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[2602.08216] Thermodynamic Isomorphism of Transformers: A Lagrangian Approach to Attention Dynamics
Summary
This paper presents a thermodynamic framework for analyzing Transformer attention dynamics, linking it to statistical mechanics through a Lagrangian approach.
Why It Matters
Understanding the thermodynamic properties of Transformer models can enhance our grasp of their training dynamics and scaling behaviors. This research offers a novel perspective that could lead to improved model designs and insights into generalization capabilities in machine learning.
Key Takeaways
- Introduces a thermodynamic framework for Transformer attention analysis.
- Establishes a connection between attention mechanisms and statistical mechanics.
- Identifies critical-like behaviors in attention energy fluctuations.
- Suggests that attention dynamics can be interpreted as emergent thermodynamic properties.
- Encourages further exploration of scaling limits in deep learning architectures.
Computer Science > Machine Learning arXiv:2602.08216 (cs) [Submitted on 9 Feb 2026 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Thermodynamic Isomorphism of Transformers: A Lagrangian Approach to Attention Dynamics Authors:Gunn Kim View a PDF of the paper titled Thermodynamic Isomorphism of Transformers: A Lagrangian Approach to Attention Dynamics, by Gunn Kim View PDF HTML (experimental) Abstract:We propose an effective field-theoretic framework for analyzing Transformer attention through a thermodynamic lens. By constructing a Lagrangian on the information manifold equipped with the Fisher metric, we show that, within the Shannon--Boltzmann entropy framework, the Softmax function arises as a stationary solution minimizing a Helmholtz free energy functional. This establishes a formal correspondence between scaled dot-product attention and canonical ensemble statistics. Extending this mapping to macroscopic observables, we define an effective specific heat associated with fluctuations of the attention energy landscape. In controlled experiments on the modular addition task ($p = 19$--$113$), we observe a robust peak in this fluctuation measure that consistently precedes the onset of generalization. While no asymptotic power-law divergence is detected in this finite-depth regime, the reproducible enhancement of energy variance suggests a critical-like crossover accompanying representational reorganization. Our framework provides a unified statistical-mechanical ...
