Cascaded Language Models for Cost-Effective Human–AI Decision-Making
Authors: Claudio Fanconi
Mihaela van der Schaar
Venue: NeurIPS 2025 poster ()
Keywords: Multi-LLM
Decision Making
Question Answering
Cascaded LLMs
Primary area: deep_learning
TL;DR: We propose a Cascaded multi-LLM framework with deferral and abstention policies and online learning to balance accuracy, cost, and abstention, delegating tasks across models and humans to improve efficiency in QA tasks.

Abstract: A challenge in human-AI decision-making is to balance three factors: the *correctness* of predictions, the *cost* of knowledge and reasoning complexity, and the confidence about whether to *abstain* from automated answers or escalate to human experts. In this work, we present a cascaded LLM decision framework that adaptively delegates tasks across multiple tiers of expertise -- a base model for initial candidate answers, a more capable and knowledgeable (but costlier) large model, and a human expert for when the model cascade abstains. Our method proceeds in two stages. First, a deferral policy determines whether to accept the base model’s answer or regenerate it with the large model based on the confidence score. Second, an abstention policy decides whether the cascade model response is sufficiently certain or requires human intervention. Moreover, to overcome static policies and accommodate changing task difficulty, we incorporate an online learning mechanism which uses human feedback. We demonstrate this approach to general question-answering (ARC-Easy, ARC-Challenge, and MMLU) and medical question-answering (MedQA and MedMCQA). Our results demonstrate that our cascaded strategy outperforms single-model baselines in most cases, achieving higher accuracy while reducing costs and providing a principled approach to handling abstentions.

Cascaded Language Models for Cost-Effective Human-AI Decision-Making
Claudio Fanconi University of Cambridge caf830cam. ac. uk
Mihaela van der Schaar
University of Cambridge
mv4720cam. ac.
Abstract
A challenge in human-Al maaiiinn-making is to balance three factors: the cor- rectness of predictions, the cost of knowledge and reasoning complexity, and the confidence about whether to abstain from automated answers or escalate to hu- man experts. In this work, present a cascaded LLM decision framework that adaptively delegates tasks across multiple tiers of expertise a base model for initial candidate answers, more capable and knowledgeable (but costlier) large model, and human expert for when the model cascade abstains. Our method proceeds in two stages. First, a deferral policy determines whether accept the base model's 's answer or regenerate it with the large model based on the confidence score. Second, an abstention policy decides whether the cascade model response is sufficiently certain or requires human intervention. Moreover, to overcome static policies and accommodate changing task difficulty, we incorporate an online learning mechanism which uses human feedback. We demonstrate this approach to general question-ant aanteirngnnswringgggg (ARC-Easy, ARC-Challenge, and MMLU) and medi- cal question-answering (MedQA and MedMCQA). Our results demonstrate that our cascaded strategy outperforms single-model baselines in most cases, achiev- ing higher accuracy while reducing costs and providing principled approach handling abstentions
Introduction
nata-driven decision support has gained increasing traction in high-stakes fields such as healthcare
[Jin et al. 2024 Fan al. 2024 Li al. 2024), finance [Li et al. 2023a Zhao al. 2024 and education Xu et al., 2024 For example, in the medical context, large language models (LLMs) can facilitate accurate diagnoses and treatment recommendations that encode vast knowledge Kim et al. (2024). However, high accuracy in such complex settings often requires substantial computational resources or multiple reasoning steps. Additionally, LLMs may hallucinate or generate incorrect outputs with severe consequences. Effecctive Auman-AI collaboration should balance correctness, cost, and abstention, ensuring Al-driven assistance integrates seamlessly with expert oversight.
The Challenge. key challenge in effective human-Al collaboration how to allocate computa- tional and human resources efficientlyddeiddii when an automated model should answer, when should escalate to a lager and more capable model, and when should defer to human expertise. Naïve strategies such always relying the cheaper model always trusting the more capable one fail to optimise this trade-off. The former increases the risk errors and hallucinations, while the latter inflates costs. Likewise, static deferral policies, fixed thresholds, one-off calibrations cannot adapt to changing task distributions or evolving model competence.
We provide the code for our experiments at https//ggiibb.oomaaaaaaccccaaaaa
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Advderton
If deliereed
Hiunaa Plckltion
Dylipe Moan
Masa
Mary
0.2
Maro
0,8
Expert
Figure 1: Cascaded LLM Human-Al Decision-Making Framework Examples. Given decision- making problem, the system (1) generates an initial response with base model, (2) verifies correct- ness probability, (2.5) defers to larger model if needed, (3) assesses response uncertainty, and (3.5) abstains to human expert if necessary. If feedback is available, deferral and abstention modules are adjusted over time. For this system to work efficiently, the modules should uphold three desiderata: pi the deferral policy regenerates responses only when necessary. D2 the abstention policy escalates to humans only when uncertainty is high, (33 the system continuously improves with feedback.
These limitations motivate three requirements for any cost-effective human-Al Al decision-making framework:
1. D1 Reduce Unnecessary Regenerations: Responses should only be regenerated by more capable model when there is sufficient evidence that the current one is unreliable..
2. D2 Abstain when Uncertain: The system should defer to human experts when uncertainty
exceeds acceptable bounds, avoiding overconfident automation in high-risk scenarios.
3. D3 Adapt over time: The framework should continuously refine its deferral and abstention policies as feedback becomes available, ensuring sustained reliability and improvement.
Together, these desiderata define the principles an effective decision- decision-making making framework must satisfy, irrespective of implementation.
Our Approach. We propose cascaded L.LM framework that explicitly satisfies these three require- ments. The framework adaptively delegates tasks across multiple tiers of expertise: a lightweight base model provides initial answers; a more capable but costlier large model regenerates responses when confidence is low; and, if uncertainty remains high in the system abstains to a human expert. An online learning mechanism continually adjusts the deferral and abstention thresholds based on human feedback, improving decision quality over time. Figure [ provides an overview of this cascaded decision flow with three example questions of varying difficulty.
responses, the
Contributions.
Our main contributions are threefold:
Cascaded LLM Human-AT Decision System: We introduce multi-tier decision- making system that coordinates LLMs of varying capacity with human experts balance accuracy, cost, and abstention.
Principled Deferral and Abstention Policies: We design confidence- and uncertainty-based decision policies that regulate when to defer to a larger model abstain to humans, guided by Bayesian calibration for reliable verification.
Online Learning for Adaptive Decision-Making: We propose an online optimi- sation schome that refines the deferral and abstention thresholds using human feedback, enabling continual adaptation to task complexity.

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2 Related Work
Multi-LLM Answer Generation. Several studies have explored collaborative frameworks that leverage multiple LLMs of varying capacities to enhance both performance and cost-efficiency beyond the capabilities of a single model [Chen et al. 2023 Ding et al. 2024 Aggarwal et al.) 2024]. Chen et al. [023] proposed cost-effective strategies such as prompt structuring, model approximation, and cascaded LLM frameworks. Similarly, Ding et al. 2024) introduced intelligent routing mechanism that dynamically assigns prompts to the most appropriate model. AAggrraa et al.) [222] developed black-box LLM framework for cost-efficient response generation, formalised as a Partially Observable Markov Decision Process (POMDP), requiring minimal training data. ZZu 2023a proposed multiplexer-basel approach that balances queries between small and a large L.MM, employing a trained BERT classifier to determine when the smaller model suffices.
al.
Šakota et al. [0244 introduced a neta-moddll-rrven selection framework that requires pre-training for optimal query distribution. In a parallel line of research, speculative decoding (Leviathan et al.) 2023], employs a lightweight model to generate multiple tokens, which a larger model subsequently verifies.
In contrast to prior research, we propose multi-tier framework for human-Al collaboration. Rather than relying solely on automation, our approach integrates human intervention when model uncer- tainty is too high, addressing a gap in previous multi-tier frameworks. Compared to speculative decoding research,
work prioritises the factual correctness of complete responses rather than token-wise distributions, enabling more robust decision-
rather than just fluent text generation. Zellinger et al. [2025] conducts concurrent line of research that is closest
work cascaded LLMs, as well as in their previous works (Zellinger and Thomson 2024 2025]. They focus on probabilistic modelling of cascading LLMs and their deferral and abstention mechanisms.
LLM Answer Verification and Uncertainty Quantification. Ensuring the reliability of LLM- generated responses requires adequate verification and uncertainty quantification mechanisms. Several studies have explored self verffictiiinntoon strategies [Weng et al.) [2023] Jiang et al., 2024 Pan et al. 2022]] often leveraging the LLM's internal knowledge [Dhuliawala et al. 2023). J. Alternative approaches
employ external knowledge sources for verification [aan et al. 2024
et al. 2023] Peng et al.
2023 Aggarwal et al. [0024] introduced verification techniques based on available contextual information, predominantly involving multiple LLM queries to validate response accuracy. Another research direction quantifies factual correctness uncertainty (Mahaut et al.) 2024] Kadavath et al.
[2022] conducted a detailed analysis of how LLMs express uncertainty through surrogate token probabilities, demonstrating their effectiveness in calibration. |Azaria and Mitchell [2023] explored internal LLM states, training classifiers to quantify uncertainty, while methods such as semantic
uncertainty estimation (Kuhn al. 2023 enhance robustness by analysing variations in semantically equivalent token sequences.
Our approach relies surrogate token probability [Kadavath et al.) 2022 as verification component. However, we extend this methodology by integrating a hierarchical escalation mechanism that dynamically transitions between models and human experts based verification results.
Selective Prediction. Selective prediction enables models abstain from uncertain queries Yaniy and Wiener 2010). crucial feature in risk-sensitive settings where errors are costly. The idea dates back to Chow's work on optical character recognition [Chow] 1957 1970). and has since been shown to improve deep learning performance [Geifman and HI- Yaniv [017]. 7J. In NI.P, abstention has been
introduced through manfidence-basel thresholds [Xin et al.) 2021 Yoshikawa and Okazaki 2023]. with recent work on uncertainty quantification for large language models advancing this line of research [Manakul et al. 2023 Farquhar et al., 2024 Lin et al. (024).
LLMs in Online Learning. Traditional L.MM research predominantly evaluates language models on static datasets. However, our work aligns with online learning paradigms, wherein policies are continuously refined in response to streaming data [Cortes et al. [018]] Ye et al.) 2024]. Our methodology is inspired by Jarrett et al. (2022). who introduced an online decision mediation framework mediating between suboptimal human decisions and an expert oracle. A similar research with the online learning approach is conducted by Zhu et al. 2023a], which extended their multiplexer mechanism to an online setting.
3

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3 Background
3.1 Cascaded Decision System
We consider two-tiered cascaded LLM decision system for question answering under resource constraints, denoted by
Mbsse -> Margee following the notation of Zellingee et al. (2025].
Let E X be a problem statement prompt, and let ) denote system-generated response. For every input æ, the models return a confidence score P;(xr) E [0, and an uncertainty score (x) E [0, oo), where i E {base, large). The decision to predict using the base model MMase to defer to the larger model Marge is based on whether the confidence exceeds deferral threshold, i.e., ((x) > Dasee Thus, prediction is only made if the base model is sufficiently confident. In contrast, abstention governed by predictive uncertainty: if this exceeds a threshold, Ex(x) Eı+ the system abstains and forwards the query to human expert.
We formally define the cascaded decision system as:
MBase (I)) if (1r) > Øbase A base (x) < Ébase
C(x)
Marzo (x)
if Drase (x) S Obase Chase (x) < Ehase A Eharge (x) S
Étarge
(I)
Ø
if E (x) Etuse
Easse (ar) Ehase
The decision flow of this cascade is also illustrated in Figure While focus two-model system here, the framework naturally generalises to cascades involving multiple L.MSs of varying sizes.
The objective is to generate accurate responses while accounting for the computational costs of the models and abstaining when the system is too uncertain. As described in Zellinger and Thomson [2024). this constitutes a multi-objective optimisation problem over three dimensions: error, cost, and abstention. Formally, minimise the system risk:
R(C)= PP(error A -abstention) + A. + A, (absteenntio))
Here, P(error A -abstention) denotes the probability of the system making an error when it does not abstain, Costt is the expected computational cost incurred, and P((asstnnion)) is the probability of the system abstaining and deferring to human expert. The terms de and Xa weight the cost and abstention penalties, respectively. We explain the system risk in more detail in Section 4.2
Assumptions. The base model is cost-efficient but less accurate, whereas the large model is more capable but computationally expensive. 2 Generating responses incurs significantly higher cost than processing imputs, especially in settings that require Chain-of-Thought (CoT) prompting WWii al. 2022 advanced test-time reasoning [Xie et al. 2024]. A3 Each response is assumed to be either correct or incorrect, with no ambiguity.
Policy (nnorraity-hasel
Reepotes
~ Mouilt)
Deteral Pailcy (owtbierra-tteadl
Bagg i Euer
Probdem Stramrrt
Bsee Misde Iheppenoe
Large Modiel Response
Magi(s)
Abstention Pollcy (unoertntyy-wvw
Bawila) Cuen
Expprt(()
Regaraation
Shage
Hurran Reeporse
Online Teedback
Figure 2: Decision flow of the two-tiered cascaded LLM system. The base model first evaluates each query. Confident, low-uncertainty responses are accepted; uncertain ones are passed the large model or, if still uncertain, deferred to a human expert. Online feedback progressively improves these policies.
3.2 Cost Calculation
To estimate the computational cost response generation, we define cost function that scales linearly with model size and token counts. Let denote the model size (in billions of parameters,

