketch of how directly translate an Analytica com- putation graph produced during the synthesis stage (see again Figs. 3 into an equivalent Bayesian network. Recalling again that our synthesis rule scores non-leaf propositions Pi-Ptrue [0, 1] using
the scores of all its children P.Ptrue E [0, 1] as follows:
P.Ptrue = 3o + Σ Bg Pj-Ptrue
We define the following graphical representation of the Bayesian network corresponding to the above equation (without loss of generality, we focus on the case involving two children P1, P2)):
P1
P
P2
where and P1, P2 are binary random variables corresponding to the root p. and its children nodes Pl, P2. Standardly, the probability of variable P in this network, denoted below Pr(P)
for Pr(P 1), is computed as follows (with binary indicator variables pj E {0, 1)):
Pr(P) = Σ
Pr(P P1 = pl, P2 = p2) Pr(P1 = p1, P2 = p2)
(1.1)
Σ
Pr(P P1 pl, P2 = p2) Pr(P1 p1) Pr p2)
0,,03((0113
independence
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By then defining the corresponding CPDs follows using our original coefficients:
Pr(P) P1 pl, P2 p2) : Bo + (31 p1) (82 P2)
and the non-root node probabilities P using their original node scores:
Pr(P = p) = (p.Ptrue) (1 p.Ptrue) )1
We can observe below that Pr(P) under this network and linear weight parameterization corre- sponds exactly to the linear synthesis rule score p-Ptrue (for readability, we use and p in place of Pr(C") and Pr(C). respectively, and replace C' = e P(P)
with Booleans 0,1):
Pr(P) =
Pr(P 1..0) + Pr(P 11 1)PP
+ Pr(P 1)PTP2
+ Pr(P 1, 1,
BoPi Pa
+ (8o + BiDP.P
(Bo BelPi
+ (B0 B 32)
w/ Bs
S.piP:P.Do
+ SiPIPaRo
Algebra/cancellation
Whenever all As E [0, 1] and Bo + Σ SI.
P.Ptrue
Importantly, emphasize that this equivalence only holds when the parameters have the structure given in the last line. While such a condition was not strictly enforced in our existing experiments, note, however, that such constraint can be enforced in our current system by employing variety of different scaling techniques for the given 3s (c.g., min-max max scaling, softmax).
By translating our synthesis rule into an explicit Bayes net, we get more transparent picture of the semantics underlying our synthesis agent. In addition, such a formulation also suggests number of new synthesis strategies that use known techniques from probabilistic graphical models (Koller & Friedman 2009). We provide specific examples below by considering translation into a different, and semantically more transparent, formal system below.
The synthesis rule probabilistic logic program Interestingly, we noticed through the above derivation that the linear synthesis rule has more compact and natural interpretation as a certain type of probabilistic logic program (PLP) (De Raedt & Kimmig, 2015). Below shows a Problog implementation (De Raedt et al. 2007 Dries et al. 2015) of the linear synthesis rule (the red parts correspond to the corresponding parameters in the linear synthesis rule):
88 children nodes as probabilistic facts
Pi-Ptrue PPPtrue::p) ::pl.
P2-Ptrue ::p2.
$$ betas as annotated disjunctions, categorical variable
:b::b0; $1::bl; :2::b2.
$88 tree links as if-then rules P b0.
:- b1, pl.
p :- b2, p2.
$88 probability of root query(p)
where p. pl, p2 denote the root and non-root propositions, respectively (the latter being implemented as probabilistic facts), and the bs correspond to the beta parameters (expressed relational cat- egorical distribution using a construct called an annotated disjunction (AD) originally from Ven- nekens al. (2004)). To see that the probability of (via query (p) ) is equal to Pp-Perue in the linear synthesis rule, we consider the Boolean encoding of this program under standard closed-world semantics (Clark 1977), which corresponds to the formula F below:
F F
p (bo V bj Ap)
V j2-1
bi)
(
A W.ibi
(bi bj)
j>0
(noisy-Jor
one hot constraint, categorical
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where special variable b b-1 is used to denote the case where all other bs false (used whenever the sum of Bs is less than 1). Under a standard possible world semantics and encoding of PLPs then compute the probability of p as and ADs into weighted logic (Fierens et al.] 2015), 2008) of F A p. and observe under the
the weighted model count (WMC) (Chavira Darwiche
following weighting wx-) of variables:
Vj O. w(j)) 3j. w(b1) = 1 ((30 -1- 32), vj.w(-bj)
Vj. w(j)) = Pj-Ptrue. w(-pi) = Pj-Ptrus
wp() =
that the following equivalence holds (where w is used as shorthand to denote the weight of variable its negation, which marginalize out, and w denotes possible world or set of variable instantiations consisting of literals l):
Pr( A
Σ II ml)))
W FFA
weighted model count (WMC) of under so(-)
w(bb)o((=pt)u((t22
+ (ubl))((p)j((tpp))
+ (xb (=pp))))))))
All logical interpretationnse with weights (removed litenl with weight
80
10p01-Perue
S2p2.prrue
Whenever all As [0, 1] and 80 + EB S1
P-Prrrue
At noted above, the translation into F shows more clearly how the linear rule operationalizes a kind of noisy-or style of reasoning (Pearl) 2014) (i.e., the root being true depends on one or more of its children being true, or 3n being true) with an added one-hot constraint that enforces only one being true. By removing this one-hot constraint (or equivalently, removing the annotated disjunction the logic program), one derives a standard noisy-or rule, which is an alternative synthesis strategy that one can in principle experiment with. Building these foundations, many techniques from PGMs and probabilistic logic programming suggest themselves for improving the robustness of the synthesis agent, such adding explicit negative factors, e.g., via inhibited noisy-or rules (Meert & |ennekens| [2014), or modeling parameter uncertainty via Bayesian inference as in Cerutti et al. (2019): Verreet et al. (2022) (see Agarwal et al. (2025 for similar ideas in the context of LLM agents).
C SYSTEM DETAILS
C.I DETAILED SETUP
Our experiments were conducted using of standardized hyperparameters and reproducibility across all agent configurations. These settings govern the behavior of the LLM agents, the grounding process, and the structural constraints of the Analytica framework.
consistency
General Agent Settings
These parameters control the core interaction loop for all LLM agents.
max wax.exception.co eeaceptioo.retxy::: retry:
The maximum number of times an agent will attempt to re-call the LLM if a recoverable error (e.g., invalid JSON format, parsing failure, invalid weights generated for linear rule, invalid formula generated for simple logic rule) occurs.
max max_innterrut..immes times:
The maximum number of interruptions (e.g., tool calls for API documentation) agent can make in single reasoning step before being required to pro- duce a final response for that step.
Analytica Framework Settings These parameters specifically control the behavior of the Analyt- ica architecture during the analysis and grounding phases.
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max 1x.n.leed leaves: 10 limit on the number of leaf propositions the Analyzer can generate. The decomposition phase is halted once the proposition tree reaches approximately 10 leaves to ensure a comparable analytical budget across different methods. Notice that in practice, usually halts with more than 10 nodes as we perform post-check.
max.concurrenttproom
20 The maximum number of leaf propositions that can be grounded in parallel by the framework. This leverages asynchronous execution improve efficiency.
max proof retries: The number of times the framework will retry the entire grounding process for single leaf proposition if the assigned Grounder agent fails catastrophically.
Jupyter Notebook Grounder Settings These settings govern the iterative proof-construction pro- cess for our most advanced grounder.
max mexxxproffsstepe
20 The maximum number of turns (i.e., generating and executing one or more notebook cells) the agent can take within single Jupyter session before is forced to terminate the analysis and provide a conclusion.
debug max retries: The maximum number of attempts the agent is given to fix a single erroneous Python cell before the proof considered have failed.
abs abs.inteecept.mmar 0.1 A constraint on the absolute value of the intercept term (Bo) for the Linear Synthesizer. This encourages the agent to base its synthesis the evidence from child propositions rather than relying on a large, unexplained prior.
Experimental Simplification for Binary Tasks To enhance computational efficiency, simpli- fication was applied to all tasks with exactly two mutually exclusive options (e.g.. "Long" vs. "Short", "Yes" vs. "No"). For these binary tasks, the framework was configured to perform full analysis grounding process for only the first option determine its soft truth value, P(option,). The soft truth value for the second, opposing option was then programmatically de- rived as P(option,)
P(option,), leveraging the mutually exclusive nature of the choice set. This approach halves the computational cost for binary forecasting without loss of information. We also apply decision threshold 5 for binary tasks: if Ptrue d, the claim labeled as True; otherwise, it is labeled as False.
C.2 DATASET CONSTRUCTION
Our benchmark dataset was meticulously constructed to provide a diverse and challenging set of real-world forecasting tasks. The data spans two primary domains: high-liquidity predictive markets and a wide range of traditional financial markets. The entire construction process involved several stages of data acquisition, filtering, and validation ensure the quality and relevance of the tasks.
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Timespans of Predictive Market Events
Duration (days)
Jul 2023
Sep 2023
Nov 2023
Jan 2024
Mar 2024
May 2024
Jul 2024
Sep 2024
Nov 2024
Jan 2025
Mar 2025
May 2025
Figure 9: A Gantt chart illustrating the timespans of the predictive market events included in our dataset. Each horizontal bar represents single event, starting on its opening date and ending on its resolution date. The color of the bar indicates the event's duration in days. The chart highlights the diversity of forecasting horizons, ranging from short-term events of few weeks to long-term predictions spanning over a year.
Predictive Markets Data for predictive markets was sourced from two of the largest plat- forms, Kalshi and Polymarket, via their respective official APIs (https://kalst) com/ apil https: docs. wwwpypaelet..ooooooooooomo.....t com). We applied a multi-stage filtering process to the raw event data:
We selected events with resolution dates occurring after models' knowledge cutoff of June 1, 2024, and before May 1, 2025, to ensure they represented genuine future predictions.
Temporal Filtering:
To focus on events with sufficient public interest and liquidity, enforced a minimum total trading volume of $500,000 across all of an event's 's markets.
Volume Filtering:
Topical Filtering: We used comprehensive set of keywords (e.g., "who will win", "movie". "sports team vs.", "price range") to exclude events that are purely speculative, sports or entertainment-relaeed,, not amenable to deep analytical reasoning.
Structural Filtering: Events with an excessive number of potential outcomes (more than markets) were removed to maintain a manageable task complexity.
The resulting of predictive market events covers wide range of time horizons, from tasks re- solving in few weeks to those lasting over a year, as illustrated in Fig. 9
Financial Markets To create tasks for financial markets, we sourced historical end-of-day price data from the Financial Modeling Prep (FMP) API. We curated diverse list of highly-liquid assets from several categories to ensure broad market coverage:
Stocks: core set of large-cap stocks was selected from major US indices, including the S&P 100, Dow Jones Industrial Average, and NASDAQ-100.
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Indices: A comprehensive list of major global and sector-specific stock market indices.
Funds: A variety of Exchange-Traded Funds (ETFs), including those focused on specific sectors, investment themes, and active management strategies.
Cryptocurrencies:
The top cryptocurrencies by market capitalization, such as BTCUSD and ETHUSD, were included.
Forex:
Major and minor currency pairs were selected to represent the global foreign ex- change market.
Commodities: list of all available commodity futures provided by the data source.
Final Curation and Validation After the initial filtering and selection, all potential tasks under- went final validation step. Each event was used construct 'Query' object, which simulates the task setup for an agent. Any event that failed during this process due to issues like incomplete historical data, invalid time span, resulting in options with distinguishable value (i.e., all outcomes having the same payoff)-was discarded from the final dataset. This final check ensures that every task in the benchmark is well-formed and evaluable.
C.3 BASIC SEARCH AND DEEP RESEARCH GROUNDERS
To benchmark framework against non-programming agents with varying levels of sophistication, we implemented two text-based grounders: Basic Search and Deep Research. Both agents are built upon common, customized search service ensure consistency in information access. This service powered by the Exa API (https: //eaa.aa//// and is strictly configured to only return web results published before the experiment's knowledge cutoff date, thereby preventing data leakage from the future.
For Basic Search grounder, the search function was provided to the agent tool. When tasked with grounding leaf proposition, it may use the tool through function calling provided by the OpenAl API. The Deep Research grounder implemented using the OpenAI DeepResearch API. We replace the default search tool with our own customized MCP server hosting the same search tool the Basic Search grounder avoid data leaking.
C.4 JUPYTER NOTEBOOK GROUNDER
The Jupyter Notebook Grounder is the most advanced grounding agent in our framework, de- signed to simulate the workflow of human expert performing quantitative and qualitative analysis. Instead of relying solely on text-based reasoning, this agent interacts with a sandboxed Jupyter Notebook environment to construct rigorous, evidence-based proof for given leaf proposition. The process is stateful, iterative, and tool-driven, allowing for complex data retrieval, analysis, and visualization.
C.4.1 SANDBOX ENVIRONMENT
Each grounding task is executed within an isolated Jupyter Session, which provides a secure and stateful computational environment. The sandbox is managed by the JupyterSandbox class, which handles the lifecycle of kernel processes and notebook files.
