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Neural Networks Learn Statistics of Increasing Complexity
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Neural Networks Learn Statistics of Increasing Complexity
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The distributional simplicity bias (DSB) posits that neural networks learn low-order moments of the data distribution first, before moving on to higher-order correlations. In this work, we present compelling new evidence for the DSB by showing that networks automatically learn to perform well on maximum-entropy distributions whose low-order statistics match those of the training set early in training, then lose this ability later. We also extend the DSB to discrete domains by proving an equivalence between token $n$-gram frequencies and the moments of embedding vectors, and by finding empirical evidence for the bias in LLMs. Finally we use optimal transport methods to surgically edit the low-order statistics of one class to match those of another, and show that early-training networks treat the edited samples as if they were drawn from the target class. Code is available at https://github.com/EleutherAI/features-across-time.
Forward citations
Cited by 4 Pith papers
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A theory of learning data statistics in diffusion models, from easy to hard
Diffusion models exhibit a distributional simplicity bias, learning pairwise input statistics at linear sample complexity while fourth-order cumulants require cubic complexity unless sharing correlated latent structure.
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A theory of learning data statistics in diffusion models, from easy to hard
Denoising diffusion learns pair-wise input statistics at linear sample complexity and fourth-order cumulants only at cubic complexity, unless latent variables are correlated.
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