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arxiv: 2605.28500 · v1 · pith:KLQ6EOEXnew · submitted 2026-05-27 · 💻 cs.CL · cs.AI· cs.LG

Functional Entropy: Predicting Functional Correctness in LLM-Generated Code with Uncertainty Quantification

Dylan Bouchard , Mohit Singh Chauhan , Zeya Ahmad , Ho-Kyeong Ra This is my paper

Pith reviewed 2026-06-29 13:20 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG
keywords functional entropyuncertainty quantificationcode generationlarge language modelsfunctional equivalencesemantic entropyhallucination detection
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The pith

Replacing NLI with LLM-based functional equivalence assessment improves uncertainty quantification for detecting incorrect LLM-generated code.

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

The paper evaluates how uncertainty quantification methods transfer from natural language to code generation across three languages, five models, and over 1700 problems. Token-probability methods work without change, but sampling methods that rely on natural language inference collapse because NLI models treat functionally different code as equivalent, pushing most outputs into one cluster. The authors replace NLI semantic equivalence with an LLM-based functional equivalence check to create a family of code-specific methods, including functional entropy as the direct analog of semantic entropy. These methods reach the highest AUROC in 11 of 15 model-benchmark pairs and show the best calibration in most cases, outperforming both NLI variants and other baselines.

Core claim

Functional equivalence methods achieve top AUROC in 11 out of 15 model-benchmark combinations and the best calibration across most settings, consistently outperforming both NLI-based counterparts and all other methods evaluated by using an LLM to assess functional equivalence rather than NLI to assess semantic equivalence.

What carries the argument

Functional entropy, the code analog of semantic entropy obtained by replacing NLI-based semantic equivalence with LLM-based functional equivalence assessment to quantify uncertainty over code samples.

If this is right

  • Token-probability-based UQ methods transfer directly to code generation tasks without modification.
  • NLI-based sampling methods fail for code because most responses collapse into a single semantic cluster.
  • Functional equivalence methods deliver higher AUROC than NLI or token baselines in the majority of evaluated settings.
  • The same methods also produce better-calibrated uncertainty estimates across most model-benchmark pairs.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Task-specific equivalence checkers may be required for reliable UQ whenever semantic similarity diverges from functional behavior.
  • The approach could be tested on other structured generation tasks whose outputs are verifiable by execution or formal means.
  • Using a separate model family for the functional assessor might reduce circularity risks when the generator and assessor share training data.

Load-bearing premise

An LLM-based functional equivalence assessor can reliably distinguish functionally distinct code without introducing systematic errors of its own or depending on the same model family being evaluated.

What would settle it

A test set where the functional equivalence LLM consistently labels distinct code as equivalent (or vice versa) while human or test-case verification shows the opposite would falsify the reliability of the assessor.

Figures

Figures reproduced from arXiv: 2605.28500 by Dylan Bouchard, Ho-Kyeong Ra, Mohit Singh Chauhan, Zeya Ahmad.

Figure 1
Figure 1. Figure 1: AUROC of NLI-Based Methods vs. Code-Adapted (Functional Equivalence) Methods [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of cluster counts for NLI-based clustering (red) and functional equivalence clustering (blue) [PITH_FULL_IMAGE:figures/full_fig_p015_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: AUROC as a function of the number of sampled responses [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: AUROC as a function of the number of sampled responses [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: AUROC as a function of the number of sampled responses [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
read the original abstract

Large language models have shown impressive capabilities in code generation, yet they often produce functionally incorrect code. Uncertainty quantification (UQ) methods have emerged as a promising approach for detecting hallucinations in natural language generation, but their effectiveness for code generation tasks remains underexplored. We systematically evaluate how UQ techniques transfer to code generation across three programming languages, five LLMs, and over 1,700 problems. We find that some token-probability-based methods generalize effectively without modification, while sampling-based methods relying on natural language inference (NLI) fail because NLI models cannot distinguish functionally different code, causing most responses to collapse into a single semantic cluster. To address this, we introduce functional equivalence methods, a family of code-specific methods that replace NLI-based semantic equivalence with an LLM-based functional equivalence assessment, including functional entropy, a code-specific analog of semantic entropy. Functional equivalence methods achieve top AUROC in 11 out of 15 model-benchmark combinations and the best calibration across most settings, consistently outperforming both NLI-based counterparts and all other methods evaluated.