When a session initiated, a special initialization cell is prepended to the notebook. This cell imports necessary libraries and instantiates the P Proxy class, which serves the agent's interface to all external data APIs. This setup ensures that the agent has immediate access to its toolsct and that all API calls configured with the correct knowledge cutoff date, preventing data leakage from the future.
The agent's interaction with the notebook is entirely programmatic. It cannot directly edit delete previous cells; it can only append new cells, ensuring a verifiable and immutable record of the analysis process.
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C.4.2 ITERATIVE PROOF CONSTRUCTION
The agent constructs its proof through an iterative, multi-step process orchestrated by the Prover agent logic. The agent reasons about the proposition and decides on course of action, which it implements by generating sequence of notebook cells.
The agent's primary output is a stream of Jupyter cells, which can be of two types, as dictated by the system prompt:
Cell Generation
Markdown Cells (<markdown.cell>>) Used for qualitative reasoning, outlining the analytical plan, summarizing intermediate findings, and structuring the final report.
Python Cells (<python_cell>): Used for quantitative tasks. This is where the agent performs data retrieval via API calls, conducts statistical analysis, and generates visualiza- tions to support its claims.
Debugging Loop After the agent submits its cells, the sandbox executes them sequentially. If Python cell fails, the execution halts, and the agent is provided with the error traceback. It then enters debugging loop, where it is prompted to provide a corrected version the single erroneous cell. This cycle can repeat for predefined number of attempts beebug_max.ree reeriie)), allowing the agent to recover from syntax errors, incorrect API usage, or data handling mistakes.
Termination The agent continues this cycle of planning, coding, and debugging until it determines its analysis is complete. It then issues a special <TERMINATE NOTEBOOK> command. At this point, the programming phase ends, and the agent is prompted to synthesize its findings from the notebook into a final, comprchensive proof and a soft truth value (Ptrue) for the proposition.
Name
Description
fmp
Financial Modeling Prep API
FMP provides the Stock Market APIs and Financial Data APIs, such as real-time stock prices, financial statements, and his- torical data. It offers a comprehensive so- lution meet all financial data needs.
132
msd
Main Street Data API
The Main Street Data API compiled over thousands of metrics related to 2,500 US companies, offering unparalleled insights into businesses beyond standard financial statements.
4
fred
Federal Reserve Economic Data
The FRED& API retrieves economic data from the FRED@ and ALFRED@ websites hosted by the Economic Research Division of the Federal Reserve Bank of St. Louis.
16
Google Trends Search API
Google Trends API scrape real-time results from Google Trends. also supports au- tocomplete, related queries, related topics, and geo locations.
8
exa
Exa Search API
Exa provides three core functionaliiiis: Find webpages using Exa's 's embeddings- based or Google-style keyword search; ob- tain clean, up-to-date, parsed HTML; and find similar pages.
Table The library external data APIs available to the Jupyter Notebook Grounder. Each proxy provides access to suite of specific endpoints for quantitative analysis. "#" means the number of endpoints.
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Pairwise significance & 95% Confidence Interval (Accuracy Difference)
10.5
Randoon
Nox Soarch
12.90
Tou Thg.
111 12.5
1.
13.00
Graph Tha.
11.00
Forest Tay.
Andlytical 1850
Pralyttcs
6.00
Anayries
0.00
Jaylee
Analydice UN
Ancltiee (M
-4.%%
Mandiom
Graph of trige
Romet of trig
Auabyica ERG
Analytica BPS
Dessi Novennc
Ansipss (ON
Anegytta CN
Asappica .o1
600
Acsipiic
Juewer
Anelyiian
Analvitia
Figure 10: Statistical significance of the results in Table computed by pairwise McNemar's tn each square, the first row denotes the P value, the second and third row denotes the upper and lower sides of the confidence interval of the accuracy difference between the model on the y-axis and the xaxxis.
C.4.3 API LIBRARY
The Jupyter environment augmented with powerful, extensible library of APIs for accessing real-world data. All API interactions are mediated through special CALL function injected into the notebook's 's scope.
The Proxy System The CALL_API function is an interface to the Proxy class, which manages access to all underlying data sources. The Proxy system is designed to be modular, with each data source (e.g., FRED, Financial Modeling Prep) implemented as separate BaseProxy sub- class. This design allows for easy integration new data sources. Before using an API, the agent instructed to retrieve.api.do function get detailed documentation endpoints and parameters, promoting correct usage. Table 4 lists the core APIs available to the agent in our experiments.
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D ADDITIONAL RESULTS
D.1 MCNEMAR'S TEST
To validate the statistical significance of our accuracy improvements, we performed pairwise Mc- Nemar's test on the prediction outcomes (correct vs. incorrect) for all evaluated methods. This test is appropriate for comparing the performance of two classifiers on the same dataset. We test the methods on the full forecasting benchmark introduced in 5.1 The results, visualized as matrix of p-values, are presented in Fig. 10
The matrix clearly shows that the improvements achieved by our top-performing configurations are highly statistically significant. For instance, Analytica-L. augmented with the Deep Research grounder shows a p-value of p=0.00 when compared against the standalone Deep Research baseline, as well as against all other baselines like Tree of Thoughts and Forest of Thoughts. This indicates that the observed 12.72% relative improvement in accuracy is extremely unlikely to be to random chance.
Similarly, the highly cost-effective Jupyter Notebook grounder with Analytica-L also demonstrates statistically significant outperformance against its standalone counterpart and the Basic Search- based methods. The test also highlights significant performance differences between the synthesis rules; the Linear (-L) and Vanilla (-V) rules consistently and significantly outperform the Simple Logic (-S) rule across different grounders, confirming the robustness discussed in 4.3 In cases where the performance difference is small, the correctly identifies it not significant (NS), such as the comparison between Analytica-V (DR) and Jupyter Notebook + Analytica-L (JN).
D.2 PERFORMANCE BY CATEGORY
Pred.
Index
Stock
Fund
Forex
Comm.
Cryp.
All
Random
46.19
55.06
43.60
47.66
50.00
50.00
37.50
48. 10
Tree of Thgt. 45.29
71.35
63.95
67.29
56.25
62.50
50.00
60.19
Graph of Thgt.
45.74
66.85
60.47
64.49
50.00
65.62
37.50
57.88
Forest of Thgt.
46.64
69.66
64.53
69.16
50.00
68.75
50.00
60.73
Basic Search
43.50
61.24
56,40
65.42
31.25
50.00
37.50
53.94
Analytica-V V
43.50
79.21
65.12
74.77
43.75
71.88
62.50
63.18
+ Analytica-S
44.84
67.98
57.56
67.29
62.50
56.25
50.00
57.61
+ Analytica-L
48.88
80.90
65.12
74.77
56.25
71.88
75.00
65.62
Deep Research
46.64
80.34
64.53
71.96
43.75
50.00
75.00
63.04
A
57.85
82.58
65.12
76.64
62.50
68.75
87.50
69.16
+ Analytica-S
53.36
79.21
63.95
74.77
62.50
68.75
75.00
66.30
+ Analytica-L
63.68
80.90
65.70
75.70
68.75
75.00
100.0
71.06
Jupyter NB
51.12
73.03
62.21
66.36
62.50
59.38
62.50
61.96
+ Analytica-V
60.54
79.78
64.53
75.70
50.00
75.00
75,00
68.89
+ Analytica-S
51.12
73.60
63.37
65.42
68.75
65.62
75.00
62.77
+ Analytica-L
60.54
81.46
65.70
74.77
75.00
78.12
75.00
70.11
Num. Tasks
223
178
172
107
16
32
736
Ratio
30.30%
24.18%
23.37%
14.54%
2.17%
4.35%
1.09%
100%
Table 5: Model accuracy (Accu. %) breakdown by task category.
Table provides a granular breakdown of model performance across seven distinct categorics: Pre- dictive Markets (Pred.), Stock Indices (Index), individual Stocks, Funds, Foreign Exchange (Forex), Commodities (Comm.), and Cryptocurrencies (Cryp.). This detailed view reveals several key in- sights into the strengths and weaknesses of the different methods.
Across the board, mnalytica-enhanee agents consistently outperform their standalone counterparts in almost every category. The most substantial gains observed in the more traditional and data-
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rich financial markets, such as Indices, Stocks, and Funds. For instance, when augmenting Deep Research, Analytica-L achieves a remarkable 100% accuracy on the cryptocurrency tasks and significantly boosts performance in Predictive Markets from 46.64% to 63.68%. This suggests that the structured, decompositional approach of Analytica is particularly effective in domains where a multitude of quantitative and qualitative factors must be weighed.
Interestingly, most models, including the more advanced ones, struggle with Predictive Market tasks, with many performing below the random baseline. This highlights the inherent difficulty of these problems, which often involve complex socio-political factors and sparse, noisy data. However, in this challenging domain that Analytica-L provides the most dramatic relative improvement, demonstrating its ability to impose a coherent analytical structure on ambiguous problems. In con- trast, performance on financial instruments like Indices and Funds strong across most models, likely due to the availability of high-quality historical data and established analytical frameworks, which the agents can effectively leverage. The Jupyter NB agent, with its ability perform quan- titative analysis, shows its strength in these data-intensive categories, and its performance is further amplified by the Analytica framework.
D.3 METHOD CONSENSUS OF ANALYTICA
Agent Consensus Matrix
Basic Search
bapyter Notebook
Deep Research
Analytica (85)
Analytica (M)
Analytica-V (DR)
Analytica-L Analyoiaal (85)
Analylica- (DR)
Analytica (85)
Analytica-S (M)
Anayyica-S (DR)
Random
(IN
Random
6.83
0.77
0.72
6.75
0.74
0.72
077
0.73
0.76
0.79
1.00
Basic Search
0.63
1:00
0.91
0.9
0.85
0.86
0.64
0.83
0.0
0.8
0.87
0.80
0.81
Jupyter
0.56
0.86
0.05
Deep Research
0.91
0.91
0.08
Analytica Vi (B5)
0.72
0.85
0.85
0.35
1.00
0.92
0.69
0.90
0.94
0.91
0.76
0.75
0.14
Consensus Score
Analytica-V (N)
0.83
0.88
0.82
2.20
0.97
0.92
0.95
0.76
0.76
Analytica-V (DR)
0.85
Analytica-l, (85)
0.72
0.03
0.83
0.95
0.90
0.90
0.90
0.93
0.74
0.70
0.75
Analyticad (N)
0.75
0.85
0.86
0.88
0.84
0.32
0.69
0.95
1.00
0.97
0.75
0.74
0.76
0.50
Anelytice-L
Analytica 5 185)
0.87
0.75
0.56
Analytica-S (N)
0.76
0.54
0.77
0.75
0.73
0.78
0.76
0.74
0.74
0.75
0.26
1.20
0.89
Analytica-5
0.81
0.75
0.74
0.76
0.76
0.26
0.75
0.89
1:00
Figure 11: Consensus matrix of final predictions across all methods. The color of each cell rep- resents the pairwise agreement score between two methods, with darker colors indicating higher consensus.
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Fig. 11 displays consensus matrix, illustrating the degree of agreement in the final predictions among all evaluated methods. The matrix reveals distinct clusters of agreement. The various "thought" architectures (Tree, Graph, Forest) form noticeable cluster, indicating that they often arrive at similar conclusions despite their different structural approaches to reasoning. This suggests they may share similar underlying reasoning patterns or biases inherited from the base L.M..
The Analytica variants, particularly those built on the same grounder (e.g., all Deep Research Analyt ica versions), show very high consensus among themselves. This is expected, they share the same foundational evidence from the grounder and differ only in the final synthesis step. more insightful observation is the relatively high agreement between the top-performing mod- els, Deep Research + Analytica- and Jupyter NB Analytica-2 This conver- gence among the best methods suggests that as performance and robustness increase, the models' conclusions become more aligned, likely approaching more objectively correct analysis. The Vanilla, Simple Logic, and Linear synthesizers for given grounder also form tight cluster, which strong indicator that the decomposition and grounding phases are the most critical drivers of the final outcome, with the synthesis rule acting as a fine-tuning mechanism for accuracy and stability.
D.4 ABLATION ON BASE MODELS
To rigorously evaluate the impact of the underlying language model on the performance and effi- ciency of the Analytica framework, we conducted a series of ablation studies. We systematically varied the models assigned the three core components: the Grounder, the Analyzer, and the Syn- thesizer.
D.4.1 SETUP
Our experiments utilize three distinct large language models, chosen to represent spectrum of ca-
pabilities and design philosophies: o3 (o3 (o3-2025-04-16) for specialized reasoning, serving as our high-performance benchmark. 2. gpt-4.1 (Hypothetical Generalist): A powerful, general-purposee model used test the framework's effectiveness with non-specialized but highly capable LLM. 3. 04-mini (Hypothetical Cost-Effective Reasoner): A cost-efficient and fast reasoning model to evaluate the framework's performance under significant resource constraints.
state-of-the-arr model optimized
This selection allows us to measure not only how performance scales with model capability but also how robust the framework is to the specific architecture of its components. We run all configurations on our benchmark set with 100 events introduced in [.I We use the Vanilla synthesis rules and basic search agents.
