Cortical Networks

Artificial Neural Networks (ANNs) are notoriously energy-inefficient compared to their biological counterparts. While biological brains operate at the thermodynamic limit of information efficiency, ANNs rely on heuristic regularization techniques (L1, L2) that do not account for the physical costs of information transport. In this work, we translate the "Theory of Thermodynamic Branching" (Marchesi, 2026) from biophysics to machine learning. We introduce "Thermodynamic Regularization", a novel penalty term derived from the optimization of cortical dendritic arbors. We demonstrate that this bio-inspired exponent (approx 2.42) outperforms both Lasso (L1) and Ridge (L2) regression on:1. Standard vision benchmarks (MNIST), achieving 69% sparsity with 95.8% accuracy.2. Transformer architectures (NanoGPT on Shakespeare), preserving language modeling capability significantly better than standard decay (Loss 2.64 vs 2.83) while inducing efficient pruning. This suggests that the branching factor alpha = 2.42 is not merely a biological curiosity, but a universal constant for efficient distributed computing.