Spilled Energy in Large Language Models

2026-02-20

AI Summary

Large language models frequently generate factual errors, biases, and hallucinations during inference, yet existing approaches struggle to detect and localize such issues efficiently. This work treats the model’s softmax classifier as an energy-based model and introduces two training-free metrics—overflow energy and marginalized energy—that analyze energy overflow during decoding and sequence-level energy consistency. By directly computing energy discrepancies from output logits, the method enables probe-free, activation-ablation-free hallucination detection. Experiments across nine benchmarks and synthetic algebraic tasks demonstrate that the approach exhibits strong robustness and generalization across multiple mainstream large language models.

Technology Category

• Natural Language Processing: (Large) Language Models
• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Large Vision Models

Application Category

• Search and Retrieval-Augmented AI: Large language models for search
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

We reinterpret the final Large Language Model (LLM) softmax classifier as an Energy-Based Model (EBM), decomposing the sequence-to-sequence probability chain into multiple interacting EBMs at inference. This principled approach allows us to track "energy spills" during decoding, which we empirically show correlate with factual errors, biases, and failures. Similar to Orgad et al. (2025), our method localizes the exact answer token and subsequently tests for hallucinations. Crucially, however, we achieve this without requiring trained probe classifiers or activation ablations. Instead, we introduce two completely training-free metrics derived directly from output logits: spilled energy, which captures the discrepancy between energy values across consecutive generation steps that should theoretically match, and marginalized energy, which is measurable at a single step. Evaluated on nine benchmarks across state-of-the-art LLMs (including LLaMA, Mistral, and Gemma) and on synthetic algebraic operations (Qwen3), our approach demonstrates robust, competitive hallucination detection and cross-task generalization. Notably, these results hold for both pretrained and instruction-tuned variants without introducing any training overhead.

Problem

• hallucination
• large language models
• energy-based models
• factual errors
• bias

Innovation

• Energy-Based Model
• Spilled Energy
• Hallucination Detection
• Training-Free Metric
• Logit Analysis