# Selection Without Signal, Recovery Through Expression: A Measurement Study of Post-Hoc Falsification Operators for Frozen Small Code Models

arXiv: https://arxiv.org/abs/2606.16999 · HTML: https://mlsanity.com/paper/2606.16999/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 46 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 30 of 33)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Is Your Code Generated by ChatGPT Really Correct? Rigorous Evaluation of Large Language Models for Code Generation](https://mlsanity.com/paper/2305.01210/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Large Language Models Cannot Self-Correct Reasoning Yet](https://mlsanity.com/paper/2310.01798/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Teaching Large Language Models to Self-Debug](https://mlsanity.com/paper/2304.05128/) (2023)
- [Quantifying Language Models' Sensitivity to Spurious Features in Prompt Design or: How I learned to start worrying about prompt formatting](https://mlsanity.com/paper/2310.11324/) (2023)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Natural Language to Code Translation with Execution](https://mlsanity.com/paper/2204.11454/) (2022)
- [Coder Reviewer Reranking for Code Generation](https://mlsanity.com/paper/2211.16490/) (2022)
- [Planning In Natural Language Improves LLM Search For Code Generation](https://mlsanity.com/paper/2409.03733/) (2024)
- [Learning How Hard to Think: Input-Adaptive Allocation of LM Computation](https://mlsanity.com/paper/2410.04707/) (2024)
- [Correlated Errors in Large Language Models](https://mlsanity.com/paper/2506.07962/) (2025)
- [Automated Hypothesis Validation with Agentic Sequential Falsifications](https://mlsanity.com/paper/2502.09858/) (2025)
- [Understanding the Dark Side of LLMs' Intrinsic Self-Correction](https://mlsanity.com/paper/2412.14959/) (2024)
- [On Leakage of Code Generation Evaluation Datasets](https://mlsanity.com/paper/2407.07565/) (2024)
- [Revisit Self-Debugging with Self-Generated Tests for Code Generation](https://mlsanity.com/paper/2501.12793/) (2025)
- [CoVerRL: Breaking the Consensus Trap in Label-Free Reasoning via Generator-Verifier Co-Evolution](https://mlsanity.com/paper/2603.17775/) (2026)
- [SEVerA: Verified Synthesis of Self-Evolving Agents](https://mlsanity.com/paper/2603.25111/) (2026)
- [Can Language Models Falsify? Evaluating Algorithmic Reasoning with Counterexample Creation](https://mlsanity.com/paper/2502.19414/) (2025)
- [Uncovering Systematic Failures of LLMs in Verifying Code Against Natural Language Specifications](https://mlsanity.com/paper/2508.12358/) (2025)

## Built on by (most cited first, 2 of 2)

- [Falsification, Not Exposure: An Internally Preregistered Placebo-Controlled Decomposition of Self-Repair Feedback in Frozen Small Code Models](https://mlsanity.com/paper/2606.31511/) (2026)
- [Form, Not Content? A Preregistered, Placebo-Controlled Evaluation of Learned Error-Conditioned Self-Repair Through Prompts and Weights in Frozen Small Code Models](https://mlsanity.com/paper/2607.12962/) (2026)

## Abstract (arXiv)

Frozen small code models (<=1.5B parameters, run locally without fine-tuning) suit offline and privacy-constrained use, but often emit plausible-but-wrong programs. A natural remedy is a post-hoc operator that selects, verifies, repairs, or re-processes the model's samples without retraining; in principled form it is Popperian: attack each candidate with a severe test, keep what survives. We measure whether such operators help. Under one deterministic execution oracle and a leakage-free, matched-compute protocol, 26 semantic post-hoc operators (selection, verification, repair, elimination, portfolios, sound vetoes, generation conditioning) are evaluated against Best-of-N (BoN); on the cells and benchmarks tested, none improves held-out accuracy over BoN. The negative is mechanistic: a coverage wall (systematic hard-task failures deeper sampling does not rescue), a capability scissors (a competent generator leaves almost no discriminable error among visible-test passers), and a near-empty consensus trap (the visible-pass-but-hidden-wrong majority a leakage-free selector needs rarely co-occurs with a correct alternative). A distribution-free do-no-harm bound cannot certify a harm rate <=alpha at zero observed harm unless n>=45. Two operators help on a different axis, outside the semantic output space. An expression-layer recovery (M1), the only accuracy gain here, recovers correct programs the standard extractor discards (robust extraction and public-test signature alignment); it does no harm (b10=0), is leakage-free, and lifts DeepSeek-Coder-1.3B by +12 tasks on HumanEval+ (p=2.4e-4). An adaptive consensus early-stop (ACE) is a calibrated compute-saving control (~19% saving, zero harm). M1 and the selection negative replicate on HumanEval+ and MBPP+ across three model cells. The lesson: fix the harness and measure coverage before blaming semantic post-hoc reasoning.