Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
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Hamprecht, Yoshua Bengio, and Aaron Courville
10 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Neural networks are known to be a class of highly expressive functions able to fit even random input-output mappings with $100\%$ accuracy. In this work, we present properties of neural networks that complement this aspect of expressivity. By using tools from Fourier analysis, we show that deep ReLU networks are biased towards low frequency functions, meaning that they cannot have local fluctuations without affecting their global behavior. Intuitively, this property is in line with the observation that over-parameterized networks find simple patterns that generalize across data samples. We also investigate how the shape of the data manifold affects expressivity by showing evidence that learning high frequencies gets \emph{easier} with increasing manifold complexity, and present a theoretical understanding of this behavior. Finally, we study the robustness of the frequency components with respect to parameter perturbation, to develop the intuition that the parameters must be finely tuned to express high frequency functions.
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Neural networks trained on crossing symmetry accurately reconstruct conformal correlators from minimal inputs due to alignment between their spectral bias and CFT smoothness.
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Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
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Deep learning-based phase-field modelling of brittle fracture in anisotropic media
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A Theory of Saddle Escape in Deep Nonlinear Networks
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Theory of the Frequency Principle for General Deep Neural Networks
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Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems
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Neural Networks Reveal a Universal Bias in Conformal Correlators
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FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
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