On the Spatiotemporal Dynamics of Generalization in Neural Networks
This addresses the fundamental gap between statistical learning and logical reasoning for AI systems, offering a novel approach to improve generalization in neural networks.
The paper tackled the problem of neural networks failing to generalize to longer sequences by proposing that generalization requires adherence to physical constraints like locality, symmetry, and stability, and it introduced the SEAD architecture, which achieved 100% accuracy on addition from 16-digit to 1 million-digit numbers.
Why do neural networks fail to generalize addition from 16-digit to 32-digit numbers, while a child who learns the rule can apply it to arbitrarily long sequences? We argue that this failure is not an engineering problem but a violation of physical postulates. Drawing inspiration from physics, we identify three constraints that any generalizing system must satisfy: (1) Locality -- information propagates at finite speed; (2) Symmetry -- the laws of computation are invariant across space and time; (3) Stability -- the system converges to discrete attractors that resist noise accumulation. From these postulates, we derive -- rather than design -- the Spatiotemporal Evolution with Attractor Dynamics (SEAD) architecture: a neural cellular automaton where local convolutional rules are iterated until convergence. Experiments on three tasks validate our theory: (1) Parity -- demonstrating perfect length generalization via light-cone propagation; (2) Addition -- achieving scale-invariant inference from L=16 to L=1 million with 100% accuracy, exhibiting input-adaptive computation; (3) Rule 110 -- learning a Turing-complete cellular automaton without trajectory divergence. Our results suggest that the gap between statistical learning and logical reasoning can be bridged -- not by scaling parameters, but by respecting the physics of computation.