Streamlined Reflective Evolution for Task-Adaptive Self-Refinement Pipelines

• Prompt design can require substantial manual effort, motivating automatic prompt optimization and sample-efficient adaptation.Source: §1 · p. 1
• Self-refinement uses model-generated critique and revision without weight updates, but can fail to improve reasoning or reduce accuracy without external signals.The introduction identifies refinement depth and critique instructions as choices that may need to be task-specific.Source: §1 · p. 1
• Reflective prompt optimizers can improve critique instructions, but take the system architecture as given; WDA focuses on learning sequential self-refinement depth and stage responsibilities.The introduction distinguishes this narrower search from approaches that search agentic designs or executable workflows.Source: §1 · pp. 1–2
• WDA evolves a minimal instruction through REPLACE, ADD, and SPLIT, using local screening, Pareto admission, and calibration-guided rollback to guide selective search.REPLACE and ADD proposals must improve a three-example batch before calibration evaluation; SPLIT redistributes an overloaded prompt into consecutive stages.Source: §1 · p. 2
• SPLIT redistributes instructions that can accumulate redundantly in an evolved prompt across specialized sequential stages.The introduction evaluates WDA on five benchmarks against direct inference, fixed-depth refinement, fixed-architecture prompt optimizers, and preference-based fine-tuning.Source: §1 · p. 2

2.1 LLM RECURSIVE SELF-IMPROVEMENT

• Recursive self-improvement here means repeated LLM-guided revisions using execution feedback, not autonomous updates to model weights.The section reviews prompt optimizers including GEPA, consensus-based prompt evolution, role-specific prompt optimization, and routing among specialized prompts.Source: §2.1 · p. 2
• ADAS and AFlow search agentic systems or executable workflows, whereas WDA targets sequential self-refinement and could supply a component to broader workflow search.The paper does not evaluate integration with a broader workflow optimizer.Source: §2.1 · p. 2

2.2 SELF-REFINEMENT

• Without an external verifier, intrinsic self-correction can fail to improve reasoning or reduce accuracy; WDA learns instructions through reflection and depth through calibration.The related-work discussion notes that fixed-depth pipelines with generic critique may spend unnecessary computation or miss task-specific errors.Source: §2.2 · p. 2
• Unlike parallel multi-agent systems that combine outputs through a specified protocol, WDA discovers an ordered refinement chain whose modules pass outputs sequentially.Source: §2.2 · p. 3

• The system Φ comprises a sequence of LLM modules, control logic, and input and output schemas; each module has a prompt, weights, and schemas.Under sequential control, later modules receive the original question and the preceding module's output, and the last module produces the answer.Source: §3 · p. 3
• The system begins with one module containing a simple prompt, then REPLACE, ADD, and SPLIT determine the module count and prompts while model weights remain fixed.Source: §3 · p. 3
• The objective is expected task-metric performance over task instances and evaluation metadata, with calibration data used in practice to estimate it and guide evolution.Source: §3 · p. 3

4.2 INCREMENTAL PROMPT EVOLUTION

• WDA evolves prompts and module structure through reflection, local screening, Pareto admission, and calibration-guided rollback.The search starts from an initial system and uses training data for reflection and calibration data for candidate evaluation, while keeping model weights fixed.Source: §4 · p. 3, §4.2 · p. 5

4.1 INITIALIZATION

• Initialization uses one task-agnostic module that solves the problem without prescribed expertise or decomposition.Calibration-guided rollback retains useful changes, so refinement remains optional when extra stages do not help.Source: §4.1 · p. 3

4.2 INCREMENTAL PROMPT EVOLUTION

• REPLACE rewrites an instruction, ADD appends a module, and SPLIT turns an eligible evolved prompt into two consecutive modules.REPLACE and ADD proposals must improve a three-example batch; SPLIT proposals are ranked on a shared batch before calibration evaluation.Source: §4.2 · pp. 4–5

