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.
arXiv preprint arXiv:2312.17044 (2024)
6 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
representative citing papers
Deriving a neural cellular automaton from locality, symmetry, and stability postulates produces 100% accurate addition generalization from 16-digit to 1-million-digit inputs.
LOOPE learns a patch ordering for positional embeddings in ViTs and introduces the Three Cell Experiment benchmark that shows 30-35% gaps in positional retention versus the usual 4-6%.
Applies optimal transport to bound OOD generalization error in Transformers via Lipschitz continuity and TC^0 circuit depth lower bounds for Dyck-k backtracking, supported by evaluations on 54 configurations.
A survey of positional encoding methods in transformer-based time series models that evaluates fixed, learnable, relative, and hybrid approaches on classification tasks and links effectiveness to data characteristics.
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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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LOOPE: Learnable Optimal Patch Order in Positional Embeddings for Vision Transformers
LOOPE learns a patch ordering for positional embeddings in ViTs and introduces the Three Cell Experiment benchmark that shows 30-35% gaps in positional retention versus the usual 4-6%.
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A Measure-Theoretic Analysis of Reasoning: Structural Generalization and Approximation Limits
Applies optimal transport to bound OOD generalization error in Transformers via Lipschitz continuity and TC^0 circuit depth lower bounds for Dyck-k backtracking, supported by evaluations on 54 configurations.
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Positional Encoding in Transformer-Based Time Series Models: A Survey
A survey of positional encoding methods in transformer-based time series models that evaluates fixed, learnable, relative, and hybrid approaches on classification tasks and links effectiveness to data characteristics.
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