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D.4.2 COST-ERFICIENCE OF MODEL COMBINATIONS
Cost Efficiency Analysis of Agent Combinations
Model Combination (Grounder Analyzer Synthesizer)
D4-Miri a 04-iin a 0440n
328.5
04-Mii 06-Mi 03
237.2
O4-iini
GPT41
257.4
03
OR-Mee 03 GPT43
285.9
O4-Mini GPS4. 0446i
252.7
173.8
04-Mii GPT4.1
08 e 04 Kini e 04 Mil
320.3
03 Miw 03
216.9
O4-Mil GPTd1
213.5
03
03 d3 GPT4.
171.1
03 GPT44.3 04466
241.9
GPT442
177.2
189.3
GP7-4.1 + 04 Kin + 04 Mnl
GPT441 or Men a
226.4
GPT4.1 04-MMi GPT41
234.8
241.1
GPS4.1
69T4.1 03 GPT4J
171.7
G e GPF41 о4
278.8
GPT42
175.0
50
100
150
200
250
300
350
Cost Efficiency (Accuracy / Cost per Query (S))
Figure 12: Cost-efficiency analysis of different model combinations for the Analytica components. The chart compares 27 configurations, varying the LLM for the Grounder, Analyzer, and Synthesizer roles. The length of the bar represents cost-efficiency, calculated accuracy divided by cost.
In Fig. 12 we present aecuuusa analysis for all 27 possible combinations of the three base models across the Grounder, Analyzer, and Synthesizer roles. The plot clearly illustrates the trade-off frontier between computational cost and predictive accuracy.
The results unequivocally show that the choice of the Grounder model is the most significant deter- minant of both cost and overall performance. Configurations using the powerful o3 model for the grounding phase consistently form a cluster in the high-accuracy, high-cost quadrant. Conversely, using the economical o4 -iini as the Grounder results in a cheaper but less accurate agent. The model choices for the Analyzer and Synthesizer have a more subtle effect, creating smaller per- formance variations within the distinct tiers established by the Grounder. This analysis serves as a practical guide, allowing users to select a configuration that aligns with their specific balance of performance requirements and resource constraints.
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D.4.3
BASE MODEL SELECTION FOR COMPONENTS
Average Performance by Model
70
06.33
60.33
66.11
66.33
05.es
0.35
0.33
0.31
0.30
50
0.26
Accuracy (%)
0.25
40
0.20
30
0.11
0.10
10
Accuracy
0.05
Cost
GPT-4.1
03
04.Mini
GPT-4.1
03
04-Mini
GPT-4.1
Q3
Q4.Mini
0.00
Grounder
Analyzer
Synthesizer
Figure 13: Marginal impact model choice on component performance. The chart shows average accuracy and cost when specific model is used for particular role (Grounder, Analyzer, Synthesizer), averaged across all other configuration choices.
Fig. 13 isolltts the marginal impact of the base LLM for each of the three agent roles, with each data point representing an average over all configurations where that model was used that specific role. The results indicate that the Analytica framework exhibits considerable robustmess to the choice of model within this family. While there is clear and expected trend where more capable models generally yield higher accuracy, the absolute differences in the final outcomes are modest. This low sensitivity suggests that the structured process of decomposition, grounding, and synthesis primary driver of performance. mitigating some of the variability that might arise from different model sizes or training objectives from the same provider.
This effect is particularly evident with the 04-mini model, which delivers performance that is competitive with its larger counterparts. This a significant finding, as it suggests the framework's 's methodical approach- ooprkich-breakkin complex problem into series of smaller, well-defined tasks effectively leverage more efficient models. By providing this structural "scaffolding", Analytica enables these smaller models contribute complex reasoning chains in way that would be difficult less constrained, end-to-end setting.
breaking
While the framework robust in this context, a hierarchy of influence among the components is still discernible. The choice of the Grounder model has the most pronounced impact on final accuracy, underscoring that the quality of foundational evidence is paramount. The system's graceful degradation in performance with less capable grounders, rather than outright failure, further supports the claim of architectural resilience. Besides, our model selections are from the same model family provided by OpenAI, while models from different providers may show a different pattern.
D.4.4 PERFORMANCE OPEN-WEIGHT AND SMALL MODELS
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Model
Accu
Imp.
Soft
Hard
BS
Cost (1k)
# Params
DeepSeek-v3.1
60.95
56.68
61.89
25.73
$3
671B (37B)
Analytica-L.
64.25
5.42
56.39
59.96
22.34
$59
GLM-4.6
52.73
53.10
55.03
30.73
$10
355B (32B)
+ Analytica-L
55.33
4.96
56.60
59.59
25.92
$100
Kimi-K2-Thinking
55,56
54,44
58.39
30.59
$25
IT (32B)
+ AAnalytic-LL
56.81
2.26
59.73
63.15
25.59
$284
Qwen3-Next-80--Thing
53.64
54.88
58.79
33.97
$10
80B (3B)
+ Analytica-L
55.55
3.56
58.36
59.65
32.77
$104
OpenAI-OSS-120B
54.72
55.97
59.18
28.20
$2
117B (5.1B)
+ Analytica-I.
62.96
15.05
55,40
55.67
22.74
$22
0 OpenAI-OSS-20B
55.57
54.79
59.24
29.56
$1
21B (3.6B)
+ Analytica-I.
64.24
15.59
56.91
58.59
23.68
$7
GPT-5-mini
62.45
56.60
64.09
24.37
$7
N/A
Analytica-L
64.37
3.07
60.31
65.79
23.27
$71
04-mini
62.63
58.49
64.27
25.56
$9
N/A
+ Analytica-L
66.
5.56
58.49
64.62
23.47
$101
Table
Evaluating Analytica on small and open-weight models.
To further validate the generality and robustness of our framework, we broadened our evaluation to include heterogeneous set of open-weight, cost-efficient small language models. The experimental configuration strictly adheres to the protocol outlined in $5.1 For each model, we conduct two runs: one using vanilla Basic Search and another employing Analytica-Linen with the Basic Search grounder.
The results in Table 0 indicate a consistent performance gain across all evaluated models, demon- strating that the benefits extend to both open-source systems and smaller architectures. The largest relative gains occur in compact, distilled models, thereby helping to democratize advanced rea- soning capabilities; for example, OpenAI-OSS-20BB enhanced with Analytica attains performance comparable to the baseline of the substantially larger 67 -B-parmetter DeepSeek-v3.1. This implies that Analytica can substantially narrow the capability gap between efficient edge models and large frontier models. Furthermore, the findings suggest that Analytica's effectivenees is only weakly dependent on model size (i.e., parameter count) and instead primarily governed by the underly- ing pre-training and post-training procedures, which shape how well model aligns with the structured decomposition tasks required by Analytica.
D.5 EVALUATION ON SCIENTIFIC CLAIMS
To assess domain transferability beyond finance, economics, and predictive markets. further evaluate our method in the Matter-of-Fact (MoF) benchmark (Jansen et al.) 2025a). We perform zero-shot evaluation on the test of MoF, which includes a large of 4.4k binary scientific claims from superconductors, semiconductors, batteries, and aerospace materials publications, and involving qualitative and quantitative claims from theoretical, experimental, and code/simulation topics.
For each instance, an agent receives single claim and required to output the probability Ptrue that the claim is correct. A decision threshold 5 is then applied: if Ptruc > 8, the claim is labeled as True; otherwise, it is labeled as False. For each model, we calibrate the threshold on the MoF validation set, which contains 1.4k claims. Concretely, for all validation claims, then search for the threshold that yields the highest overall accuracy, and finally use this threshold on the test set. Our evaluation includes GPT-4o-mini and 04-mini, as reported in the original paper, and additionally the two most recent models, GPT-5.1 and GPT-5- mini. Each model is evaluated under standard Basic Search configuration and under Analytica-
first collect the predicted Ptrue values
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Linear configuration using Basic Search grounders. We use each claim's publication date as the cutoff for the searches. Following Jansen et al. (202aa), we report both overall and per-category accuracy, well the associated costs.
Overall Accu.
Accuracy by Category
Cost
Model
True
False
Qual.
Qnt.
Exp.
Code
Ther.
Int.
(x 1k)
Random
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
0.50
GPT-4o-mini
0.66
0,90
0.42
0.72
0.72
0.68
0.63
0.61
0.58
$1
+ Analytica-L
0.59
0.87
0.30
0.55
0.58
0.59
0.59
0.60
0.60
$7
04-mini
0.61
0.34
0.88
0.60
0.57
0.63
0.62
0.59
0.63
$6
Analytica-L
0.64
0.95
0.30
0.57
0.60
0.73
0.62
0.68
0.66
$38
GPT-5.1
0.62
0.27
0.97
0.58
0.56
0.59
0.69
0.66
0.62
$9
Analytica-L
0.70
0.85
0.55
0.73
0.75
0.71
0.67
0.70
0.64
$78
GPT-5-mini 0.71
0.60
0.82
0.69
0.76
0.66
0.64
0.75
0.72
$3
Analytica-L
0.73
0.70
0.75
0.75
0.77
0.69
0.67
0.79
0.67
$27
Table Experiment results for scientific claims on the Matter-of-Face benchmark.
The results, summarized in Table 7 demonstrate that Analytica's structured reasoning framework generally generalizes effectively to scientific domains, though with notable exceptions. We observed significant performance uplifts for several architectures; for instance, the GPT-5.1 model improved from 62% to 70% accuracy, and GPT-5-mini saw gains from 71% to 73%. However, the impact was not universally positive: GPT-4o-miní experienced a performance regression, dropping from 0.66 to 0.59 accuracy, which is also the only negative case we observed in our experiments. A plausible explanation is that this is the oldest model among all the base models evaluated in this work and may lack the capacity required for robust complex reasoning. Nevertheless, the consistent improvement across the majority of tested models validates the broader utility of the framework in the scientific domain.
D.6 ERROR ANALYSIS
To better understand the conditions under which our methods succeed or fail, we conducted a de- tailed error analysis.
D.6.1 TASK CORRECTNESS DISTRIBUTIONS
Diarbattinn Task Comectness Robes (AB)
Destibution of "aok Correctness Sates (Predittvve Marti
Distrbution of Tast Comettwes Rahes (Steel)
Decontaae Thabe
122%
21% 23% 30%
coos
cass eles
Genecnnee Sara Gegmere
Ceverheess Rabe Segmenze
Genecnnes Sara Segmere
25%
Disoriuciion of lak Cor recnnesss Saces (inde:
Diar bution of Task Correcrress Ratos (Fud))
D'strlution of lask Comrccr es Rates 100
20%
Nurtanbage of
10%
23%
B819
Comectness Rabe Segment
Semectress Rate segmin:
Comocnees Rate Sepmen:
Figure 14: Distribution of task correctness rates across all models for different categories. The
histograms show the percentage of tasks falling into different correctness rate buckets.
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Fig. 14 (task correctness plots) shows the distribution of prediction correctness across different task categories. The distributions for financial tasks (Stock, Index, Fund) tend to be more concentrated towards higher correctness scores, especially for the oop-perfrmmng models. In contrast, the dis- tribution for Predictive Markets is flatter and more spread out, confirming that these tasks are more challenging and that model performance is less consistent. This visual analysis reinforces the finding that the models are more reliable in domains with structured data and established patterns.
D.6.2 TASK FEATURES AND CORRECTNESS
Compattion Volat Distibutiors
Compatiio Pays Battes Number Opticnn
Comparison Lag-rddume Distribu ions
2.30
V0locito
2.99
Jur IDA bos vort
peisican past Sarippo pussiite Number Options
Categary
Callegor
Figure 15: Correlation between task features and model performance. The boxplots show that higher asset volatility (left) and lower market volume (right) are associated with lower pass rates.
The boxplots in Fig. 15 explore the relationship between task characteristics and model perfor- mance. We observe a negative correlation between the volatility of financial asset and the models' prediction accuracy. This is intuitive: highly volatile assets inherently less predictable. Simi- larly, for predictive markets, events with a shorter time horizon (less time to gather information and for trends to stabilize) and lower market volume (less collective wisdom draw upon) associ- ated with lower accuracy. This suggests that the models' performance is sensitive to the inherent uncertainty and information scarcity of the task.
D.6.3 TOP AND BOTTOM PERFORMING TASKS
Finally, the tables listing the top and bottom 10 performing tasks provide qualitative insights.
Top 10 Pass rate
Bottom 10 Pass rate
MSFT shareholders vote for Bitcoin investment?
Who will be Trump's Secretary of Labor?
Will Biden announce resignation by July 31?
Trump gets more black voters than in 2020? Fed decision in January?
Will Biden speak the DNC?
Will Trump be Speaker by January 1?
Will Ukraine hold Kursk through Aug 31? Ukraine agrees to Trump mineral deal?
Trump and Biden debate before Election?
Trump nominates Elon Musk to Cabinet?
Yoon arrested by Friday?
Will the US confirm that aliens exist in 2024?
Trump and Harris agree Sept 10 debate?
Will Kanye launch a coin in February?
Will Assad remain President of Syria?
Will Kamala Harris win all 6 swing states?
Which states will move the right?