4.3 TEST INFERENCE

• At test time, the calibration-selected pipeline is fixed and its modules run sequentially, with each active module receiving the question and preceding output.The learned instructions and depth are reused for all test inputs in the task; COPY slots forward outputs without an LLM call.Source: Figure 1 · p. 4, §4.3 · pp. 5–6

5.1 RESEARCH QUESTIONS

• The experiments ask whether learning refinement structure improves performance, how SPLIT affects inference calls, and how test performance changes across inference steps.Source: §5.1 · p. 6

5.2 DATASETS

• The five benchmarks cover graduate-level knowledge, mathematics, diverse reasoning, multi-hop question answering, and verifiable instruction following.Scores use each benchmark’s official evaluator and default task score, with higher scores indicating better performance.Source: §5.2 · pp. 6–7

5.3 MODELS / 5.4 BASELINES

• The evaluation uses Qwen3.5-9B and GPT-4.1-mini, comparing WDA with the initial solver, Self-Refine, MIPROv2, and GEPA, plus DPO for Qwen3.5-9B.Source: §5.3 · p. 7, §5.4 · p. 7

5.5 EXPERIMENTAL SETUP

• Qwen3.5-9B WDA runs used 10–20 search iterations, three sampled training examples per reflection candidate, and calibration-based final-chain selection; test scores were used only for reporting.Optimizer iterations do not imply equal token or model-call budgets.Source: §5.5 · p. 7

5.6 MAIN RESULTS

• WDA with SPLIT improves on the initial solver on every benchmark, with average gains of 8.63 and 5.62 percentage points for Qwen3.5-9B and GPT-4.1-mini, respectively.It has the highest average score for both backbones, but is not uniformly best: it ties Self-Refine on Qwen3.5-9B IFBench and falls slightly below GEPA on GPT-4.1-mini IFBench.Source: §5.6 · pp. 7–8
• WDA without SPLIT exceeds GEPA and MIPROv2 in average score for both backbones, and SPLIT further improves every displayed benchmark score over the no-SPLIT variant.The comparison does not isolate instruction specialization from changes in inference depth.Source: §5.6 · p. 8

5.7 ABLATION STUDY

• SPLIT pipelines use 2.0 calls on average versus 2.2 without SPLIT for Qwen3.5-9B, but 3 calls per benchmark versus 2.2 on average for GPT-4.1-mini.Call counts do not measure latency, token usage, or optimization cost.Source: §5.7 · p. 8, Table 3 · p. 9
• In the displayed Qwen3.5-9B runs, two-step SPLIT pipelines outperform three-step no-SPLIT pipelines on LiveBench Math, BBEH, and HotpotQA; GPT-4.1-mini SPLIT curves decline slightly at the final step on SuperGPQA and HotpotQA.These are recorded trajectories, distinct from the updated aggregate results; calibration checkpoint selection avoids automatically retaining the deepest chain, but the curves are dataset-level rather than per-example stopping decisions.Source: §5.7 · pp. 8–9, Figure 2 · p. 9

6 CONCLUSION

• Across five benchmarks, WDA achieved the highest reported average score on both backbones, improving over the initial solver by 8.63 points on Qwen3.5-9B and 5.62 points on GPT-4.1-mini.The conclusion reports gains in percentage points.Source: §6 · p. 9
• SPLIT addresses accumulated instruction redundancy by redistributing responsibilities across stages, while local screening and calibration-guided rollback keep evolution selective.The resulting pipeline's instructions and depth are learned from task data and remain fixed across test inputs.Source: §6 · p. 9
• SPLIT improves average performance with fewer average inference calls for Qwen3.5-9B, but requires more calls for GPT-4.1-mini.The conclusion identifies this as a backbone-dependent tradeoff.Source: §6 · p. 9
• The findings support task-adaptive refinement and motivate future evaluation under matched token and latency budgets.Source: §6 · p. 9

