SIPDO: Closed-Loop Prompt Optimization via Synthetic Data Feedback
Authors: Yaoning Yu
Ye Yu
Peiyan Zhang
Kai Wei
Haojing Luo
Haohan Wang
Venue: ICLR 2026 Poster (2026)
Keywords: Synthetic Data
Prompt Optimization
Primary area: foundation or frontier models, including LLMs

Abstract: Prompt quality plays a critical role in the performance of large language models (LLMs), motivating a growing body of work on prompt optimization. Most existing methods optimize prompts over a fixed dataset, assuming static input distributions and offering limited support for iterative improvement. We introduce SIPDO (Self-Improving Prompts through Data-Augmented Optimization), a closed-loop framework for prompt learning that integrates synthetic data generation into the optimization process. SIPDO couples a synthetic data generator with a prompt optimizer, where the generator produces new examples that reveal current prompt weaknesses and the optimizer incrementally refines the prompt in response. This feedback-driven loop enables systematic improvement of prompt performance without assuming access to external supervision or new tasks. Experiments across question answering and reasoning benchmarks show that SIPDO outperforms standard prompt tuning methods, highlighting the value of integrating data synthesis into prompt learning workflows.

Published as a conference paper at ICLR 2026
SIPDO: CLOSED-LOOP PROMPT OPTIMIZATION VIA SYNTHETIC DATA FEEDBACK
Yaoning Yu Ye Yu' Peiyan Zhang² Kai Wei Haojing Luo2 Haohan Wang'
University of Illinois at Urbana- Chaana-hamppiin, Sttarc.Institue, UUniversity of South Florida
ABSTRACT
Prompt quality plays critical role in the performance of large language mod- els (LLMs), motivating growing body of work on prompt optimization. Most existing methods optimize prompts over a fixed dataset, assuming static input distributions and offering limited support for iterative improvement. We intro- duce SIPDO (Self- Imerovinp Prompts through Data-Augmenter Optimization), a closed-loop framework for prompt learning that integrates synthetic data gen- eration into the optimization process. SIPDO couples a synthetic data generator with a prompt optimizer, where the generator produces new examples that reveal current prompt weaknesses and the optimizer incrementally refines the prompt response. This feedback-driven loop enables systematic improvement of prompt performance without assuming access to external supervision new tasks. Ex- periments across question answering and reasoning benchmarks show that SIPDO outperforms standard prompt tuning methods, highlighting the value of integrating data synthesis into prompt learning workflows.
INTRODUCTION
Large language models (LLMs) have demonstrated strong performance across a wide range of nat- ural language tasks, including classification, question answering, and reasoning Liu et al. (2025);
Chen et al. 2025a However, their output quality is highly sensitive to prompt design small changes in phrasing, structure, or formatting can lead to significant variations in performance (He) al. 2024, Spiess al., 2025). This sensitivity has made prompt optimization core challenge in adapting LLMs to downstream applications, where consistency and reliability are crucial. In do- mains such as healthcare and finance, the inability to ensure stable, predictable performance makes prompt optimization more than desirable enhancement, but critical necessity for reliable system deployment.
The core challenge of prompt optimization is multifaceted. Unlike traditional hyperparameter tun- ing, the search space of prompts is discrete, non-differentiable, and vast. Small modifications to prompts have unpredictable effects LLMs' behavior, and the gradient-based methods that typically power optimization in machine learning are not directly applicable. Furthermore, LLMs often perform well on fixed, curated test set, but their performance can deteriorate when faced with novel linguistic variations, edge cases, or adversarial queries. This makes prompt optimization particularly challenging, as a prompt that performs well in one scenario may fail when the input distribution shifts, leading to issues such as catastrophic forgetting or fragile performance across different contexts.
Prior work in prompt optimization has explored manual tuning, discrete search, and gradient- methods improve model responses (Wang et al. [2023) (Shin al., 2020) Cui al., 2024 Kwon et al., 2024 Zhang et al.) 2024 Chen et al. 2025b). While effective in some settings, these ap- proaches do not address the dynamic nature real-world inputs, where the input space evolves over time. As result, they can produce prompts that perform well on average but lack robustness when the input distribution changes.
In contrast, data augmentation has long been used in supervised learning to improve robustness by exposing models to diverse conditions (Mikolajezyk & Grochowski 2018 Wang et al. 2022). In
"These authors contributed equally.

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the context of prompt learning, the ability of LLMs to generate high-quality synthetic data presents an exciting opportunity to improve prompt optimization. However, existing prompt optimization methods do not leverage synthetic data in dynamic. feedback driven manner (Singh et al., 2023
Gilardi et al. 2023] Tang et al. 2023; Gao et al.) 2023 Yu et al. 2025). Moreover, it is not sufficient to simply produce more data; the challenge is generate data that purposeful and stressful that targets the current failure modes of the prompt and provides a progressive challenge that helps guide its evolution. The synthetic data must also be carefully crafted to ensure that it does not overwhelm the model with trivially easy or overly difficult cases, but instead exposes latent weaknesses that need to be addressed.
To address these challenges, we propose SIPDO (Self-Improving Prompts through Data- Augmented Optimization), closed-loop framework for prompt optimization that integrates syn- thetic data generation directly into the learning process. SIPDO consists of two components: Syn- thetic Data Generator that produces inputs specifically designed challenge the current prompt, and Prompt Optimizer that uses these examples to iteratively refine the prompt. This feedback loop enables the prompt to evolve continuously over time, adapting to new, previously unseen inputs with minimal supervision for each new scenario individually by providing a general idea of the task type and what needs to be in mind without manually constructing a new prompt. Particularly, SIPDO addresses the unique challenges of prompt optimization by transforming the optimization process from a static, one-time procedure to a dynamic, self-adaptive learning loop. This shift is critical for ensuring prompt robustness in the face of evolving input distributions.
Contributions. This paper makes the following contributions:
We introduce a feedback-driven framework SIPDO that integrates synthetic data generation into prompt optimization, providing a novel pathway for improving prompt robustness.
We develop a method construct synthetic examples that dynamically stress-test prompts, reveal- ing failure modes and guiding refinement.
We empirically demonstrate that augmenting prompt optimization with synthetic data improves performance across multiple reasoning benchmarks, surpassing existing prompt tuning methods.
2
RELATED WORK
2.1 AUTOMATIC PROMPT ENGINEERING
Automatically discovering optimal prompts has become a key challenge in the era of large language models (LL.Ms). Automatic Prompt Engineering (APE) employs optimization-baste based, generative, and template-drivee approaches. Optimization techniques include gradient-based based search (Shin et al.) 2020 reinforcement learning (Ouyang et al.] 2022; Kwon et al., (024), and evolutionary algorithms (Cui et al., 2024). Generative methods use models like GPT and Gemini to generate candidate prompts, with StablePrompt (Kwon et al. 2024) optimizing prompts via reinforcement learning- Additionally, PromptAgent (Wang et al. (023) breaks down prompt creation into sub- goals. while template-driven approaches, like fill-in-the blank formats, ensure clarity (Chen et al., 20224). Recent work has expanded on automatic prompt optimization techniques. REVOLVE <Zhang et al. 2024) treats prompt optimization as an iterative text editing process that uses changes in model outputs across rounds to make updates more stable. In addition, [Chen et al. (2025b) stresses that good prompts should give consistent results despite randomness, and proposes measuring semantic stabil- ity to guide prompt improvement. In parallel, AutoPDL (Spiess et al. (2225) automates the discovery of optimal configurations for agents which successive halving to explore the space of agentic and non-agentic prompting patterns. The sequential optimal learning approach for automated prompt engineering (Wang et al. 2025) uses Bayesian regression and Knowledge-Grradeee Gradient policies to effi- ciently identify effective prompt features. Progressively Automatic Prompt Optimization (Qu et al.) colluutio-bbssee algorithm to optimize prompts for visual classification tasks.
2025) introduces Adopting LLM as a feedback loop to refine prompts has recently emerged. Self-Refine (Madaan et al. 2023) improves the model by generating feedback based on the previously generated outputs and using that feedback to refine the next output. In Promptbreeder (Fernando et al.) 2023). it uses an iterative feedback loop to select better prompts from the original prompts and mutation prompts, while Recursive In- Context Learning for Autonomous Prompt Generation in Large Language Mod- els: A Self-Instrueted Approach (Yilar et al. 2024) introduces framework that refines prompts
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through iterative loops based generated outputs. More recently, SPO(Self-Supervise) Prompt Optimization) (Xiang et al. 2023) uses iterative feedback to refine prompts by comparing the out- puts of the current prompt and its revised version without relying ground truth, and DLPO (Peng et al. 2025) optimizes prompts within loops by mimicking deep learning style where it uses textual loss, gradients, and feedback process to update prompts. CriSPO (He et al.) 2025) also extends iterative feedback loop optimization using critique guides to update prompts with multi-metric.
We propose hybrid framework integrating LLM-driven rewriting with natural language feedback (Pryzant et al. 2002)), alongside self-reflection (Shinn et al. (024) and planning (Wang et al. 2023 enhancing prompt adaptability and precision.
2.2 DATA SYNTHESIS
Using large language models (LLMs) for data synthesis is a relatively new and rapidly evolving
approach. Recent advancements have shown that LLMs possess the capability to generate text with fluency and quality comparable human output (Li et al. 2023 Mukherjee et al., 2023] Eldan &
Li 2023). For instance, prior work (Gao et al. 2023) ) has explored leveraging pre- traindddd language models (PLMs) to generate task-specifie text data that can be used to train and evaluate. Recent work Magpie (Xu et al., 2024) leverages the auto-regressive nature of aligned L.MSs to generate high-quality instruction data. Additionally, Synthetic Text Generation for Training Large Language Models via Gradient Matching (Nguyen et al. (2025) proposes novel approach to generate synthetic text that matches the gradients of human data. However, these studies have not fully incorporated advanced methodologies such as chain-of- offthoghhttt (CoT) reasoning, in-context learning, or data synthesis driven by prompts that integrate task descriptions and label information.
In this study, we systematically experimented with range of techniques, including in-context learn- ing and prompt-driven data synthesis, combining task descriptions and label information. Our results show that these approaches generate high-quality synthetic data. By introducing a difficulty tier, we further enhanced the data's robustness and applicability. These findings demonstrate the potential of combining advanced LLM capabilities with tailored prompting strategies to improve data synthesis for prompt optimization.
3 METHOD
In this work, we introduce SIPDO, a two-agent system for optimizing prompts using data augmenta- tion techniques. The workflow has two cooperating agents: (i) Data Generator creates synthetic data with increasing difficulty levels to expose weaknesses in the prompt, and (ii) Auto Prompt Optimizer iteratively analyzes errors and rewrites the prompt to maximize task performance. An overview of SIPDO is shown in Fig I
Notation. We define the true data distribution as S, which governs input-label pairs (x, y) E X x V. Let N denote the size of i.i.d. dataset drawn from S, denoted as {( 1:) S. We consider LLMs equipped with a prompt E P, and define its output function as f(p, x) E y Prediction accuracy is measured using bounded surrogate loss L(J(p, ())(),))))) where E [0, 1]. We introduce a synthetic data generator defined by a distribution (ā, û). parameterized by di E W, which produces synthetic samples forming a dataset D {( ū.) M. where M is the number of generated examples. To ensure that the synthetic labels remain realistic, we estimate the population label prior with y" (y) and use this to regularize the generator.