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e.g., 1lama3.1-8B + = 8), Em and fout the numbers of input and output tokens, and p > 0 the output-to-inpe token cost ratio accounting for the higher cost of generation. The total cost given by:
Cost(8, lin, four P) = s (fim + p. fvai)
This provides a simple yet effective way to compare models of different sizes under a unified cost metric, independent of infrastructure-specifie pricing. Additional cost components can be incorporated as needed.
4 Methods
4.1
Calibrated Confidence and Uncertainty Estimation
Effective deferral and abstention decisions in a cascaded system critically depend accurately quan- tifying model confidence ((x) and uncertainty E(x) for each input æ. Overconfident or miscalibrated predictions can lead to errors, while excessive uncertainty may result unnecessary escalations. Therefore, the first part of our method focuses on analysing a range of techniques to estimate these quantities reliable and cost-efficient manner. To this end, we evaluate four complementary methods that approximate the probability that response is correct.
(1) Self- Verification. Given an input æ and model response yhuse MM, (2x). we prompt the same model quantify how likely the response is correct by generating new response (Li al. 2023b] The model returns raw confidence score by outputting either a scalar value token in response to a verification prompt (see Appendix B.2). The outputted probability serves uncalibrated estimate of correctness.
(2) Consistent Self- Verificaaaa.. We repeat the self eef--veification process n times under stochastic sampling (e.g., with temperature), and aggregate the resulting probabilities. The empirical mean forms the uncalibrated confidence score. This approach inspired by self-consistency in (Aggarwal ct al. 2024].
(3) Surrogate Token Probability. We adopt the approach of Kadavath et al. [2022], where the model M; is asked to verify whether a generated response y is correct, and we extract the next-token probability over the discrete label set YES/NO. Specifically:
MYES
x. y)
(x
MYES
y) + (NO x,y)
(4) Monte-Carle Surrogate Token Probability. To obtain better confidence estimates, we apply Monte Carlo Dropout Gal and Ghahramani] at test time when computing the surrogate token probability. For each of stochastic forward passes, we sample estimate pi (x)), mean forms the uncalibrated confidence score:
(),))))) and the empirical
(x( = T Σ (I)
(5)
Model Evaluation by Larger Models. For each of the above methods, the evaluating model M; either be the same model that generated the original response, or larger model in the cascade, if available. While self-evaluation is cheap and self-contained, verifying small model's output using a larger model is still substantially cheaper than generating a new response from seratch-parte -aracch-particularlyy when generation involves long-form reasoning, as per Assumption A2. Additionally, larger models tend to be better calibrated and may yield more reliable verification, improving downstream deferral and abstention decisions [Zhu et al. 2023bb Chhikara 2025
Bayesian Calibration. ensure that the extracted confidence scores are comparable across models and consistent with empirical correctness, we fit a Bayesian logistic regression model on small
calibration set of 100 samples. This is a Bayesian version of Platt scaling (Platt 2000). and we assume Normal distribution prior. We follow Zellinger and Thomson 20024] approach and
5

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apply a non-linear transformation on the raw confidence score before inputting it into the Bayesian model, spread out the clusters of overconfident probabilities.
log( I-pt
1
p; 2 0.5
Per Ptr (p:) =
log(2) log(
if ps 0.5
Subsequently, the Bayesian Logistic Regression outputs posterior distribution over correctness. The mean of the posterior predictive distribution defines the calibrated confidence (xx) while we use standard deviation as model-based uncertainty estimate E(x), as in [Fanconi et al. 2023
4.2 Online Improvement
To enable online learning 13), parameterise the deferral and abstention thresholds and optimise them online. Given a dataset ((t) at time t with previous problem statements and ground truth labels, update the thresholds using stochastic gradient descent. While the system is deployed, we assume that we will receive a ground truth response (v") at the end of every decision if the system abstains. Thus, our dataset continually increases ( = D(t-1) {2, y²} every time the cascade abstains.
Our objective function the system risk R(C) (Equation 2p. We expand this risk into the concrete, differentiable losses. Throughout, let
(x(x)) [0, 1],
E,(x) E [0, 1], E (base, large)
denote the calibrated probability of correctness (posterior predictive) and uncertainty score (i.c. posterior predictive standard deviation) returned by model for an input The optimisation variables are
obaee Ebuses Étarge (0, 1),
For numerical stability treat their raw, unconstrained versions base Shase Stargo optimisation parameters and map them (0, 1) with sigmoid funetion:
R as the true
O buss
of Ohase
Etuse of Tuuse )
Starge = of raw
To keep the loss fully differentiable, we replace every Boolean test with soft logistic step, where k determines the steepness
1f2 > 0} - gx(z) = x(k2).
With this convention the three mutually exclusive masks at the base stage are
Pabsti (x) g Ebssc (x) Ebase).
(7)
Mpredt (x) = mabsit) gu( Drese - croase)
(8)
Malferl (x) = (1 Mabsll) gel Drmse Pbase (I=)),
(9)
and the masks at the large stage are
Pabsaz (x) = Maeferl (z) gi(EEtage( Eturge),
(10)
Mpreaz (x) ) = Mideferl (z) (1 - gk (Etaree (x) - Starpe)
(11)
Probability of abstention. The cascade abstains two mutually exclusive ways, so P(abstention)
Pahsal
+ Paha2-
(12)
Expected correctness. Only the prediction masks contribute non-zero probability of correctness; we weight each by the calibrated confidence:
[CCorret
Mypredll
Prase]
Mmprred2
Prange)
(13)
Expected cost. Let C1 be the costs from the base model, which consist of the generation cost and the verification cost (cither by itself or by a larger model). Furthermore, C2 is the generation cost and the verification cost caused by the large model. The first term is incurred on every query; the second is incurred only we defer:
[[Cost] eı + E Maater] C2-
(14)
System-risk objective. Substituting the three expectations above into Eq. 22 produces the differen- tiable loss that is back proppprrpeg during threshold optimisation in online learning:
R(C)= = -[/Correct] + A₂ B[Cost] + d (Pabstl + Pabaz).
(15)

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Experiments
In this section, we empirically assess whether the desiderata D1 D2 and 03. introduced in Section are satisfied. For (1) and ( we analyse in Section 5.1 the performance of various confidence estimation techniques with respect to calibration and cost-efficiency. Subsequently, in Section 5.2 we investigate whether the system improves through online learning.
General Setup. We evaluate cascade of two LLMs, specifically (Qwen-2.5-13 5-
Qwen-2.5-7B). Additional results for other cuscades-(LLes) (Llama3. + Llama3. 1-8B).
(Llama3. 2-1B + Llama3. 1-8B), and (Qwen-2.5-30 - Qwen-2 2.577BB are reported in Ap- [ These model pairs are selected due to their open-source availability and our ability to them on an NVIDIA A100 GPU.
pendix
To evaluate the generalisability of our framework across domains, we use five question-answeriig datasets: (1) ARC2-Easy and (2) ARC2-Challenge [Clark et al.) 2018), which are part of the A12 Reasoning Challenge and require reasoning over grade-school science; (3) Massive Multitask Language Understanding (MMLU) benchmark [Hendrycks et al. 202T]. which covers subjects ranging from complex STEM international law, nutrition, and religion; and two medical QA benchmarks: (4) MedQA Jii et al., 2020]. consisting of US medical board exam questions, and (5) McdMCQA [Pal et al. 2022 comprising entrance exam questions from the Indian medical school curriculum. All datasets are in multiple-choice format, with ground-truth answers satisfying Assumption A3 Chain-of-Thouud
reasoning is employed generate answers. The cost proportion between input and output tokens is set to p = 5, consistent with Anthropic's s current pricing to date (Anthropic 2025 Details on generation and verification prompts can be found in Appendix BB2
5.1
Cost-Benefit Analysis of Verification Methods
We begin by empirically analysing which verification method from Section is most suitable for estimating the confidence of generated response. Once calibrated via Bayesian logistic regression, these confidence estimates determine whether to defer a prediction from the base model to the larger model.
To assess both cost-efficiency and accuracy, we compare the calibrated base model confidence Prase against two baselines: (1) using only the base model (Qwen-2. 1aren-2.5-11
and (2) using only the large model (0wen-2.5-7B) In Figure 3] we visualise accuracy versus cost per sample across the datasets. We use threshold- aggnsstic strategy where deferral to the large model is performed with probability Dbsse (z). We evaluate four methods: Self- Verification (SV, n=1),, Surrogate Token Probability (STP, n=1), Consistent Self- Verification (SV, n=5), and Monte Carlo STP (MC-STP, n=5). For the latter two, we perform five regenerations or stochastic passes. Each experiment is conducted once using Mbuse the verifying LLM, and once using Maarge
As shown in Figure 3 (and Figures 10 and 13 Appendix C. using larger model for verification generally yields a better cost-benefit profile, particularly simpler datasets (ARC2-Easy, ARC2- Challenge, MMLU). In contrast, base-model verification provides only marginal gains. On the more complex medical datasets (MedQA and MedMCQA), all methods struggle. STP (n=1) is the most effective the ARC2-Eatt -asy and ARC2- Challenge dataset.
To quantitatively assess cost-efficieccy, we compute the Incremental Benefit per Cost (IBC) metric from Aggarwal et 2024), defined as:
P Peascade Phase
Plunge
Pouse
IBCaascude
IBChase
Chase
Change
Obuse
where P denotes accuracy and C denotes cost. We then compute the relative gain:
IBCeuscade
IBChase
ABBC =
1000
IBCbus
Higher AIBC values indicate improved cost-efficiency over the baseline.
As seen Table verifying with Marge consistently leads to higher AIBC scores, particularly on ARC2-Easy ARC2- Challenge, and MMLU, On the medical datasets, no single method consistently
7

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(A) ARC2-Eay
(6) ARC2-Challege
(c) MMLU
0.96
1.56
0.71
0.50
0.55
0.00
0.66
0.75
0.50
2
1.01
1.5
2.5
310
Cost per Samgle
-107
Cos per Strple
X00
Cost Sample
K10T
MedQA
(e) MedMCQA
0.50
0.53
0.30
0.30
Acorscc
2.45
0.45
0.40
0.40
0.00
0.
1.0
Cort per Sample
Coe Sample
X0077
1)
12
STr (n--1)
bare Model
SVa (e- 9)
STD (o
SMawp (a 53
STRuge (n-55
Figure 3: Cost-Aceuracy Trade-off for Calibrated Verification Methods (Qwen-2.5 1.5B+7BB.
Accuracy versus cost per sample shown for the cascaded model using various verification methods. Performance above the linear interpolation line between base and large model baselines indicates positive cost-benefit. Error bars represent standard error.
ARC2 Easy
ARC2 Challenge
MMLU
MedQA
MedMCQA
SV (n=1)
-2.4 :: 32.6
-11.6 2: 20.5
-18.7 4.9
-27.3 1 14.3
-24.8 : 9.5
Base
SV (m=5)
10.2 29.6
-26.2 + 19.1
-19.4 + 4.9
-25.4 + 13.4
-19.5
STP (n=1)
-16.9 +: 33.2
-19.3 20.9
-20.4
-23.9 + 14.7
-22.9 9.7
MC-STP (n=5)
-37.4 28.8
-16.0 21.0
-27.3 2.2.6
13.7
-22.2 9.4
SV (m=1)
258.44+39.1
70.5 26.0
7.77
-6.1 15.8
-11.6 10.0
Large
SV (n=5)
188.5 31.5
23.7
-11.9 2.9
14.7
-11.0 9.8
STP (n=1)
242.7 + 36.3
89.3 + 26.2
5.2
16.3
-10.0 = 10.1
MC-STP (m=5)
171.4 + 36.4
39.2 22.0
22,44
4.0
-16.8 + 14.5
19.7 = 9.3
Table 1: Calibrated AIBC Scores for Qwen-2.5 (1.5B+7B) Each row indicates a verification
method (SV or STP) with = 1 or n. 5, grouped by whether the base large model was used for verification.
outperforms the others significantly. Moreover, we see that on the medical datasets, the AIBC standard error rates for the verification scores using the large model are around O, indicating no cost-benefit compared to the easier datasets. report additional results for the other cascades in Tables 5 o Appendix C Interestingly, the uncalibrated confidence scores appear to yield higher ATBC, albeit with a significantly higher standard error, suggesting the instability of uncalibrated confidence scores. We conduct ablation study of the size of the calibration set in Appendix C.5) which demonstrates that the calibration size between 50-500 samples, does not lead to significant performance change. Moreover, we report the various subjects of the MMLU dataset in Appendix Section C.6) which reveals a stark difference ABCC scores across different areas of expertise.
5.2 Online Improvement of the Decision System
Desideratum
D3 requires that "the framework should continuously refine deferral and abstention policies feedback becomes available, ensuring sustained reliability and improvement". We simulate

