Long-range dependency in integer multiplication is a mirage from 1D representation; a 2D grid reduces it to local 3x3 operations, letting a 321-parameter neural cellular automaton generalize perfectly to inputs 683 times longer than training while Transformers fail.
Arithmetic Transformers Can Length-Generalize in Both Operand Length and Count
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Deriving a neural cellular automaton from locality, symmetry, and stability postulates produces 100% accurate addition generalization from 16-digit to 1-million-digit inputs.
Parameter reconstruction algorithm for SNN training obtained by extending convexification of parallel feedforward threshold networks to the recurrent case that subsumes SNNs.
citing papers explorer
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On the Mirage of Long-Range Dependency, with an Application to Integer Multiplication
Long-range dependency in integer multiplication is a mirage from 1D representation; a 2D grid reduces it to local 3x3 operations, letting a 321-parameter neural cellular automaton generalize perfectly to inputs 683 times longer than training while Transformers fail.
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On the Spatiotemporal Dynamics of Generalization in Neural Networks
Deriving a neural cellular automaton from locality, symmetry, and stability postulates produces 100% accurate addition generalization from 16-digit to 1-million-digit inputs.
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Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction
Parameter reconstruction algorithm for SNN training obtained by extending convexification of parallel feedforward threshold networks to the recurrent case that subsumes SNNs.