Uncertainty Estimation in Code Generation

• Uncertainty estimation in code generation is a set of techniques that quantify model confidence using entropy, sample-based, and decision-theoretic methods.
• These methods enhance code correctness and safety through calibrated thresholds, Bayesian ensembles, and semantic clustering integrated into decoding pipelines.
• Empirical results demonstrate improvements up to 15.5% in pass rates using adaptive decoding strategies, underscoring practical benefits for software engineering.

Uncertainty estimation in code generation encompasses a rich spectrum of algorithmic, probabilistic, and decision-theoretic methodologies to quantify the confidence—or lack thereof—in outputs produced by LLMs during program synthesis. Due to the rigid requirements of code correctness, semantic equivalence, and safety in software engineering, these techniques often diverge from their analogues in natural language generation, both in theoretical formulation and empirical efficacy. This article surveys leading uncertainty estimation methods as developed and evaluated across recent literature, with an emphasis on mathematical formulations, empirical behavior, calibration, and integration with code-generation pipelines.

1. Information-Theoretic and Token-Level Approaches

Information-theoretic measures form the backbone of most single-query uncertainty estimators in code LLMs, leveraging properties of the model’s output distributions over tokens.

• Normalized Entropy: Shannon entropy $H(p) = -\sum_{i=1}^V p_i \log p_i$ for the predicted token distribution is often normalized as $U_e(p) = H(p)/\log V$, ensuring a range in $[0, 1]$ for direct comparability regardless of vocabulary size. This measure is sensitive to flatness in the distribution and increases with model uncertainty (Zhu et al., 19 Mar 2025, He et al., 10 Jun 2025).
• Probability Differential: Defined as $U_d(p) = 1-(p^1-p^2)$, where $p^1$ and $p^2$ are the top two predicted probabilities, this metric assigns high uncertainty when the leading choices are closely ranked, and vice versa (Zhu et al., 19 Mar 2025).
• Entropy Thresholding and Adaptive Cutoffs: Thresholds for "high" uncertainty are generally tuned empirically. For example, UnCert-CoT uses $\tau\approx0.2-0.3$ for entropy measures, and up to $0.7$ for the probability differential (Zhu et al., 19 Mar 2025). AdaDec learns model-specific thresholds by fitting logistic regression to ground-truth-referenced entropies, providing data-driven, architecture-aware selection of pause points for alternative decoding strategies (He et al., 10 Jun 2025).
• Empirical Performance: On MHPP and HumanEval, uncertainty-aware pipelines that trigger chain-of-thought reasoning or reranking at high-uncertainty steps (but use greedy decoding otherwise) consistently outperform untargeted or all-CoT baselines, improving pass rates by up to 6.1% (UnCert-CoT on MHPP) and as much as 15.5% on MBPP for AdaDec (Zhu et al., 19 Mar 2025, He et al., 10 Jun 2025).

2. Sample-Based and Bayesian Methods

Sample-based methods approximate epistemic uncertainty by examining the variability or divergence among multiple samples from the model's conditional distribution.

• Variation Ratio (VR) and Variation Ratio w.r.t. Original (VRO): VR is computed as $$1 - \frac{1}{T} \sum_{t=1}^{T} \mathbb{I}[\hat{y}_t = \text{mode}(\{\hat{y}\})]$$, while VRO quantifies average dissimilarity (e.g., using CodeBLEU for code) between generation variants and a canonical output. Sample-based VRO attains AUCs up to 0.825 for flagging buggy code on HumanEval (Huang et al., 2023).
• Perturbation-Based Augmentation: By injecting high (or low) entropy tokens at "critical" generation points and greedily continuing, it is possible to estimate output robustness through changes in the resulting code. While conceptually aligned with test-time augmentation, these methods are more computationally involved and empirically offer lower precision than stochastic sampling (Huang et al., 2023).
• Bayesian Ensembles and Monte Carlo Dropout: Ensembles of independently trained models or repeated runs with dropout simulate distributional uncertainty, supporting metrics such as expected entropy and probability variance. These approaches show high efficacy in calibration and OOD detection under code distribution shifts (e.g., Deep Ensembles, MCD) but introduce significant inference cost (Li et al., 2024).

3. Structured and Localized Uncertainty: Spans, Regions, and Patches

Uncertainty in code is often localized to specific tokens, lines, or AST regions rather than entire outputs.

