Distributional Energy-Based Models for Uncertainty-Aware Structured LLM Reasoning

• URL: http://arxiv.org/abs/2605.18871v1
• Date: Fri, 15 May 2026 17:08:27 GMT
• Title: Distributional Energy-Based Models for Uncertainty-Aware Structured LLM Reasoning
• Abstract summary: Large Language Models produce structured outputs such as travel plans or code solutions.<n>Individual reasoning steps may appear correct while the output as a whole violates budgets, fails test cases, or contradicts earlier deductions.<n>We propose a learned quality scorer with deterministic analytical constraint penalties for verifying structured LLM outputs.
• Score: 40.342912574072024
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: When Large Language Models produce structured outputs such as travel plans, code solutions, or multi-step proofs, individual reasoning steps may appear correct while the output as a whole violates budgets, fails test cases, or contradicts earlier deductions. We propose a decomposed energy function that combines a learned quality scorer with deterministic analytical constraint penalties for verifying structured LLM outputs. The quality scorer is a heterogeneous ensemble of low-rank adapters on a single frozen encoder (3% trainable parameters); the ensemble mean ranks candidates while the standard deviation quantifies epistemic uncertainty, driving a two-pass inference loop that triggers targeted regeneration or abstention. Across five benchmarks (GSM8K, MuSR, TravelPlanner, TACO, Knights & Knaves), our 149M-parameter verifier orchestrating a pool of 7-26B open generators outperforms single-shot Qwen-72B on every benchmark, matches Claude Sonnet 4.6 on MuSR (67.7% vs. 68.0%), and reduces constraint violations by 53% relative to Opus 4.6 on TravelPlanner (oracle 0.028, random 0.231). The two routes are complementary: structural verification wins when constraints are checkable (the verifier captures signal frontier models cannot self-detect), while pretraining-scale priors win where they are not (narrative inference, code semantics). A cross-dataset confounding analysis confirms genuine quality discrimination on four reasoning tasks and identifies a model-identity shortcut on code, mitigated via last-layer retraining. Scorers trained on difficult data transfer zero-shot: a MuSR-trained scorer achieves 93.9% on GSM8K without seeing a math problem.

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