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an online setting in which the system selects among Musee Margee or a human expert, adjusting its thresholds based on feedback from abstentions.
500
700
Base
Base
Base
600
Large
Large
600
400
Cascade
400
Cascade
Cumulative Regret
200
Cascade
500
4000
200
3030
200
100
1000
800
1000
600
Online time (t)
Online time (+)
Online time
(a) ARC2-Easy
(b) ARC2-Challenge
(c) MMLU
700
Largo Cascade
600
Large
Cascade
Cumulativ Regeet
600
Comulativ Begnet
500
400
200
Online time steps (t)
Online time steps (t)
(d) MedQA
(e) MedMCQA
Figure 4: Cumulative Regret in Online Setting (Qwen-2.5 1.5B ++ 7B). Cumulative system risk over time. Training data is collected only when abstentions occur. The cascaded system consistently achieves lower regret.
Specifically, the experiment streams 1,000 unseen questions in random order simulate production traffic. Before the first query, the deferral probabilities are calibrated using the values learned from the 100-sample calibration set. Thereafter, answered by an oracle expert to a replay buffer. This replay buffer is used to perform the ADAM optimiser [Kingma and Ba 2014) updates on the differentiable risk[with with learning rate 0.05 and a batch size of I0, on the delerral and abstention thresholds 0 = { (oasse Ehase, Starge J. The prediction made on an unseen query and the regret is calculated on it. query added to the replay buffer, the regret associated with it has already been calculated, and the sample now becomes training sample; however, it is not further evaluated. We compare the cascaded system C' using only Mosse and only Marge with single abstention threshold Ç. The system risk for single model is explained more detail Appendix A.T we are considering a deployed system, we track the cumulative regret over time, which we define as follows:
add queries that
marked for abstention and
Regret(M)lr) = Σ R(M
where M E {C, Mpase Marge and (t) evolves based on abstention feedback D,. We chose regret the metric for this experiment, inspired by the work online decision mediation (Jarettt et al.) 2022]. Regret is the running sum of our per-query risk. Because error, compute, and human-hande already weighted into the same units, adding them over time tells you the exact "bill" the system has paid. A lower regret curve indicates a higher benefit, as represents combination of abstentions, correct predictions, and costs, and curve illustrates how quickly a policy learns online and whether early mistakes are compensated for later.
grow time in deployed setting. The regret
We initialise the thresholds at ( (0.5, 0.05, 0.05}. where & = 0.05 corresponds to the standard deviation of 5% confidence. For the single model baselines, we initialise the abstention threshold

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as with = 0.05, and keep the rest of the hyperparameters the same. Throughout this experiment, we employ the STP (n 1) verification strategy, which was found to be the most competitive in the previous section, To avoid trivial solutions (e.g., always selecting one model), we balance system risk using A = 10-5 and Aa 0.1, in line with Zellinger et al. (2025).
Figure 4 shows that the cascaded system yields lower cumulative regret over 1000 test samples on ARC2-Easy, ARC2-Challenge. MMLU, and MedMCQA, compared to using either model in isolation. On MedQA, gains are less clear, likely due to poor confidence estimation, which was also observed in the section above. Similar trends are observed in other cascades (see Figures 9 12 13 Appendix(C).. Nevertheless, in four of the five cases, the cascaded LLM system demonstrates lower cumulative regret than when using single models online, where feedback received when abstaining from action. Additionally, we experiment by comparing our proposed gradient-bare -ased approach to traditional grid search over 0 Appendix
No Label Flippigg 20% Fligiigii
5.3
The Effect of Imperfect Expert
50% Flippin
To recall the system risk objective in Equation 15 the part where wrong human annotations will have impact is the
100% Label-Flpping
Cumulative Regeet
expected correctness (Equation 13). More precisely, the
calibrated confidence scores 4 Poase and $ Inrge-- The noisier
the feedback is. the more uncalibrated Dasse and D large will become. Therefore, optimisation of the cascaded model will become unreliable.
200
We demonstrate this through additional experiments in the online setting, where we progressively swap correct incorrect predictions while calibrating the model, and how this affects the trajectory on the ARC-Easy dataset with 2.ve-2..51.555 + Qwen-2.5-1 5-B. The results are dis- played in Figure[5] We observe that the higher the percentage of label corruption is in the calibration set, the higher the cumulative regret becomes while deploying the decision- making system.
100
02.0
1000
Onfine time staps
Figure 5: Imperfect Experts. We in- crease the percentage of flipped labels during system calibration, simulating imperfect experts, which in turn in- creases the system's 's risk of error.
Limitations
Our cascaded multi-LLM decision-making framework strikes a balance between accuracy, cost, and abstention, but it has limitations. Sensitivity to cost and abstention variations can impact efficiency, leading to trivial solutions (only using the cheapest model the model with the lowest error rate). Discrepancies in model performance or relative costs may lead to over-reliance on specific models, thereby reducing adaptability. Furthermore, parameter initialisation affects the convergence of the deferral policy. Additionally, the framework relies on human feedback, which may hinder adaptation if it is sparse noisy in real-world scenario. Finally, fitting Bayesian logistic regression model is usually more complex than fitting a regular one, depending on the different posterior approximations or sampling strategies employed.
7 Conclusion
We proposed a multi-tier decision-making framework that escalates tasks between a base model, a large model, and human experts. By leveraging deferral and abstention policies, our approach aims to enhance performance, accuracy, and abstention while adapting through online learning. Our experiments show that the framework outperforms single-model baselines by reducing unnecessary escalations and improving response correctness on the ARC2- ARC2-Challenge. MMLU, and MedMCQA datasets. On MedQA, cascaded model did not outperform the single model approach. potentially due to the complexity of the dataset. Nevertheless, we believe that this proposed system could be beneficial where performance, costs, and abstention of LLMS need to carefully balanced. Future work should investigate different uncertainty quantification methods of LLMs to enhance abstention. Moreover, it would be crucial to examine whether there are theoretical guarantees that justify the application of cascaded LLMs.
10

---

Acknowledgements and Disclosure of Funding
We want extend our gratitude to Alan Jeffares, Paulius Rauba, Yusuke Kano, Jeremy Voisey, and Alison Smithard for their insightful discussions and valuable feedback. Canon Medical Systems Corporation funds CF's studentship. This work was supported by Microsoft's Accelerate Foundation Models Academic Research initiative.
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A Additional Method Details
A.1 Single-model System Risk
For completeness we report the risk of running either model alone. g is that model's abstention threshold and its total cost,
siinge (M) = [ Mabat )00 + Aoc + A(maml
where Mabaa (z) = 9h (3(x)= E).
Implementation Details
The code for this paper, to reproduce the results is provided at https:/ggituu.coo////noocccccca Iims All experiments implemented in Python |Van Rossum and Drake Jr 1995] with Py-
Torch Paszke al. 2017) and Hugging Face Transformers Wolf et al. 2020
Compute.
Experiments are conducted on a single A A100-class GPUs.
B.1
Generation Models
Policies initialised from instruction tuned checkpoints and trained with the learned reward signal. The following policy backbones are used:
meta 1 ama 1tt
O0enn/heen2.5-3B-Innttu
Jvenn/heen2.5-7B-Intrrre
B.2 Prompts
Throughout this paper, we use prompts to make decision predictions using Chain-of-Thought and verification prompts determine a response's 's factual correctness or uncertainty.
Response Generation Prompt ARC2-Easy + ARC2-Challenge
You are helpful AI.
Answer the following multiple-choice question using step-by-step reasoning, then conclude with final stating the answer.
Question: {question}
Choices:
{choice_03
{choice_1) 1}
(choice_2)
{choice_3) ((choice_4))
Let's reason step- then conclude with: "The best anaver is: <X>"
Reasoning:
16

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Response Generation Prompt MMLU
You expert in (subject). Anawer the following multiple-choice question using step-by-step reasoning, then conclude with a final stating the best ansver.
Question: {question)
Choices:
{choices)
Let's reason step-by-step, then conclude with: "The best answer is: <D>
Reasoning:
Response Generation Prompt MedQA
You are medical doctor taking the US Medical Licensing Examination. Answer the following multiple-choice question using step-by-step reasoning, then conclude with final stating the best answer.
Question: {question}
Choices:
{choice_0}
{choice_1) 1]
{choice_25
{choice_3) (choice_4)
Let's reason step- then conclude with: "The best ansver is: <X>"
Reasoning:
Response Generation Prompt MedMCQA
You medical doctor answering real world medical questions. Answer the following multiple-choice question using step-by-step reasoning, then conclude with a final 1ine stating the best ansver.
Question: {question)
Choices:
{choice_0)
(choice_1)
{choice_2) 2}
(choice_3)
Let's reason step-by-step, then conclude with: "The best anaver is: <X""
Reasoning:
17

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Self Verification Prompt
Given the following question and the model's answer, please evaluate correctness. Question: {question)
Model Answer: (candidate_ansven)
Please give confidence score scale of 0.0 to 1.0 for this prediction.
Answer:
Surrogate Token Probability Prompt
Given the following question and the model's answer, please evaluate correctness. Reapond with a single token: [yes_token) or {no_token}
Question: {question)
Model Answer: {candidate_answer)
Is this answer correct: (yes_token) fno_token??
Answer:
18

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C
Additional Results
C.1
Qwen-2.5 1.5B + 7B
C.1.1
Uncalibrated
(a] ARC2-Easy
(b) ARC2-Chalknge
(c) MMLU
6.00
0.00
0.70
0.85
Accurty
6.00
Accurtyy
0.05
0.88
0.60
Cost per Sample
Cost per Sample
Cost per Sample
(d) MedQA
(e) MedMCQA
0.50
Hell
0.50
Acceracy
0.15
0.40
0.35
0.4
0.6
0.5
1.0
1.2
Cost per Samale
Cost per Sample
x000
Modal
SMane IN 1)
Dow (nr 13
X SMi (u-m 1]
STR
Large Mooel
SVam
STPuw
Figure Benefit-Cost Analysis of Uncalibrated Verification Methods (Qwen-2.5 1.5B-7B). We dis- play the cost vs accuracy of the various verification methods, using the cascade (Qwen-2. 1rven-2.5-11 5-1.5B - Qwen-2.5-77 Verification methods, which are located above linear interpolation between the base or large models, indicate a positive cost-benefit ratio. The eтror bars indicate the standard error.
ARC2 Easy
ARC2 Challenge
MMLU
MedQA
MedMCQA
(n=1) 1)
278.5 237.3
80.5 174.1
-18.7 4.9
-5,88
89.0
Base
SV (n=5)
93.3 +: 112.7
-15.6 + 104.2
-19.4
-65.6 1 55.3
29.3 1 63.2
STP (n=1)
-100.0 948.0
-100.0 - 847.4
-20.4
-87.0
-100.0 + 835.5
MC-STP (n=5)
-66.3 + 142.6
-74.3 + 143.4
-24.6 4.2
-69.7 4 72.9
-71.6 + 114.7
SV (n=1)
280.5
84.8 4: 24.6
5.0
24.7 1. 21.0
32.0 1 14.0
Large
SV (n=5)
219.7 + 35.8
66.5 + 22.3
-7.0 4.8
13.9 + 18.9
24.6 + 13.8
STP (n=1)
284.5 40.4
96.9 + 24.2
7.5 5.5
21.6 19.4
35.0 + 14.2
MC-STP (m=5)
66.5 19.2
21.3 4: 14.6
-5.7 4.9
-10.5 4 14.6
-3.5 10.2
Table Uncalibrated AIBC Scores for Qwen-2.5 (1.5B >7B). Each row indicates a verification
method (SV or STP) with 1 or n 5. grouped by whether the base large model was used for verification.
19