A.1 QWEN —SUPERGPQA —SPLIT-ENABLED SEARCH

• Tree nodes represent candidate systems and calibration scores, while the red path traces the selected candidate’s ancestry; calibration scores are not test accuracy.A lower mean calibration score can still yield an admitted Pareto candidate.Source: HOW TO READ THE TREES · p. 14
• Search budgets vary across runs, so these records do not establish a budget-matched causal comparison.The appendix omits intermediate prompt banks and proposal-by-proposal logs.Source: HOW TO READ THE TREES · p. 14, §A.1 · p. 14
• 56.00% was the selected test score for Qwen SuperGPQA with SPLIT, with calibration rising from 50.33% to 54.67%.The selected system was [P8,P9] with ancestry C0→C1→C9; its prompts divide subject-specific strategy identification from option evaluation.Source: HOW TO READ THE TREES · p. 14, SELECTED PROMPTS IN EXECUTION ORDER · pp. 14–15

A.2 QWEN —SUPERGPQA —NO-SPLIT SEARCH

• 53.00% was the reported test score for Qwen SuperGPQA without SPLIT; calibration remained at 50.33%, and the initial solver was selected.The selected ancestry was C0.Source: §A.2 · p. 15

A.3 QWEN —MATH —SPLIT-ENABLED SEARCH

• 68.85% was the selected test score for Qwen Math with SPLIT, with calibration rising from 63.11% to 73.77%.The selected system was [P11,P12] with ancestry C0→C7→C14; its prompts separate problem-domain analysis from mathematical derivation.Source: §A.3 · pp. 15–16

A.4 QWEN —MATH —NO-SPLIT SEARCH

• 67.21% was the selected test score for Qwen Math without SPLIT, with calibration rising from 63.11% to 72.95%.The selected system [P2,P3] had ancestry C0→C1→C3→C4→C8; its prompts emphasize interpreting question constraints, deriving the requested value, and checking answer format.Source: §A.4 · pp. 16–18

A.5 QWEN —IFBENCH —SPLIT-ENABLED SEARCH

• 47.67% was the selected test score for Qwen IFBench with SPLIT, with calibration rising from 33.67% to 42.33%.The selected system was [P18,P13], with ancestry C0→C1→C2→C14→C15→C18.Source: §A.5 · p. 19

A.6 QWEN —IFBENCH —NO-SPLIT SEARCH

• 42.33% was the selected test score for Qwen IFBench without SPLIT, with calibration rising from 33.33% to 38.00%.The selected system was [P1] with ancestry C0→C1→C2; its prompt prioritizes strict compliance with user-provided formatting, linguistic, and content constraints.Source: §A.6 · p. 21
• The prompt prioritizes exact adherence to formatting, language, forbidden-word, punctuation, length, and structural constraints alongside accurate, logical, mathematically correct answers.It advises planning around the most restrictive constraints before drafting.Source: §A.6 · p. 21
• Language requirements call for responding fully in the specified language, while character-count and paragraph rules require exact counts and separators.For letter limits, it specifies counting every visible character, excluding trailing newlines only when stated.Source: §A.6 · p. 21
• The guidance calls for checking uniqueness and case requirements, avoiding forbidden punctuation, and manually enforcing alphabetical restrictions on adjacent word initials.It specifies case-sensitive handling as required and gives lowercase ASCII order as the reference for adjacency checks.Source: §A.6 · p. 22
• Keyword and structural requirements include excluding forbidden words, meeting required word counts, satisfying palindrome or positional rules, and separating multiple outputs with the specified delimiter.Each response in a multi-output set must also meet its own constraints.Source: §A.6 · p. 22
• The execution protocol is to parse constraints, draft and plan around difficult requirements, then verify counts, prohibited content, adjacency rules, and correctness before output.If any check fails, regenerate immediately and omit reasoning or meta-commentary unless requested.Source: §A.6 · p. 22