3.1 DATA GENERATOR
The Data Generator supplies fresh, well-targeted examples that expose the weakness by creating new synthetic-pain whose difficulty is designed beyond prompt's 's current reach.
Sampling rule. The data generator first draws target label ÿ py)).. By sampling a latent variable 2 (2 S) that captures the structure few-shot S, the decoder qo produces = (2, 7. where is a controlled difficulty tier.
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Synthetic data of difficulty level <auestion>> <Answer>>
Prompt Optimizer
fail
Analysis
True Data <Ruussiion <Answer?
If pass
TEST
Recommendation
0.
Refinement
Generator
Revised Prompt
Figure Starting from true data distribution S, the Data Generator(left) produces a synthetic question-answer pair at difficulty level c. The Auto Prompt Optimizer(right) evaluates the cur- rent prompt on this synthetic data via three sub-modules-eree analysis, recommendation, and refinement-and outputs revised prompt. The revised prompt is tested on present failures and all previously solved examples. the prompt still makes errors, then return to the Auto Prompt Opti- mizer for further refinement; if passes, move the next sample(with higher c). The eycle repeats until no етто remains or the budget is reached, yielding self-improved prompt.
Learning objective. The parameters & are learned by minimizing a hybrid objective that balances the KL penalty and the bounded surrogate loss:
min R(b) + ( v)],
Note that, we penalize deviations from the true label distribution using the Kullback-Leibler diver- gence term R(*)) (L (v) pl*
(y)). scaled by factor X R(t) during training.
Progressive difficulty. To address tasks of varying difficulty, we introduces a progressive difficulty parameter where {I...., n.. so that prompts could be tested on gradually more challenging examples. This allows the prompts to progressively improve and generalize effectively across task of increasing difficulty. Since qy is conditioned yield n difficulty- variants
single latent template (z, y) therefore
(a [(m)) = (g0 1), (x(,,y,))
For curriculum generation, an ordered sequence c1 < ... < Cn is sampled and feeds the output of the previous level back into the generator,
(1) (z, y. c1), (2()) au (ho (2: y, o2), (n) ) = (h (2: y, Cn),
where he is summarizer that distills the previous sample into latent cue, allowing semantic depth to accumulate across levels. The sequence ej < C2 <.... < Cn guarantees monotone growth of problem difficulty, providing rich gradient of difficulty for the prompt to learn from.
3.2 AUTO PROMPT OPTIMIZER
After each new synthetic instance is calibrated, the Auto Prompt Optimizer probes the current prompt, identifies the weaknesses, and repairs them before the next instance drawn. This stage builds prompt that is both robust, suitable, and generalizable for specific tasks.
Accuracy score. At iteration / E {l...., MM. the optimizer improves the current prompt y using the feedback collected from synthetic log D. {ã 3 3 C y. For any prompt p and set A C X x V, we define
(p) =
Σ
1f(p,T) = ū].
(2)
A
(5.0)EA
T[-] is the indicator function that evaluates to I the prompt's output matches the target label, and otherwise.
Step Error analysis. We first evaluate ((() on the whole set and collect the current error slice
{()) {(, ( ,,)
5}
(3)

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If g()) Ø, the prompt already "covers" all unseen cases, therefore, terminate and return p" =0 otherwise, we proceed to the next step.
Step2: Recommendation.
A reflection module Ry inspects E(0) (7, 7), pl), and f(p(") and produces a textual-patch suggesting how to modify the prompt: A Rd(p(t) g(h,, (I, ū), f(p(t, (f)) This summarizes why the prompt failed and how it can be amended(e.g. clarify/revise instructions, drop distracting details).
3: Targeted refinement. A prompt editor Uo applies the patch A (9) to revised prompt pl0 in order to fix the current error: p(() Us A (1) ,p)),, g()).
Local confirmation. We then test revised prompt p( only on the current errors: sgoo (pt9) < 1, some errors still remain. In this case, we make the revised prompt new baseline prompt by setting p(*) + p(o, updating E(0), and repeating Step 2 to generate more sufficient patch A (1); otherwise, proceed global confirmation.
Global confirmation. Solving the local error slice is not enough-we must ensure that revised prompt "covers" all seen cases. Therefore, we evaluate jit) on the entire synthetic history collected seen so far by (p(tt) During evaluation, if g(t) of Ø at any previous data, we treat them as new error set and sent them back to step 2 with new g()) to fix the current error. If g(t) = Ø, we accept the revision, set p(t+1) = f( draw the next synthetic example, and restart from Step until f == M.
Convergence guarantee. Because (p())) non-decreasing and bounded above by 1, the pro- cess stops at most M successful corrections or the user-chosen cap T Tmax- The final output p" arg maxegegt sp(p(9) achieves perfect coverage (p") = 1) whenever it is attain- able within the budget.
By iteratively applying this feedback-driven process, it systematically refines prompts to improve clarity, adaptability, and overall performance, making the framework highly generalizable across tasks and domains.
3.3 THEORETICAL GUARANTER
Since one of our goals in SIPDO is to demonstrate that, data augmentation, a popular branch of performance improvement in deep learning, also be used in prompt optimization context, aim to offer similiar performance guarantees as done in previous data augmentation literature (Wang al. 2022 Chen et al. 2020 Dao al. 2019).
Assumptions. We first offer the assumptions that we need for the theoretical guarantees.
A1 (Label-prresevvation) For all 1/ v and for any (xc y). the generator's conditional satisfies
Pręy lū = y i 2 (x. v))
We require the generator never flips the ground- -ruth label of the base example it is derived from (it may, however, hallucinate novel inputs as long as their labels match the intended classes). In practice, because L.MMs sometimes assign unexpected labels, first generate the label and then sample å conditioned on that label. For tasks and domains where producing valid synthetic data is difficult, we apply a three-voter check: three expert agents independently verify each generated item for label-input consistency and basic factual correctness.
- R-( The A2 (Approximate maximizer). Let 3²* = aig max+ew Egg L(f
inner-loop training of the generator attains a value at most E below this supremum. A perfect maximizer would be ideal but is infeasible; we only need the learned generator to be good enough-within e of optimal. The residual e directly appears in the bound.
A3 (Uniform convergence). (Wang et al. 2022) For every prompt p. the empirical loss deviates from its population counterpart by at most ((P), n, 8) with probability 1 - 6., where standard
form of q(PP), n, 5) is Ô log (P|+)og(1/8)
N
PAC(probably approximately correct) guarantee: empirical performance generalizes provided n large enough.
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sst
2nd iteration
3rd
Final Result
MMI.U Subject
Method
iteration
iteration
(Comparative Acc.)
TextGrad
85
88
86
89( 4.0) 89(, 4.0)
M-TextGrad
85
87
College Computer Science
REVOLVE
85
88
89
90(1 3.0) 93
SIPDO
TextGrad
84.8
87.5
82.1
88 4Q 5.4)
M-TextGrad
85.5
85.4
85.3
85.0(1 8.8)
Machine Learning
REVOLVE
85.7
86.6
85.7
88 88.4Q 5.4)
ANN
90. 90.1(4..7
SIPDO
93.8
TextGrad REVOLVE
95.1
97.2
95.1
96.5( 0.0)
College Biology
96.5
96.1
97.2
96.5( 0.0)
SIPDO
96.5
Table 1: Results MMLU Machine Learning. College Computer Science, and College Biology subject by GPT-4o, demonstrating SIPDO's 's effectiveness on different subjects
A4 (Alignment of risks). For any prompt and generator vb,
Eqg L(f(p.))).))) s EsL(f(p, x). v)
X R(v).
The KL penalty controls how far the generator may wander: if it manufactures rare-label outliers, R(O) increases and the bound tightens. We can verify that (v) is always absolutely-contimme w.r.t. p" (y); KL is then finite and the inequality follows from the classical variational formula.
A5 (Surrogate link). The 0-1 loss is upper-hounded by the surrogate loss: (ff * (p v).
s
This is needed in order to translate guarantees on the differentiable training loss the classification error(e.g. cross-entropy, hinge, logistic).
Theorem 3.1 Regularised Worst-case Data Generation. Under Assumptions A1-A5, for any fixed prompt E P, with probability at least - 8 over the draw of the training set, we have
sup Eg Lff * New
L (f((.xz)).))
+ R(vb)
+ (IP), (2)
KL penalty of hardest generator
population worst-case ervor
empirical
Practical implication. The inequality states that if the empirical loss of the prompt is low, and no generator can inflate that loss without paying high KL tax, then even a hypothetically all aow-pouerful adversary (generator) cannot cause the prompt to misclassify more than the RHS. Selecting larger X tightens the KI. tax, thus lowering the worst-case error but potentially harming cesuurcc-prreiseeee the pobustness-performaan trade-off observed empirically in Experiments Section 4 In addition, detailed proof theorem can be found in Appendix
4 EXPERIMENTS
4.1 EXPERIMENTAL SETUP
We use following baseline methods are for comparison across the different datasets and benchmarks: Chain of Thought (CoT) (Suzgun et al. 2022) guides models through explicit step-by-step reason- ing; Automatic Prompt Engineer (APE) Wang et al. (023)) refines prompts via Monte Carlo search and model feedback; PromptAgent (Zhou et al. (0222 also uses Monte Carlo Tree Search to iter-
atively improve prompts: Seuro-Symbolic (Pan et al. 2023) converts LLM outputs into structured
forms for rule-based inference: TextGrad (Yuksekgonul al. 2024) treats textual feedback

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first-order gradient for prompt updates; Momentum-Enhanced TextGrad YYuksekgonul et al.) 2024) adds momentum, enlarging updates when feedback aligns; REVOLVE (Zhang et al. 2024) adjusts prompts using the trajectory of model responses second-order signal; and ANN (Ma et al. 2025) models agent collaboration as a layered neural network.
We test SIPDO five main datasets across reasoning tasks:
BIG-Bench. We include all 4689 instances from six BIG-Bench tasks: Penguins Table, Geo- metric Shapes, Epistemic Reasoning, Object Counting, Temporal Sequences, and Causal Judgment (Srivastava et al. 2022). For these tasks, SIPDO is compared to Chain of Thought (CoT) (Suzgun al. 2022). Automatic Prompt Engineer (APE) (Wang al. 2023), and PromptAgent (Zhou al.