US inauguration on January 20?
Romania Parliamentary Election
Table 8: Top and Bottom 10 performing events predictive markets.
For predictive markets, the models excel at forecasting high-profile, binary events, particularly within the realm of US politics. The Top 10 tasks are questions about major political figures like Joe Biden and Donald Trump, revolving around widely publicized events such as debates and convention speeches. These topics generate a massive volume of news articles, social media chatter, and opinion polling, creating dense information environment where sentiment and likelihood can be effectively gauged by synthesizing public discourse.
Predictive Markets
The models fail when faced with questions that require more nuanced, specialized, or multifaceted reasoning. The Bottom 10 list includes tasks that involve predicting specific cabinet appointments, complex voter demographic shifts, the outcomes of intricate geopolitical conflicts. These ques-
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tions cannot be answered by simply aggregating headlines; they require deeper, causal understand- ing of political systems and human behavior, which remains a significant challenge.
Top Pass rate
Bottom 10 Pass rate
MetLife, Inc. (MET)
Target Corporation (TGT)
Johnson & Johnson (JNJ)
AstraZeneca PLC (AZN)
Microsoft Corporation (MSFT)
ConocoPhillips (COP)
AbbVie Inc. (ABBV)
Chevron Corporation (CVX)
Take-Two Interactive Software, Inc. (TTWO)
PACCAR Inc (PCAR)
Bristol-Myers Squibb Company (BMY)
Micron Technology, Inc. (MU)
Intuitive Surgical, Inc. (ISRG)
MongoDB, Inc. (MDB)
Mondelez International, Inc. (MDLZ)
Synopsys, Inc. (SNPS)
Axon Enterprise, Inc. (AXON)
UnitedHealth Group Incorporated (UNH)
Mercadol Inc. (MELI)
Alphabet Inc. (GOOGL)
Table 9: Top and Bottom 10 performing stocks.
Stocks For individual stock (Table 9). the models demonstrate clear preference for large, es- tablished companies with extensive public records and relatively stable business models. The Top 10 performers include blue-chip names from diverse sectors such as insurance (MetLife), pharma- ceuticals (Johnson & Johnson, AbbVie), technology (Microsoft), and consumer goods (Mondelez). These companies are heavily covered by financial analysts and news media, providing a rich and consistent stream of information for the agents to process. Their performance is often driven by broad economic trends and predictable business cycles, which align well with the models' ability to synthesize macroeconomic data.
Conversely, the Bottom 10 list is populated by companies whose performance tied to more volatile, cyclical, speculative factors. This includes energy giants (ConocoPhillips, Chevron) subject to commodity price swings, semiconductor firms (Micron Technology) in a notoriously cyclical in- dustry, and high-growth tech companies (MongoDB, Synopsys) whose valuations are sensitive to shifting market sentiment and competitive pressures. Even large, stable companies like Target and Alphabet appear here, suggesting that factors like consumer spending shifts or complex regulatory challenges can introduce a level of unpredictability that is difficult for the models to capture.
Top 10 Pass rate
Bottom 10 Pass rate
HANG SENG INDEX ("HSI)
IDX30 Index (IDX30)
Oslo Bors All-Share Index ("OSEAX)
Thailand Stock Exchange Index (SET)
New Zealand Exchange Index ("NZ50)
Copenhagen Exchange Index (OMXC20)
ASX 200 Telecommunication ("AXTJ)
NASDAQ Biotechnology (NNBI)
Toronto Stock Exchange Index (TSX60)
Nikkei 225 ("N225)
MSCI World Index (MSCIWORLD)
BIST Food Beverage Index (XGIDA.IS)
Intuitive Surgical, Inc. (ISRG)
S&P/ASX 200 Energy ('AXEJ)
Dow Jones U.S. Semiconductors ("DJUSSC)
Malaysia Stock Exchange Index (KLSE)
Australia Stock Exchange Index (ASX200)
S&P Biotechnology Select Indust ("SPSIBI)
S&P Global 100 ("OOI)
BIST Tourism Index (XTRZM)
Table 10: Top and Bottom 10 performing indices.
Indices Table 10 reveals that the models are most successful when forecasting broad, diversified, major market indices. The Top 10 list is dominated by global or major national benchmarks like the MSCI World Index, Australia's ASX200, and Hong Kong's Hang Seng Index. These indices reflect aggregate economic activity and are driven by macroeconomic narratives that are widely discussed and debated in public forums, making them ideal subjects for LLM-based analysis.
The models struggle significantly with more specialized volatile indices. The Bottom 10 list features sector-specific indices in notoriously unpredictable fields like Biotechnology ŠPSTBI)
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and Energy (ÁXEJ). It also includes indices from smaller or emerging markets (Thailand, Malaysia, Indonesia), which may be influenced by local political and economic factors that are less covered by the global information sources the models primarily rely on. This indicates a gap in handling niche domains and region-specific complexities.
Top 10 Pass rate
Bottom 10 Pass rate
Capital Group Dividend Value ETF (CGDV)
Global X Copper Miners ETF (COPX)
Fidelity Total Bond ETF (FBND)
iShares U.S. Home Construction ETF (ITB)
iShares Global Infrastructure ETF (IGF)
Direxion Semiconductor Bull 3X (SOXL)
The Industrial Select Sector SPDR Fund (XLI)
iShares Global Clean Energy ETF (ICLN)
Vanguard Communication Services ETF (VOX)
iShares Biotechnology ETF (IBB)
BlackRock U.S. Carbon Transition ETF (LCTTU)
Global Upstream Natural Resources (GUNR)
First Trust NASDAQ-1000 HEA-DAQ-10--Technoolee 100Teochnyyggy (QTEC)
The Energy Select Sector SPDR Fund (XLE)
Vanguard Global ex- U.S. Real Estate (VNQI)
JPM Nasdaq Equity Premium Income (JEPQ)
VanEck Gold Miners ETF (GDX)
Dimensional U.S. Targeted Value ETF (DFAT)
Invesco Aerospace & Defense ETF (PPA)
Vanguard Materials Index Fund ETF (VAW)
Table 11: Top and Bottom 10 performing funds.
Funds Similar to the stock and index categories (Table [T]. the models perform best with broad, diversified, and well-established ETFs. The Top 10 includes funds representing core sectors of the economy, such as Industrials (XLI,, Infrastructure (IGF), and Communication Services (VOX), as well as bond funds (FBND) and funds tracking precious metals (GDX). These investment vehicles are generally less volatile than individual stocks, and their performance is tied to clearer, more persistent macroeconomic trends.
The Bottom 10 is almost exclusively composed of highly cyclical, thematic, or leveraged ETFs. This includes funds focused on volatile sectors like Copper Miners (COPX), Home Construction (ITB), Clean Energy (ICLN), and Biotechnology (IBB). The inclusion of a 3x leveraged semiconductor ETF (SOXL) is particularly telling, as these instruments are designed for short-term trading and are extremely sensitive to market volatility, making long-term forecasting exceptionally difficult.
Top 10 Pass rate
Bottom 10 Pass rate
TRON (TRXUSD)
Solana (SOLUSD)
Micro Gold Futures (MGC)
Micro E-mini Russell 2000 Futures (RTY)
Dogecoin (DOGEUSD)
Ethereum (ETHUSD)
Mini DJI Index Futures (YMUSD)
Artificial Liquid Intelligence (ALIUSD)
E-Mini S&P 500 Futures (EMUSD)
Brent Crude Oil (BZUSD)
XRP (XRPUSD)
AUD/EUR (AUDEUR)
Feeder Cattle Futures (GFUSX)
Rough Rice Futures (ZRUSD)
Soybean Oil Futures (ZLUSX)
USD/CNY (USDCNY)
Bitcoin (BTCUSD)
NZD/USD (NZDUSD)
Micro Silver Futures (SILUSD)
CHF/CAD (CHFCAD)
Table 12: Top and Bottom 10 performing commodity, forex, or crypto.
Other (Commodity, Forex, Crypto) In Table 12 performance is mixed, but pattern emerges. The Top 10 includes futures contracts on major stock indices (F-Mini S&P 500, Mini DJI), which driven by the same broad market sentiment that makes the underlying indices predictable. It also includes some of the largest and most discussed cryptocurreneies (Bitcoin, XRP, Dogecoin), where the sheer volume of online discourse may provide sufficient signal for the models to latch onto.
The Bottom 10 list highlights the difficulty of forecasting assets driven by complex and interlocking global factors. It features several currency pairs (AUD/EUR, USD/CNY, NZD/USD), whose move- ments are determined by the interplay of multiple national economies' monetary policies, trade bal- ances, and political stability. It also includes volatile commodities like Brent Crude Oil and Rough
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Rice, alongside major but notoriously volatile cryptocurrencies like Ethereum and Solana, reinfore- ing the conclusion that high intrinsic volatility remains primary obstacle to accurate forecasting.
D.7 RESYNTHESIS
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What If Labor market sudconly shows hard recession?
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(PEES)
BT serde (14555
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Figure 16: An example of the resynthesis feature for "what-if" scenario analysis. An analyst man- ually changes the probability of leaf node (P2. to reflect counterfactual assumption. The framework efficiently recalculates only the affected branch, providing a rapid update the root proposition's 's probability and quantifying the impact of the change.
key feature of the Analytica framework is its support for efficient, interactive "what-if" scenario analysis via process called resynthesis. As described in 4.1 once proposition tree is fully grounded and synthesized, user can manually alter the truth value of any node to explore coun- terfactual scenario. The framework's locality principle ensures that only the affected branch of the tree needs to be re-symthesized, making the process computationally inexpensive.
Fig. 16 provides concrete example of this process. The initial analysis (left) of the proposition "Federal Reserve will cut rates this year" results in a probability of 0.58. An analyst wishing to test the system's sensitivity to labor market conditions can pose the counterfactull "What the Labor market suddenly shows hard recession?". This is implemented by manually changing the probability of the relevant leaf node, P2. 1, from its original value to 0.0, reflecting the new assump- tion. The Resynthesis process is triggered, and the new probability is propagated up its branch. The truth values of unaffected nodes (like P1) remain unchanged. The fast recalculation yields a new root probability of 0.48, providing immediate quantitative measure of the labor market's 's impact on the overall forecast. This capability transforms Analytica from a static forecasting tool into a dynamic environment for decision-making and risk assessment.
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Random
Basic Search
Deep Research
Jupyter Notebook
w/o Analytica
48.10
53.94
63.04
61.96
Linear
65.62
71.06
70.
Average Random
63.59
67.39
66.71
62.09
66.44
65,90
Table 13: Replace the weights with random values, or make the models an unweighted average.
D.8 SYNTHESIS RULES
Distribution of Beta and Beta 0 Values
2500
All Betas
Beta
2000
Frequency
1500
1000
-0.2
0.6
Value
Figure 17: Distribution of the learned weights (3,) and intercept (3g) for the Linear synthesis rule. The concentration of weights low positive values demonstrates the rule's noise-dampening prop- erty, as formally proven in $ A.I
Linear Rule The stability of the Linear rule, = = is predicated on its ability to act as weighted average that dampens noise from its inputs. Our experiments confirm that the Synthesizer leams to implement this property. Fig. 17 shows the distribution of all leamned child weights (8,) and intercept terms (3p) across our experiments. The child weights are predominantly positive and concentrated in the [0, 0.5] range, ensuring that single child proposition has outsized impact and that errors are smoothed rather than amplified. The intercept term, .o, is tightly centered around zero, indicating that the agent relies primarily the evidence provided by the child propositions rather than a strong independent bias. This behavior is encouraged by constraining the intercept's absolute value (e.g., |Bol < 0.1), which prevents the model from ignoring the grounded evidence.
In Table 13
we replace all the weights by random numbers ('Average'), or degrade the linear rule to simple unweighted average ('Average') while removing the intercept, and compare it with the Analytica with the linear rule for different grounder and the grounder itself without Analytica. The degraded performance shows that the linear weights provide informative ensemble of evidence.
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Formula
Assumption
PA
1.1. OR (P1.1.2 AND
Fuel costs stay stable, capacity constraints manageable, and Fed policy avoids significant slowdown.
0.65
P1.1.3) OR (P1.1.2 AND PA)
AND P2 AND P3 AND PA)
No unmodeled political or platform de- 0.8 velopments (e.g., surprise rule changes, cebate-defiiition di sputes, or market tech- nical disruptions) will materially alter Pl, P2, or P3.
(P1 AND P2 AND P3) OR PA
Residual catalysts (ETF flows, China re- opening travel, idiosyncratic M&A) can occasionally override modeled drivers to make long KWEB best even one core condition fails.
0.05
(P1 AND P2 AND P3 AND PA)
No large unmodeled regime shifts or 0.85 market-structure shocks beyond those cap- tured in P1-P3.
(P1. 1 AND P1.2 AND P1.3 AND
Additional supportive factors (e.g.. fiscal 0.7 policy. corporate buybacks. cross-border flows) remain in place, offsetting valuation headwinds.
P1.5 AND NOT P1.4) OR PA
(P1.1 AND P1.3 AND P1 AND
No major geopolitical or macroeconomic shocks will trigger risk-off shift in market sentiment.
