Modeling Pruning as a Phase Transition: A Thermodynamic Analysis of Neural Activations

Computers, Materials and Continua. 2026. Vol. 86. No. 3. Article 99.

- Р. М., Sergei Koltcov, Surkov A., Ignatenko V.

Activation pruning reduces neural network complexity by eliminating low-importance neuron activations, yet identifying the critical pruning threshold—beyond which accuracy rapidly deteriorates—remains computationally expensive and typically requires exhaustive search. We introduce a thermodynamics-inspired framework that treats activation distributions as energy-filtered physical systems and employs the free energy of activations as a principled evaluation metric. Phase-transition–like phenomena in the free-energy profile—such as extrema, inflection points, and curvature changes—yield reliable estimates of the critical pruning threshold, providing a theoretically grounded means of predicting sharp accuracy degradation. To further enhance efficiency, we propose a renormalized free energy technique that approximates full-evaluation free energy using only the activation distribution of the unpruned network. This eliminates repeated forward passes, dramatically reducing computational overhead and achieving speedups of up to 550× for MLPs. Extensive experiments across diverse vision architectures (MLP, CNN, ResNet, MobileNet, Vision Transformer) and text models (LSTM, BERT, ELECTRA, T5, GPT-2) on multiple datasets validate the generality, robustness, and computational efficiency of our approach. Overall, this work establishes a theoretically grounded and practically effective framework for activation pruning, bridging the gap between analytical understanding and efficient deployment of sparse neural networks.

Keywords: термодинамика, thermodynamics, ренормализация, свободная энергия, free energy, renormalization, activation pruning, model compression, sparsity, разреживание активаций, сжатие модели, разреженность

Publication based on the results of: Analysis of Human Interaction with Information and Improvement of Algorithms of Information Processing (2025)