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

1 major / 2 minor

Summary. The paper evaluates UQ methods for detecting functional incorrectness in LLM-generated code across three languages, five LLMs, and >1700 problems. It reports that NLI-based sampling methods fail because NLI cannot distinguish functional differences (causing cluster collapse), and introduces LLM-based functional equivalence methods (including functional entropy as a code analog of semantic entropy). These achieve top AUROC in 11/15 model-benchmark combinations and best calibration in most settings, outperforming NLI-based and other baselines.

Significance. If robust, the work fills a gap in code-specific UQ by adapting semantic entropy ideas to functional equivalence, supported by a broad multi-language, multi-model evaluation. This could improve reliability assessment for code generation. The systematic scope across 1700+ problems is a clear empirical strength.

major comments (1)
  1. [Abstract and Experimental Setup] Abstract and Experimental Setup: the central claim that functional equivalence methods (replacing NLI with an LLM judge) deliver reliable gains rests on the assessor's labels being independent of the generator's failure modes. No cross-family ablation (different model family for judge vs. generator) or execution-based ground-truth validation of equivalence labels is reported. This is load-bearing, as correlated blind spots (e.g., on off-by-one or type errors) would under-count distinct failures and inflate AUROC.
minor comments (2)
  1. Add explicit citations and version numbers for all benchmarks and the 1700+ problems to allow reproduction.
  2. [Methods] Clarify prompting details for the LLM functional equivalence judge (e.g., exact instructions or few-shot examples) in the methods section.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The concern about potential correlation between the functional equivalence judge and generator models is valid and directly relevant to the robustness of our claims. We respond point-by-point below and commit to revisions.

read point-by-point responses

  1. Referee: [Abstract and Experimental Setup] Abstract and Experimental Setup: the central claim that functional equivalence methods (replacing NLI with an LLM judge) deliver reliable gains rests on the assessor's labels being independent of the generator's failure modes. No cross-family ablation (different model family for judge vs. generator) or execution-based ground-truth validation of equivalence labels is reported. This is load-bearing, as correlated blind spots (e.g., on off-by-one or type errors) would under-count distinct failures and inflate AUROC.

    Authors: We acknowledge this is a substantive limitation not addressed in the current manuscript. The experiments rely on LLM-based functional equivalence without reported cross-family ablations or execution-based validation of the labels, leaving open the possibility of correlated blind spots inflating AUROC. We agree this assumption is load-bearing for the central claim. In the revised manuscript we will add a cross-family ablation (e.g., using a distinct model family for the judge) and include execution-based validation on a subset of problems with available test cases, along with discussion of remaining limitations such as test coverage. These additions will appear in the Experimental Setup section and be noted in the abstract. revision: yes

Circularity Check

0 steps flagged

No circularity; purely empirical evaluation with no derivations or self-referential reductions

full rationale

The paper reports an empirical study comparing UQ methods on code generation tasks across LLMs, languages, and benchmarks. The central result (functional equivalence methods topping AUROC in 11/15 settings) is obtained by direct measurement of AUROC and calibration on held-out problems, not by any equation, parameter fit, or first-principles derivation that reduces to the inputs by construction. No self-definitional steps, fitted-input predictions, or load-bearing self-citations appear in the abstract or described claims. The introduction of functional entropy is presented as an empirical replacement for NLI clustering rather than a mathematical derivation. The work is therefore self-contained against external benchmarks and receives the default non-circularity finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only view supplies no information on free parameters, background axioms, or new entities; the functional equivalence assessor is treated as an off-the-shelf component whose reliability is assumed.

pith-pipeline@v0.9.1-grok · 5728 in / 1021 out tokens · 23843 ms · 2026-06-29T13:20:26.484163+00:00 · methodology

discussion (0)

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