0.75
(P1.2 2 OR PA))
(P1 AND P2) AND PA
Assumes that platform execution, liquidity, and unmodeled market/political tail-risks do not invalidate P1 P2 before resolu- tion.
0.8
(P1.1 AND P1.2) OR (P1.5 AND
PA captures other supporting factors 0.5 (global risks, post-election fiscal changes) that bolster hike under loose financial and expansionary fiscal conditions.
P1.6) OR (P1.3 AND P1.4 AND PA)
AND (P2 OR PA)
Residual factors (e.g. large M&A, extraor- dinary buybacks, regulatory shifts in agri- culture, geopolitical events) may still tip returns in favor of long DE even if short's modcled inferiority weakens.
0.1
(P1 AND P2 AND PA)
No extreme political shocks, contract re- designs, or acute liquidity dislocations oc- invert the EV risk-adjusted rank- ing of the PC contract relative to alterna- tives.
0.85
Table 14: Random real examples of logical formulas, assumption descriptions, and assumption probabilities (PA) generated by the Simple Logic Synthesizer agent.
Simple Logic Rule Table presents selection of formulas generated by the agent in our experi- ments. These examples showcase how the agent uses combination of AND, OR, and NOT operators, along with the PA variable, build a causal or evidential case the parent proposition. For in- stance. proposition might be true if several core conditions met (P1 AND P2 AND PA) or if one of several alternative scenarios occurs (P1.1 AND P1. 2) OR (P1.3 AND PA) )
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Child Proposition 1.1 Published as a conference paper at ICLR 2026
E PROMPTS
E.1 ANALYZER
System Prompt for Analyzer
You are an expert logical strategist and project manager for team of advanced research agents (grounders) in financial, economic, business, social, and political analysis. Your primary mission is to decompose a complex 'Proposition to Analyze' into a tree financial, economic, business, social, and political propositions, where the truthfulness of the parent proposition is based on the truthfulness of the children.
You should firstly give an analysis and planning of how to decompose the proposition, and explain your framework of analysis, use the professional knowledge and analysis framework in financial, economic, business, social, and political analysis. You are encouraged to apply professional analysis framework that are used academia or industry. Please refer them in your analysis. A proposition tree is like the following:
Parent Proposition
Child Proposition 1
* Child Proposition 1.2
Child Proposition 2
* Child Proposition 2.1
Child Proposition 2.2
You should progressively derive it in your analysis. Then, provide your proposition tree in list of ISON objects wrapped in a single 'ijson '. in the following format:
vrijson [
"parent": "proposition.id" # the id of the parent
proposition
"children";
"propositton.id": "proposition.contentt, the content of the child proposition
"causality: "..." # the causality of how the childres lead to, imply, support, impact the parent proposition (...)
...
Each ISON object should be a single proposition and its children. You should mark each child with *unique* proposition_id The id of input proposition is always "PO". Then mark the children with "PI", "P2", "P1.2", "P1.3.2.1", etc. not allowed to reuse the same proposition for different propositions. The propositions should form a tree structure rooted at "PO".
Notes:
1. A proposition is a single sentence statement, with financial, economic, business, social, and political meaning that can be associated with boolean value True or
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False. The decomposition should illustrate the causal relation that how children factors lead to, imply, support, or impact the truthfulness of the parent proposition.
2. The decomposed propositions should be self-contained, not dependent on the par- ent proposition. Which means it can be understood without the parent proposition as context. For example, should not refer to the parent proposition using terms like "it", "this metric", "this event", etc.
3. You not expected to decompose the proposition into low-Ievel fine- ane-ggained propositions. Instead, it is ideal to decompose the proposition into high-level and meaningful financial, economic, business, social, and political factors, assump- tions, hypotheses, etc.
4. You should keep the tree to be in-depth but not redundant, this means that you do not need to create commonsense as child proposition. You can have some compromise on rigorousness, the key is to illustrate clear, indepth and professional analysis.
5. Try provide really insightful information from your analysis and the outcome de- composition tree that creates "alpha" for the user. Think comprehensively, deeply, and professionally. You are encouraged give really deep analysis and very deep decomposition tree.
6. Do not make redundant propositions. such as the rewrite of the same proposition or the ones that can be simply derived from the negation of other children.
Ideal Decomposition (Example for Linear rule):
Ideally, a parent proposition can be represented as a multiple linear combination of its children's propositions, i.e. P. true beta + beta 1 ptrueell beta 2 ... Deta_n"P_truee + eps, where P _ttuu is the probability of the parent proposition being true; beta_0 is the intercept, representing bias probability of the parent proposition being true that reflects the information beyond the children propositions; beta_1, beta_2, .... beta_n are the weights of the children's ' P_true; and eps is the eтror term. As a result, an ideal set of child propositions should be less correlated with each other, and representing the most dom- inant factors that affect the parent proposition. Left those less important factors to the parent proposition the intercept and explain your decisions in your analysis process.
E.2 SYNTHESIZER
System Prompt for Synthesizer (Vanilla)
You are an expert for a team of advanced research agents (grounders) in financial, eco- nomic, business, social, and political analysis. The grounders have access external databases and information sources that support their analysis. They also possess qualitative and quantitative analysis skills using Jupyter Notebook help them analyze the proposition.
Your task is to aggregate the analysis of children's propositions from the grounders, and estimate the probability of truthfulness (P (P_true) of proposition based on their proofs and estimated P true.. Each proposition contains financial, economic, business, social, or political statement, which can be associated with boolean value, True or False, represented as a float number P_true between and 1, where means False and I means True. And they are decomposed into set of child propositions that may have causal, evidential, or other relationships with the parent proposition, which are already analyzed by the grounders.
You will need to use your professional skills and analytical frameworks financial, economic, business, social, and political analysis estimate the P_true of the parent proposition, with a comprehensive, natural language "Proof" that explains your entire reasoning process, which proves or disproves the parent proposition that supports your
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estimated P_true.
### INSTRUCTIONS
You will receive a ISON object with the parent proposition information and its children, along with their proofs and P P_true. First, write comprehensive and in-depth "Proof" that explains your entire reasoning process. Then, reweight the children's proposition factors based on your confidence in their proofs and their importance to the parent proposition. You are also required to provide a risk assessment of the proposition, and explain the risk factors that might lead to the proposition being false. Please make your analysis more specific and detailed as possible, do not miss any important information especially the data and evidence from the grounders. You encouraged present the data and evidence in table and other visualizations. Finally, synthesize the probability of the parent proposition based on the reweighted children factors, and provide your conclusion single "sjsonn in the following format:
vrison
"p.true": <float> # the probability of the proposition
being true, between 0 and "key.factor"; <string> the key factors that why the proposition likely to be true or false, one or two sentences
### NOTES
You are encouraged use the knowledge and theory from academia or industry and cite them in your proof.
2. You need to think beyond the given data and provide a more comprehensive, in- depth, and broad analysis especially for the points that might be omitted by the grounders.
3. It is also your task to check the consistency of the children's proofs and their P_true, well as the quality of the proofs themselves.
System Prompt for Synthesizer (Linear)
You expert for team of advanced research agents (grounders) in financial, nomic, business, social, and political analysis. The grounders have access to external databases and information sources that support their analysis. They also possess qualitative and quantitative analysis skills using Jupyter Notebook to help them analyze the proposition.
Your task is to aggregate the analysis of children's propositions from the grounders, and estimate the probability of truthfulness (P (P.true) of proposition based on their proofs and estimated P P.true. Each proposition contains financial, economic, business, social, or political statement, which can be associated with boolean value, True or False, represented as a float number P. P.true between O and 1, where ( means False and I means True. And they are decomposed into a set of child propositions that may have causal, evidential, or other relationships with the parent proposition, which are already analyzed by the grounders.
You will need to your professional skills and analytical frameworks in financial, economic, business, social, and political analysis to estimate the P_true of the parent proposition, with comprehensive, natural language "Proof" that explains your entire reasoning process, which proves or disproves the parent proposition that supports your estimated P_true. The P.true of the parent proposition is represented multiple linear
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combination of the children's P_true, i.e. P_true beta_0 heta_1*P_true" beta_2*1 P_truee +... + "itaannP_ttuuaa + eps, where beta_0 is the intercept, representing bias probability of the parent proposition being true based on your own knowledge and analysis; beta. beta.2, ... beta.n are the weights of the children's P.true, based on your confidence of the value from their proofs and your judgment of their importance to the parent proposition; and eps is the error term.
### INSTRUCTIONS
You will receive JSON object with the parent proposition information and its children, along with their proofs and P true. First, write a comprehensive and in-depth "Proof" that explains your entire reasoning process. You also required to provide risk assessment of the proposition, and explain the risk factors that might lead to the proposition being false. Then, analyze the weights the children's proposition factors based on your confidence in their proofs and your judgment of their importance to the parent proposition. Please make your analysis more specific and detailed as possible, do not miss any important information especially the data and evidence from the grounders. You should try to compute the resulting true of the parent proposition based on the weights and the intercept you derived and iteratively refine them, to make sure the final P P_ture is reasonable and valid (between O) and 1). The eps usually small and can ignored, do not include in your final result. You are encouraged to present the data and evidence in table and other visualizations. Finally, provide your conclusion in single jjson
1 in the following format:
'ijson
{
"beta": H{
"beta.0": <float>, the intercept, the key must be <float>, for example, "P1", # the weights of the children's s proposition factors, all children must be included
"beta.0"
"<child "P2", "P1.1", "P1.2", etc.
H
"key-factor"; <string> the key factors that why the proposition likely to be true or false, one or two sentences }}
#*# NOTES
You are encouraged use the knowledge and theory from academia or industry and cite them in your proof.
2. You need to think beyond the given data and provide a more comprehensive, in- depth, and broad analysis especially for the points that might be omitted by the grounders, they are the core factors you need to consider in deriving the intercept, the intercept can be seen as an assumption those omitted factors and the risk factors, remember to clearly state those assumptions in your proof and explain how they affect the intercept.
3. The weights do not necessary to be from the intercept beta. () can be negative, but its absolute value should be less than (abs_interce) mate the final P_rrue after the weights and intercept are applied must be between 0 and 1. Please compute yourself first to make sure the final P.true is valid before providing your conclusion in the JSON block.
can be any real number, and
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System Prompt for Synthesizer (Simple Logic)
You are an expert for a team of advanced research agents (grounder) in financial, eco- nomic, business, social, and political analysis. The grounders have access to external databases and information sources that support their analysis. They also possess qualitative and quantitative analysis skills using Jupyter Notebook to help them analyze the proposition.
Your task is to aggregate the analysis of children's propositions from the grounders, and estimate the probability of truthfulness (P true) of a proposition based on their proofs and estimated P true. Each proposition contains financial, economic, business, social, or political statement, which can be associated with a boolean value, True or False, represented as a float number P_true between 0 and 1, where means False and I means True. And they are decomposed into a set of child propositions that may have causal, evidential, or other relationships with the parent proposition, which are already analyzed by the grounders.
You will need to use your professional skills and analytical frameworks financial, economic, business, social, and political analysis estimate the P_true of the parent propo- sition, with a comprehensive, natural language "Proof" that explains your entire reasoning process. The P_true of the parent proposition is represented children's P true, i.c. P true = (P truel AND true2) OR (P true3 AND true4) OR OR (P true n-1 AND P true n), where P 1u P true2, P true of the children propositions being true. Here we use probabilistic logic to represent the logical combination, where a logical AND of P_truel and P_true2 is represented as: P_truel AND P_true2 = P_truel P_true2: a logical OR of P P_tueel and P P_true2 is represented as: P.truel OR P_true2 P_truel P P_true2 P_truel P_true2; and a logical NOT of P_true is represented as: NOT P P_truel = P truel, you can also use NOT to negate the parentheses.
logical combination of the
the probabilities
### INSTRUCTIONS
You will receive a JSON object with the parent proposition information and its children, along with their proofs and P. P.true. First, write a comprehensive and in-depth "Proof" that explains your entire reasoning process. You are also required to provide risk assessment of the proposition, and explain the risk factors that might lead to the proposition being false. Then, analyze the logical combination of the children's proposition factors based your confidence their proofs and your judgment of their importance to the parent proposition. Please make your analysis information especially the data and evidence from the grounders. Specially, you can include special assumption variable to capture the less important factors, and include in the formula. Notice that the assumption variable id in the formula should ALWAYS BE "PA", and all the other variables the formula should be the proposition id of the children in the input proposition information. You should use ALL the children propositions in the formula, and the formula should a valid logical combination of the children's P_true. You are encouraged to present the data and evidence in table and other visualizations. Finally, provide your conclusion in single jison
specific and detailed possible, do not miss any important
1 in the following format:
Vjjson
{[
"formula": <string>, # e.g., (P1 AND P2) OR (P3 AND NOT PA)
"assumption": {f
"detail": <string>, I detailed assumptions, one or two
sentences
"probability": <float>, # the probability the assumption being true, between 0 and 1
}}
" factorr"
<string> key factors, two sentences
}
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### NOTES
1. You are encouraged use the knowledge and theory from academia or industry and cite them in your proof.
2. You need to think beyond the given data and provide a more comprehensive. in- depth, and broad analysis especially for the points that might be omitted by the grounders, they are the core factors you need to consider in deriving the formula, remember clearly state those assumptions in your proof and explain how they affect the formula.
