LLM Reasoning as Attractor Dynamics: Gibbs-Weighted Energy Minimization for Latent Memory Retrieval

arXiv CS · · 1 min read · Engineering & Technology

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Key Takeaways

  • LLMs function as high-dimensional Dense Associative Memories, storing reasoning patterns as latent attractors.
  • Correct reasoning chains correspond to deep, wide attractor basins ('flat minima') in the model's output distribution.
  • Hallucinations manifest as sharp, unstable local minima.
  • A retrieval mechanism, based on a Gibbs measure of spectral entropy and inverse energy weighting ($P \propto e^{-\beta E}$), effectively approximates the equilibrium distribution of the associative memory.
  • This mechanism improved Microsoft Phi-3.5 performance on GSM8K by 5.38% (84.7% to 90.1%).
  • Inference is better modeled as a dynamic settling process into an attractor basin rather than greedy next-token prediction.

Why This Matters

The proposed mechanism offers empirical improvements in LLM performance on mathematical reasoning tasks. By re-conceptualizing LLM inference as a dynamic settling process, this research provides an alternative framework for understanding and potentially enhancing LLM reliability and accuracy in complex reasoning tasks.

Overview

Large Language Models (LLMs) are conventionally characterized as autoregressive generators. This work presents an alternative perspective, viewing LLMs as high-dimensional Dense Associative Memories. Within this framework, complex reasoning patterns are considered to be stored as latent attractors. The research investigates the energy landscape associated with mathematical reasoning. It proposes that accurate reasoning chains correspond to deep, wide attractor basins, termed 'flat minima,' within the model's output distribution. Conversely, hallucinations are posited to correspond to sharp, unstable local minima.

Approach

To leverage the identified geometry of the energy landscape, a retrieval mechanism was developed. This mechanism is based on a Gibbs measure of the trajectory's spectral entropy. The methodology involves sampling multiple reasoning paths. These paths are then weighted by their inverse energy, expressed as $P \propto e^{-\beta E}$. This weighting process approximates the equilibrium distribution of the associative memory, facilitating the system's relaxation into a robust solution.

Findings

The application of this physics-inspired mechanism resulted in empirical improvements. Specifically, Microsoft Phi-3.5's performance on the GSM8K benchmark increased by 5.38%. This improvement moved the performance from 84.7% to 90.1%. These findings suggest that the inference process in LLMs can be more effectively modeled as a dynamic settling into an attractor basin, rather than solely as a greedy next-token prediction.

Research Context

The study reframes the understanding of LLM operation from that of a sequential generator to a collective computation system operating as a high-dimensional Dense Associative Memory. This conceptual shift provides a framework for analyzing reasoning within LLMs through the lens of attractor dynamics and energy landscapes. The identification of 'flat minima' for correct reasoning and 'sharp, unstable local minima' for hallucinations provides a geometric interpretation of model accuracy and failure modes.

Research Information

Institution
arXiv CS
Original Study
View Publication
Source
arXiv CS

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