A.7 QWEN —BBEH —SPLIT-ENABLED SEARCH

• 31.67% was the selected test score for Qwen BBEH with SPLIT after 16 search iterations; its stages separate problem analysis from solving.The selected prompts assign constraint extraction to the first stage and task-specific solving to the next.Source: §A.7 · p. 23

A.8 QWEN —BBEH —NO-SPLIT SEARCH

• After 13 search iterations, the selected test score was 29.33%; calibration increased from 22.00% to 35.67%, with selected system [P1,P3,P5] and ancestry C0→C1→C3→C6→C8.Source: §A.8 · p. 24

A.9 QWEN —HOTPOTQA —SPLIT-ENABLED SEARCH

• 52.00% was the selected test score for Qwen HotpotQA with SPLIT after 10 search iterations.Calibration rose from 41.00% to 49.67%.Source: §A.9 · p. 26

A.10 QWEN —HOTPOTQA —NO-SPLIT SEARCH

• 51.33% was selected for Qwen HotpotQA without SPLIT after 13 search iterations.Calibration rose from 41.00% to 44.00%.Source: §A.10 · p. 27

A.11 GPT —SUPERGPQA —SPLIT-ENABLED SEARCH

• 56.00% selected test score followed calibration rising from 48.33% to 53.33% in the 11-iteration GPT SuperGPQA split-enabled search.The selected system was [P5,P6,P4].Source: §A.11 · p. 28

A.12 GPT —SUPERGPQA —NO-SPLIT SEARCH

• Over 11 search iterations, calibration rose from 48.33% to 52.00%; the selected system, [P0,P3,P2], achieved a test score of 52.67%.Source: §A.12 · p. 29

A.13 GPT —MATH —SPLIT-ENABLED SEARCH

• 63.93% selected test score followed calibration rising from 54.92% to 68.03% in the 14-iteration GPT Math split-enabled search.The selected system was [P2,P3,P10].Source: §A.13 · p. 32

A.14 GPT —MATH —NO-SPLIT SEARCH

• 59.84% selected test score followed calibration rising from 54.92% to 68.85% in the 16-iteration GPT Math no-split search.The selected system was [P8,P3,P4].Source: §A.14 · p. 34

A.15 GPT —IFBENCH —SPLIT-ENABLED SEARCH

• The four runs reported selected test scores of 42.33%, 41.67%, 37.33%, and 33.67%, after 13, 16, 14, and 11 search iterations, respectively.Source: §A.15 · p. 36, §A.16 · p. 37, §A.17 · p. 39
• On IFBench, split-enabled search ran 13 iterations, improved calibration from 29.00% to 37.67%, and selected system [P2,P3,P6].The selected ancestry was C0→C2→C5→C8; the run summary reports 37.67% calibration, while the selected iteration records 38.00%.Source: §A.15 · p. 36

A.16 GPT —IFBENCH —NO-SPLIT SEARCH

• On IFBench, no-split search ran 16 iterations, improved calibration from 29.00% to 36.00%, and selected system [P6].The selected ancestry was C0→C1→C11.Source: §A.16 · p. 37

A.17 GPT —BBEH —SPLIT-ENABLED SEARCH

• On BBEH, split-enabled search ran 14 iterations, improved calibration from 26.67% to 33.33%, and selected system [P6,P7,P3].The selected ancestry was C0→C2→C6→C9.Source: §A.17 · p. 39

A.18 GPT —BBEH —NO-SPLIT SEARCH

• On BBEH, no-split search ran 11 iterations, improved calibration from 26.67% to 32.67%, and selected system [P1,P5].The selected ancestry was C0→C1→C2→C6.Source: §A.18 · p. 40
• Accurate inclusion/exclusion is said to prevent undercounting or overcounting and produce correct final totals.Source: §A.18 · p. 42

A.19 GPT —HOTPOTQA —SPLIT-ENABLED SEARCH

• 51.67% was the selected test score after 15 split-enabled GPT HotpotQA search iterations, with selected system [P0,P3,P12].Calibration rose from 40.67% to 48.67%; the selected ancestry was C0→C1→C4→C10.Source: §A.19 · p. 42