• Minimal Patch Calibration and Supervision: Localized patch datasets, constructed via minimal test-verified repairs of generated code, enable supervised learning of auxiliary "probe" models that emit calibrated probabilities for tokens, lines, or arbitrary spans being correct. Max-pooling of intermediate-layer embeddings, followed by span-level logistic regression, achieves line-wise Brier Skill Score (BSS) up to 0.33 and Expected Calibration Error (ECE) ≈ 0.02 (Gros et al., 31 Dec 2025).
• Self-Consistency and Reflective Confidence: Black-box methods, such as self-consistency (counting token survival across temperature-diversified samples) and reflective prompting (requesting explicit confidence statements from the LLM), provide useful but slightly less calibrated local uncertainty signals. After Platt scaling, line-level BSS reaches 0.13-0.19 (Gros et al., 31 Dec 2025).
• Edit Likelihood Prediction: Highlighting tokens by empirically or model-predicted edit likelihood (rather than low-generation probability) robustly correlates with programmer action and improves human correction time and edit efficiency (Vasconcelos et al., 2023).

4. Semantic, Decision-Theoretic, and Structured Output Approaches

Higher-order methods interpret uncertainty at the semantic or decision-theoretic level.

• Semantic Entropy via Equivalence Clusters: By sampling outputs and clustering by semantic equivalence (e.g., symbolic execution or behavioral traces), entropy over these clusters quantifies functional uncertainty. This "semantic entropy" aligns more closely with correctness than raw decoding probabilities (Sharma et al., 17 Feb 2025).
• Epistemic Mutual Information: Iterative sampling and conditional clustering enable computation of epistemic uncertainty (distinguished from aleatoric) via mutual information between samples, providing an orthogonal signal to entropy-based proxies (Sharma et al., 17 Feb 2025).
• Decision-Theoretic Utility/Minimum Bayes Risk: R-U-SURE defines optimal code suggestions as those maximizing expected utility over random sampled user intents, solved efficiently with dual decomposition over binary region-marking variables (Sure/Unsure at each token/region). This achieves higher utility and better edit-localization F1 than threshold-based heuristics (Johnson et al., 2023).
• Prediction Sets with PAC Guarantees: Structured conformal prediction for code synthesis constructs prediction sets as partial programs (programs with AST-aligned holes) that, with high coverage probability, contain the correct completion. This approach balances set size (node removals) and empirical coverage by integer linear programming and monotonic calibration, strictly dominating top-k or token-thresholding methods (Khakhar et al., 2023).

5. Calibration, Multicalibration, and Group-Aware Methods

Calibration aims to ensure model-generated confidence estimates reflect true correctness likelihood, with multicalibration extending this guarantee to fine-grained subpopulations or code problem characteristics.

• Calibration Metrics: Expected Calibration Error (ECE), Brier Score (BS), and Brier Skill Score (BSS) are standard; BSS>0 indicates improvement over naïve base-rate prediction (Campos et al., 9 Dec 2025, Gros et al., 31 Dec 2025).
• Histogram Binning, Platt Scaling, Isotonic Regression: Post-hoc transformations align predicted confidence to observed correctness via data-driven remapping over bins or grouped features (Campos et al., 9 Dec 2025, Chouraqui et al., 2023).
• Multicalibration: Calibration is enforced within every subgroup defined by code complexity, language, or code length. Iterative grouped binning or regression adjusts likelihoods to minimize calibration error simultaneously across overlapping groups. Methods such as IGLB and LINR consistently achieve the lowest group-averaged squared errors and the highest skill score increments on modern code LLMs and diverse multilingual benchmarks (Campos et al., 9 Dec 2025).
• Geometric Separation: Input-output proximity in embedding space (e.g., CodeBERT or pretrained encoder) provides a group-agnostic, geometry-driven calibration signal that, when coupled with isotonic regression, sharply reduces calibration error relative to raw token likelihoods (Chouraqui et al., 2023).

6. Integration with Decoding and Inference Pipelines

Recent research explores tight integration of uncertainty estimation into the decoding process of autoregressive code LLMs.