2022
Logical Reasoning Tasks. To assess logical reasoning, we sample 600 examples from the depth-5 subset of ProofWriter with a balanced label distribution (Tafjord et al. 2022 1) use 204 test examples from FOLIO that require first-order inference over short passages (Han al. 2024). and select the 500 most challenging 5-hop scenarios from the actional-charace
version of PrOntoQA (Saparov)
He 2022). For these tasks, SIPDO is compared Chain Thought (CoT) (Suzgun et al. 2022). Neuro-Symbolic (Pan et al.
2023 and REVOLVE Zhang et al. 2024).
MMLU (Massive Multitask Language Understanding). To test expert-level factual knowledge and problem solving in LLMs, we evaluate on MMLU (Hendrycks et al. 2020), focusing on college- level subject areas: Biology (1 instances), Computer Science (100 instances), and Machine Learn- ing (112 instances). For this benchmark, SIPDO is compared with TextGrad (Yuksekgonul et al.
2024). REVOLVE (Zhang et al. 2024), and ANN (Ma et al. 2025).
4.2
IMPLEMENTATION
Data Generation and Prompt Improvements. We specify maximum level and data generated with level of difficulties in prior iterations so that model is aware of the difficulty level of each previous example. To illustrate this, we provide detailed example of generating a Causal Judgment QA pair from BIG-Bench below.
Causal Judgment Prompt Template
(System Input You are an expert in generating logical causal-attribuie questions and answers. Your task generate pair of causal attributions causation. One is causation statement, and another a non-causation statement.
[User Input];
Guidelines:
Make sure that data generated different.
2. Use clear and direct words in the question, avoiding overly complex phrasing, trickiness, or ambiguity.
3. Do not make the logic in the statement overly complicated; the statement and question should be understood
fair level.
4. creative and diverse. Only follow logic and flow
diverse with the content and not limited the given example. given examples, but be creative
5. Only one data instance needs to be generated cach time.
6. Generate only output: the generated content should strictly follow the output format from the examples below.
7. Difficulty should increase with each iteration with total difficulty level: (max difficulty level] (current
difficulty level: [c)).
8. Make sure the generated data is sufficient and robust without any errors, especially logic.
9. The generated samples suppose challenge the model's ability reason and answer the question
correctly.
Past generated samples: (Generated data with difficulty)
Below the Examples with expected data format:
(True Data 1) (Tree Data 2)
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Accuracy (%)
Avg. Acc. (%)
Method
Penguins
Geume.
Epistemic
Obj. Count
Temporal
Causal
(Comparative Acc.)
CoT
79.8
79.1
79.3
98.0
67.8
81.5(4 7.6)
GPT-4o
APE
84.8
65.3
84.8
86.0
99.2
74.0
82.4C] 6.7)
PromptAgent
96.
83.0
91.6
88.2
98.4
77.8
89.2(1 0.1)
SIPDO
%6.4
86.3
91.1
99.3
79.0
89.1
CrT
75.8
68.6
85.2
81.5
94.9
63.6
78.3(J 9.0)
GPT-4o-mini
APE
83.7
44.5
81.6
86.3
97.2
75.6
78.2(1 9.1)
PromptAgent
86.0
84.3
84.6
85.201 2.1)
SIPDO
92.1
73.2
85.1
87.5
98.0
88.0
87.3
COT
70.4
68.3
85,5
90.1
94.0
66.8
79.2(} 3.7)
Gemini- 1.5 flash
69.4
71.61, 11.3)
PromptAgent
67.4
70.3
81.6
86.3
94.2
67.9
78.0KL 4.9)
SIPDO
87.0
98.4
73.2
CoT
82.6
92.8
61.5
79.5CL 3.9)
Gempni-1.3-pro
APE
40.2
56.6
88.7
78.6
86.0
65.7
69,3(L 14.1)
PromptAgent
73.6
58.3
83.8
72.6
98.4
74.2
76.8() 6.6)
SIPDO
79.3
64.3
89.3
91.3
98.0
78.3
83.4
Table Results on BIG- tasks across multiple LLMs. SIPDO consistently outperforms stan- dard prompting baselines (CoT, APE, PromptAgent) across most tasks and models, demonstrating generalization and effectiveness of the prompt optimization by synthetic data feedback.
We the difficulty budget 10 for all benchmarks except Penguins In Table and Geomet- ric Shapes from BIG-Bench, where = 25 accommodates their complex reasoning. The number of training iterations is tied the difficulty level, with c to ensure progressively harder sam- ples. The model temperature is set to 0.5 for data generation to maintain coherence. We fix the target label ý and prompt the model to generate a matching question for data validity. For chal- lenging MMLU benchmarks, three expert agents review each generated item, and only those with unanimous approval are passed
auto-prompter. This minimizes hallucinations and ensures ac- curate question-answer answer pairs. Examples of synthetic BIG-Bench Causal Judgment data at different difficulty levels are shown in Appendix
For further prompt optimization, set the model temperature to 0.0 during error analysis and im- provement steps to ensure deterministic, high-quality outputs. However, we use a higher temperature of 0.7 for generating recommendations, which encourages the model produce more diverse and creative suggestions. This combination stabilizes the error analysis and prompt improvement phases while simultaneously enhancing the breadth and quality of recommendations. The full prompt- improvement process for BIG-Bench Penguins In a Table is in Appendix D
Geometric Data Generation. Constructing complex irregular shapes exceeds the limits of few- shot methods, so we introduce three safeguards for SVG path generation in the geometry task: (1) precision normalization-cal
coordinate rounded two decimal places, preventing floating- point drift that makes downstream parsers miscount line (L) and are (A) commands; (2) template- guided retrieval a retriever selects an SVG path template whose instruction pattern matches the target shape (e.g., "4 L" for a rectangle, "I A" for sector), and the generator perturbs only vertex coordinates, ensuring syntactic correctness while adding variety; (3) reverse- generatin check-because the shape label is known in advance, rule-based decoder parses the generated path, tallies L/A commands, and rejects any sample whose inferred label disagrees. Examples appear in Appendix E
4.3 RESULTS AND ANALYSIS
We tested SIPDO across various LLMs with temperature of 0.0 on all benchmarks, including BIG- Bench, FOLIO, PrOntoQA, ProotWriter, and three subjects from MMLU, Specifically, we ran SIPDO GPT-4o, GPT--o-mini, Gemini-1.5-faas and Gemini-1.5-pro, so that all synthetic-data calls and prompt refinements in result were driven by the same model.
MMLU. We first evaluate SIPDO three subjects from the MMLU benchmark: Machine Learning, College Biology, and College Computer Science. As shown in Table SIPDO achieves the highest results in all three subjects, while TextGrad and REVOLVE tie in the Biology subject. Specifically,
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GPT-4o
GPT-4o-mini REVOIVE
Vanilla
Neuro-5
REVOLVE
SIPDO
ProofWriter
54.0
79.6
48.6
79.3
FOLIO
71.2
79.2
72.6
65.7
83.2(1 4.0)
51.2
73.2
69.3
62.8
81.1(1 7.9)
PrOntoQA
80.4
85.2
85.4
96.3(t 0.7)
79.3
83.4
91.3(1 2.0)
Average
70.0
86.4(t 4.2)
64.9
83.91 6.5)
Table 3: Performance(%) (%) on ProofWriter, FOLIO, and PrOntoQA by Neuro-Symbolie, CoT, RE- VOLVE, SIPDO, and Baseline Prompting methods across GPT-4o and GPT-4o-mini.
Model
PENGUINS
GEOME.
EPISTEMIC
OBI.CNT.
TEMPORAL
CAUSAL
Avg.
73.2
68.1
81.9
53.8
97.0
68.4
73.7
GPT-4o
24.1%)
17.2%)
5.1%)
(L 40.9%)
( 2.3%)
(4 13.4%)
(U 17.3%)
GPT-4o-
69.6
47.5
80.0
39,9
92.1
67.4
66.1
mini
(L (1.4%)
(4 35.1%)
() 6.0%)
(4 51.4%)
(L 6.0%)
(4 23.4%)
(4 24.3%)
Table 4: Accuracy (%) after removing the difficulty gradient. Numbers in parentheses show absolute drop (4) relative to the performance with difficulty gradient placed.
we set up the SIPDO pipeline using the GPT-4o model, except for the GPT-4o-mini during the testing phase, in order to provide greater insight into the reasoning weaknesses of LLMs.
BIG-Bench. We then evaluate SIPDO on six BIG-Bench tasks As shown in Table GPT-4o, GPT- 4o-mini, and Gemini-1.5-fias demonstrate particularly strong performance in Temporal Reason- ing, Object Counting, Penguins In a Table, and Causal Judgment. While Geometric Shapes exhibits comparable accuracy across GPT-4o and GPT-4o-mini, SIPDO achieves the highest overall accuracy across all LLMs except for GPT-4o, trailing PromptAgent by only 0.1%, 1%, yet still demonstrating that LLMs benefit from synthetic data generation for reasoning improvements, whereas other methods primarily rely on existing datasets. To further illustrate the generated different difficulty data in Causal Judgment tasks iteration and difficulty increase, the actual logical turns display mono- tonic trend in figure 2
FOLIO, PrOntoQA, and ProofWriter. We further test SIPDO on FOLIO, PrOntoQA, and ProofWriter, assess- ing the methods' ability perform structured logical reasoning. As shown in Table 3 SIPDO outperforms all approaches on FOLIO and PrOntoQA and achieves the highest average accuracy. In PrOntoQA, SIPDO surpasses all methods, demonstrating its capability to generate structured logical proofs. Similarly, for FO- LIO, SIPDO outperforms Neuro-Symbolic, CoT, and RE-
Jadgment Complexity lterations
Extmissed narge Maa Sure
Resoortg lure Uested
VOLVE, further validating its effectiveness in formal logic inference.
While neuro-symbolic reasoning remains the best per- former on ProofWriter, SIPDO achieves highly compet- itive results ProofWriter, trailing by only 0.4% GPT-4o-mini and 2% on GPT-4o, underscoring its strong adaptability structured reasoning tasks. Crucially, un- like neuro-symbolic approaches that rely on predefined rule-based datasets, SIPDO trained entirely on generated synthetic data, demonstrating the effec- tiveness of LLM--riven data augmentation for enhancing logical inference across diverse reasoning benchmarks. SIPDO outputs revised prompt that surpasses baselines, validating effectiveness for prompt design and performance gains. All generated prompts appear in Appendix B
Figure 2: Generated BIG-Beneh Causal Judgment task in different difficulties
4.4 ABLATION STUDY
Difficulty Gradient. To assess the contribution the difficulty gradient, we conduct an ablation study by comparing without difficulty level. As Table 4 shows, every BIG-Bench sub-task suffers

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Published as a conference paper at ICLR 2026
when the difficulty gradient is absent. On average, GPT-4o loses 17.3% accuracy, while the weaker GPT-4o-mini drops 24.3%, confirming that smaller models depends even more on the difficulty gradient. The steepest declines appear tasks Object Counting (40.9 % and 54.4 %) and Geometric Shapes (17.2 % and 35.1 %). Even comparatively simple tasks-Temporal Sequences and Epistemic Reasoning- still lose up %. We also provide detailed analysis of how different difficulty levels affect performance in Table These results indicate that within the OpenAI model family, the weaker model is more sensitive the absence of a difficulty gradient and the benefit of progressive difficulty schedule becomes more pronounced. Without this gradient, generated prompts tend to be shorter and easier, often failing capture complex reasoning patterns (details Appendix [C).