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C.2 LLama3 1B - 8B
C.2.1 Calibrated
ARC2-Easy
(b) ARC2 Challenge
0.16
0.20
0.5
0.63
0.00
Accorey
Accuracy
Accuracy
0.7
0.05
0.50
0.45
0.5
2
Sample
X10
Cost
Sample
106
Samole
X207
(d) MedQA
(c) McdMCQA
0.7
0.00
0.35
Acamacy
Acomacy
0.50
0.5
0.45
0.40
9
Cost par Sample
per Sample
x0007
Rose Model
SMa (N 1) I
STP (n 12
E Shagr 1]
I
STR (a
Large
Suaus (s - 5)
STP (n B)
Σ
SVage (x- B)
Σ
STRug (n 5)
Figure 7: Benefit-Cost Analysis of Calibrated Verification Methods (Llama3 1B 18). We display the cost vs accuracy of the various verification methods, using the cascade (Llama3. 2-BB - Llama3. Llama3.1-8B). Verification methods, which are located above the linear interpolation between the base or large models, indicate a positive cost-benefit ratio. The error bars indicate the standard error.
ARC2 Easy
ARC2 Challenge
MMLU
MedQA
MedMCQA
SV (n=1)
-8.8 1 16.4
-13.2 i 11.4
2.6
-8.0 1 9.5
-9.9 199.80 8.9
Base
SV (n=5)
-12.8 + 16.5
-19.6 + 10.8
+11.9
-21.3
-15.6 8.7
STP (n=1)
-4.4 + 16.7
-522 11.7
-6.8
4.8 -13.6
MC-STP (n=5)
0.8 1 15.2
.9.0 11.4
-9.0
-9.4 9.2
-11.2 1 8.8
SV (m=1)
14.551455
28-11.11
2.6.64266
4.T49. 9.9
0.00
Large
SV (n=5)
50.1 13.7
10.7 11.8
..3.7
9.17
+..1
STP (n=1)
118.3 1 15.8
38.1 13.7
-.22
9.7
-3.7 9.2
MC-STP (n=5)
97.7 + 14.4
15.4 + 11.7
2.5
-6.8
2.6 9.0
Table 3: Calibrated AIBC Scores for Llama3 (IB+8B), Each row indicates a verification method
(SV or STP) with or 5, grouped by whether the base or large model was used for verification.
20

---

C.2.2
Uncalibrated
(a] ARC2-Easy
[b) ARC2-Challege
(c) MMLU
0.10
0.70
6.00
0.00
0.85
Azcurayy
Acceracy
0.7
Accunt
6.90
0.55
0.70
0.6
0.30
6.70
0.45
0.66
0.80
Cost per Sample
Cos: per Sample
Cost por Sample
MedQA
MedMCQA
0.00
0.35
0.5
Acourggy
0.30
0.45
0.4
0.25
0.50
0.75
1.00
1.25
Cost Sample
X300
Cost per Sample
X31
Base Model
SVam (n 1)
STP ban (n 11
X SMare (o- 1]
X
STr (n-
Model
SVam
SMage
STr
Figure 8: Benefit-Cost Analysis Uncalibrated Verification Methods (Llama3 1B -8B). We display the cost vs accuracy of the various verification methods, using the cascade (Llama3, 2-1B Llama3. 1-8B). Verification methods, which are located above the linear interpolation between the base large models, indicate positive cost-benefit ratio. The eπror bars indicate the standard error.
ARC2 Easy
ARC2 Challenge
MMLU
MedQA
McdMCQA
SV (n=1)
6.5 13.1
2
2.6
-38.9 1 98.5
.4.2 12.0
Base
SV (n=5)
16.1 21.3
-11.3 18.4
-1.9
-55.7 + 82.4
-14.4 + 18.6
STP (n=1)
344.3
-30.0 211.7
2.88
-21.2 :: 159.6
MC-STP (n=5)
42.5
-39.0 113.6
2.7
-19.8 = 107.9
-42.9 68.9
SV (n=1)
1
89.3
2.79
9.9 10.2
73.3 = 32.8
Large
SV (n=5)
143.4 + 33.6
83.1 31.6
2.6
10.1 = 10.2
63.5 = 32.0
STP (n=1)
129.4 + 19.1
59.1 + 16.5
1.6 3.0
7.3
30.0 = 11.8
MC-STP (n=5)
71.0 = 17.2
24.0 16.5
0.3 + 2.9
4.2 = 10.0
9.2 = 13.2
Table 4: Uncalibrated AIBC Scores for Llama3 (1B -BB). Each row indicates verification
method (SV or STP) with n = 1 or n 5, grouped by whether the base or large model was used for verification.
21

---

C.2.3 Online Learning
500
600
1030
Large
Largo Cascade
Cimulatbe Regret
400
Cascade
Cumulathe Regret
500
Cascorde
Cumulatbo Regrat
800
400
300
600
300
200
100
Online time (t)
Online time steps (t)
Online time steps (t)
(a) ARC2-Easy
(h) ARC2-Challenge
(c) MMLU
Rase
Rase
Large
Large
600
Cascado
800
Cumulative Regres
Cumulazive Regres
400
200
0
200
400
600
800
1000
200
400
600
800
1000
stops (+)
stops (+)
(d) McdQA
(c) MedMCQA
Figure 9: Cumulative Regret in Online Setting (Llama3 1B -8). We display the cumulative
regret of the system risk when using Cascade (Llama3 2-1B - Llama3. 1-8B). Points are only added to the training if abstention is made. The error bars indicate the standard error.
22

---

C.3 LLama 3B + 8B
Due to the large size of the MMLU dataset and the costs associated with making predictions on it, we omit this for the (Llama3. 2-3B - L1 ama3. 3 1 1-8B) combination in this subsection.
ARC2 Easy
ARC2 Challenge
MedQA
MedMCQA
col.
uscal.
uncul.
col.
cal.
SV (1=11) 1)
267.7 2 364.0
38.1: 96
322.3 = 335.2
-11.5 R14
15.7 4 205.7
46.9 -8.66
93.6 + 154.5
-27.8 = 20.9
SV (xm6))
247.2 359.8
32.1 100.9
352.2 325.3
0. 84.4
12.5 200.0
-28.2
49.4
96.1 + 146.7
.3.5 +
STP (m=1)
272.7 +: 338.6
34.9 4: 99.6
279.7
à: 337,5
-0.7 1: 80.9
35.6 à: 199.1
88.2 1: 89.3
91.2 + 153.0
-19.2 :9.9
MC-STP 8)
272.4 325.0
4400 96.
279.9 +: 3126
33.0 100.0
-92 - 2049
23.2:2:52.
119.0 : 154.3
-5.0 20.0
(xxm))
312.2 321.9
84.2 1106
237.4 2776
2005 4 84.8
-124 136.7
20.3
$1.0 4 100.1
SV ()=5)
257.4 4: 324.7
63.2
106.4
281.6
292.7
37.4
83.1
4.7 4 131.5
-3.4 4:48
$4.8 4: 107.0
-14.2 à: 22.1
STP (m=1)
331.9 1: 287.7
77.0 1: 112.2
254.6 2: 291.8
-0.7 + 83.7
-888
+ 1268
-34.4
462
96.7 : 99.5
-38.6
20.3
MC-STP 6)
422.2 = 328.8
78.2 1098
325.5 306.1
- 78.7
+
150.7
+8.
91.4 100.3
-11.5
Table 5: ATBC scores for Llama3 (3B > across datasets and calibration settings. Rows show
methods (SV or STP) with n = 1 or n 5, grouped by whether probabilities come from the base or large model, All values are rounded to decimal place.
(4) ARC2-Emy
(b) ARC2-Challeng
(d) MedQA
(e) MedMCQA QA
C0.08
0.98
Accuracy
0.92
Accueacy
0.54
0.56
10.38
0.64
0.91
0.52
0.56
0.50
00.30
-0.62
0.50
00778
10.52
0.58
0.6
1.0
1.0 Cost por Sampla
Cost
Sumple
X107
per Samola
Cost per Sample
x100
X10
Buse Model Model
SVau [nim 1) X
STRuw (n 1)
X SMang (n 1] X
STP (n 1)
SMau (pem
STR (nim
SVany 5]
wg (nim 5)
Figure 10: Benefit-Cost Analysis of Calibrated Verification Methods (Ilama3 3B 38). We display the cost accuracy of the various verification methods, using the cascade (Llama3, 2-3B - L 1BB). Verification methods, which are located above the linear interpolation between the base or large models, indicate a positive cost-benefit ratio. The error bars indicate the standard error.
(4) ARC2-Easy
(b) ARC2-Challenge
(d) MeeQA
(v) MedMCQA
0.94
00.5
0.68
10.00
0.50
0.52
0.56
Arruney
0..5
Accupoy
0.04
0.50
0..50
-0.62
0.54
0.59
00.78
00.50
10.52
0.4
0.6
0.5
1.0
1.0
1.3
Cost per Somple
x107
Cost per Sample
X300
Cost per Sample
x110
Cost per Sample
X007
Base Model
SMam (+--
STPL
SYuge
X
STP ag
Large Model
SV (1- 5)
STP (n
SVany (a 5]
STP fn 5)
Figure 11: Benefit-Cost Analysis of Uncalibrated Verification Methods (Ilama3 3B- 38B). We display the cost vs accuracy of the various verification methods, using the cascade (Llama3. 2-3B -> Llama3. 1 1B).. Verification methods, which are located above the linear interpolation between the base or large models, indicate a positive cost-benefit ratio. The error bars indicate the standard error.
23

---

Candative Rage
903
Conuallo Rugss
Casuedi
030
-00
#9]
-000
9:3
300
-00
100
303
(28)
65.0
803
1000
201
-181
12.0
600
1000
200
-381
1241
600
1100
202
-181
0201
500
1100
Ontine oma strps (1)
Oxiss cmn StB0e
Uniis cm steps (1)
Osiie cee (1)
(a) ARC2-Easy
(b) ARC2-Challenge
(c) MedQA
(d) McdMCQA
Figure 12: Cumulative Regret in Online Setting (Llama3 3B >8B). We display the cumulative regret of the system risk when using Cascade (Llama3. 2-3B + Llama3. 1-8B). Points are only added the training if abstention is made. The error bars indicate the standard error.
C.4 Q wen 3B 7B
Due the large size the MMLU dataset and the costs associated with making predictions on we omit this for the (Qwen-2. 2.5-3B - Qwen-2. mioon-.5-770 combination in this subsection.
ARC2 Easy
ARC2 Challenge
MedQA
MedMCQA
oul.
ancol.
(m=1)
72.6 67.1
98.5
458
37.5
46.2
-3100 21.1
Haxe
377
13.7 76.4
39.0
-54.6
13.5
STP (xe1))
-194 23.5
44.7
-2.1
168
-3.6
57.0
.1155 41.5 12.1
-52.0 15.5
37.5 - 10.6
-31.
MC-SIP (mmm)
42.11:21.1 21.8
755
43.3 18.1
.532 838
4478 + 11.9
-50.4
13.7
39.9 11.0
45.5 14.0
(mx=])
2704 125.5
46.3
15.4
216
(m=5))
99.0 60.4
139.1
58.11
34.9
43.0
13.4 1327
149
STP (xxm))
342.9 121.3
313.9 + 135.6
96.1 57.9
99.4
75.8
-8.3 +:
20.0
23.77
4: 17.4
16.3
22.2
.17.1
16.5
MC (m==5)
21.0 1: 35.6
97.2 89.8
-194 24.9
16.2
1:
-2.8
11.1
44.77
142
37.4 12.9
29.5
1 14.9
Table AIBC scores Qwen-2.5 (3B
BB)) across datasets and calibration settings. Rows show methods (SV or STP) with n = or 5. grouped by whether probabilities come from the base or large model. All values are rounded decimal place.
ARC2-Easy
ARC2.Challenge
MedQA
(e) MedMCQA
0.50
T.550
00.5
42555
0.02
0.500
Accuracy
0.94
0.475
0.50
0.86
0.52
0.52
5.5
Sumple
Samole
per Sample
Coot
Base Model
SVau (x 1)
STP (n 1) STr (n
I SVinp (n 1] SVige B)
Σ
STP (n m) am (n
Modal
Figure 13: Benefit-Cost Analysis of Calibrated Verification Methods (Qwen-2.5 3B 3B- +7B). We display the cost accuracy of the various verification methods, using the cascade (Qwen-2.5 5-BB Qwen-2.5-77 5-7B). Verification methods, which are located above the linear interpolation between the base large models, indicate positive cost-benefit ratio. The error bars indicate the standard enror.
24

