Algorithmic Separation between Constant-Depth and Logarithmic-Depth Neural Networks

arXiv:2607.25200 · cs.LG, stat.ML · Submitted 2026-07-28 · Read on arXiv

Yunwei Ren, Zihao Wang, Jason D. Lee

cs.LG, stat.ML

Submitted: 2026-07-28

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Accuracy — 13× in this paper · explained in 1 episode
• Editor — 11× in this paper · explained in 2 episodes
• Chebyshev Polynomials — 9× in this paper · explained in 2 episodes
• Sparsity — 3× in this paper · explained in 5 episodes
• Hierarchical Structure — 2× in this paper · explained in 3 episodes
• Absorb — 1× in this paper · explained in 1 episode
• Feature Selection — 1× in this paper · explained in 4 episodes
• Phase Transition — 1× in this paper · explained in 3 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Representation Learning — 1× in this paper · explained in 3 episodes
• Sample Complexity — 1× in this paper · explained in 20 episodes
• Structural Properties — 1× in this paper · explained in 2 episodes

Sources

• The Multiscale Single-Index Model: A Stylized Model for Hierarchical Feature Learning
• Deep Networks Learn Deep Hierarchical Models
• Deep Learning of Compositional Targets with Hierarchical Spectral Methods
• A Spectral Condition for Feature Learning

Related papers

• Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation
• AIRL-S: Unifying Reinforcement Learning and Search-Based Test-Time Scaling via Adversarial Inverse Reinforcement Learning
• Transformers as Bayesian In-Context Experimenters: Smoothness-Adaptive Efficient ATE Estimation
• Convergence issues in Relational Concept Analysis based on AOC-posets
• Beliefs Beyond Posteriors: The Predictive Cost of ELBO Binding
• Understanding Diffusion Models via Ratio-Based Function Approximation with SignReLU Networks