One-Shot Extremes. We experimented with replacing the step-wise difficulty gradient by a one- shot extremes sampler that tells the generator to create the most unusual examples. On our synthetic suites this shortcut delivered no measurable gain. The "extreme" samples were either solved in- stantly or only slight perturbations of original cases, leaving the optimizer with no fresh errors to exploit. We suspect the idea will pay off in real-world corpora (e.g. financial statements) where genuine edge cases abound and can expose blind spots that our synthetic tasks do not capture.
CONCLUSION
We presented SIPDO, a data-centric framework that converts augmentation into live feedback sig- nal for prompt optimization. A generator creates progressively harder examples, and an auto- proo-pp optimizer uses them to expose and correct prompt weaknesses. This coupling produces consistent accuracy gains across diverse reasoning benchmarks, outperforming several leading baselines. Be- yond these empirical results, SIPDO shows how data-generation strategies and prompt optimization reinforce one another, linking ideas from curriculum learning and adaptive optimization with LLM practice. Further investigation on domain specific corpora such as financial filings and clini- cal notes and exploration of fully automated variants that refine prompts through continuous model feedback will clarify SIPDO's broader value and extend its principles to new settings.
ACKNOWLEDDMENT
This work was partially supported by the National Artificial Intelligence Research Resource (NAIRR) Pilot under awards NAIRR250400 and NAIRR240283, and Standing Up to POTS.
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A DETAILED ABLATION TABLE STUDIES
In this section, we provide more comprehensive and detailed ablation studies that demonstrate our studies and findings.
GPT-4o mini
GPT-4o
Task
Difficulty
Run Time (6)
Cost (S)
Tokens
Acc. (%)
Run Time (8)
Cost (S)
Tokens
Acc. (%)
217.43
0.0130
67269
83.7
58.55
0.1089
35426
91.3
Penguins
10
1078.47
0.0929
527358
92.59
561.05
1,2100
410807
93.33
2226.68
0.21774
1250646
92.59
2342.25
6.4528
2275582
96.0
20
19753,99
2,6698
16695611
93.33
3452.01
7,8194
2759306
96.67
49.07
0.0027
14297
75.33
119.28
0.1401
42985
78.0
Epistemic
686. 18
0.0420
227607
76.0
555.86
0.6814
224480
79.0
15
1471.69
0.1
640713
80.33
[440.52
2,0357
695678
83.67
20
3279.38
0,2583
1483605
80.0
2885.80
4,0457
1418053
84.0
$1,70
0.00369
19079
35,33
106.06
0,0955
27548
50.0
690.22
0.03237
144212
49.17
560.95
0.4726
133780
67.67
Geomettic
15
1326.86
0,06710
296540
72.22
964.28
0,9158
268912
80.0
20
2503.59
0.20610
571178
78.06
1334.71
1.4882
45U575
87.78
103.80
0.0064
causal judgeninnee
10
899,33
0.0699
385346
66.66
156.22
0.2761
101715
81.6
2066.
79.67
534.45
237519
20
443,71
0.0388
236561
67.89
3033.81
4,8447
1738332
79.49
35.40
0,0016
7650
94.0
39.27
0.0283
7813
99.67
147.00
0.0066
26538
97.5
647.34
0.8005
267894
99.33
temporal
15
2166.98
0.1876
1034249
99.67
1432,008
2.1206
736935
99.33
1255135
190.52
0.0122
60765
91.0
115.30
0,1660
49776
97.0
object counting
1094.08
0.0684
363795
92.0
512.40
0.7296
232588
98.0
2592.44
0,2069
1148406
96.0
1396.33
1,8831
624918
99.33
20
5078.75
0,3968
2260081
96.0
2848.81
4,3167
1459739
99.33
Table 5: SIPDO's cost (time, money, tokens) and accuracy across tasks and difficulty levels for GPT-4o-mini and GPT-4o.
Perguina
Epeacesic
Gomnetrcc
Tarpera
Inspreeni
Oitecct Countnng
litn Vime
Ran
Rie
Run
Ree Thee
Acc
Time
79675
10619
83.0
01389
18313
77.8
6398
8933
201M|
95.01
48012
72.9
00953
96A
1HM7
84B
41477
M4.3
SUIDI
81.5
Table 6: Run time and accuracy tasks for SIPDO and PromptAgent
Cost in time (s)
Cost in money (S)
Performunce (Sr)
Task
Remove voters
With voters
Remove voters
With voters
Remove voters
With voters
College Biology
763
912
0.0167
0.0221
95.14
96.5
Machine Learning
375
680
0.0096
0.7974
76.79
93.8
College Computer Science
432
1311
0.0104
1,8880
88.00
93.0
Table 7: Impact of SIPDO's voters on cost and performance across tasks.
Accuracy (%)
Cost in time
Task
w/o generator
w/o error analysis
wlo revisor
w/o generator
wl envor analysis
w/o revisor
College Biology
95.83
95.83
95.14
331
677
314
Machine Learning
77.68
1622
353
College Computer Science
94.00
90.00
89.00
2405
2852
2861
Table 8: Ablation results on accuracy and time cost when removing each component of SIPDO.
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B OPTIMZED PROMPTS FOR DIFFERENT TASKS
In this section, we demonstrate optimized prompts by Chain-of-Thought (CoT), Automatic Prompt Engineering (APE), PromptAgent, and SIPDO with Accuracys respectively.
Table 9; Comparison of Optimized Prompts for Object Counting task, including CoT, APE, PromptAgent, and SIPDO
Approach
Optimized Prompt
Accuracy
CoT
Your task is to count the total number of objects mentioned question. Follow these simple steps to ensure accurate counting:
0.928
**tepps to Follow:** 1. **Identify Items**; Read the question carefully and list all objects mentioned. 2. **Count Quantities**; For each item, check if quantity is provided. no quantity mentioned, assume one. **Add Totals**; Add up the quantities all items to calculate the total count. 4. **Verify the Total*;; Double- check to ensure no item is missed or counted twice.
+* "xxample:** Question: "Count the apples, oranges, and bananas. There are 2 apples, orange. and bananas." Step 1: Identify items: apples, oranges, bananas. Step 2: Count quantities: apples, I orange. bananas. Step 3: Add totals: 2 + Step 4: Verify: All items are accounted for, total is 6. #*Output*** "The total count is 6."
Use this step-by-ster method for every question to ensure accurate and clear results. Calculate the overall total of all items even those spoken in groups.
APE
0.863
PromptAgent
Carefully examine the provided information. Identify and catalog each mentioned item, ensuring that explicitly stated quantities are accurately recorded. If no quantity is spec- ified for an item, assume it as single unit. However, for items with defined quantities, count each unit separately and include it in the total. If collective terms or categories are mentioned, break them down into their individual components and associate each with its stated count. When computing the total for such categories, ensure that the sum reflects all individual units rather than just the number of groups or types. Each item should be counted independently, but related items belonging to a common category should he grouped together, with their specific quantities contributing precisely to the final total. Avoid assumptions regarding the classification or nature of ittem-adheer adhere standard, widely accepted definitions. Finally, summarize the count by explicitly listing the quantity of each identified item category, and provide comprehensive total of individual units rather than just category counts, unless otherwise specified.
0.882
SPIDO
Task Requirements:
0.923
The task involves counting the total number of objects listed in a question. Each distinct object should be considered as part of the total count, regardless of its type or variation. The output should be formatted correctly specified. Problem Rule Application: Identify all items listed in the question. Count each item exactly once, regardless of type, to determine the total number of objects. Ensure accuracy by verifying that all listed items have been included in the final count. Provide the final result in the re- quired format: The number should be presented in both word form and numerical form, separated by comma (e.g.. "nine, 9"). No extra symbols, characters, or explanations should be included. Judgment Criteria: (Strictly follow these rules) Complete Identification:
Extract and recognize all objects in the given list. Do not overlook any item mentioned in the question. Accurate Counting:
Each item must counted exactly once. Ensure items omitted double- counted. Verification Process: Double-check the list to confirm that all objects are included. Cross-verify the final count to avoid errors.
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Table 10: Comparison of Optimized Prompts for Penguins In A Table task.
including CoT. APE, PromptAgent. and SIPDO
Approach CoT
Optimized Prompt
Accuracy
You are tasked with answering questions about a table of penguins and their attributes. Use step-hy-step reasoning, to ensure accuracy in calculations and comparisons. The table is as follows: ".. Name, Age, Height (cm). Weight (kg) Louis. 7. 50, 11 Bernard, 5, 80, 13 Vincent, 9, 60, 11 Gwen, 8, 70. 15 .
0.818
Identify the target attribute (age, height, or weight) and the type of operation (comparison, ranking, filtering.. 2. Extract the relevant rows or columns hased on the question's 's requirements. 3. Perform the required operation step-by-step using the extracted data. 4. Clearly summarize the answer based the operation's 's result.
**Reasoning Steps for Each Question:**
Example Workflow: Question: "Who is the tallest penguin?" Step 1: Identify the target attribute: Height. Step 2: Extract the height values and corresponding names: [(Louis, 50), (Bernard, 80), (Vincent, 60), (Gwen, 70)]. Step 3: Find the maximum height: Bernard (80 cm). Step 4: Output the result: "Bernard is the tallest penguin with height of cm."
Follow this workflow for every question to ensure clarity and correctness. Carefully scrutinize the provided table or tables. Understand the query in relation to the information given. Pinpoint the pertinent data and carry out the vital computations comparisons determine the right answer from the given choices.
APE
0.848
PromptAgent
Answer questions about a table of penguins and their attributes. considering both the penguin table and any additional relevant tables. Please provide step-by-step reasoning for your answers, and ensure to clarify any criteria used for filtering or sorting data. Here is table where the first line is a header and cach subsequent line is penguin: name, age, height (cm), weight (kg) Louis, 7, 50, Bernard, 80, Vincent, 9, 60, Gwen, 8, 70, 15
0.961
For example: the age of Louis is 7, the weight of Gwen is 15 kg. the height of Bernard is 80 cm. What is the name of the last penguin sorted by alphabetic order? Options: (A) Louis (B) Bernard (C) Vincent (D) Gwen (E) James
List the names of the penguins. 2. Sort names alphabetically and present the sorted list clearly. 3. Identify the last name in the sorted list and indicate the corresponding option letter from the provided options. 4. If the last name does not match any of the options, select the name that is closest to the last name in the original list of penguins.
**Istructioons**
At end, show the answer option bracketed between janswer; and j/answer..