---

ARC2-Easy
ARC2-Challege
MedIQ
(e) MedMCQQA
10.66
0.55
0.54
00:00
0.02
Accuraty
Accuract
0.62
0.50
50.50
00.62
0.93
10.60
0.92
Sample
Samale
por Sample
Base Model
SVam [ss 2)
STP (n
SVany (n 1] SYrgg 5)
STP (a 1)
Model
wa (n
Figure 14: Benelit-Cost Analysis of Uncalibrated Verification Methods (Qwen-2.5 3B +BB) We display the cost accuracy of the various verification methods, using the cascade (Qwen-2. 5-3B (w-7)..5-7BB. Verification methods, which are located above the linear interpolation between the base large models, indicate positive cost-benefit ratio. The error bars indicate the standard error.
300
700
Large
Large
Cincldiie Rignt
Casquéte
Candaaive Raget
991
Cansards
Condldine Runni
600
Casquate
Caupliee
300
(00
000
190
100
100
650
1000
500
Orfinc
Onfin
(a) ARC2-Easy
(b) ARC2-Challenge
(c) MedQA
(d) MedMCQA
Figure 15: Cumulative Regret in Online Setting (Qwen-2.5 3B +BB) We display the cumulative regret of the system risk when using Cascade (Qwen-2.8 3B - Qwen-2. 5-7B). Points only added to the training set an abstention is made. The error bars indicate the standard error.
C.5 Ablation of Different Calibration Size
We conducted an ablation study to investigate the effect of calibration size on deferral probability verification, using STP (n 1). The results can be found here Table 7
Generally, it appears that the calibration size has little influence on these magnitudes. we examine the standard error across the various sizes, of them is significantly better than the others. The only thing that we noted was that with a too small calibration set, we would have more diverging chains in the Bayesian Logistic Regression sampling.
Model
Datasel
Cal. Size = 50
Cal. Size = 100
Cal. Size 200
Cal. Size = 500
ARC2 Easy
239.5 36.1
242.7 36.3
273.5 i 42.7
254.9 1. 43.5
Challenge
87.8 24.3
89.3
4 25.4
28.7
Qwen-2.5 (L.58-+BB)
McdQA
-3.0 15.4
1.7 + 16.3
-7.7 16.6
-16.6 = 18.6
McdMCQA
-7.5 9.9
10.00 + 10.1
-8.0
-: 9.9
.5.7 = 10.4
ARC2 Easy
121.9 1: 15.6
118.3 1: 15.8
122.6 1: 16.5
102.8 1: 16.0
Laama 3 (IB (IB-+8B)
Challenge
38.1
13.7
4: 12.8
McdQA
10.1 9.7
9.7
5.3 10.0
9.8 11.9
McdMCQA
9.4
3.7
6.7 9.1
7.0
Table AIBC scores across different calibration sizes for Qwen-2.5 and Llama-3 models on multiple datasets, using STP (n 1) verification strategy.
25

---

C.6 MMLU Subject
Subject
AIBC (Base
Large)
International
US Foreign Policy
54.20
Jurisprudence
45,95
Business Ethics
33.53
Sociology
66.72
High School Psychology
31.38 37.80
High Schnol Govermment And Politics
29.64 35.23
Logical Fallacies
28.68 87.21
World Religions
23.14 68.51
Human Aging
20.88 47.71
Philosophy
18.97 44.90
Computer Security
16.8 + 440.64
Miscellanzous
16.78 20,86
Management
16,30 61.84
High School Microcconomics
15.60 27.56
High School Geography
13.66 29.49
Marketing
12.23 61.58
Prehistory
11.94 33.99
High School Biology
11.23 42.87
Security Studies
10.47 50.74
Medical Gemetics
8.21 +: 34.18
Cullege Biology
8.20 1: 39.82
Professional Psychology
4,43 22.52
High School US History
4.28
Clinical Knowledge
3.93 48.4
Formal Logic
+ 46.67
Sexuality
All Subjects (Average)
2,52 5.23
Anatomy
2.32 +: 54.35
Relations
1.82 152.51
College Medicine
= 46.04
Global
+: 51.04
High School Macroeconomics
High School European History
Abstract Algebra
Nutrition
-1.55
Professional Accounting
-1.67 31.01
High School Chemistry
-1.85 26.87
Iligh School Mathematics
2.46 29.03
Machine Learning
2.84 40.49
Moral Disputes
-3366 + 36.88
Elementary Mathematics
3.60 + 23.81
Conceptual Physies
-3.78 + 29.27
High School Computer Science
4,81 44.225
Professional Law
6.00 21.39
High School Physies
4.81 21.16
College Physics
+002 + 28.6
Astronomy
8.60 + 30.55
High School Statistics
-10.18 + 26.16
Econometrics
-10.50 1 36.09
Electrical Engineering
-10.79 + 41.71
College Mathematics
-12.30 1 62.39
1ligh School World History
.16.96 1 53.38
Professional Medicine
-18.75 + 21.12
Moral Scenarios
22.65 + 16.20
College Chemistry
Collage Computer Science Virology
25.63 + 35.75
Table 8: AIBC Scores by Subject (Qwen-2.5). Values show the change in IBC from the cas- caded LLM framework using the surrogate token probability method, sorted by subject for the (Qwen-2.55 5-1.5B - 0xen-2.5-1 2-BB7B combination, after calibration.
26

---

Subject
ABBC (Base
Large)
World Religions
35.95 35.25
Anatomy
Virology
Miscellaneous
High School Psychology
Clinical Knowlodge
Prchistory
14.27
Marketing
US Foreign Policy
13.70 34.01
Conceptual Physies
13.37 22.75
High School Geugraphy
12.50 29.38
Jurisprudence
12.22 42.25
Logical Fallacics
11.77 32.46
Moral Disputes
11.12 21.71
High School Biology
7.66 + 16.00
Management
6.73 1: 35.36
College Medicine
5.84 1: 26.08
International Law
4.88 +: 24.42
High School Microecomemies
4.38 + 15.48
Human Aging
4.16 + 39.64
High School Macrocconomics
2.51 = 14:27
Sociology
2.05 1: 22.75
Astronomy
1.97 + 19.43
Philosophy
:: 20.96
Electrical Engineering
0.33 1: 26.12
Nutrition
0.31 + 19.88
College Biology
0.30 + 23.37
Abstmact Algehra
Computer Security
All Subjocts (Average)
-1.16 + 2.87
Medical Genetics
-1.39 27.97
Business Ethics
-1.59 35.09
High School Govemment Politics
-1.61
Formal Logic
-2.11 43.78
Professional Psychology
High School Computer
29.56
Human Sexuality
Sccurity Studies
Public Relations
61.18
Fconometrics
-..67 29.45
College Computer Science
-7.06 29.54
llggh School Statisties
-7.70 15.34
lligh School Physics
9.27 25.92
College Physics
99.43 + 15.95
Moral Scenarios
9963 + 13.23
Professional Medicine
10.05 + 18.46
Elementary Mathenaties
11043 1: 8.50
Professional Accounting
-10.99 1: 17.82
High School World History
-10.72 + 19.96
High School US History
-11.81 1: 17.55
High School Mathematics
-12.64 + 11.41
High School Chemistry
-13.66 + 17.31
Professional Law
-1433 + 10.24
High School Eurogean History
-17.91 + 24.25
Cullege Chemistry
17.922 1: 38.05
College Mathematics
17.95 1. 26.48
Machine Learning
20.64 + 19.84
Global Facts
-35.32 + 36.23
Table 9: A IBC Scores by Subject (Llama3). Values show the change IBC from the cascaded LLM framework using the surrogate token probability method, sorted by subject for the (Llama3. 2211B Llama3.1 1 1-8B) combination, after calibration.
27

---

C.7 Grid-Search over Threshold Parameters
we perform an additional experiment on the ARC2-Easy dataset with the (Qxen-2.5-1.53 Qwen-2. 5-7B) combination. We perform a grid search with every parameter = {orase Ebase Etarge over {0.5, 0.15, 0.25, 0.35, 0.45, 0.55, 0.65, 0.75, 0.85, 0.953. The search grid's time complexity is cubic, (n))), and increases with the addition of expert data to the replay buffer, becoming computationally extremely expensive compared
the gradient-based approach. We report our findings in Figure T6. We observe from the results, that the gradient-based approach achieves lower cumulative regret, compared the grid-search approach, on single-model strategies, and also on the cascsaded LLM framework.
1000
Base
Base
500
Large
Large
800
Cascade
Cascade
Cumulative Regret
400
Cumulative Regret
600
300
400
200
200
100
0
0
200
400
600
800
1000
200
400
600
800
1000
Online time steps (t)
Online time steps (t)
(a) Gradient-based Optimisation
(b) Grid Scarch
Figure 16: Gradient-Based vs. Grid-Search. Online learning performance of the cascaded LLM framework over 1000 samples using the proposed gradient-based (16a) approach against grid-search 16b over the threshold parameters 0.
28