3. The assumption variable id the formula should ALWAYS BE "PA", and all the other variables in the formula should be the proposition id of the children in the input proposition information.
4. You should use ALL the children propositions in the formula, and the formula should be valid logical combination of the children's P.true.
5. You are encouraged to present the data and evidence in table and other visualiza- tions.
6. The available operators include AND, OR, NOT and parentheses.
E.3 GROUNDER
General Grounder Prompt
You are an expert in financial, economic, business, social, and political analysis. You will be provided with proposition, and your task is provide comprehensive proof that either proves disproves the proposition. It should include the bullet points of your analysis, such as the key findings, data, evidence, and quantitative analysis. Please be more specific and detailed as possible, do not miss any important information especially the data and evidence. You are encouraged to present the data and evidence table and other visualizations.
After you have written the complete textual proof, append single jsson block. Inside this block, provide single ISON object with exactly two keys:
1. "p-true". ": Your estimated probability (a float between 0.00 and 1.00) that the proposition true, based on your proof and notebook analysis.
2. "key-factor"s A brief (1-2 sentences maximum) statement of single most critical factor from your analysis that influenced this probability.
Example of the final part of your response:
(end of your textual proof)... ... The evidence strongly suggests the proposition is false due to factor X and factor Y.
'' ''json
"p true": 0.12,
"key factor"" "The consistent downtrend in the primary dataset combined with negative macroeconomic indicators."
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System Prompt for Jupyter Notehook Grounder
You are an expert in financial, economic, business, social, and political analysis. You primarily use propositional logic and are skilled in both qualitative and quantitative methods for your analysis. Your primary goal is to prove or disprove the given proposition. The final outcome will be the probability of the proposition to be true, accompanied by detailed proof or disproof. You use Jupyter Notebook environment as your analysis tool. You will progressively write code and markdown cells in the notebook to analyze the proposition and construct your proof. Please read these instructions carefully.
## Jupyter Notebook Environment
You will work by generating content for a Jupyter Notebook. Every time you respond, you will provide one or more cells.
1. Python Cells:
Wrap Python code in <python.cell> s/python.cell> tags. Use these for quantitative analysis, data processing, API calls, visualizations (using matplotlib plotly, avoid altair due to rendering issues), etc.
2. Markdown Cells: Wrap markdown content
<markdown.cell>
< s/markdown.cen
tags. Use these for notes, qualitative analysis, inter-
mediate reports, summaries, and to structure your overall analysis.
3. Cell Order: Cells are added to the notebook the order you provide them.
4. Sequential Execution: Cells executed sequentially.
5. Error Handling: If a Python cell execution fails, you will be informed of the error and required provide corrected version of *that specific cell*, The notebook will then re-run from the corrected cell.
6. Immutability: You cannot delete or edit previously submitted cells. Each response appends new cells.
7. Output Availability: the *current* response. Outputs from previous turns are part of the dialog history.
You will only receive the outputs of the cells you wrote in
## APT Library Usage
You have access to API library within your <python.cell> blocks. The system will execute these for you:
CALL API (api path: str, api params: dict): Use this to call an API end- point.
Example:
response CALL ("re@I("mmppll ("fmp/crypto" end-of-dar miistorcal--prcc-eeo///oo (orii","""""" {("symbol": "BTCUSD",
"from": "2023-C1-01"})
A directory of available APIs is provided below.
1. Consult Documentation First: ALWAYS make sure you have retrieved and read the documents of the API endpoints you are going use *before* you write Python cell that uses CALLAAPT function, unless you have retrieved that specific documentation earlier in this session. This prevents incorrect API usage.
2. Use API: ALWAYS use the CALL API function to interact with APIs. API keys are managed by the backend.
API:
## Terminating Analysis
When your analysis is complete and you are ready construct your final proof, use the following instruction *by itself* in your response (do not include any <python cell>> in that same response):
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Published as a conference paper at ICLR 2026
<TERMINATE NOTEBOOK>
You will then be prompted to provide your final proof and conclusion.
## API Directory
{api dirttoryy
Additional Notes:
Avoid rendering libraries like Altair due potential display issues. Matplotlib Plotly are preferred for visualizations.
Do not repeatedly request the same API documentation if you've ve already retrieved it.
It's generally more efficient to retrieve documentation for several APIs you antici- pate using in one go, rather than retrieve multiple rounds of dialogs.
Concluding Instructions for grounder
Please conclude your analysis into a report of your analysis. First, provide a comprehensive proof that either proves disproves the proposition. This proof should be based on your entire analysis in the Jupyter notebook, summarizing the key findings, data, and reasoning steps. should include the bullet points of your analysis, such as the key findings, data, evidence, and quantitative analysis. Please be more specific and detailed as possible, do not miss any important information especially the data and evidence. You are encouraged to present the data and evidence in a table and other visualizations.
After you have written the complete textual proof, append single ''json block. Inside this block, provide single JSON object with exactly two keys:
1. "p. truee: Your estimated probability (a float between 0.00 and 1.00) that the proposition true, based on your proof and notebook analysis.
2. "key_factor"; A brief (1-2 sentences maximum) statement of the single most critical factor from your analysis that influenced this probability.
Example of the final part of your response:
... (end of your textual proof) ...
The evidence strongly suggests the proposition is false due to factor X and factor Y.
''jsonn
"p "p.true": 0.12,
"actor" "The consistent downtrend the primary dataset combined with negative macroeconomic indicators."
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Published as a conference paper at ICLR 2026
F EXAMPLES
F.1 PROPOSITION TREE WITH LINEAR SYNTHESIS
PO: Long stock NVDA and hold for one year is the best option (Pirwe 0.872)
Proof key point: Superior risk-adjusted return for longs (P2) combined with mate- rially higher carrying costs for shorts (P3) makes long NVDA the best option. (See full report below)
Formula: PO 0.05 + 0.2 PI + 0.3 * P2 + 0.3 P3 0.15 P4
Causality: If NVIDIA is expected to rise (PI), offers better risk-reward (P2), while shorts incur higher costs (P3) and face an upside-skewed distribution (P4), then going long and holding for year dominates going short, making it the best option.
Proof report of PO
We assess the proposition "Long stock NVDA and hold for one year is the best option" by in- tegrating four independent dimensions-absolute upside potential (PI), relative risk-adjusted performance (P2), asymmetric carrying costs (P3), and return distribution skewness (P4)- and by explicitly considering omitted macro, competitive, and regulatory factors that shape the baseline probability (intercept).
1. Synthesis of Child Propositions
(Prue 0.7895): Positive total shareholder return over 12 months
P2 (Prne 0.9040): Long's risk-adjusted return & short's
P3 (Puue 0.9320): Shorting NVDA is materially
expensive
P4 (Pune
0.7550): One-year returns are positively skewed
Causality: If NVDD is likely to rise (PI). delivering superior risk-adjusted returns (P2), while shorts face higher costs (P3) and the upside greatly dominates downside (P4), then long hold dominates short + hold.
2. Omitted Factors and Intercept (3p +0005)
We set modest +5% baseline bias to capture:
Equity risk premium and upward drift in broad markets (Ibbotson & Chen, 2003)
Management execution, capital allocation optionality (M&A, partnerships)
Secular Al tailwinds beyond near-term catalysts
Regulatory, geopolitical, or macro shocks that affect longs and shorts symmetrically
Netting these, we assume small positive baseline that reflects the default tendency for well- capitalized, growth-oriente equities to outperform shorts in normal conditions.
3. Weight Allocation
We allocate weights based each factor's direct bearing the "best option" judgment and our confidence in the children's 's proofs. The weights sum to So = 0.95:
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Child Proposition
Ptrue
Weight (5,)
Justification
P1
0.7895
0.20
Underpins absolute upside, but influenced by valuation and macro.
P2
0.9040
0.30
Directly compares long short risk- adjusted terms.
P3
0.9320
0.30
Captures persistent cost drag shorts that alone tips the balance.
P4
0.7550
0.15
Shapes payoff' asymmetry; strong posi- tive skew favors longs.
Sum
0.95
4. Computation of Ptrue
Paue :. + ΣB: Bc Pune.
0.05 + (0.20 0.7895) + (0.30 0.9040) - (0.30 0.9320) + (0.15 -0.5550)
0.05 0.1579 0.2712 + 0.2796 + 0.1133
0.8720 (87.2%)
5. Risk Assessment
Key risks that could materially lower this probability include:
A sudden, deep global recession or credit-market shock reversing equity drift
Unanticipated, severe export controls on NVIDIA's China business
Technological leapfrogging by AMD, Intel, or hyperscaler custom silicon
Rapid Fed tightening that compresses high-growth multiple far than growth beat justifies
Corporate-govermane govemaance or execution missteps on next-gen product ramps
Each of these will reduce one or more child factors (P1-P4) introduce asymmetric shocks not captured above.
The combination of robust upside potential, dominant risk-adjusted profile for longs, elevated costs for shorts, and fat right tail yields high probability (~87%) that long + hold is the best option over one year.
Conclusion:
P1: NVIDIA stock is likely to deliver a positive total sharcholder return over the next twelve months, (Pirue 0.790)
Proof key point: Robust AI-driven earnings growth combined with stable/cxpanding valuation multiples, supported by buybacks and potential consensus upside, makes positive TSR highly likely. (See full report below)
Formula: P1 0.05 + 0.25 P1.1 0.25 P1.2 + 0.3 P1.3 + 0.15 P1.4
Causality: Sustained fundamental growth that meets/exceeds expectations (P1.1 & P1.2), combined with stable or expanding multiples (P1.3) a supportive macro backdrop (P1.4), yields high probability of positive total return.
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Published as a conference paper at ICLR 2026
Proof report for
Proof for Proposition P1
We evaluate the proposition "NVIDIA stock is likely deliver a positive total shareholder return (TSR) over the next twelve months" by combining four pillars:
1. Fundamental growth (P1.1): NVIDIA's revenue and earnings are set to grow strongly in FY2025 (Pune = 0.855). Explosive Al-accelerator demand, secured advanced-node supply, and a durable performancc/ecoossttr moat underpin this forecast.
2. Consensus upside (P1.2): Market expectations are too conservative and likely be exceeded (Piee = 0.79). Independent TAM estimates and the upcoming Blackwell launch imply material beats vs. consensus.
3. Valuation support (P1.3): Multiples should remain stable or expand as growth mo- mentum persists (Prme = 0.815). A scarcity premium pure-play Al hardware and outsized upward earnings revisions offset interest-rate pressures.
4. Macro backdrop (P1.4): Broad macro/sector conditions will remain supportive of high-growth semiconductor equities (Pine 0.5586) given likely Fed easing and sec- ular tailwinds AI/5G/cloud, partially offset by recession risk and geopolitical head- winds.
Positive TSR requires (a) earnings growth 2 required return hurdle, (b) stable or expanding P/E, and (c) no severe drawdown from macro or idiosyncratic shocks. Each child proposition addresses one of these drivers.
Omitted Factors and Intercept (Bp)
NVIDIA's large buyback program (> S7 B/year) further boosts TSR.
No dividend: TSR = price return + buybacks + optionality.
Downside risks: sharper Fed tightening, broad tech de-rating, surprise supply-chain disruptions, accelerated competitive inroads by AMD/Intel or in-house hyperscaler chips.
Net of these, assume small positive bias from buybacks and optionality, setting 30 +0.05.
Weight Allocation
We allocate relative importance based each pillar's direct influence TSR and our confi- dence in the underlying analysis:
Fundamentals (P1.1): 0.25 the primary driver of intrinsic value via earnings growth.
Consensus upside (P1.2): 0.25 reinforces the growth beat narrative and a will-to-pay premium.
Valuation support (P1.3): 0.30 critical to convert earnings into price return; con-
traction would crase gains.
Macro backdrop (P1.4): 0.15 shapes discount-rate trends; less certain given mixed cyclical signals.
Intercept (8p): 0.05 captures buybacks and optionality net unmodeled risks.
Calculation
Prue pparent)
+ P1. + 32 P1.2 83 P1.3 84 P1.4
-0.05 + 0.25 0.855 + 0.25 0.79 + 0.30 0.815 + 0.15 -0.5586
0.05 0.2138 0.1975
0.2445 + 0.0838
2 0.7896 (79.0%)
Risk Assessment
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Published as a conference paper at ICLR 2026
Macroeconomic risk: A sharper-than-expeceed Fed tightening cycle or deep recession could reverse valuation multiples and curb enterprise Al spending.
Valuation rotation: A rotation out of high-growth/AI into value or cyclicals would compress NVIDIA's P/E.
Competitive disruption: fester-than-exper inroads by AMD, Intel, Google TPU, or custom hyperscaler silicon could erode pricing power.
Geopolitical/supply shocks: New export restrictions, Taiwan-China tensions, or foundry yield setbacks could throttle shipments.
Execution risk: Unforeseen delays in Blackwell ramp or disappointing Al software adoption could dent earnings beats.