SIPDO
Answer questions about a dynamic, comprehensive table of penguins and their attributes that allows penguins and other animals to be added and removed. Perform calculations and comparisons based the questions asked. Read the question carcfully to determine which attribute is being compared (age, hoight, weight). When comparing an attribute, extract the name and that attribute, and then compare, ignoring the other attributes. Ensure the extracted value is from the correct column corresponding to the requested attribute. When using the table, align the data that the first number is age, the second is height, and the third is weight. Understand the question correctly, find the key words from it, and then perform calculations or comparisons based on the key words The current table is as follows:
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Name, Age. Height (cm), Weight (kg)
Louis, 7, 50. 11
Bernard, 5, 80, 13
Vincent, 9, 60, 11
Gwen, 8, 70, 15
**Question Rules to Apply:
Identify the
columns that meet the specified conditions. Retrieve the value the required attribute from identified rows or columns.
When we modify this table (by adding new penguins or removing existing penguins or adding giraffes), we first confirm whether the information we added is penguin giraffe, and then solve the problem of comparing, ranking, and filtering based on attributes between penguins or giraffes, depending the problem.
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Table 11:
Comparison of Optimized Prompts for Geometric Shapes task, in- cluding CoT, APE, PromptAgent, and SIPDO
Approach
Optimized Prompt
Accuracy
CoT
Your task is to identify the geometric shape represented by given SVG path data.
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Follow these steps to ensure accuracy:
**eepp to Identify the Shape: 1. **Check for 'A' Instructions If the path con- tains 'A' determine: **Cincle*#; 2 more "A' instructions. *= 'A' instruction. 2. **Count Instructions If there are no 'A' instructions, count the 'L' instructions to determine the polygon's 's shape: ***inn**
'I.. **Trian- gle**: 3 'L' + *Rectangle**; 4 "L", Pcntagon**: 'L'. *cxxagoo*** 6 'L' * **Heptagon** * 'L'. *Octagon**; 8 'L', **Kite**; 4 'L' 3. **Povvide the Shape N; Output only the of the shape (e.g.. "circle". "triangle", "hexagon") **Example=** Input:
zn Step 1: 'A' instructions. Step 2: Count 'L' instructions: LL' Step 3: Shape is *#Retanggeest, '*"Output**: "rectangle".
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Use this st-seby-step process for all inputs to determine the correct shape. Determine the shape each SVG path element is drawing. then pair it with the corre- sponding letter from the available choices. In this case, C symbolizes hexagon, G for pentagon. signifies sector, and B stands heptagon.
APE
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Table 11: Comparison of Optimized Prompts for Geometric Shapes task (con-
tinued)
Approach
Optimized Prompt
Accuracy
PromptAgent
Analyze the SVG path data to identify geometric shape represents. Follow these comprehensive and retined steps to ensure accurate identification:
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1. *oolistic Path Closure**; Determine if the path forms a closed shape by check- ing if the last point connects hack the starting point. If multiple "M" commands are present, analyze the segments collectively identify any closed loops. Treat the entire path as single entity thorough analysis. 2. **Segment and Side Analysis**; Iden- tify the types of segments used in the path: **Line Segments**; Count the number of distinct line segments to determine the number of sides. Ensure accurate counting by considering all segments collectively. **Are Segments** For paths using the 'A' command, note that these represent elliptical ares. Pay attention to the parameters distinguish between circles and ellipses. 3. *IIn-depth Geometric Propertics**; For line segments, analyze the relative lengths of sides and angles between them. Consider properties such parallel sides, equal side lengths, and right angles distinguish be- tween different types of polygons. Evaluate the overall shape formed by all segments. For are segments, examine the parameters are equal, which indicates a circle. + the radii differ, consider the shape as an el- lipse. 4. Shape Identification and Classification Use the geometric properties to classify the shape: For polygons, identify specific types like rectangles, kites, and trapezoids based their properties. Pay special attention the number of sides and the relationships between them. Consider the entire path as a single shape to ensure accurate classification. - For ares, determine if the shape is a circle or an ellipse based the radii. 5. **Options Selection and Interpretation*** Choose the most appropri- shape from the given options. Consider multiple interpretations of the path data, especially when multiple 'M' commands are present, to ensure accurate classification. If the path represents multiple shapes, prioritize the most complex or relevant shape. 6. ** Ambiguity Resolution In cases where the path data could represent multiple shapes, provide rationale for selecting the most complex or relevant shape. Consider the context and any additional information that might influence the classification. Visiuaal Verification
'A' command: Check the radii
possihle, visualize the path confirm the identified shape. This step can help resolve any remaining ambiguities and ensure the accuracy of the classification. 8. **Itrrative ** If the initial classification is uncertain, re- visit the analysis steps refine the identification. Consider alternative interpretations and re-evaluate the geometric properties. **Contextual Considerations Take into account any contextual information or additional data that might influence the shape classification, especially in ambiguous cases.
Provide your answer by selecting the correct option and enclosing within "janswer," and '/annwery"" tags.
** **Exmplee:** SVG Path: 'path d="M 8.10,55.86 1.74,25.57 L 12.08,23.40
18.44,53.69 L 8. 10.55.86" Analysis: The path forms a closed quadrilateral with op- posite sides parallel and equal, indicating a rectangle. Answer: "janswer,H H/anwerr SVG Path: 'path d='M 16.33,5.98 A 8.87,8.87 275.02 1,0 14.78,23.64 A 8.87.8.87 275.02 1,0 16.33.5.98'/ Analysis: The path uses elliptical ares with equal radii, form- ing a closed loop, indicating a circle. Answer:
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Table 11: Comparison of Optimized Prompts for Geometric Shapes task (con-
tinued)
Approach SIPDO
Optimized Prompt
Accuracy
Given following SVG path data: "input" options, identify the geometric shape it represents and provide **ONLY** the name of the shape as the 'target'. **Task Requirements:** 1. Count the instructions in the SVG path 2. Judge the shape of the graphic according to the judgment criteria 3. Provide the exact name of the shape as output.
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You need to count how many instructions ** are the SVG path:
**Problem Rule Application:** 1. Visualize the path data to understand the overall structure. 2. Find out whether there is instruction #* ***## in the instruction. If so. deter- mine whether it is circle
sector according to the number of instructions "*A"". If not, determine how many sides 3. For polygons, pay attention the number of edges to identify the shape. The following are the number of instructions correspond- ing to different shapes: **triangle** * L. **rectangle**; L. **hexagon**; 6 L pentagon 5 L. **octagon*** * 8 I. **heptagon * 7 L **itt**; 4 L +* L. ** 2 more A **secto**=
** **Jugmment criteria:* (Please strictly abide by this rule) No need to pay attention "M" instructions !! First identify whether there is an instruction "A" in the SVG path. If so, first determine whether it is a circle sector. !! If there is no instruction "A", determine the number of sides of the polygon based the instruction "L.". A polygon with *n sides requires *n* "I." instructions. (Please strictly abide by this rule)
Table 12:
Comparison of Optimized Prompts for Causal Judgment tasks, in- cluding CoT, APE, PromptAgent, and SIPDO
Approach
Optimized Prompt
Accuracy
CoT
Respond inquiries about causal attribution by identifying the key causes and their contributions to the outcome. Follow the steps below ensure accurate and clear reasoning:
Task:
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**Steps to Analyze Causation: 1. **Identify Key Entities*:; Read the question care- fully and highlight the specific entities factors being discussed. 2. **Detemmine Relevant Causes**; Analyze the context to identify immediate and incidental causes contributing to the outcome. Immediate causes: Directly lead the outcome. Inci- dental causes: Indirectly influence the outcome but may still contribute. Interactions** Consider how multiple causes might interact to produce the observed effect (e.g., synergy independent contributions). 4. **Provide the Answer**, Clearly the primary and secondary causes, well their roles in creating the outcome. Avoid unsupported assumptions.
**Evaluate
Use this structured reasoning approach to analyze each inquiry and provide a clear and logical explanation.
APE
For each situation, decide if the result was caused deliberately not. If the individual or party behind the event was aware of the potential result and chose go ahcad, select 'Yes'. they didn't intend the result to happen, even if they knew it could possibly occur, select 'No'."
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Approach
Optimized Prompt
Accuracy
PromptAgent
When addressing questions about causal attribution, ensure comprehensive analysis by considering both individual and collective actions that contribute to an outcome. Clearly differentiate between necessary and sufficient causes, and recognize that mul- tiple causes simultaneusly contribute to an outcome. Emphasize the importance of understanding both general and specific intentions, especially when outcomes are unintended. Define "intentional" actions as those where the actor or group had control over maintaining or altering the conditions necessary for the outcome, even if the spe- cific result was not desired. Address scenarios where unintended consequences arise from intentional actions, and provide answers that reflect nuanced understanding of how different elements interact to produce a result. Use diverse examples illustrate key concepts like "direct causation," "simultancity," and "unintended consequences," ensuring balanced consideration of necessary and sufficient causes. Simplify com- plex scenarios by breaking them down into clear, manageablc components, and provide definitions or examples of key initions of key terms such as "necessary," "sufficient," "intentional." and "unintended consequences" to ensure precise understanding. Highlight the importance of interac- tions between multiple causes, especially in complex scenarios, and offer strategies for analyzing scenarios where simultaneity is erucial. Explore the nuances of intentional actions and unintended consequences more deeply, and encourage use of diverse examples to illustrate different aspects causation. Pay special attention to role individual actions in maintaining necessary conditions and the distinction hetween col- lective and individual causation. Emphasize that in collective decision-making the out- come can be intentional if it aligns with the group's goals, disagree. Reinforce the distinction between necessary and sufficient causes, ensuring the model understands that necessary causes alone do not determine the outcome. Clar- ify that following a protocol does not remove intentionality if the outcome aligns with organizational priorities. Highlight that intentionality can be attributed if the outcome was a foresccable consequence of the action, regardless of individual opposition.
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guide your analysis. Additionally, clarify def-
if individual members
SIPDO
Task Requirements Determine whether a given event (cause) directly leads to another event (effect). Assess the causal relationship based on logical reasoning, ensuring a clear and definitive answer. The final ouiput must be only "Yes" or "No", strictly ad- hering the required format. Problem Rule Application Identify the cause and effect within the question. Assess necessity: Determine if cause is essential to occur. Evaluate causation: If the cause did not happen, would the effect still occur? If the effect only happens when the cause is present, then the cause directly leads to the effect. If the effect can still happen independently, then the relationship is not causal. Judgment Criteria Direct Causation: If the cause directly leads to the effect and a necessary condition, answer "Yes". the effect would not have occurred without the cause, answer "Yes". Example: "Dropping a glass caused it to shatter." -> Yes. No Direct Causation: If the effect can occur without the cause, answer "No". If the cause is only correlated but not necessary, answer "No", Example: "Wearing a red shirt caused the stock market rise." No. Verification Process: Check whether the absence of the cause results in the absence of the effect. Ensure logical consistency in the causal assessment.