---

NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: For assumptions section 3 for results see section 5 where the experiments represent the claims made the abstract and introduction.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No or
NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations the work performed by the authors?
Answer: [Yes]
Justification:
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Reviews:
[{"review_id": "pSdktI1vCz", "reviewer": "Reviewer_wErX", "summary": "The paper proposes an end-to-end risk-aware cascade for large-language-model (LLM) question answering that (i) routes queries first to a cheap base model, (ii) decides—via a calibrated confidence/uncertainty gate—whether to accept that answer, defer to a large verifier, or abstain to a human, and (iii) learns all routing thresholds online by stochastic gradient descent on a differentiable objective that simultaneously prices accuracy, compute cost, and human escalation.  The key technical pieces are a surrogate-token probability verifier that costs only a single forward pass of the big model and a soft-mask formulation that makes a three-way routing policy differentiable.  Experiments on four multiple-choice QA benchmarks show sizable cost–accuracy gains over either single model and illustrate the limits of the approach on harder medical tasks.", "questions": "- Have you run an offline grid-search or Bayesian-optimisation baseline that chooses a single-gate confidence threshold (or a two-gate confidence + uncertainty router) on a validation split, and if so, how does its cost–risk trade-off compare to your differentiable soft-mask policy?\n- Do you have empirical data on expert latency, monetary cost, and inter-annotator disagreement for the tasks you study? If so, can you rerun the risk analysis with those measured λₐ values instead of the assumed constants (λₐ = 0.1, λ_c = 10⁻⁵)?\n- How sensitive is performance to the size of the calibration set? Could you show ΔIBC curves for 50, 200, and 500 calibration examples?", "limitations": "yes", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths:\n- The paper turns the well-trodden two-tier cascade into a principled, self-optimising, and empirically validated framework for multiple-choice QA. Its main innovations—the risk objective, STP verification, and online threshold learning—are theoretically clean and practically useful.\n- Breadth of study—two model families, four benchmarks, extensive ablations—gives credible evidence that the cascade can deliver cost savings. Reproducible: code is released, and ablations clarify which components matter.\n- The method is drop-in for discrete-choice QA pipelines and shows clear Pareto improvements on science-QA tasks.\n\nWeaknesses；\n- No real human-in-the-loop experiment. The “human tier” is an oracle that instantly returns the benchmark label; consequently  - 1）the framework never measures human turnaround time or error; and 2) λ_a (abstention cost) is set by fiat, not from empirical data. This makes all online-learning curves optimistic.\n- Dual gates, soft-mask logistics, and multiple verification variants may be over-engineered. Does simpler grid-searched thresholds (or even single-gate routers) obtain similar gains?\n\nOverall, the work is a solid incremental contribution for production-minded QA systems, but further research is required before the approach can be called a general solution for LLM deployment.", "was_revised": true, "final_justification": "The author addressed the concern on not using real human experts and robustness of the result given varying calibration size. The requested comparison to simpler grid search is not addressed; it's a more expensive method though. Overall, I think the new results validate the correctness of the paper.", "rebuttal": "We thank the reviewer for their constructive feedback. We’re glad the reviewer finds the approach principled, as well as the breadth of experiments and the empirical results promising and effective.\n\nWe address their concerns and questions below:\n\n---\n### **W1) Noisy Human in the Loop**\n>No real human-in-the-loop experiment. \n>1）the framework never measures human turnaround time or error;\nThe reason why we used the Oracle labeller was to isolate the optimisation behaviour of the cascade. Using an oracle, let us measure the *best‑possible* value of deferring to humans. Nevertheless, we acknowledge that this is a strong assumption. \n\nHowever, let’s have a look at the defined risk from a mathematical perspective, if we assume that we have an imperfect labeller (such as not all labels are correct)\n\nTo recall the system risk objective, which is being optimised, is:\n\n$$\\mathcal{R}(C)\n= 1-\\mathbb{E}[\\text{Correct}] + \\lambda_c \\mathbb{E}[\\text{Cost}] + \\lambda_a \\mathbb{P}[\\text{Abstention}]$$ \n(eq.12, page 6)\n\nNow, the part where wrong human annotations will have an impact is at \n\n$$\\mathbb{E}[\\text{Correct}] = \\mathbb{E}\\bigl[m_{\\text{pred1}}\\cdot\\Phi_{\\text{base}}\\bigr] +\n\\mathbb{E}\\bigl[m_{\\text{pred2}}\\cdot\\Phi_{\\text{large}}\\bigr]$$\n\nmore precisely on the calibrated confidence scores $\\Phi_{\\text{base}}$ and $\\Phi_{\\text{large}}$. The noisier the feedback is, the more uncalibrated $\\Phi_{\\text{base}}$ and $\\Phi_{\\text{large}}$ will become. Therefore, optimisation of the cascaded model will become unreliable. \n\nWe show this on some simple additional experiments in the online setting, where we increasingly swap correct to incorrect predictions, when calibrating the model, and how this affects the trajectory on the ARC-Easy dataset with `Qwen2.5-1.5B-Instruct` → `Qwen2.5-7B-Instruct`\n\n| **Online Step** | **0%**  | **20%** | **50%** | **100%** |\n| --- | --- | --- | --- | --- |\n| **200** | **28.66** | 44.75 | 74.39 | 97.54 |\n| **400** | **77.01** | 127.12 | 204.69 | 303.3 |\n| **600** | **126.12** | 208.42 | 321.77 | 506.24 |\n| **800** | **183.54** | 294.01 | 435.38 | 698.95 |\n| **1000** | **240.68** | 380.16 | 548.74 | 885.77 |\n\nWe observe that the cumulative regret in the online setting increases as the number of wrongly labelled data points increases, which calibrates the $\\Phi_{\\text{base}}$ and $\\Phi_{\\text{large}}$.\n\n**ACTION**: highlight this point further in the limitations and add this analysis to the manuscript.\n\n---\n### **W2 & Q2) Abstention Cost**\n>2) λ_a (abstention cost) is set by fiat, not from empirical data. This makes all online-learning curves optimistic.\n>Do you have empirical data on expert latency, monetary cost, and inter-annotator disagreement for the tasks you study?\n\nThanks for pointing this out. We want to emphasise that this multi-objective problem is highly dependent on the initial assumptions of $\\lambda_a$ and $\\lambda_c$. For example, setting $\\lambda_a=\\infty$ and $\\lambda_c=0$, the trivial solution is always to choose the best-performing model, while, e.g., $ \\ lambda_a=0$ and $\\lambda_c=\\infty$, the trivial solution is to always choose the cheapest model.\n\nOur choice for $\\lambda_a = 0.1$ and $\\lambda = 10^{-5}$ originates from Zellinger et al.’s paper [3], where they analyse the multi-objective problem between performance, cost, and abstention, in various combinations of $\\lambda_a$ and $\\lambda_c$. From their Figure 3, we see that the choices of $\\lambda_a = 0.1$ and $\\lambda = 10^{-5}$ are sensible initial assumptions for this multi-objective problem, which are worth investigating on various datasets without yielding trivial solutions.\n\n[3] Michael J. Zellinger, Rex Liu, and Matt Thomson. Cost-Saving LLM Cascades with Early Abstention, March 2025. arXiv:2502.09054\n**ACTION** Justify this part better in the manuscript as well as to acknowledge this limitation\n\n---\n### **W3) Over-engineered method and grid-search**\n>Dual gates, soft-mask logistics, and multiple verification variants may be over-engineered. Does simpler grid-searched thresholds (or even single-gate routers) obtain similar gains?\n>Have you run an offline grid-search or Bayesian-optimisation baseline that chooses a single-gate confidence threshold (or a two-gate confidence + uncertainty router)\n\nThank you for pointing this out. First of all, we wish to point out that the exploration of the multiple verification methods is independent of the dual gates and is used to determine which verification is a sensible choice. We agree that a simple threshold grid search might be sufficient. However, a main concern about grid search is that, depending on the granularity of the search, the computational cost can become significantly higher than the differentiable soft-gate. While we have not currently managed to provide the results here, we will introduce a comparison for the camera-ready version\n\n**ACTION** Add comparison to grid search to the appendix of the paper\n\n\n---\n### **Q3) Sensitivity to Calibration set size**\n>How sensitive is performance to the size of the calibration set? Could you show ΔIBC curves for 50, 200, and 500 calibration examples?\n\nThank you for this question. We reran the experiments on 50, 200, and 500 calibration examples, and these are the results:\n\n| **Model** | **Dataset** | **Cal. Size = 50** | **Cal. Size = 100** | **Cal. Size = 200** | **Cal. Size = 500** |\n| --- | --- | --- | --- | --- | --- |\n| **Qwen 2.5 (1.5B–7B)** | ARC2 Easy | 239.5 ± 36.1 | 242.7 ± 36.3 | **273.5 ± 42.7** | 254.9 ± 43.5 |\n|  | ARC2 Challenge | 87.8 ± 24.3 | **89.3 ± 26.2** | 68.7 ± 25.4 | 62.1 ± 28.7 |\n|  | MedQA | -3.0 ± 15.4 | **1.7 ± 16.3** | -7.7 ± 16.6 | -16.6 ± 18.6 |\n|  | MedMCQA | -7.5 ± 9.9 | -10.0 ± 10.1 | -8.0 ± 9.9 | **-5.7 ± 10.4** |\n|  |  | | | |  |\n| **LLaMA 3 (1B–8B)** | ARC2 Easy | 121.9 ± 15.6 | 118.3 ± 15.8 | **122.6 ± 16.5** | 102.8 ± 16.0 |\n|  | ARC2 Challenge | **45.7 ± 13.1** | 38.1 ± 13.7 | 40.3 ± 12.8 | 43.4 ± 15.6 |\n|  | MedQA | **10.1 ± 9.7** | 5.6 ± 9.7 | 5.3 ± 10.0 | 9.8 ± 11.9 |\n|  | MedMCQA | **7.4 ± 9.5** | -3.7 ± 9.2 | 6.7 ± 9.1 | 7.0 ± 9.3 |\n\nGenerally, it appears that the calibration size has little influence on these magnitudes. If we examine the standard error across the various sizes, none of them is significantly better than the others. The only thing that we noted were with a too small calibration set, we would have more diverging chains in the Bayesian Logistic Regression sampling.\n\n**ACTION**: Include this analysis in the appendix of the paper."}, {"review_id": "t9AwlTo4zZ", "reviewer": "Reviewer_zGHi", "summary": "This paper proposes a cascaded framework for human-LLM decision-making by generating predictions with a small base model, deferring to a more capable but costlier model (e.g. more compute budget) when uncertain, and abstaining to a human expert if even the costlier model is uncertain. The authors further show that across multiple interactions, cumulative regret can be minimized by training the deferral and abstention policies continually in an online fashion when feedback is available.", "questions": "Kindly address the questions regarding missing details from the \"Weaknesses\" section.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 3, "strengths_and_weaknesses": "### Strengths\n\n- **Important and well-motivated problem**\n\n- **Well-designed experiments and analyses:** The experimental design seems fairly sound appropriate for the research questions they are trying to answer. The results seem solid, consistent and convincing. Overall, I am convinced that uncertainty-based LLM cascades are a useful paradigm for cost-effective human-AI collaboration.\n\n- **Writing is clear and easy to follow.** The motivation and contributions are very clear. The methodology is fairly easy to understand.\n\n\n\n### Weaknesses\n\n- **Missing details:**\n    - Calibration errors/Brier scores for the various confidence calibration methods. A further analysis between miscalibration of the conf estimation method and overall accuracy of the cascaded system would be interesting to see.\n    - Who are the human experts in your experiments? Does the accuracy in Figures 3 include the correctness of the experts' predictions, when the large model defers to the expert?\n    - How is uncertainty estimation calculated? In L113, it is mentioned that uncertainty $\\in [0, \\infty]$, but in section 4, it is not clear how this is estimated, or whether it is estimated using the same function as the confidence estimation function. In fact, it is not even clear how confidence and uncertainty scores are different. \n- **Low ecological validity of tasks:** The selected datasets are not representative of realistic use cases of LLM systems (grade-school science and medical exam questions).", "was_revised": true, "final_justification": "The authors have adequately addressed the concerns I raised, and I am raising my score to an Accept accordingly.", "rebuttal": "We thank the reviewer for their positive feedback. We’re glad the reviewer finds the problem important and our analyses well-designed with promising results.\n\nWe address the weaknesses below.\n\n---\n\n### **W1) Calibration**\n\n>Calibration errors/Brier scores for the various confidence calibration methods. A further analysis between miscalibration of the conf estimation method and overall accuracy of the cascaded system would be interesting to see.\n\nThank you very much for this observation. We agree with you. Unfortunately, due to the limited time in this rebuttal period, we prioritised the other experiments and, therefore, did not manage to complete this analysis in time. \n\nWe did however at least inspect how different sizes of the calibration impact the $\\Delta$IBC score\n\n| **Model** | **Dataset** | **Cal. Size = 50** | **Cal. Size = 100** | **Cal. Size = 200** | **Cal. Size = 500** |\n| --- | --- | --- | --- | --- | --- |\n| **Qwen 2.5 (1.5B–7B)** | ARC2 Easy | 239.5 ± 36.1 | 242.7 ± 36.3 | **273.5 ± 42.7** | 254.9 ± 43.5 |\n|  | ARC2 Challenge | 87.8 ± 24.3 | **89.3 ± 26.2** | 68.7 ± 25.4 | 62.1 ± 28.7 |\n|  | MedQA | -3.0 ± 15.4 | **1.7 ± 16.3** | -7.7 ± 16.6 | -16.6 ± 18.6 |\n|  | MedMCQA | -7.5 ± 9.9 | -10.0 ± 10.1 | -8.0 ± 9.9 | **-5.7 ± 10.4** |\n| **LLaMA 3 (1B–8B)** | ARC2 Easy | 121.9 ± 15.6 | 118.3 ± 15.8 | **122.6 ± 16.5** | 102.8 ± 16.0 |\n|  | ARC2 Challenge | **45.7 ± 13.1** | 38.1 ± 13.7 | 40.3 ± 12.8 | 43.4 ± 15.6 |\n|  | MedQA | **10.1 ± 9.7** | 5.6 ± 9.7 | 5.3 ± 10.0 | 9.8 ± 11.9 |\n|  | MedMCQA | **7.4 ± 9.5** | -3.7 ± 9.2 | 6.7 ± 9.1 | 7.0 ± 9.3 |\n\nFrom here, we can see that increasing the calibration set does not significantly increase the final $\\Delta$IBC score, particularly given the overlap in standard errors.\n\n**ACTION**: Add Brier score analysis to the appendix of the manuscript for better understanding of the calibration.\n\n---\n\n### **W2) Information about Experts**\n\nWho are the human experts in your experiments? Does the accuracy in Figures 3 include the correctness of the experts' predictions, when the large model defers to the expert?\n\nFirst of all, no, the accuracies in Figure 3 do not include the correctness of the expert predictions. This is also not the case in Figure 4.\n\nIn our experiments, we do not use human experts directly; instead, we assume the presence of an oracle that returns the correct answer if the cascaded system decides to abstain from making a decision. Therefore, the human experts are indirectly the people who labelled the 4 datasets respectively.\n\nThis might be an oversimplification, and we acknowledge this shortcoming. To this end, we conducted experiments on the datasets, incorporating random noise when returning feedback that is consistent with human error on these tasks.\n\nWe show this on some simple additional experiments in the online setting, where we increasingly swap correct to incorrect predictions, when calibrating the model, and how this affects the trajectory on the ARC-Easy dataset with Qwen2.5-1.5B → Qwen2.5-7B\n\n| **Online Step** | **0%**  | **20%** | **50%** | **100%** |\n| --- | --- | --- | --- | --- |\n| **200** | **28.66** | 44.75 | 74.39 | 97.54 |\n| **400** | **77.01** | 127.12 | 204.69 | 303.3 |\n| **600** | **126.12** | 208.42 | 321.77 | 506.24 |\n| **800** | **183.54** | 294.01 | 435.38 | 698.95 |\n| **1000** | **240.68** | 380.16 | 548.74 | 885.77 |\n\nWe observe that the cumulative regret in the online setting increases as the number of wrongly labelled data points increases, which calibrates the $\\Phi_{\\text{base}}$ and $\\Phi_{\\text{large}}$.\n\n**ACTION**: highlight this point further in the limitations and add this analysis to the manuscript.\n\n---\n\n### **W3) Explain Uncertainty**\n\nHow is uncertainty estimation calculated? In L113, it is mentioned that uncertainty , but in section 4, it is not clear how this is estimated, or whether it is estimated using the same function as the confidence estimation function. In fact, it is not even clear how confidence and uncertainty scores are different.\n\nThank you for your question. This is a great point that we should highlight more effectively. The model we use to calibrate our verification data is Bayesian logistic regression (BLR). Compared to a standard logistic regression, a BLR returns a posterior predictive distribution, rather than a single point estimate.  This serves us for two purposes: Firstly, the mean of the predictive distribution is used to recalibrate the confidence scores (just like in a standard logistic regression). Secondly, we utilise the spread of the posterior predictive distribution, specifically the standard deviation, to quantify uncertainty, which we then use to determine abstention.\n\n**ACTION**: Make this distinction clearer in the main manuscript\n\n---\n\n### **W4)Low ecological validity of tasks**\n\nThe selected datasets are not representative of realistic use cases of LLM systems (grade-school science and medical exam questions).\n\nThank you for pointing this out. To this extend we have run our experiments during this short rebuttal time on MMLU [4], to assess the wider variety of the cascaded model systems on questions beyond grade-shool science question, but also including foreign politics, international law, logic, or management\n\nWe report the results here:\n\n**All MMLU categories**\n\n**$\\Delta$IBC**\n\n| **Step** | **Qwen2.5 1.5B → 7B**  | **LLaMA3 1B → 8B** |\n| --- | --- | --- |\n| $\\Delta$IBC (STP n=1) | 6.2 ± 5.44 | 5.3 ± 10.57 |\n\nWe see that in both cases the $\\Delta$IBC is positive. However, it is clearer in the Qwen2.5 cascaded system, where the standard error does not cross zero. \n\n**Online Experiment**\n(While we cannot provide an image, we try our best to give an informative table below)\n\n|  | **Qwen2.5 1.5B → 7B**  |  |  |  | **LLaMA3 1B → 8B** |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| **Online Step** | **Cascaded** | **Base** | **Large** |  | **Cascaded** | **Base** | **Large** |\n| **200** | **73.1** | 95.97 | 104.97 |  | **100.46** | 102.92 | 139.61 |\n| **400** | **205.66** | 269.08 | 281.64 |  | **296.33** | 302.75 | 398.17 |\n| **600** | **328.77** | 394.4 | 411.07 |  | **472.75** | 475.32 | 615.78 |\n| **800** | **452.75** | 516.18 | 530.5 |  | 631.86 | **630.86** | 839.49 |\n| **1000** | **589.03** | 649.55 | 665.2 |  | 818.74 | **813.61** | 1042.03 |\n\nWe observe that on the combined MMLU dataset, the cascade system still has the lowest cumulative regret after 1000 steps.\n\n**MMLU Subcategories**\n\nHere we also demonstrate some subcategories in an ordered fashion on the **Qwen2.5 1.5B → 7B** cascade, based on $\\Delta$IBC\n\n| Subject | $\\Delta$IBC ± SE |\n| --- | --- |\n| Computer Security | 113.38 ± 553.75 |\n| High School Psychology | 62.69 ± 41.61 |\n| Sociology | 54.23 ± 77.31 |\n| Public Relations | 47.91 ± 176.82 |\n| … |  |\n| Human Aging | 7.61 ± 47.08 |\n| **All** | **6.20 ± 5.44** |\n| Econometrics | 6.11 ± 42.79 |\n| … |  |\n| High School US History | -21.87 ± 29.37 |\n| Global Facts | -24.72 ± 43.40 |\n| College Physics | -27.22 ± 26.32 |\n| College Chemistry | -29.80 ± 39.77 |\n| Electrical Engineering | -34.56 ± 40.97 |\n\n**ACTION:** Add this new analysis in the main part of the manuscript\n\n[4] Hendrycks, Dan; Burns, Collin; Basart, Steven; Zou, Andy; Mazeika, Mantas; Song, Dawn; Steinhardt, Jacob (2021). \"Measuring Massive Multitask Language Understanding\". ICLR. arXiv:2009.03300."