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| Format: | Preprint |
| Published: |
2026
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| Online Access: | https://arxiv.org/abs/2602.01651 |
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| _version_ | 1866917424403578880 |
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| author | Wei, Zichao |
| author_facet | Wei, Zichao |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01651 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Spatiotemporal Dynamics of Generalization in Neural Networks Wei, Zichao Machine Learning Artificial Intelligence 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. |
| title | On the Spatiotemporal Dynamics of Generalization in Neural Networks |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2602.01651 |