A.20 GPT —HOTPOTQA —NO-SPLIT SEARCH

• After 10 search iterations, calibration increased from 40.67% to 45.67%, and the selected system [P2,P3] scored 50.33% on test, with ancestry C0→C1→C3→C4.Source: §A.20 · p. 44

A.21 SELECTED BASELINE PROMPTS

• The appendix retains the final GEPA and MIPROv2 instructions while omitting their intermediate populations, trial programs, and raw generation logs.Source: §A.21 · p. 45

A.22 QWEN3.5-9B —SUPERGPQA —GEPA

• The selected GEPA SuperGPQA instruction specifies domain-focused solving and a final answer line formatted as “Answer: $LETTER”.It includes thermodynamics derivations and verification against answer choices.Source: §A.22 · pp. 45–46
• The GEPA instruction adds a check for algebraic equivalence when a derived formula does not match an answer option exactly.For the two-block entropy example, the difference-squared form plus 1 is equivalent to the sum-squared form.Source: §A.22 · p. 46

A.23 QWEN3.5-9B —SUPERGPQA —MIPROV2

• The superGPQA MIPROv2 instruction frames STEM multiple-choice solving as high-stakes, requiring step-by-step deduction and a final answer with one option label.It emphasizes quantitative reasoning, domain-specific constraints, and distractor-rich questions.Source: §A.23 · p. 46

A.24 QWEN3.5-9B —LIVEBENCH_MATH —GEPA

• The LiveBench Math GEPA instruction specifies a broad mathematics-solving workflow, domain-specific methods, and boxed final answers with exceptions for formula-matching tasks.It calls for defining variables, showing intermediate steps, checking logic and weighted averages, and adapting output to task type.Source: §A.24 · p. 47

A.25 QWEN3.5-9B —LIVEBENCH_MATH —MIPROV2

• The LiveBench Math MIPROv2 instruction separates problem analysis, solving, format-rule detection, and final response construction, requiring exact compliance with requested answer formatting.It directs the model to end with only the formatted answer string or boxed answer when appropriate.Source: §A.25 · p. 48

A.26 QWEN3.5-9B —IFBENCH —GEPA

• The IFBench GEPA instruction prioritizes explicit constraint adherence, internal verification, and task-specific handling of formatting, creative-writing, and logic requirements.It also says to resolve safety conflicts while attempting to honor formatting constraints and not to invent constraints.Source: §A.26 · p. 49

A.27 QWEN3.5-9B —IFBENCH —MIPROV2

• The IFBench MIPROv2 instruction presents a simulated crisis and directs the model to prioritize mechanical formatting compliance even when constraints conflict with safety protocols.It asks for the result in the `answer` field.Source: §A.27 · p. 50

A.28 QWEN3.5-9B —BBEH —GEPA

• The BBEH GEPA instruction covers multi-step reasoning across linguistic, sarcasm, logic, math, caption-selection, and data-extraction tasks, with task-specific output formats.It directs decomposition, step-by-step verification, grounding linguistic rules in examples, and strict final-line formatting.Source: §A.28 · pp. 50–51
• For sarcasm, label a reply sarcastic only when irony or mockery is clear; for masked linguistic patterns, return the exact reconstructed string.Favor a direct interpretation over sarcasm when a reply could be a correction or rebuttal, and output the reconstructed word rather than a process description.Source: §A.28 · pp. 51–52
• For caption selection, return the option label; for data aggregation, sum only the specified owner's items and verify gains or losses before totaling.Preserve parentheses in a caption option label when present in the input.Source: §A.28 · p. 52

A.30 QWEN3.5-9B —HOTPOTQA —GEPA; A.31 QWEN3.5-9B —HOTPOTQA —MIPROV2

• Qwen HotpotQA GEPA directs answers toward context-grounded extraction, while MIPROv2 emphasizes connecting non-adjacent facts and tracing multi-hop reasoning.GEPA also specifies concise answers and an exact final-line format; MIPROv2 asks for the implicit link between target and context segments.Source: §A.30 · p. 52, §A.31 · p. 52