}, {"review_id": "T3PAQ3YwJZ", "reviewer": "Reviewer_D2qF", "summary": "The paper proposes a three-tier cascade that routes tasks from a lightweight LLM to a larger LLM or a human expert via calibrated confidence-based deferral and abstention thresholds, updating these thresholds online to balance accuracy, cost, and risk. Across four multiple-choice benchmarks (ARC-Easy/Challenge, MedQA, MedMCQA), the cascade cuts inference cost while maintaining or improving accuracy.", "questions": "please refer to weakness", "limitations": "please refer to weakness", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n\n1. The exploration of multi-agent collaboration—combining small models, large models, and human experts—is an interesting direction that has the potential to further push the limits of LLM capabilities.\n2. The paper is clearly written and easy to follow.\n\n**Weaknesses:**\n\n1. The experimental setup lacks clarity, especially regarding which versions of LLaMA and Qwen were used. It remains unclear whether the improvements from cascading would diminish as base models become stronger. This missing analysis is critical.\n2. The evaluation is limited to a few multiple-choice tasks. Key benchmarks like MMLU, MATH, and AIME, which test general and reasoning ability, are missing. It’s important to assess whether the proposed framework is still effective—and whether it can enhance LLMs further—in more challenging scenarios.\n3. The paper does not compare against other multi-agent coordination methods. It remains unclear how this cascade framework performs relative to existing autonomous agent collaboration strategies.\n4. As shown in Figure 4(c), the cascade fails to outperform a single large model on MedQA, suggesting that its generalization to complex, domain-specific tasks needs further validation.\n5. In real-world settings, accurate human feedback can be sparse or noisy, which would make online threshold tuning difficult and limit the applicability of the framework.\n6. The overall novelty of the work is relatively limited.", "was_revised": true, "final_justification": "I appreciate the authors’ detailed responses, which address some of my concerns. However, there are still several important aspects that should be included in the camera-ready version of the paper. Therefore, I would like to keep my score unchanged at this time. I strongly recommend that the authors incorporate a more comprehensive evaluation in the final version.", "rebuttal": "We thank the reviewer for their constructive feedback and appreciate that they view this as an interesting problem.\n\nWe address the weaknesses above in our responses below\n\n---\n\n### **W1) Clarity of Experimental Setup**\n\n>The experimental setup lacks clarity, especially regarding which versions of LLaMA and Qwen were used. It remains unclear whether the improvements from cascading would diminish as base models become stronger. This missing analysis is critical.\n\nThank you for pointing this out. Apologies for not having specified this clearer in the paper. We use the following models:\n- `meta-llama/Llama-3.2-1B-Instruct`\n\n- `meta-llama/Llama-3.2-3B-Instruct`\n\n- `meta-llama/Llama-3.1-8B-Instruct`\n\n- `Qwen/Qwen2.5-1.5B-Instruct`\n\n- `Qwen/Qwen2.5-3B-Instruct`\n\n- `Qwen/Qwen2.5-7B-Instruct`\n\nAs our experiments require accessing the logits and, in some instances, also altering the architecture slightly (e.g., Monte Carlo Dropout), we are running all our experiments locally. To this end, we are unfortunately limited to our available compute resources, specifically a single A100 NVIDIA GPU, which makes it impossible to run large models. While larger models lead to better performance, they also vastly increase the number of parameters.\n\nTo address this problem, we have tried an experiment with `Qwen/Qwen2.5-1.5B-Instruct` and `Qwen/Qwen2.5-14B-Instruct` And we report the results here:\n\n**ACTION**: Add a more detailed explanation of the models and experiments in the main paper, as well as in the appendix\n\n---\n\n### **W2 & W4) Additional Benchmarks**\n\n>The evaluation is limited to a few multiple-choice tasks. Key benchmarks like MMLU, MATH, and AIME, which test general and reasoning ability, are missing. It’s important to assess whether the proposed framework is still effective—and whether it can enhance LLMs further—in more challenging scenarios.\n\n>As shown in Figure 4(c), the cascade fails to outperform a single large model on MedQA, suggesting that its generalization to complex, domain-specific tasks needs further validation.\n\nThank you for this comment. We ran some experiments and you can find the results here on **Qwen2.5 1.5B → 7B**:\n\n**All MMLU categories**\n\nThank you for pointing this out. To this extend we have run our experiments during this short rebuttal time on MMLU [4], to assess the wider variety of the cascaded model systems on questions beyond grade-shool science question, but also including foreign politics, international law, logic, or management\n\nWe report the results here:\n\n**All MMLU categories**\n\n**$\\Delta$IBC**\n\n| **Step** | **Qwen2.5 1.5B → 7B**  | **LLaMA3 1B → 8B** |\n| --- | --- | --- |\n| $\\Delta$IBC (STP n=1) | 6.2 ± 5.44 | 5.3 ± 10.57 |\n\nWe see that in both cases the $\\Delta$IBC is positive. However, it is clearer in the Qwen2.5 cascaded system, where the standard error does not cross zero. \n\n**Online Experiment**\n(While we cannot provide an image, we try our best to give an informative table below)\n\n|  | **Qwen2.5 1.5B → 7B**  |  |  |  | **LLaMA3 1B → 8B** |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| **Online Step** | **Cascaded** | **Base** | **Large** |  | **Cascaded** | **Base** | **Large** |\n| **200** | **73.1** | 95.97 | 104.97 |  | **100.46** | 102.92 | 139.61 |\n| **400** | **205.66** | 269.08 | 281.64 |  | **296.33** | 302.75 | 398.17 |\n| **600** | **328.77** | 394.4 | 411.07 |  | **472.75** | 475.32 | 615.78 |\n| **800** | **452.75** | 516.18 | 530.5 |  | 631.86 | **630.86** | 839.49 |\n| **1000** | **589.03** | 649.55 | 665.2 |  | 818.74 | **813.61** | 1042.03 |\n\nWe observe that on the combined MMLU dataset, the cascade system still has the lowest cumulative regret after 1000 steps.\n\n**MMLU Subcategories**\n\nHere we also demonstrate some subcategories in an ordered fashion on the **Qwen2.5 1.5B → 7B** cascade, based on $\\Delta$IBC\n\n| Subject | $\\Delta$IBC ± SE |\n| --- | --- |\n| Computer Security | 113.38 ± 553.75 |\n| High School Psychology | 62.69 ± 41.61 |\n| Sociology | 54.23 ± 77.31 |\n| Public Relations | 47.91 ± 176.82 |\n| … |  |\n| Human Aging | 7.61 ± 47.08 |\n| **All** | **6.20 ± 5.44** |\n| Econometrics | 6.11 ± 42.79 |\n| … |  |\n| High School US History | -21.87 ± 29.37 |\n| Global Facts | -24.72 ± 43.40 |\n| College Physics | -27.22 ± 26.32 |\n| College Chemistry | -29.80 ± 39.77 |\n| Electrical Engineering | -34.56 ± 40.97 |\n\nAs shown above, different domain-specific tasks can vary significantly in how the cascaded model performs in a static setting. We hope that this further analysis sheds more clarity on the effect of the domain-specificity for our framework.\n\n**AIME (Math reasoning):**\n\nWe tried to run some experiments on the AIME 2022 - 2024 validation set (`AI-MO/aimo-validation-aime`). However, given the limited time during this rebuttal period, we ran into some challenges on this set:\n\n1. The validation set is only very small, having 30 questions per year a (total of 90 questions).\nThis hinders the performance of a good and stable calibration with the Bayesian Logistic Regression.\n2.  We were having trouble achieving competitive results with available open-source models that would fit our computing resource limitations. We used `Qwen/Qwen2.5-Math-1.5B-Instruct` and `Qwen/Qwen2.5-Math-7B-Instruct` for the cascade of models, where they achieved an accuracy of 8.88% and 14.44%, respectively. These low accuracy values also hinder proper calibration, as the base model should not be trusted solely, and the cascaded system should always abstain.\n\nWe apologise for not being able to provide more detailed results on this front at this time; we are working to find a comparable reasoning dataset (e.g. GMS8K), which is not QA for the final version of the manuscript\n\n**ACTION**: Add these results to the main paper\n\n---\n\n### **W5) Noisy human feedback**\n\n>In real-world settings, accurate human feedback can be sparse or noisy, which would make online threshold tuning difficult and limit the applicability of the framework.\n\nWe conducted experiments on the datasets, incorporating random noise when returning feedback that is consistent with human error on these tasks.\n\nWe show this on some simple additional experiments in the online setting, where we increasingly swap correct to incorrect predictions, when calibrating the model, and how this affects the trajectory on the ARC-Easy dataset with Qwen2.5-1.5B → Qwen2.5-7B\n\n| **Online Step** | **0%**  | **20%** | **50%** | **100%** |\n| --- | --- | --- | --- | --- |\n| **200** | **28.66** | 44.75 | 74.39 | 97.54 |\n| **400** | **77.01** | 127.12 | 204.69 | 303.3 |\n| **600** | **126.12** | 208.42 | 321.77 | 506.24 |\n| **800** | **183.54** | 294.01 | 435.38 | 698.95 |\n| **1000** | **240.68** | 380.16 | 548.74 | 885.77 |\n\n---\n\nWe observe that the cumulative regret in the online setting increases as the number of wrongly labelled data points increases, which calibrates the $\\Phi_{\\text{base}}$ and $\\Phi_{\\text{large}}$.\n\n**ACTION**: highlight this point further in the limitations and add this analysis to the manuscript."}, {"review_id": "yl337MvtcJ", "reviewer": "Reviewer_Jo6m", "summary": "This is an interesting framework that represents an effort to advance the deployment of large language models for human-algorithmic joint decision-making. The effort estimates the cost of doing so and also provides a pathway for on-line deployment and dynamic improvement, evaluating smaller local large language models (LLaMA/Qwen 1B/7B) to provide a proof of concept across several benchmark datasets.", "questions": "What is the actual quantifiable benefit for specific use cases?\nHow would the performance change with larger models?\nAre there other benchmarks that would better unify the goals of the authors under this framework?", "limitations": "Yes", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "This framework considers both cost and performance, estimates uncertainty, and accounts for on-line use of large language models in human-algorithmic interaction for decision-making. The cost-benefit analysis is interesting, and the use of different verification methods anchored by base models of different complexities (albeit both small models). \n\nThe use of very small models to answer more complex questions is a major limitation, since the largest open source models are up to 405B parameters. Does the improvement persist with more complex models?The datasets used to test this appear to use multiple choice questions, which are inherently limited in testing for human-AI collaboration, and appear unsuited for on-line use. In the medical domain (MedQA, MedMCQA), there is typically more unstructured question and answer, with variable amounts of information provided throughout the interaction. The authors acknowledge this and then perform the on-line experiment - however, the on-line experiment is poorly described, and the use of Regret should be justified further. How does it actually reflect benefit?", "was_revised": true, "final_justification": "While I appreciate the limitations that are acknowledged and clarified, I am still unsure if this would be a useful framework without empirical results for larger more commonly available, larger, and updated models. In response to the area chair, my concerns still persist on 1) model level - need to test more complex, widely used, and updated models 2) dataset level - while understandable, the severe limitations of the dataset limit confidence in the findings 3) despite adding a dataset (MMLU), this is supposed to be for clinical applications and 4) I am unconvinced that regret is sufficient since the original work has not been widely adopted or accepted as a viable metric for clinical applications.", "rebuttal": "We thank the reviewer for their feedback. We address their concerns below:\n\n---\n\n### **Q1) Use of Larger Models**\n\n>The use of very small models to answer more complex questions is a major limitation, since the largest open source models are up to 405B parameters. Does the improvement persist with more complex models?\n\n>How would the performance change with larger models?\n\nAs our experiments require accessing the logits and, in some instances, also altering the architecture slightly (e.g., Monte Carlo Dropout), we are running all our experiments locally. To this end, we are unfortunately limited to our available compute resources, specifically a single A100 NVIDIA GPU, which makes it impossible to run large models. While larger models lead to better performance, they also vastly increase the number of parameters.\n\nWe are sorry that we can not provide more details on this matter.\n\n---\n\n### **Q2) Non-QA Datasets**\n\n>The datasets used to test this appear to use multiple choice questions, which are inherently limited in testing for human-AI collaboration, and appear unsuited for on-line use. \n\nThanks for pointing this out. We tried to run some experiments on the AIME 2022 - 2024 validation set (`AI-MO/aimo-validation-aime`). However, given the limited time during this rebuttal period, we ran into some challenges on this set:\n\n1. The validation set is only very small, having 30 questions per year a (total of 90 questions).\nThis hinders the performance of a good and stable calibration with the Bayesian Logistic Regression.\n2.  We were having trouble achieving competitive results with available open-source models that would fit our computing resource limitations. We used `Qwen/Qwen2.5-Math-1.5B-Instruct` and `Qwen/Qwen2.5-Math-7B-Instruct` for the cascade of models, where they achieved an accuracy of 8.88% and 14.44%, respectively. These low accuracy values also hinder proper calibration, as the base model should not be trusted solely, and the cascaded system should always abstain.\n\nWe apologise for not being able to provide more detailed results on this front at this time; we are working to find a comparable reasoning dataset (e.g. GMS8K), which is not QA for the final version of the manuscript\n\n**ACTION**: Try GSM8K for mathematical reasoning and include it in the main paper, or further acknowledge this shortcoming.\n\n---\n\n### **Q3) Unstructured Medical Data**\n\n>In the medical domain (MedQA, MedMCQA), there is typically more unstructured question and answer, with variable amounts of information provided throughout the interaction. \n\nWe agree with you that in the medical domain, conversations are more unstructured, and we believe this is a crucial point to address in the future. However, this slightly exceeds the scope of the current paper, as we are interested in the methodologies of a cascaded system and how it can be optimised when deployed online. MedQA and MedMCQA are, nevertheless, both question-and-answer datasets that test specific medical domain knowledge.\n\n---\n\n### **Q4) Further Describe the Online Experiment**\n\n>the on-line experiment is poorly described, \n\nWe apologise for the brevity of the online‑learning description and will expand it in the revision.  Specifically, the experiment streams 1,000 unseen questions (ARC-Easy, ARC-Challenge, MedQA, MedMCQA) in a *random order* to simulate production traffic.  Before the first query, verification methods are calibrated using the values learned from the 100-sample calibration set; thereafter, we add queries that were marked for abstention and answered by an oracle expert to a replay buffer. This replay buffer is used to perform Adam updates on the differentiable risk (Eq. 2) with a learning rate of 0.05.  Please note that the prediction is made on an unseen query and the regret is calculated on it. If a query is added to the replay buffer, the regret associated with it has already been calculated, and the sample now becomes a training sample; however, it is not further evaluated.  We compare against two baselines assessed on the *same* stream: (i) the single base model, and  (ii) the single large model. We hope this clarifies the matter.\n\nWe hope that this clarifies any concerns the reviewer may have had.\n\n---\n\n### **Q5) Justification of Regret**\n\n>the use of Regret should be justified further. How does it actually reflect a benefit?\n\nWe chose regret as the metric for this experiment, inspired by the work on online decision mediation [4]. More precisely, we believe that regret is a good indicator because:\n\n1. Regret is just the running sum of our per‑query risk. Because error, compute, and human‑hand‑off are already weighted into the same units, adding them over time tells you the exact “bill” the system has paid.\n2. A lower regret curve indicates higher benefit, as a combination of abstentions, correct predictions and cost, and we can see it grow over time in a deployed setting.\n3. Unlike a static accuracy figure, the regret curve illustrates how quickly a policy learns online and whether early mistakes are compensated for later.\n\nThus, cumulative regret is an additive, monetisable ledger that directly reflects the practical benefit of one routing policy over another.\n\n[4]  Daniel Jarrett, Alihan Hüyük, and Mihaela van der Schaar. Online Decision Mediation. October\nICLR 2022. \n\n---\n\n### **Q6) Other Benchmarks**\n\n>Are there other benchmarks that would better unify the goals of the authors under this framework?\n\nAnother benchmark proposed by the reviewers that could be interesting to evaluate is the MMLU benchmark, which tests QA in various domains, including management, foreign relations, and science. Etc. \n\nWe have run our experiments and report the following:\n**All MMLU categories**\n\n**$\\Delta$IBC**\n\n| **Step** | **Qwen2.5 1.5B → 7B**  | **LLaMA3 1B → 8B** |\n| --- | --- | --- |\n| $\\Delta$IBC (STP n=1) | 6.2 ± 5.44 | 5.3 ± 10.57 |\n\nWe see that in both cases the $\\Delta$IBC is positive. However, it is clearer in the Qwen2.5 cascaded system, where the standard error does not cross zero. \n\n**Online Experiment**\n(While we cannot provide an image, we try our best to give an informative table below)\n\n|  | **Qwen2.5 1.5B → 7B**  |  |  |  | **LLaMA3 1B → 8B** |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- |\n| **Online Step** | **Cascaded** | **Base** | **Large** |  | **Cascaded** | **Base** | **Large** |\n| **200** | **73.1** | 95.97 | 104.97 |  | **100.46** | 102.92 | 139.61 |\n| **400** | **205.66** | 269.08 | 281.64 |  | **296.33** | 302.75 | 398.17 |\n| **600** | **328.77** | 394.4 | 411.07 |  | **472.75** | 475.32 | 615.78 |\n| **800** | **452.75** | 516.18 | 530.5 |  | 631.86 | **630.86** | 839.49 |\n| **1000** | **589.03** | 649.55 | 665.2 |  | 818.74 | **813.61** | 1042.03 |\n\nWe observe that on the combined MMLU dataset, the cascade system still has the lowest cumulative regret after 1000 steps.\n\n**MMLU Subcategories**\n\nHere we also demonstrate some subcategories in an ordered fashion on the **Qwen2.5 1.5B → 7B** cascade, based on $\\Delta$IBC\n\n| Subject | $\\Delta$IBC ± SE |\n| --- | --- |\n| Computer Security | 113.38 ± 553.75 |\n| High School Psychology | 62.69 ± 41.61 |\n| Sociology | 54.23 ± 77.31 |\n| Public Relations | 47.91 ± 176.82 |\n| … |  |\n| Human Aging | 7.61 ± 47.08 |\n| **All** | **6.20 ± 5.44** |\n| Econometrics | 6.11 ± 42.79 |\n| … |  |\n| High School US History | -21.87 ± 29.37 |\n| Global Facts | -24.72 ± 43.40 |\n| College Physics | -27.22 ± 26.32 |\n| College Chemistry | -29.80 ± 39.77 |\n| Electrical Engineering | -34.56 ± 40.97 |\n\n**ACTION:** Add this new analysis to the central part of the manuscript\n\n[4] Hendrycks, Dan; Burns, Collin; Basart, Steven; Zou, Andy; Mazeika, Mantas; Song, Dawn; Steinhardt, Jacob (2021). \"Measuring Massive Multitask Language Understanding\". ICLR. arXiv:2009.03300.\n\n---\n\nWe thank the reviewer for their time and hope that we could clarify and address their concerns and hopefully showcase the relevance of our work."}]