Conclusion
Given the strength of Al-driven fundamentals, anticipated consensus beats, supportive valua- tions, and moderately favorable macro backdrop- offset by identifiable downside risks-we we estimate 79% probability that NVIDIA stock will deliver positive total shareholder return over the next twelve months.
P1.1: NVIDIA's revenue and earnings will grow strongly year-on-year in FY2025 driven by accelerating demand Al accelerators. (Perue 0.855)
Proof key point: Explosive Al-accelerator demand combined with secured advanced- node supply and a durable performance/ccossstem moat underpins strong FY2025 rev- enue and earnings growth. (See full report below)
Formula: P1.1 = 0.05 + 0.4 P1.1.1 + 0.35 P1.1.2 + 0.25 P1.1.3
Causality: Explosive demand (P1.1.1) convert to realized revenue only if NVIDIA can supply product (P1.1.2) and maintain competitive lead (PI.1.3); together they drive strong earnings growth.
Proof report for P1.1
Proof for Proposition P1.1
We assess NVIDIA's likelihood of delivering "strong" year-on-year (YoY) growth in revenue and earnings for FY2025 by synthesizing three critical child propositions:
P1.1.1 (Global Al compute demand > 50% YoY)
11,1.2 (NVIDIA's supply chain ramp advanced-node GPUs)
1.. (NVIDIA maintains performance and ecosystem lead)
Strong top-line growth requires (a) sufficient end-user demand, (b) the ability to supply prod- uct meet that demand, and (c) competitive moat that supports pricing power and margin leverage.
1. Demand driver (P1.1.1, Ptrue 0.90, weight = 0.40)
Q1 FY2025 Data Center revenue grew 427% YoY to $22.6 B, dwarfing the 50% baseline.
Q2 guidance implies 50%+ YoY growth in total revs, with Data Center above that. Hyperscalers (AWS/Azure/GCP) and analysts (IDC, Gartner, McKinsey) uni- formly forecast > 50% annual growth through 2025.
Conclusion: Global demand for AI accelerators is exploding, driving strong revenue potential.
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2. Supply ramp (P1.1.2, Ptrue = 0.90, weight = 0.35)
NVIDIA has locked in wafer allocations at TSMC's nm and nm nodes; TSMC is expanding both via extra shifts (5 nm) and new fabs (3 nm in Q2 2024 ramp, Arizona setup).
Long-lead times are mitigated by multi-year reservations and customer prioritiza- tion.
No reported delays in ASML EUV tool deliveries or foundry capacity build-outs.
Conclusion: The supply chain is aligned meet surging GPU orders, removing key constraint on YoY growth.
3. Competitive moat (PI.1.3, Ptree = 0.92, weight 0.25)
Real-world MLPerf benchmarks show NVIDIA's sustained throughput 30-50% above AMD/Google offerings, preserving performance leadership.
CUDA's deep software ecosystem (20+ optimized libraries, mature debug- ging/profiling tools, and 230 active open-source projects) far outstrips ROCm and TPU stacks.
This fosters sticky customer relationships, premium pricing, and less vulnerability competitor inroads.
Conclusion: NVIDIA's performance and ecosystem advantage secures pricing power and margin expansion.
Model and Weight Allocation
Combining these factors, we model the parent probability as:
Piuce (parent) 3o 0.90 82 0.90 + A3 0.99
We choose:
31 0.40 (demand is the primary driver),
f2 0.35 (supply ramp is essential),
f3 0.25 (competitive moat underpins pricing/margins).
So 0.05 to account for macro-risk (potential enterprise capex caution, geopoliti- cal/export controls, chip pricing pressure, or supply-chain disruptions).
Calculation
P -0.05 + 0.40 x 0.90 + 0.35 x 0.90 + 0.25 x 0.92
0.05 + 0.36 0.315 + 0.23
0.855 (85.5%)
This comfortably lies between and and reflects strong but not certain growth given resid- ual macro and execution risks.
Risk Assessment
Macroeconomic slowdown: A broader IT' capex pullback cautious forecasting by enterprises could damp order timing.
Geopolitical/export controls: New U.S. or Chinese export restrictions could hamper shipment volumes prolong lead times.
Competitive catch-up: AMD, Intel, or custom Al chips from hyperscalers may nar- row NVIDIA's edge faster than expected.
Pricing pressure: In highly competitive bids, NVIDIA may need targeted price ad- justments that compress margins.
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P1.11: Global demand for generative Al compute by lyperscalers and enterprises will grow at > 50% year-on--ear through 2025, (Porue = 0.900)
Proof key point: NVIDIA's QI Data Center revenue grew 427% Yo establishing a concrete basis that hyperscaler demand for generative AI compute is expanding far beyond 50% annually. (See fill report below)
Proof report for P1.1.1
Final Proof: Global Demand for Generative AI Compute Z 50% YoY Through 2025
We evaluate the proposition by synthesizing (1) NVIDIA's QI FY2025 actuals and Q2 FY2025 guidance, (2) hyperscaler infrastructure announcements, and (3) third-party market forecasts.
1. NVIDIA Q1 FY2025 Actuals vs. Q1 FY2024 Baseline
Metric
Q1 FY2024
Q1 FY2025
YoY Growth
Data Center Revenue
$4.29 B
$22.60 B $19.00 B*
+427%
Compute (GPU) Revenue
$3.77 B*
>
YoY (>> 400%)
"Estimates derived from disclosed growth multiples transcript.
Key Evidence
Management: "Data Center revenue of $22.6 B... up 427% YoY..."
"Compute revenue grew more than 5x from last year."
These exceptional Q1 results far exceed the 50% threshold.
2. NVIDIA Q2 FY2025 Guidance vs. Q2 FY2024 Baseline
Metric
Q2 FY2024 (Actual)
Q2 FY2025 (Guidance) Implied YoY Growth
Total Revenue
$16 B
$24 B
+50%
Key Evidence
Transcript: "Revenue of S26 B... well above outlook $24 B."
Baseline Q2 FY2024 revenue was $16 B.
$24 B guidance implies exactly +50% YoY; given the Data Center segment is the fastest-growing part, its compute sub-revenue will exceed 50%.
3. Hyperscaler Infrastructure Announcements
We surveyed public hyperscaler news (AWS, Azure, GCP) for signs of compute-capace scaling:
AWS launched multiple H100 GPU clusters (P5 instances) in every major region in H1 2024.
Azure introduced "ND series v5" supercomputers powered by H100 GPUs in April 2024.
GCP expanded "A3" TPU and "A2" A100 GPU pods with > 2x capacity versus prior genera- tion.
These deployments indicate professional-scale growth trajectories well above 50% YoY in compute pacity.
Third-Party Market Forecasts
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Published as a conference paper at ICLR 2026
Source
Forecast Horizon
CAGR YoY Growth
Notes
IDC (2023)
2023-2025
56% CAGR
"AT infrastructure spending to grow >> 50% annually."
Gartner (2023)
2023-2025
52% CAGR
Enterprise and hyperscaler capex combined.
McKinsey (2024)
2023-2025
50%+ YoY
Focus on generative Al compute budgets.
Key Evidence
All major industry analysts project well above 50% annual growth Al infrastructure spend through 2025.
Logical Synthesis
1. Empirical Baseline:
NVIDIA's QI FY2025 YoY growth in Data Center and compute segments is +400%++ far surpassing 50%.
2. Forward Guidance: Q2 FY2025 guidance implies at +50% total revenue YoY; Cen- ter will exceed this benchmark.
3. Hyperscaler Behavior:
AWS/Azure/GCP public launches confirm 50% YoY capacity ex-
pansion plans.
4. Analyst Consensus: IDC, Gartner, and McKinsey forecasts all predict > 50% YoY growth for generative Al infrastructurc.
Therefore, global demand for generative Al compute by hyperscalers and enterprises will grow at 50% YoY through 2025.
For the remaining propositions, will omit the proof reports they are similar to the examples above.
P1..2: NVIDIA can secure sufficient advanced-node supply from TSMC and its sup-
ply chain to meet increasing GPU orders. (Porwe 0.900)
Proof key point: TSMC's confirmed 3 nm ramp timelines and NVIDIA's advance wafer reser- vations for nm/3 nm nodes drive high confidence supply sufficiency.
P1.13: Competing accelerator offerings lag NVIDIA in performance and the depth of the CUDA software ecosystem. (Perue 0.920)
Proof key point: Real-world sustained MLPerf benchmarks consistently show NVIDIA's Ten- sor Cores deliver 30-50% higher throughput combined with a far more mature CUDA toolchain.
P1.2: Consensus market expectations for NVIDIA's growth are still too conser- vative and are likely be exceeded, P.... 0. 0.790)
Proof key point: Systemic underestimation of Al-accelerator TAM and proven architecture-led outperformance combine to bias consensus growth forecasts materi- ally downward.
Formula: P1.2 0.07 0.45 P1.2.1 + 0.45 P1.2.2
Causality: If TAM and new product impact are modeledddeeed (P1.2.1, P1.2.2), actual results are likely to beat consensus, supporting price appreciation.
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P1.2.1:
Equity analysts underestimate total addressable market for Al accelera- tors in 2024-2025, (Prrue 0.850)
Proof key point: Implied NVIDIA market share falls below its historical 80-90% range under consensus forecasts, signaling an artificially small TAM.
P1.2.2: The forthcoming Blackwell architecture, shipping by Q4 2024, will provide incremental upside to revenue versus current estimates. (1 0.750)
Proof' key point: Management guidance and historical architecture-Ier outperformance indicate Blackwell's revenue impact is underappreciated in consensus estimates.
P1.3: Valuation multiples for NVIDIA are likely to remain stable or expand as growth momentum persists. (Porue = 0.815)
The combination of concentrated investor demand for scarce pure- play AI hardware and outsized upward earnings revisions underpins stable or expand- ing valuation multiples for NVIDIA.
Proof key point:
Formula: P1.3 = 0.05 + 0.45 P1.3.1 + 0.45 P1.3.2
Causality: High demand for scarce Al exposure (P1.3.1) and rising earnings (P1.3.2)
keep or expand NVIDIA's valuation multiple.
P1.3.1: 1: Investor risk appetite for leading Al platform companies will stay elevated scarcity of pure hardware plays. (Perue 0.850)
Proof key point: The scarcity of publicly traded pure-play Al hardware names concentrates investor demand into the few available leaders, sustaining elevated valuation multiples.
P1.3.2: Upward earnings revisions will offset potential multiple compression pres- sures. (Ptrue 0.930)
Proof' key point: NVIDIA's median historical EPS growth of 50% exceeds the 43% needed to offset even 30% P/E compression.
Macro-economic and sector conditions will remain supportive of high- growth semiconductor equities over the next year. (Pevus 0.559)
P1.4:
Proof key point: Fed-induced rate cuts are the dominant driver lowering the equity discount rate, making semiconductor valuations sensitive monetary easing.
Formula: PL.4 0.05 0.5 P1.411 + 0.3 PL4.2
Causality: Lower discount rates (P1.4.1) and healthy capex (P1.4.2) create support- ive macro environment for growth tech equities.
P1.41:: The U.S. Federal Reserve is expected to shift to modest rate cuts, lowering the equity discount rate. (Piras 0.800)
Proof key point: The persistent decline in market-implied short-term yields and easing yield- curve inversion signaling priced-in Fed rate cuts.
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Published as a conference paper at ICLR 2026
P1.4.2: The U.S. economy projected to avoid recession and maintain robust tech capex in 2024-2025. (Perue = 0.362)
Proof key point: The persistent yield curve inversion-negattie spread on every trading day over the last six months- dominatess all other expansion signals.
P2: The risk-adjusted return profile a long position NVIDIA is supe- rior to that of a short position over the next twelve months. (Prrue 0.904)
Continuous cost drag and extreme-loss asymmetry for shorts severely degrades their Sharpe ratio and tail-risk profile relative to longs.
Proof key point:
Formula: P2 0.1 + 0.25 P2.1 + 0.2 P2.2 + 0.4 P2.3
Causality: Because risk of extreme loss and ongoing costs are higher for shorts (P2.1-P2.3), the risk-adjusted return is better for longs given similar absolute pected move.
P2.1: A long equity position has losses capped at 100% of capital, whereas short position has theoretically unlimited loss potential. (Perue 1.000)
Proof key point: The mathematical derivation that stock prices cannot go below zero bounds long-pose oong-ooitiion losses at 100%, while short losses are unbounded.
P2.2: Realized volatility in NVIDIA is positively skewed; large upward price gaps earnings releases impose greater risk shorts. (Prrue 0.850)
Proof key point: The earnings-day gap distribution shows heavy right tail-2 out of 26 events (77.7%) had +5%+ jumps and none had comparable negative gaps.
P2.3: Stock-borrow fees and collateral requirements increase drawdown risk and lower the Sharpe ratio for short position. (Ptrae = 0.960)
Proof key point: The continuous cost drag (borrow fee + collateral) worsened the short Sharpe from -1.73 to -1.82 and deepened drawdown from -90.22% -90.90%
P3: Market frictions and structural costs make maintaining short posi- tion in NVIDIA materially more expensive than holding long position. (Pirue 0.932)
Persistently high borrow fees and substantial margin financing drite- by constrained lendable float and corporate actions-make shorting NVDA materially more expensive than holding long.
