Proves that Rademacher complexity of depth-d compositional trees over finite operator vocabulary is controlled by (K b L)^{d} / sqrt(n) under Lipschitz conditions on operators.
L., Foster, D
6 Pith papers cite this work, alongside 174 external citations. Polarity classification is still indexing.
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abstract
This paper presents a margin-based multiclass generalization bound for neural networks that scales with their margin-normalized "spectral complexity": their Lipschitz constant, meaning the product of the spectral norms of the weight matrices, times a certain correction factor. This bound is empirically investigated for a standard AlexNet network trained with SGD on the mnist and cifar10 datasets, with both original and random labels; the bound, the Lipschitz constants, and the excess risks are all in direct correlation, suggesting both that SGD selects predictors whose complexity scales with the difficulty of the learning task, and secondly that the presented bound is sensitive to this complexity.
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representative citing papers
Adaptive elastic net SAEs (AEN-SAEs) mitigate feature starvation in SAEs by combining ℓ2 structural stability with adaptive ℓ1 reweighting, producing a Lipschitz-continuous sparse coding map that recovers global feature support under mild assumptions.
The paper claims ReLU Transition Graphs of ReLU networks are expanders whose spectral gap, region entropy, and edge KL divergence bound generalization and capacity; the proofs are sketches, and the empirical checks are weak.
Review of neural scaling laws and their relation to constraints and inductive biases when applying machine learning to physics problems.
citing papers explorer
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Sample Complexity of Scientific Discovery: PAC Learnability of Compositional Function Trees
Proves that Rademacher complexity of depth-d compositional trees over finite operator vocabulary is controlled by (K b L)^{d} / sqrt(n) under Lipschitz conditions on operators.
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Feature Starvation as Geometric Instability in Sparse Autoencoders
Adaptive elastic net SAEs (AEN-SAEs) mitigate feature starvation in SAEs by combining ℓ2 structural stability with adaptive ℓ1 reweighting, producing a Lipschitz-continuous sparse coding map that recovers global feature support under mild assumptions.
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Discrete Functional Geometry of ReLU Networks via ReLU Transition Graphs
The paper claims ReLU Transition Graphs of ReLU networks are expanders whose spectral gap, region entropy, and edge KL divergence bound generalization and capacity; the proofs are sketches, and the empirical checks are weak.
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Statistical Properties of Training & Generalization
Review of neural scaling laws and their relation to constraints and inductive biases when applying machine learning to physics problems.
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