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Comparison of Optimized Prompts for Epistemic task, including CoT. Table 13:
APE, PromptAgent, and SIPDO
Approach
Optimized Prompt
Accuracy
CoT
Task: Analyze the logical relationship between a given premise and hypothesis. Your goal is to determine if the premise guarantees the truth of the hypothesis. Choose one of the following answers: 'entailment" or non-entailment',
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**eps to Follow:** 1. **Understand the Premise and Hypothesis**: Carefully read the premise and hypothesis to identify the key information in both statements. 2. *n alyze the Logical Relationship**: Determine whether the information in the premise confirms the truth of the hypothesis. If the premise logically supports and guarantees the hypothesis, choose 'entailment'. If the premise does not confirm the hypothesis, if there is uncertainty, choose 'non-entailment.. 3. **Provide the Answer* Based on your analysis, oulput the correct answer (" e'entailment' or "nonnentailment".
Use this step-by-step approach for all premise and hypothesis pairs to ensure accurate reasoning.
APE
Determine whether the hypothesis is directly implied by the premise or not. If the premise's statement is direct claim or conviction of the individual mentioned in the hypothesis, choose 'entailment'. However, the premise is formed on the belief or sup- position of somcone other than the subject in the hypothesis, opt for 'non-entailment. Determine the relationship between two sentences by evaluating whether the first sen- tence provides direct logically implied evidence for the second. Choose from the options 'entailment" or 'non-entailment".
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PromptAgent
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Consider the following: ** Entailment The first sentence directly or through logical implication confirms the truth of the second sentence, even if it involves a chain of beliefs perceptions, long the chain logically supports the hypothesis. -*Non- entailment**: The first sentence does not confirm the truth of the second sentence, often involving unsupported assumptions, beliefs, or suspicions that do not logically lead to the hypothesis.
Guidelines for Analysis: 1. **Clarify Belief Chains and Logical Implications Un- derstand how beliet chains work and when they logically support the hypothesis. Pay attention to verbs indicating beliefs, assumptions, or suspicions (e.g.. "thinks," "as- sumes," "suspects") versus those indicating direct evidence (e.g.. "learns," "knows," "remembers")) ) Consider how these verbs interact in helief chains and what they imply about the subject's own beliefs. 2. **Evaluate Direct and Implicd Evidence**; De- termine the premise provides direct logically implied evidence for the hypothesis, considering how belief chains can logically support the hypothesis. Recognize that in- direct beliefs about another person's recognition can imply one's own belief about a situation, especially when the belief chain is logical and straightforward. 3. **Consider Perspective and Source of Information Note any differences in perspective souree of information (c.g., who remembers or assumes something) and how these perspectives contribute to the logical implication of the hypothesis. 4. *Connduct a Comprehensive *nalysis**: Use a step-by-step approach to ensure all relevant details and logical im- plications considered in the analysis. Balance the emphasis on direct evidence with the recognition of logical implications from indirect beliefs.
Example: Premise: "Charlotte thinks that Richard recognizes that a boy is standing in a pool getting splashed with water." Hypothesis: "Charlotte thinks that boy is standing in pool getting splashed with water." Options: (A) entailment (B) non- eot-ennallment Analysis: 1. Understanddin the Premise**:; The premise indicates that Charlotte thinks Richard recognizes a specific situation involving boy pool. 2. **Under- standing the Hypothesis**; The hypothesis states that Charlotte thinks a boy is in a pool getting splashed with water. 3. ** AAssessing the Relationship**: The premise implies that Charlotte has belief about the situation (through Richard's recognition). which logically supports the hypothesis. Charlotte's belief about Richard's recognition suggests she also believes the situation's occurrence. 4. **Conclusion The re- lationship is one of entailment because Charlotte's 's belief about Richard's recognition logically implies her belief in the situation. Therefore, the correct answer is: <answer>A</ answer>> Identify the relation between the following premises and hypotheses, choosing from the options 'entailment' or 'non-entailment.. At the end, show the answer option bracketed between <answer> and </answer>.
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Approach
Optimized Prompt
Accuracy
SIPDO
Task Requirements:
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Analyze a given premise (primary sentence) and determine whether it fully supports the truth of a hypothesis (subsequent sentence). Classify the relationship as either "Entail- ment" or "Non- "Non-Entailment based the logical and factual connections between the Provide the classification only the final ouiput. Problem Rule Application: Entailment:
The premise explicitly confirms the hypothesis with clear, direct evidence. No addi- tional information, assumptions, or interpretations are required to validate the hypothe- sis. Non-Entailment:
The premise does not fully explicitly confirm the hypothesis. If there ambiguity, uncertainty, or missing logical links, label it as Kon-EEntilment. Judgment Criteria: (Strictly follow these rules)
Language of Uncertainty:
Words like "assumes." "believes," "thinks," "feels" "suspects" indicate subjectivity and should not be considered definitive proof. These terms suggest a possibility rather than an explicit factual connection. Specific vs. General Statements:
A specific premise (e.g., mentioning "full face mask") does not necessarily contradict general hypothesis (c.g.. referencing "mask" in general). However, if the premise is too general to confirm the specific claim, classify as Non- Non-Entailment. Objective Rea- soning:
Only use the logical and factual ties within the given statements. Do not rely on external knowledge, assumptions, interpretations unless directly supported by the premise. Decision Process:
Determine whether premise fully supports the hypothesis without needing extra inference - Entailment. If the premise only partially supports or fails to confirm the hypothesis + Non-Entain con-Entailment.
Table Comparison Optimized Prompts for Temporal task including CoT, APE, PromptAgent, and SIPDO.
Approach
Optimized Prompt
Accuracy
CoT
Your task is to determine the available time slot for an event, based on a schedule of occupied times. Follow these steps to ensure accuracy:
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**Steps Identify Free Time Slots:** 1. **List Occupied Periods** Organize all occupied time slots chronological order. **Find Gaps**; Identify gaps between the occupied periods where no activities are scheduled. 3. **Check Constraints*** **: Ensure that the free time slots fall within operational constraints (c.g., facility closing times). 4. **Select the Slor**; Choose the correct free time slot that satisfies all criteria. **Output Result #ormat:** **_ Present the selected free time slot clear format, such as "Xpm to Ypm" or "Xam Yam".
Use this step-by-step method to ensure that the identified time slot is accurate and does not overlap with any occupied periods.
APE
Identify the period when the individual was unnoticed and had the possibility visit the specified place before closing time.
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Approach
Optimized Prompt
Accuracy
PromptAgent
Analyze the timeline of events determine possible time frames during which certain events could have occurred, even if they were not explicitly observed. Start by con- structing a comprehensive timeline, clearly listing all observed and unobserved time slots. Identify gaps where the subject is unobserved, ensuring these gaps fit within any given constraints, such opening and closing times. Emphasize the importance of constraints by verifying them after identifying potential gaps. Use step-by-step rea- soning approach to systematically evaluate all available information, and include a final review to check for potential errors or overlooked details before finalizing the answer. Define key terms like "unobserved" and "constraints" to ensure clarity in the task re- guirements. Provide examples to illustrate the reasoning process and expected output format, guiding the model analyzing timelines and identifying possible time frames for unobserved events. Additionally, incorporate a checklist to ensure all steps are fol- lowed, and highlight common pitfalls to avoid during the analysis. Finally, include a summary of the reasoning process reinforce understanding and emsure the model's conclusions are well-supported.
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To further enhance the model's performance, include additional examples that cover wider range of scenarios and constraints, such as overlapping time slots or multiple constraints. Provide explicit guidance on handling complex constraints and ambiguous information. Incorporate interactive feedback mechanisms to help the model learn from mistakes and improve over time. Ensure the prompt is concise and focused, avoiding unnecessary repetition while maintaining clarity and comprehensiveness Additionally, introduce section for handling exceptions unusual cases, offering strategies for dealing with incomplete confficting data. This will help the model adapt to broader range world scenarios and improve its robustness in timeline analysis tasks. **Task Requirements:** Determine the possible time period during which an event could have occurred, based on a detailed schedule of occupied times. Your goal is to identify the correct time slot that fits all the provided criteria without any overlap. ** **Problem Rule Explanation:* * Analyze the schedule to identify all time slots during which the person occupied. 2. Determine the available time slots by identifying gaps between these occupied periods. 3. Consider any additional constraints, such as closing times, that may limit the available time slots. ** **Problem Rule Application:** Identify gaps between these occupied slots where the person is free Ensure that the free time slots do not conflict with constraints like closing times.
SIPDO
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List all the occupied time slots chronologically.
**Result Verification:** adheres to any constraints. Double-check against all occupied periods to ensure there is overlap. Avoid selecting time slots that are partially accupied or overlap with any scheduled activities.
Confirm that the identified time slot is completely free and
*#ttput Result #ormat:+* Present the correct time slot in a straightforward manner, using the format "Xpm to Ypm" or "Xam to Yam" as appropriate. Ensure the output is clear and free of any extrancous symbols or text.
** "Common Mistakes to Avoid Do not include time slots that extend beyond the closing time of the facility. Avoid selecting time slots that overlap with any scheduled activities. Ensure the selected time slot is entirely free and does not partially overlap with any occupied period.
** +*General Rules and Analysis: Identify all occupied periods and list them chrono- logically. Look for gaps between these periods where the person is not scheduled for any activity. Verify that these gaps fall within any operational constraints, such as closing times. Ensure the selected time slot is entirely free and does not overlap with any occupied periods.
By following these guidelines, you can accurately determine the available time slot for the event in question. Avoid errors by ensuring that the selected time slot is entirely free and does not overlap with any occupied periods.
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C
OPTIMIZED PROMPTS WITHOUT DIFFICULTY SCALING IN SYNTHETIC DATA
Table 15: Optimized Prompts Without Difficulty Scaling in Synthetic Data
Tasks
Optimized Prompt
Accuracy
Penguins
You are provided with two tables containing data about penguins and giraffes. Your task is to focus solely the giraffe data to answer a specific question regarding the tallest
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giraffe.
**Penguin Data:
Name
Age
Height (cm) Weight (kg)
Louis 7 - 50 11
Bernard - 5 5-80
80
13
Vincent
60 11
Gwen
70
15
James 122
90
12
**Giraffe
Data:*
Name Age Height (cm) Weight (kg)
Jody - 5 430 620
Gladys - 10 420 - 5500
Marian
2 12--310 310 410
Domna 9 440
650
*TTask Requirements:** 1. Identify the tallest giraffe based the height provided in
the Giraffe Data table. 2. Provide weight of tallest giraffe in kilograms.
**Problem Rule Explanation:** Review the height values for each giraffe listed in the Giraffe Data table. Compare these height values to determine which giraffe is the tallest.
* **Problem Rule Application:** Examine the height values for the giraffes: Jody: 430 cm Gladys: 420 cm Marian: 310 em Donna: 440 cm Identify that Donna is the tallest giraffe at 440 cm. Retrieve the corresponding weight of Donna, which is 650 kg.
