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arxiv: 2605.09023 · v1 · submitted 2026-05-09 · 💻 cs.SE

Recognition: 1 theorem link

· Lean Theorem

Using Semantic Distance to Estimate Uncertainty in LLM-Based Code Generation

Weilin He , Arindam Sharma , Cristina David
Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:03 UTC · model grok-4.3

classification 💻 cs.SE
keywords LLM code generationuncertainty estimationsemantic distanceprogram execution behaviorcorrectness proxysample-based methodstaxonomycode benchmarks
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The pith

Semantic distance between execution behaviors of sampled programs estimates uncertainty in LLM code generation more accurately than binary disagreement measures.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a taxonomy to organize existing sample-based uncertainty estimators for LLM-generated code, highlighting variations in identifying, aggregating, referencing, and comparing behaviors. It proposes semantic distance-aware estimation as a new design point that quantifies the degree of behavioral difference rather than mere presence of disagreement. Evaluated on benchmarks including LiveCodeBench, MBPP, HumanEval-X, and BigCodeBench across Python, Java, and C++, these metrics serve as stronger proxies for correctness. They outperform prior methods on closed and open-source models while requiring less computation time. This matters because it provides a practical tool to gauge the reliability of generated code without accessing model internals or using additional LLM evaluations.

Core claim

The authors argue that measuring semantic distances in the execution behaviors of multiple sampled programs yields uncertainty estimates that correlate more strongly with actual correctness than existing sample-based baselines, and that this approach is robust and efficient across diverse models and languages.

What carries the argument

Semantic distance-aware uncertainty estimation, which calculates the severity of differences in program execution behaviors instead of just counting disagreements.

Load-bearing premise

The assumption that semantic distances derived from execution behaviors on the selected benchmarks capture the real-world importance of behavioral differences and extend reliably to untested fuzzing and sampling conditions.

What would settle it

A demonstration that semantic distance metrics fail to outperform disagreement-based baselines on correctness prediction when applied to a new benchmark suite or under significantly altered fuzzing parameters.

Figures

Figures reproduced from arXiv: 2605.09023 by Arindam Sharma, Cristina David, Weilin He.

Figure 1
Figure 1. Figure 1: Sensitivity of DSDE to the number of fuzz inputs [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Joint cost-effectiveness analysis of DSDE on [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: End-to-end evaluation pipeline for execution-based uncertainty estimation in code genera [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Case A: two LiveCodeBench tasks with identical execution-behaviour cluster structures but [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
read the original abstract

LLMs show strong performance in code generation, but their outputs lack correctness guarantees. Sample-based uncertainty estimators address this by generating multiple candidate programs and measuring their disagreement. However, existing estimators make different design choices about how behaviours are identified, aggregated, referenced and compared, making them difficult to assess. We therefore first introduce a taxonomy that disentangles these choices and reveals a missing design point: semantic distance-aware uncertainty estimation, which measures not only whether sampled programs disagree, but how severely their execution behaviours differ. Across LiveCodeBench, MBPP, HumanEval-X and BigCodeBench, spanning Python, Java and C++, our metrics provide strong proxies for correctness, and consistently outperform state-of-the-art sample-based baselines across both closed-source models (GPT-3.5-Turbo, GPT-4o-mini, Gemini-2.5-Flash-Lite, Claude Opus 4.5) and an open-source model (DeepSeek-Coder-V2). The method is practical: it requires neither model internals nor LLM-as-judge calls, remains robust across models, languages, sampling temperatures and fuzzing settings, and reduces runtime by approximately 48-79% relative to existing baselines.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a taxonomy of design choices in sample-based uncertainty estimation for LLM code generation (how behaviors are identified, aggregated, referenced, and compared) and fills a gap with semantic distance-aware metrics that quantify not just disagreement but the severity of differences in execution behaviors across sampled programs. It evaluates these metrics empirically on LiveCodeBench, MBPP, HumanEval-X, and BigCodeBench (Python, Java, C++) using multiple models (GPT-3.5-Turbo, GPT-4o-mini, Gemini-2.5-Flash-Lite, Claude Opus 4.5, DeepSeek-Coder-V2), claiming they serve as strong proxies for correctness, consistently outperform state-of-the-art sample-based baselines, require no model internals or LLM-as-judge calls, remain robust across temperatures and fuzzing settings, and reduce runtime by 48-79%.