Author rebuttal:

Meta-review: This paper presents a cascaded LLM framework for cost-effective human-AI decision-making that routes queries through a multiple-tier system comprising a base model, a larger and higher-capability verifier model, and human experts. The system optimizes a multi-objective risk function designed to balance accuracy, computational cost, and human intervention cost. Experiments across multiple benchmarks (including MMLU, newly added) demonstrate consistent cost-accuracy improvements over single-model baselines.

All reviewers acknowledge this addresses an important practical challenge in LLM deployment, i.e. balancing performance, cost, and human oversight. The framework is methodologically principled and combined well-established techniques in a novel cascade architecture with gradient-based optimization. The results are also consistent across multiple model families and datasets. Reviewers comment also that paper is well-written, and the discussion was helpful in resolving concerns and improving the paper's contributions.

However, the reviewers' scores are split. This is largely due to a few noted weaknesses, among which the most significant in my view are:
- Reviewer D2qF argues (1) the evaluation could be more comprehensive. This is partially mitigated due to the inclusion of MMLU results, (2) limited generality, based on the MedQA results and real-world feedback characteristics, partially mitigated by the noise experiments
- Limits to generality arising from the use of small models (though this is understandable due to computational constraints, and this is not necessarily a direct threat to validity of the core methodology)
- Potentially limited clinical applications, per Jo6m
- Somewhat limited overall novelty
- No comparison to simpler grid-search threshold optimization, though authors acknowledge this would be computationally expensive and commit to including it in the final version (and I strongly recommend that they do so)

On balance, I think this work makes a solid, if modest, contribution to an important problem with technically sound methodology and a compelling empirical validation. So, despite acknowledging some limitations that may constrain its immediate impact, I recommend acceptance.
Decision: Accept (poster)