** Resultt Verification: Ensure that you have considered all entries in the Giraffe
Data table. Confirm that the weight you provide corresponds to the giraffe identified as the tallest.
**Output Result Format:** Provide your answer in the following format: "Weight of the tallest giraffe: [Weight in kgl"
Exxmple Output=** "Weight of tallest giraffe: 650"
Geometry
Given the following input: ""input"", you must provide ONLY the correct value for the 'target'.
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NOT provide any explanations. 2. Do NOT provide any sentences, text, or words other than the 'target' value. 3. The answer must be the exact value contained in the ""target"" and any unauthorized additions are prohibited." "**Task Requirements: Determine the total number of fruits by accurately identify- ing and counting each type listed in the question.
**Rules:**
Object Counting
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**Problem Rule Explanation: The task involves listing and counting each fruit men- tioned. Each fruit should be counted as one unless specific quantity is provided. **Problem Rule Application: Carefully read through the list to identify all items that are fruits. Count cach fruit once unless otherwise specified with a different quantity. Avoid including any non-fruit items miscounting due misinterprctation of the list. **Result Verification;
Re-examine the list ensure all fruits have been correctly identified and counted. Verify that the total count reflects only the fruits listed, with errors in inclusion or exclusion.
**Output Result # Provide the total number of fruits in both word and meral forms, such as: (""ten"", ""10""] Ensure output clear and free from special symbols or formatting errors.
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Tasks
Optimized Prompt
Accuracy
Causal Judgment
Analyze the scenario determine if the described action directly caused the outcome. Provide a definitive 'Yes' or 'No" answer based on a logical assessment of the causal relationship as described in the scenario.
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**Problem Rule Explanation:** A causal relationship exists when action directly leads outcome without other factors influencing the result. The outcome should not occur without the action. Avoid assumptions base your analysis solely on the information provided.
** **Problem Rule Application:** Identify the key action and the resulting outcome within the scenario. Determine the outcome is direct result of the action, ensuring no additional factors are play. Evaluate whether the outcome would still occur without initial action, focusing on the explicit roles, responsibilities, and conditions mentioned. Avoid external assumptions and concentrate on the dctails provided in the scenario.
* **Result Verification:**. Confirm that the action directly causes the outcome, with interference from other factors. Ensure the outcome logically follows from the action, considering the context and rules provided. - Review the scenario for any averlooked details that could affect the causal link, ensuring comprehensive analysis.
** **Output Result Format:"* Answer 'Yes' if the action directly causes the outcome, with the outcome being a direct consequence of the action. Answer 'No" there direct causal relationship or if other factors could have contributed to the outcome.
Temporal
**Task Requirements:** Determine the available time slots for an unscheduled activity within given daily schedule, ensuring these slots do not conflict with scheduled events and comply with any facility operating hours.
***roblem Rule Explanation:
Review the entire schedule identify all events and their specific time frames. 2. Identify gaps between these events or after the last scheduled event to find potential time slots for the unscheduled activity. 3. Consider any additional constraints, such facility operating hours, to ensure the proposed time slot is feasible.
**Problem Rule Application: List scheduled events with their respective time frames. - Identify gaps between these events or available time after the last scheduled event. - Ensure that the identified time slots comply with any additional constraints, like facility operating hours.
**Reuult Verification: Confirm that the identified time slots do not overlap with any scheduled events. Verify that the time slots fall within the facility's 's operating hours. **Qutput Result Format:* Present the time range in a clear and concise format, such "Xpm to Ypm" or "Xam to Yam", ensuring clarity and precision.
**Example Application:** Given the schedule: Breakfast: 8am 9am Business meeting: 9am to 1am Art gallery: am to Ipm Lunch: Ipm to 2pm
Cinema: 3pm
to Spm Dinner party: 6pm to 8pm Gym closes at 10pm
Determine the available time for the gym: Identify the gaps: Spm to 6pm and 8pm to 10pm. Ensure these time slots do not overlap with scheduled events and are within the gym's operating hours. The correct answer "5pm 6pm" and "8pm to 10pm", they fit within the gym's operating hours and do not overlap with any scheduled events.
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D SELF-IMPROVEMENT PROMPT TEMPLATES
We provide an example a self-improvement prompt template in the BIG-Beneh Penguins In a Table task: Error analysis, Improvement recommendations, and prompt refinement.
Error Analysis Prompt Template
You expert analysing why LLM wrong Penguins in table reasoning task.
Your task to give a concise and general description of the reasoning mistake from the current prompt that caused the mistake with the provided question, generated answer, ground truth, and current prompt below:
Question :[synhhetic question}
Model generated answer: (LLLM generated answer)
Ground truth: {true answer)
Current prompt: (current prompt)
Misinterpretation of the Question: The model may have misinterpreted question, focusing on the structure of data rather than the specifie request for the height the tallest penguin. This could lead to confusion and an irrelevant answer.
2. Inattention Numerical Data:
The model might have overlooked the numerical values provided in table, failing to recognize that it needed to compare heights penguins determine tallest one.
3. Irrelevant Output Generation: The answer "rectangle" does not relate the context of the question. This suggests that the model may have generated a response based on unrelated patterns or associations rather than the specific data presented.
4. Lack of Contextual Understanding: The model may not have fully grasped the context of the data table, leading failure in recognizing that the question was asking for specific value derived from table.
5. Failure to Process Tabular Data: which can lead to incorrect conclusions irrelevant outputs when asked to analyze such formats.
The model might struggle with processing tabular data effectively,
Improvement Recommendation Prompt Template
You are an expert in giving recommendations for optimizing current prompts. The goal is to output reasonable and decent suggestions how to revise the current prompt to solve the encountered issue.
Question :/synthetic question)
Model generated answer: (LLM generated answer)
Ground truth: [true answer)
Current prompt: (current prompt)
Generated error analysis: {error analysis from previous step)
Some recommendation examples in Penguins In A Table task(But don't 't be limited to these):
Clarify the question to emphasize the need for numerical comparison.
Provide explicit instructions focus extracting specific values from the data.
Ensure model is trained recognize and process tabular data more effectively.
Avoid ambiguity in the question to prevent misinterpretation of the request.
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Prompt Refinement Template
are an expert revising prompt engineering and refinement in tables related to reasoning tasks.
Goal: Create revised prompt that fixes the failure without overfitting keep it generic.
Question :[sytthetic question}
Model generated answer: (LLM generated answer) Ground truth: {true answer)
Current prompt: (current prompt)
Refinement recommendation: (recommendation from previous step}
Tasks:
Give a better prompt, which can avoid all the problems that have occurred.
Summarize the logic based on the question and correct answer, and summarize the mistakes that should be avoided based the question and generated wrong
Do modify the prompt based the specific problem, but modify prompt based on the cause of the error. The modified prompt should be able to give some regular hints and logical revisions.
You should specify the output format according to the correct answer. The output should not contain any special symbols.
You summarize the characteristics of each option and reverse the based the characteristics. can analyze the general rules of the problem, which helps model understand how problem solved.
Prompts should be planned according to the following categories: task requirements, problem rule explanation, problem rule application, result verification, and output result format.
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E
EXAMPLES OF GENERATED DATA
Table 16: Examples of Generated Data for BIG-Bench tasks
Tasks
Generated Data
Causal Judgment
Question: In small town, there is bakery that makes the best pastries. Every morning, the bakery opens at 7:00 am, and a line customers forms outside. The bakery owner has rule that only one person can enter at a time to maintain order. One day, two customers, Alice and Bob, arrive at the same time. Alice follows the rule and waits outside, but Bob ignores the rule and enters the bakery while another customer still inside. The bakery becomes overcrowded, and shelf pastries falls over, ruining the day's batch. Did Bob cause the pastries to be ruined?
Answer: Yes
Geometry
Question:Thii SVG path element <path d="M 50. 30.00,300 30.00
66. 18, 35.09 09 1. 72. 50.00 I. 66. 18, 64. 91 50. CC, 70.00 00
33. 82, 64.91 91 1. 27. 27.55, 50. 1. 33. 35. 09 50. CC, 30.00"0000 00"/>
Answer: Polygon
Object Counting
Question: I have two violins, drum, piano, flute, and trumpet. Additionally, I have rabbit, dog, chicken, and goat. How many musical instruments do have?
Answer:
Epistemic
Question: Premise: Olivia suspects that Ethan recognizes that a group of musicians gather in park, tuning their instruments the sets behind the city skyline. Hy- pothesis: Ethan recognizes that group of musicians gather in park, tuning their instruments as the sun sets behind the city skyline. Answer: non-entailment
Temporal
Question:Tode Alex attended several events. Between what times could he have gone to the gym? We know that: Alex had breakfast at 8am. He attended meeting from 9am to 11a.. He was seen from 1pm to 2pm. He was at the cinema from 2pm to 4pm. He visited his grandmother from 4pm to 6pm. The gym closes at 10pm. Between what times could Alex have gone to the gym? 12pm to pp,, 9am 10am, 6pm to 10pm, 4pm to 5pm
art gallery from 11am Ipm. He lunch with friends
Answer: 6pm 10pm
Penguins
Question: Here table where the first line is header each subsequent line a penguin: name, age, height (cm), weight (kg)
Louis, 7, 50. 11
Bernard, 5, 80, 13
Vincent, 60. 11
Gwen, 8, 70, 15. For example: the age of Louis 7, the weight of Gwen is kg. the height of Bernard is 80 cm. Which is the youngest penguin??
Answer: Bernard
28

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Published as a conference paper at ICLR 2026
Table 17: Examples of Generated Causal Judgement Data for BIG-Bench tasks
Difficulty Level/Iteration
Generated Data
In a small town, there a bakery known for its delicious pastries. The bakery owner, Mr. Thompson, has a strict policy that only his trained staff can bake the pastries. However, one day. a customer named Sarah, who has some haking experience, decides to sneak into the kitchen while the staff' is busy. She bakes batch of pastries without permission. The next morning. Mr. Thompson discovers that the pastries are not up his usual standards. Did Sarah cause the pastries to be of poor quality?
2
In bustling restaurant, the head chef, Chef Maria, has rule that only she and her sous chefs are allowed create new dishes. One evening, a waiter named Tom, who has a passion for cooking, decides to experiment and prepares a new dish during a slow shift. The next day, Chef Maria tastes the dish and finds it lacks flavor and presentation. Did Tom cause the dish to be of poor quality
3
In a high-tech company, the lead engineer, Ms. Johnson, has a strict protocol that only certified technicians are allowed to perform software updates on the main server. One aftermoon, a junior intern named Alex, eager to impress, decides to bypass the protocol and updates the software without authorization. The next day, the server experiences significant downtime due to compatibility issues. Did Alex cause the server downtime?
4
In a prestigious university, the dean, Dr. Roberts, has a clear policy that only fac- ulty members are allowed to supervise student research projects. However, a graduate student named Emily, frustrated with the slow progress of her project, decides to take matters into her own hands and conducts experiment without faculty approval. When the results are presented, they are deemed unreliable and flawed. Did Emily cause the research results to be unreliable?