• Adaptive Decoding: AdaDec pauses and reranks output only at high-entropy steps, using cheap greedy selection elsewhere. This low-latency, selective reranking is guided by learned entropy thresholds, maximizing functional code correctness while minimizing overhead (mean pause rates <12%) (He et al., 10 Jun 2025).
• Uncertainty-Guided CoT: UnCert-CoT activates computationally expensive multi-sample chain-of-thought reasoning only at points of high uncertainty, thereby avoiding overthinking and error propagation on trivial lines while improving accuracy on hard cases (Zhu et al., 19 Mar 2025).
• Uncertainty-Aware Contrastive Decoding: USCD uses a “lame prompt” (few-shot context removed) to identify output noise; softmax distributions under standard and negative prompts are contrasted at high-uncertainty steps (as determined by the standard deviation of log-probabilities), with contrastive scoring and rationality-constrained vocabulary pruning. This plug-and-play method consistently improves pass@1 by 1–19% across multiple LLMs and languages (Wang et al., 2024).

Decoding Strategy	Uncertainty Signal	Activation Trigger (Typical)	Notable Gains (Benchmarks)
UnCert-CoT (Zhu et al., 19 Mar 2025)	Norm. entropy / diff	$U(p)>\tau$ (per line)	+6.1% (MHPP pass rate)
AdaDec (He et al., 10 Jun 2025)	Token entropy	$H_t>\tau^\mathrm{LM}$	up to +15.5% (MBPP Pass@1)
USCD (Wang et al., 2024)	Log-prob stddev	$u_i>\delta$ (per token)	up to +19% Pass@1 (Incoder-6B)

7. Practical Considerations, Limitations, and Future Directions

• Computational Efficiency: Single-inference methods are cheap (one forward pass) but capture only first-order uncertainty; Bayesian, sample-based, and test-time augmentation methods provide richer signals at increased cost (Huang et al., 2023, Li et al., 2024).
• Semantic Clustering Overhead: Symbolic execution or behavioral clustering for semantic entropy is computationally expensive but yields meaningful, correctness-correlated signals (Sharma et al., 17 Feb 2025).
• Calibration Tradeoffs: Multicalibration and geometric separation substantially reduce calibration error across code and problem subgroups, but require access to representative validation data and high-quality embeddings (Campos et al., 9 Dec 2025, Chouraqui et al., 2023).
• Limitations: Token-level uncertainty often under-detects subtle logical errors and is insensitive to missing code paths. Human-in-the-loop evaluation reveals that naive highlighting of low-probability tokens is not helpful unless it aligns with probable edit locations (Vasconcelos et al., 2023).
• Open Challenges: Detecting rare bugs in otherwise high-quality code remains difficult; combining uncertainty signals with static analysis or test feedback may augment sensitivity. Efficient, model-agnostic semantic clustering and embedding-based proximity methods invite further development for deployment in real-time or safety-critical settings.
• Future Directions: Adaptive thresholds, hierarchical (multi-token) uncertainty, integration with runtime test or debugger feedback, and extension to other structured prediction modalities remain active areas of exploration (Zhu et al., 19 Mar 2025, He et al., 10 Jun 2025).

• "Uncertainty-Guided Chain-of-Thought for Code Generation with LLMs" (Zhu et al., 19 Mar 2025)
• "Look Before You Leap: An Exploratory Study of Uncertainty Measurement for LLMs" (Huang et al., 2023)
• "Uncertainty Estimation based on Geometric Separation" (Chouraqui et al., 2023)
• "Towards Better Code Generation: Adaptive Decoding with Uncertainty Guidance" (He et al., 10 Jun 2025)
• "R-U-SURE? Uncertainty-Aware Code Suggestions By Maximizing Utility Across Random User Intents" (Johnson et al., 2023)
• "Uncertainty Awareness of LLMs Under Code Distribution Shifts: A Benchmark Study" (Li et al., 2024)
• "Multicalibration for LLM-based Code Generation" (Campos et al., 9 Dec 2025)
• "Assessing Correctness in LLM-Based Code Generation via Uncertainty Estimation" (Sharma et al., 17 Feb 2025)
• "The Creation of Puffin, the Automatic Uncertainty Compiler" (Gray et al., 2021)
• "PAC Prediction Sets for LLMs of Code" (Khakhar et al., 2023)
• "Localized Calibrated Uncertainty in Code LLMs" (Gros et al., 31 Dec 2025)
• "Generation Probabilities Are Not Enough: Uncertainty Highlighting in AI Code Completions" (Vasconcelos et al., 2023)
• "$\mathbb{USCD}$: Improving Code Generation of LLMs by Uncertainty-Aware Selective Contrastive Decoding" (Wang et al., 2024)