Significance. If the results hold, the work offers a practical, efficient, model-agnostic approach to uncertainty estimation for code generation that could improve reliability of LLM-based tools without added inference costs. The taxonomy clarifies the design space and the semantic-distance approach provides a new point that measures behavioral severity rather than binary disagreement, with potential to reduce false positives in correctness proxies.

major comments (2)
  1. [Evaluation methodology] Evaluation methodology (implicit in results sections): Semantic distance is computed from execution traces on the same benchmark fuzzers and test suites (HumanEval, MBPP, etc.) used to derive correctness labels. This risks overestimating proxy strength, as two programs may agree on the limited exercised inputs (yielding low distance) yet diverge on untested inputs where one is incorrect; the reported outperformance and 'strong proxy' claims are measured exactly against these labels. The robustness claims across fuzzing settings do not address generalization to held-out or real-world inputs.
  2. [Results] Results presentation: The abstract and results claim consistent outperformance and 'strong proxies' across models and benchmarks, but without reported statistical significance tests, effect sizes, or variance across runs, it is difficult to determine whether gains exceed noise or are benchmark-specific. Exact definitions of behavior aggregation, reference choice, and distance computation (e.g., how traces are compared) are needed to reproduce and verify the taxonomy's missing design point.
minor comments (2)
  1. [Abstract] Abstract: The runtime reduction is stated as 'approximately 48-79%'; reporting per-benchmark or per-model values and the exact baseline comparison would improve precision and allow readers to assess practical impact.
  2. [Taxonomy] Taxonomy section: The taxonomy disentangles choices but could benefit from a table or diagram explicitly mapping existing baselines to the four axes (identification, aggregation, reference, comparison) to make the 'missing design point' visually clear.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback. We address each major comment below, indicating planned revisions where appropriate while defending the core contributions of the work.

read point-by-point responses

  1. Referee: [Evaluation methodology] Evaluation methodology (implicit in results sections): Semantic distance is computed from execution traces on the same benchmark fuzzers and test suites (HumanEval, MBPP, etc.) used to derive correctness labels. This risks overestimating proxy strength, as two programs may agree on the limited exercised inputs (yielding low distance) yet diverge on untested inputs where one is incorrect; the reported outperformance and 'strong proxy' claims are measured exactly against these labels. The robustness claims across fuzzing settings do not address generalization to held-out or real-world inputs.

    Authors: We acknowledge the potential for overestimation when semantic distance and correctness labels are derived from the same test suites, which is a common challenge in code generation benchmarks. Our use of fuzzers generates substantially more diverse inputs than the original test cases to approximate behavioral semantics, and the consistent gains across four benchmarks with differing test characteristics (LiveCodeBench, MBPP, HumanEval-X, BigCodeBench) provide evidence that the approach captures meaningful differences. Robustness across fuzzing settings (varying input counts) further suggests the metric is not brittle to exact test coverage. However, we agree this does not fully address generalization to truly held-out or real-world inputs. We will add an explicit limitations subsection discussing this gap and its implications for proxy strength. revision: partial

  2. Referee: [Results] Results presentation: The abstract and results claim consistent outperformance and 'strong proxies' across models and benchmarks, but without reported statistical significance tests, effect sizes, or variance across runs, it is difficult to determine whether gains exceed noise or are benchmark-specific. Exact definitions of behavior aggregation, reference choice, and distance computation (e.g., how traces are compared) are needed to reproduce and verify the taxonomy's missing design point.

    Authors: We agree that statistical tests, effect sizes, and variance reporting would strengthen the presentation. In revision we will include standard deviations over multiple runs (different random seeds) and apply paired statistical tests (e.g., Wilcoxon signed-rank) with p-values and effect sizes to quantify whether improvements exceed noise. On definitions, Sections 3 and 4 already detail the taxonomy (behavior identification via execution traces, aggregation functions, reference selection, and semantic distance computation on normalized traces). We will expand these with formal equations, pseudocode for trace comparison and distance calculation, and explicit parameter settings to ensure full reproducibility. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical evaluation

full rationale

The paper defines a taxonomy of uncertainty estimation design choices and proposes semantic-distance metrics as an additional point in that space. Its strongest claims rest on direct empirical comparisons of these metrics against sample-based baselines across fixed benchmarks (LiveCodeBench, MBPP, HumanEval-X, BigCodeBench) and multiple LLMs, using correctness labels derived from the same test suites. No equations, self-definitional reductions, fitted-parameter predictions, or load-bearing self-citations appear in the provided text; the reported outperformance numbers are measured against external labels rather than being forced by the metric definitions themselves. The evaluation is therefore self-contained against the chosen benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated. The approach implicitly assumes that execution traces or outputs can be compared meaningfully across samples and that the chosen benchmarks are representative.

pith-pipeline@v0.9.0 · 5506 in / 1065 out tokens · 25711 ms · 2026-05-12T02:03:19.331687+00:00 · methodology

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