Asymmetric Scaling Laws from Sparse Features

• URL: http://arxiv.org/abs/2605.23591v1
• Date: Fri, 22 May 2026 13:00:52 GMT
• Title: Asymmetric Scaling Laws from Sparse Features
• Abstract summary: We introduce a model for neural scaling laws under sparse activations.<n>Test loss is often dominated by rare coordinates that are never observed in the training input.<n>We show that the sparsity-induced effect persists under nonlinear activations.
• Score: 2.7838875470471858
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a model for neural scaling laws under sparse activations. In the model, test loss is often dominated by rare coordinates that are never observed in the training input. This mechanism induces a novel bottleneck absent from dense models. We derive the asymptotic population loss in both the underparameterized and overparameterized regimes, and show that the loss exhibits a double-descent peak near the interpolation threshold -- where the number of parameters is just sufficient to fit the training data -- resulting in a loss curve governed by two distinct scaling exponents -- one for the overparameterized regime and one for the underparameterized regime -- with a gap determined by the degree of sparsity. Additionally, we derive a compute-optimal frontier that favors increasing dataset size over model capacity under fixed compute budgets. We also analyze gradient-descent dynamics and identify a scaling law for the probability that fixed-step gradient descent becomes unstable. We further show that the sparsity-induced effect persists under nonlinear activations.

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