Proof key point:
Formula: P3 = 0.02 + 0.38 Pa.1 + 0.42 Pa.2 + 0.2 P3.3
Causality: Persistent borrow fees (P3.1), financing costs (P3.2) and corporate-action risk (P3.3) raise the effective hurdle rate for profitable short, making it less attractive than a long.
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Published as a conference paper at ICLR 2026
P3.1: Shart-berrow fees for NVIDIA shares are elevated due to high demand and limited lenduble float from index funds. (Perue 0.850)
Proof key point: The extremely low days-to-cover 0.9 trading days) of lendable NVDA shares indicates severe supply squeeze driving high borrow fees.
P3.2: Short sellers must post collateral and are subject margin calls, increas- ing financing cost over time. (Prrue 0.950)
Proof key point: High probability 66% per year) of collateral-requiring margin calls under NVDA's volatility combined with an 8.2% annual financing cost.
P3.3: Corporate actions such share buybacks potential stock splits can increase borrow difficulty and cost for shorts. (Piree 0.950)
Proof key point: Sustained share buybacks substantially reduce the available lendable float, directly tightening supply and driving up borrow costs.
P4: The probability distribution of NVIDIA's future one-year price out- comes positively skewed, offering asymmetric upside longs and asym- metric risk shorts. (Pirue 0.755)
Proof key point: High-frequency. high-impact upside catalysts generate fat right tail that outweighs the partially discounted downside risks.
Formula: 0.05 0.6 Pa.1 + 0.3 P4.2
Causality: Because upside catalysts (P4.1) earry larger potential price impact than the partially-priced downside risks (P4.2), the distribution is positively skewed, fa- voring longs over shorts.
P4.1 Multiple upside catalysts including new architecture launches, strategic partnerships, index weight increases, and aggressive buybacks could drive large positive price moves. (Perue 0.800)
Proof key point: Discrete jump events (architecture launches and partnerships) generate con- sistent, large positive returns, producing fat right tail in return distribution. (See full report below)
P4.2: Key downside risks (export controls China, competitive pressure, macro slowdown) are at least partially discounted current valuation. 0.850)
(Ptrue
Proof key point: NVIDIA's 22.3% trailing P/E contraction over the past year despite strong fundamentals indicates material risk discounting.
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F.2 JUPYTER NOTEBOOK EXAMPLE
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58

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Published as a conference paper at ICLR 2026
NVIDI PEE vs. Tech Sector P/E
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IVE Railo
2016
2017
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59

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Published as a conference paper at ICLR 2026
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60

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Published as a conference paper at ICLR 2026
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61


Reviews:
[{"review_id": "KaZbdpe7A7", "reviewer": "Reviewer_ebpb", "summary": "The paper presents an LLM-agent architecture, Analytica, for propositional reasoning. The framework consists of three major components: 1) an Analyzer that establishes a tree structure to decompose the reasoning process; 2) a Grounder that verifies leaf propositions and assigns soft truth values; and 3) a Synthesizer that recursively aggregates children's estimations to their parents to obtain the final estimation of the proposition. The authors provide theoretical analysis demonstrating that the method achieves lower variance and bias in performance. In the experiments, the authors show that the proposed method exhibits better performance in terms of both accuracy and efficiency.", "questions": "Please see the above section.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 4, "contribution": 3, "strengths": "- The paper's writing and presentation are of high quality, with clear explanations and details about the proposed framework.\n\n- The proposed Soft Propositional Reasoning is an interesting and innovative solution to the proposition reasoning problem.\n\n- The paper presents a practical, modular architecture with strong tooling. The Jupyter Notebook grounder is a well thought-out contribution, and the framework is applicable to various grounder backends.", "weaknesses": "- The framework relies heavily on the grounder’s ability to estimate and assign numerical probabilities, which is inherently difficult to calibrate. While the tree structure enables systematic problem decomposition, it also introduces the potential for error accumulation across multiple grounders.\n\n- The theoretical analysis relies strongly on linear decomposability and i.i.d. error assumptions, which may not hold in real-world applications.\n\n- The evaluation tasks—mainly financial market forecasting—are somewhat ill-posed. It is difficult to justify that the model can fully reason about market movements using only searchable information. Moreover, such forecasting problems often lack a clear linear structure, which challenges the assumptions underlying the proposed framework.\n\n- The framework is highly sensitive to prompt design. A sensitivity analysis examining how performance varies under prompt perturbations would strengthen the paper’s robustness claims.\n\n- The baseline comparisons understate stronger alternatives. Tree-, Graph-, and Forest-of-Thought baselines are evaluated only with the Basic Search grounder, whereas Analytica is paired with more powerful grounders such as Deep Research and Jupyter Notebook, making the comparison uneven.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "pdSFlpaLWz", "reviewer": "Reviewer_Hjk1", "summary": "The authors introduce an agentic reasoning pipeline called Analytica. The framework uses soft propositional reasoning (SFR) to structure the LLM reasoning process by estimating the soft truth values of different potential outcomes, by initially decomposing the question into facts that are evaluated using the agents. Their main contributions include improved reasoning accuracy, as well as computational efficiency through their jupyter notebook grounder.", "questions": "Are there any interesting failure cases? Does this pipeline fail in specific scenarios? Would be good to analyze.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "-\tPromising results, particularly on reasoning-tuned LLMs (o3 and 04), with similar trends in general purpose LLMs\n-\tThe number of tasks used to evaluate the framework is large and diverse, highlighting generalizability of the framework. \n-\tBaselines used to compare analytica to are sufficient and relevant to the reasoning task explored by the authors.", "weaknesses": "-\tSome figures, such as Fig. 6 are unclear and somewhat cluttered. Readability and understanding of the figures should be improved. \n-\tHigh dependency on problem decomposition quality. This could affect the whole pipeline negatively. Some more discussion needs to be added regarding this point.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "QgyVFYrlN3", "reviewer": "Reviewer_kYvf", "summary": "The paper proposes a hybrid reasoning framework that combines propositional logic with statistical estimation to tackle real-world forecasting tasks. events. It decomposes queries into a tree of soft-valued propositions, grounds leaves with data tools (including a Jupyter agent), and combines beliefs via a learned linear model. On 736 finance/politics tasks it attains ≈71 % accuracy, outperforming chain-of-thought and deep-research baselines while scaling near-linearly with tree size. Contributions are the SPR formalism, modular architecture, and reproducible cost/robustness analyses—incremental but solid.", "questions": "Suggested experiment: \n\nreplicate Table 2 with at least two openly available models.\n\nrun tasks from DiscoveryBench to verify transfer.", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The design of SPR is welcoming. SPR departs from pure text-based prompting, providing a middle ground between symbolic and neural reasoning. Sec. 3 Eq. (1) decomposes MSE into bias/variance, offering a clear objective.\n\nIt offers modular architecture with strong ablations. Table 2 compares three synthesis rules; Linear achieves best accuracy/variance trade-off. Sec. 5.3 noise-injection robustness confirms Linear rule stability (Fig. 5).\n\nTable 1 reports 54× node growth vs. only 12× wall-clock increase, supporting near-linear parallel scaling, which provides good evidence for scalability.", "weaknesses": "All experiments use o3-2025-04-16 only (Sec. 5.1); no evidence for GPT-4, Claude, or open-weight models, which undermines generality claim of \"diverse base models\" (Line 026).\n\nAbstract claims “domain-agnostic” without a cross-domain Table. Dataset restricted to finance/politics (Sec. 5.1); no medical, legal, or scientific forecasting tasks. The domain transfer was not demonstrated.\n\nSynthesis-rule statistical comparison underpowered. McNemar test (Fig. 10) uses 100 tasks; confidence intervals not shown. Simple-Logic rule failure attributed to noise amplification without formal test for interaction.\n\nPotential data-leakage in financial data, also lack of adversarial robustness check.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "LehTR1h4oo", "reviewer": "Reviewer_sApi", "summary": "This paper proposes a method of structural reasoning and forecasting called Analytica, based on soft propositional reasoning. The method breaks the task up into a tree of sub-propositions with an Analyzer, and probabilistically analyzes and answers leaf queries with a Grounder (Web search, deep research, Jupyter Notebook). The query results are then aggregated with a synthesizer, both linearly and with a more complicated LLM logic process. This approach aims to minimize both bias and variance, with bias minimization motivated by the power of grounders on more simple tasks and the heuristic assumption that more atomic propositions carry less bias than their more complex counterparts. Variance is managed through the linear synthesis of probabilities with (assumed) minimal covariance throughout the reasoning tree. Finally this paper empirically tests their approach, showing both cost, time and accuracy improvement over existing baselines.", "questions": "With clarification of the following questions and addressing of the outlined weaknesses, I would be willing to increase my score. \n\n- Could the authors clarify whether Analytica primarily performs reasoning (logical inference) or prediction (forecasting)? These are conceptually distinct, and understanding which is central to the framework would clarify its intended contribution.\n\n- Who is the target user or application domain for Analytica? A discussion of the framework’s practical utility and deployment scenarios would help contextualize its significance.\n\n- Several steps in the theoretical sections appear heuristic but are presented as if formally justified. Could the authors explicitly identify which parts are heuristic assumptions versus those supported by formal derivation or proof?\n\n- The approach seems to assume independence among subclaims, which may not hold in many reasoning tasks. Do the authors have proposed methods for modeling or mitigating dependencies between subclaims?\n\n- Has Analytica been evaluated with smaller or weaker LLMs, particularly for the decomposition stage, even if grounding and synthesis use stronger models? This would clarify whether the framework depends on scale or transfers across model capacities.\n\n- The Jupyter Notebook–based grounding method is described briefly yet achieves the strongest results. Could the authors provide a more detailed example or description in the main text to illustrate how this component operates?\n\n- Was this approach evaluated on non-predictive/financial market tasks? Was the dataset compiled by the authors or another source, how did the authors ensure it is representative of the tasks the paper claims to perform well on?", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "This paper presents a well-motivated and clearly framed approach to an important problem: how to structure LLM-driven reasoning to improve both accuracy and computational efficiency.\n\nOriginality: While the individual components - task decomposition and result aggregation - draw on prior ideas, the integration into a unified “Soft Propositional Reasoning” framework is novel and conceptually appealing. The work offers a formulation of structured reasoning that can operate with black-box LLMs, extending applicability to settings where model internals are inaccessible. This synthesis of theoretical framing and modular architecture has utility within the current reasoning-agent literature.\n\nQuality: The paper demonstrates empirical validation, testing multiple variants of the core algorithm and comparing them to strong baselines. The experiments are diverse and convincingly show that the proposed method improves both accuracy and computational efficiency, and supporting the authors’ claims about bias–variance tradeoffs.\n\nClarity: The introduction and framing are particularly strong, offering a clear motivation and well-scoped research question. Figure 1 effectively summarizes the system’s architecture and serves as a helpful reference throughout the paper. Although some experimental details could be clearer, the paper overall maintains a coherent narrative and logically connects earlier sections.\n\nSignificance: The ability to coordinate structured reasoning over black-box models has broad implications for scaling LLM applications in analysis, forecasting, and decision support. The framework’s emphasis on cost–accuracy tradeoffs and robustness under modular substitution makes it practically valuable, especially as computational efficiency becomes increasingly central in large-scale LLM deployment.", "weaknesses": "Clarity and Readability of Figures:\n- Figure 6 contains overlapping text, which makes key labels difficult to read.\n- Figure 2 is visually dense and difficult to interpret; the motivation for including each column and how they relate to the overall analysis should be made explicit. I also find there are too many variations to analyze coherently, a more compact version may be easier to understand. \n- More generally, the empirical section would benefit from clearer organization — e.g., separating results by contribution type (efficiency, accuracy, stability) — and simplifying figure layouts to highlight the main findings.\n\nNovelty and Framing of Contributions:\n- The individual components of the framework—decomposing tasks into subpropositions and aggregating subresults—are not individually novel, having clear precedents in prior work such as Tree of Thoughts (Long, J et al. 2023) and Question Decomposition Tree for Answering Complex Questions over Knowledge Bases (Huang et al., 2023).\n- The paper could better emphasize what is genuinely new about their integration or about the soft propositional reasoning perspective, possibly by formalizing how Analytica’s synthesis differs from prior decomposition or ensemble reasoning methods.\n\nTheoretical Rigor:\n- The theoretical sections (particularly §4.2–4.4) rely heavily on heuristic reasoning presented as if more formally derived. For example, the claim that bias decreases with decomposition depth is asserted but not proven, and “smaller” propositions are not formally defined.\n- These sections could be improved by (a) explicitly labeling heuristic arguments as such and emphasizing empirical adherence or (b) adding formal assumptions or bounds where possible\n\nEmpirical Structure:\n- Although the results are compelling, the presentation could better connect each experiment (and corresponding figure) to a specific hypothesis derived from the theory (e.g., variance reduction, robustness to model scale) or a contribution highlighted earlier in the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)