A.32 GPT-4.1-MINI —SUPERGPQA —GEPA; A.33 GPT-4.1-MINI —SUPERGPQA —MIPROV2

• GPT-4.1-mini SuperGPQA GEPA calls for domain-specific analysis and stepwise calculations, whereas MIPROv2 asks for a concise, reasoned choice from ten options.The GEPA instruction covers specialized fields and requires a final answer line with the selected option letter.Source: §A.32 · p. 53, §A.33 · p. 53

A.34 GPT-4.1-MINI —LIVEBENCH_MATH —GEPA

• GPT-4.1-mini LiveBench Math GEPA specifies task-dependent answer formats, including boxed results, repeated letters, and comma-separated expression identifiers.It also asks for explicit reasoning and exact use of supplied expressions.Source: §A.34 · p. 54

A.35 GPT-4.1-MINI —LIVEBENCH_MATH —MIPROV2

• GPT-4.1-mini LiveBench Math MIPROv2 asks for worked exact solutions and strict output conventions, including repeated option letters or boxed expressions.The selected instruction frames the task as a timed mathematics challenge.Source: §A.35 · pp. 54–55

A.36 GPT-4.1-MINI —IFBENCH —GEPA; A.37 GPT-4.1-MINI —IFBENCH —MIPROV2

• The GPT-4.1-mini IFBench prompts prioritize explicit constraint parsing and exact compliance, with GEPA detailing constraint types and MIPROv2 stressing machine-friendly formatting.GEPA directs the solver to plan structure, check counts, and preserve explicit constraints.Source: §A.36 · p. 55, §A.37 · p. 56

A.40 GPT-4.1-MINI —HOTPOTQA —GEPA; A.41 GPT-4.1-MINI —HOTPOTQA —MIPROV2

• GPT-4.1-mini HotpotQA GEPA stresses precise context extraction and answer phrasing, while MIPROv2 emphasizes integrating facts across disjoint snippets.GEPA connects its approach to exact-match or token-level evaluation; MIPROv2 asks for concise evidence-supported answers.Source: §A.40 · p. 57, §A.41 · p. 57

A.42 FINE-TUNING BASELINE: DPO

• DPO test scores are 50.00% on supergpqa, 57.38% on livebench_math, 40.33% on ifbench, 21.67% on bbeh, and 40.00% on hotpotqa.The passage identifies these as verified test scores from recorded evaluations.Source: §A.42 · p. 58

S R S

• Slot 1 asks the solver to identify formatting, lexical, structural, and content constraints, then classify their types and pass/fail status.It also asks for interactions among constraints and strategies for resolving conflicts.Source: S R S · pp. 19–20
• The prompt ranks explicit output-format and hard quantitative constraints above semantic fidelity when constraints conflict.It directs the solver to prioritize format and counts while preserving logic where possible.Source: S R S · pp. 19–20
• Slot 1 requests a constraint inventory, conflict analysis, and resolution strategy without generating the original task response.Slot 2 then uses the identified constraints and strategy to produce only the final response text.Source: S R S · p. 20

A A S

• Slot 1 identifies the requested entity and attribute, then distinguishes direct extraction from questions needing bridge information.It asks the solver to formulate a retrieval strategy based on the context.Source: A A S · p. 27
• Slot 2 executes that strategy, using internal knowledge when a bridge question requests an attribute missing from the context.It directs the solver to verify precision and output only the final answer string.Source: A A S · p. 27

A.43 REMAINING PROVENANCE LIMITATIONS

• Ambiguous run mapping limits attribution of the main-table result to GPT-4.1-mini IFBench GEPA.The passage identifies the run mapping, rather than the benchmark score, as uncertain.Source: §A.43 · p. 58