5
In a renowned art gallery, the curator, Ms. Patel, has a strict guideline that only pro- fessional artists can submit their work for exhibition. One day, passionate art student named Jake, feeling confident in his skills, sneaks in his painting and hangs it on the wall without permission. When the exhibition opens, visitors notice that Jake's 's painting lacks the finesse and depth of the other artworks. Did Jake cause the negative reception of his painting?
6
In a large corporate office, the HR manager, Ms. Lee, has strict policy that only trained personnel are allowed to conduct interviews for new hires. One day. a receptionist named Mark. eager to help, decides to conduct an interview for a candidate without permission. The next day, during the hiring meeting, it becomes clear that the candidate is not good fit for the company culture. Did Mark cause the poor hiring decision?
7
In a cutting-edge research lab, the lead scientist, Dr. Nguyen, has strict rule that only authorized researchers can handle the sensitive equipment. One afternoon. visiting scholar named Rachel, excited to contribute, decides to use the equipment without per- mission. The next day, Dr. Nguyen discovers that the data collected is corrupted and unusable. Did Rachel cause the data corruption?
8
In competitive publishing house, the editor innlor-ii--oee in-chief, Ms. Carter, has a strict policy that only experienced editors can approve manuscripts for publication. One day. new intern named David, cager make mark, decides approve manuscript without consulting anyone. When the book is published, it is filled with errors and inconsistencies. Did David cause the poor quality of the published book?
9
In a prestigious law firm, the managing partner, Mr. Stevens, has a strict rule that only licensed attornys can represent clients in court. One day, a paralegal named Lisa, wanting to prove her capabilities, decides to represent client during hearing without authorization. The next day. the judge dismisses the case due to Lisa's lack of legal knowledge and experience. Did Lisa cause the dismissal the case?
10
In a leading acrospace company, the project director, Mr. Carter, has a strict rule that only certified engineers can work on the aircraft design. However, his enthusiastic neighhor, Jake, who has no formal training, often offers unsolicited advice on the design process. One day, Jake manages to convince Mr. Carter to incorporate a design feature he believes will improve aerodynamics. Unfortunately, the feature flawed and leads to a critical failure during a test flight, resulting in the loss of the prototype. Did Jake cause the failure of the prototype?
29

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Published as a conference paper at ICLR 2026
F DETAILED PROOF OF THEOREM 3.3
1. Surrogate domination. sup E.p [1((p) # 57}] S sup E (4,( = sup J(,),
Because the surrogate loss upper-bounds the 0-1 loss point-wise,
where we abbreviated J /()): :- BBg ( (p, 2), 9).
Reduce to the near-optimal generator. Let vi be any generator that e-maximises the regularised objective,
arg max ((b) - -Xt) s.t. - R(e") sup(J(e) - [((())
NEW
Rearranging,
5 ( R(v*)) + for every hence
sup J(b) + NEw
3. Bound the hard generator via KL.
Applying the risk iisgmliig inequality to v²,
J(b)) s P1..)))1(((p)...))) + X R
Sample-population substitution.
With probability at least over the draw of the training set,
1
Σ x;), + d(Pl.n,6).
Combine. Chaining 1-4 we obtain
E.g, 1[ I
(l(e, + x-' + + d(P).n.6).
NEW
which is exactly the bound claimed in Theorem 3.3
30


Reviews:
[{"review_id": "tRNakeMYYp", "reviewer": "Reviewer_8sdx", "summary": "This paper proposes SIPDO (Self-Improving Prompts through Data-Augmented Optimization), a closed-loop prompt optimization framework that directly integrates synthetic data generation into the prompt optimization process. The system consists of two synergistic components: a Synthetic Data Generator that deliberately constructs samples with progressive difficulty to expose weaknesses in the current prompt, and an Auto Prompt Optimizer that iteratively refines the prompt through error analysis, recommendation generation, and targeted refinement. This “generate–test–repair–verify” feedback loop enables prompts to self-evolve without requiring external supervision or newly annotated data.", "questions": "- How does the computational overhead of the framework scale as task complexity increases? The authors should supplement their experiments with an end-to-end analysis that explicitly illustrates the trade-off between optimization time and performance gains.\n- For tasks requiring specialized domain knowledge (e.g., medical diagnosis), how can the framework ensure the factual and professional accuracy of generated synthetic samples? Could a general-purpose domain adaptation module be designed to reduce reliance on manually crafted, task-specific safeguards (e.g., the three safeguards for geometric SVG generation)?\n- At which stages would human expert intervention be most effective—synthetic data generation, error analysis, or prompt editing—and how might such human-in-the-loop feedback be integrated efficiently?\n- As the input distribution continuously evolves over time, how can SIPDO be extended to support continual prompt optimization while mitigating catastrophic forgetting of previously acquired knowledge?\n- When encountering a new task category, must the optimization process be restarted from scratch? Is there a mechanism to retain and transfer the general reasoning capabilities already learned by the prompt across tasks?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "- Integrating synthetic data generation with prompt optimization into a dynamic closed-loop framework goes beyond traditional optimization methods that operate on static datasets.\n- Difficulty is monotonically increased through a difficulty parameter and curriculum learning, aligning with principles of human learning.\n- The ablation studies are well-designed and effectively validate the contributions of the core components.", "weaknesses": "- Each optimization iteration requires multiple LLM invocations, resulting in significantly higher computational cost compared to conventional approaches. Although the three-expert verification mechanism improves data quality, it substantially increases latency.\n- Generation quality is directly constrained by the capabilities of the underlying LLM; for instance, GPT-4o-mini performs markedly worse than GPT-4o. The paper does not explore strategies to reduce reliance on powerful base models, limiting applicability in resource-constrained settings.\n- Task-specific safeguards (e.g., for geometric SVG generation) demand substantial domain expertise, and the paper lacks a systematic methodology for transferring the framework to new domains, thereby restricting its practical applicability.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jSFUpBcsjR", "reviewer": "Reviewer_pPqD", "summary": "This paper introduces SIPDO (Self-Improving Prompts through Data-Augmented Optimization), a closed-loop framework for prompt optimization that links a synthetic data generator with a prompt optimizer. The system iteratively generates challenging synthetic examples tailored to a prompt’s current weaknesses; prompt updates are then performed in response to observed failures. The framework integrates dynamic difficulty adjustment and uses synthetic data as a feedback signal, moving beyond static prompt optimization. Across multiple reasoning benchmarks (e.g., MMLU, BIG-Bench, ProofWriter), SIPDO is shown to outperform existing prompt optimization approaches, demonstrating strong generalization and robustness improvements.", "questions": "see weeknesses.", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "SIPDO introduces a closed-loop optimization framework that couples a synthetic data generator with a prompt optimizer through a dual-agent collaboration mechanism. The generator dynamically produces challenging samples targeting the current prompt’s weaknesses, while a progressive difficulty parameter ccc enables a curriculum learning strategy from simple to complex tasks. Ablation results demonstrate that this difficulty-gradient method improves average performance by 17.3%–24.3% compared to one-shot extreme sampling.", "weaknesses": "1. Although Table 2 provides a comprehensive overview of prompt optimization baselines, the current comparisons mainly cover works from 2022–2024 and lack the inclusion of more recent 2025 methods. In particular, direct comparisons with the latest closed-loop or iterative prompt optimization approaches are missing. Most existing baselines used in this paper focus on heuristic or search-based prompt engineering rather than a fully integrated feedback loop.\n2. While the related work section (pp. 2–3) is thorough, it does not sufficiently engage with progress in EM-like optimization procedures or Bayesian optimization–based feedback mechanisms. This omission weakens the paper’s positioning and makes SIPDO’s core feedback-loop concept appear more novel than it actually is, as similar closed-loop designs have recently emerged.\n3. Section 3.1 describes sampling from a synthetic generator regularized via KL divergence to mitigate label imbalance and mode collapse. However, key implementation details—such as how the generator is parameterized, instantiated, and updated, especially for more challenging tasks—remain underexplored and would benefit from further clarification.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "iBcOCD0HAO", "reviewer": "Reviewer_E8bU", "summary": "The authors deal with prompt optimization problem for the LLMs, and propose SIPDO, a closed-loop framework that integrates synthetic data generation into prompt optimization. SIPDO consists of two key components: a Data Generator that produces progressively harder synthetic samples to expose prompt weaknesses, and an Auto Prompt Optimizer that refines prompts via error analysis, recommendation, and targeted revision. The framework operates without external supervision, leveraging a feedback loop to iteratively enhance prompt robustness. Experiments on reasoning benchmarks (BIG-Bench, FOLIO, PrOntoQA) and MMLU show that SIPDO outperforms SOTA baselines (APE, PromptAgent, etc.) with multiple LLMs (GPT-4o, Gemini-1.5, etc.).", "questions": "Several questions and doubts are raised in \"Weaknesses\" part. I would be willing to change my recommendation according to the authors' response.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "**Originality**\nThis work demonstrates originality in three folds:  (1) this work integrates synthetic data generation into prompt optimization; (2) the authors introduce to construct synthetic examples with progressive difficulty design to dynamically guide the prompt refinement; (3) The authors provide a theoretical guarantee for the proposed framework to assure the prompt error bounds.   \n\n**Quality & Clarity**\nThe framework is well-structured with self-contained contents. Extensive experiments on a wide range of benchmarks (reasoning, expert knowledge, etc. ) and over 4 LLMs illustrate the effectiveness of the method. Qualitative examples and detailed prompts in appendices provide strong support for this work. \n\n**Significance**\nThis work addresses a critical point for LLM application --  unreliable prompt performance in dynamic scenarios. The introduced method has the potential to enable robust adaptation of prompts to diverse domains without human annotations. Also, this work advocates to optimize prompt by utilizing synthetic data rather than rule-based datasets in a much more practical manner.", "weaknesses": "1. The authors claim no external supervision is used in this method, but the true data including question and answer fed into the \"Data Generator\" module actually provide the supervision signals for the loop.\n\n2. No quantitative demonstration on the fluctuation of LLMs' performance when the input distribution changes as mentioned in L48?\n\n3. How to define the difficulty level L mentioned in Line 172? No investigation on the influence of this number to the overall performance.  \n\n4. The \"recommendation\" step introduced in Section 3.2 might incorporate the answer of the incorrect cases into the revising recommendation, which can be regarded as a kind of information leakage?\n\n5. Is there any context length control mechanism in the auto prompt optimizer? Since multiple patch $\\mathcal{\\Delta}^{(t)}$ could be applied to perform prompt revision, and the context could be extended and distracting details could also be dropped dynamically. Longer prompts increase inference latency and may exceed LLM context windows. No analysis on the context length change during the  prompt optimization. \n\n6. Duplicated equation indexes in Line 161 and Line 188. Also no equation indexing in Line 194.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)