How Long Does Infinite Width Last? Signal Propagation in Long-Range Linear Recurrences

arXiv:2605.05113 · cs.LG · Submitted 2026-05-06 · Read on arXiv

cs.LG

Submitted: 2026-05-06

Updated: 2026-09-25

Terminology

• Trace — 29× in this paper · explained in 2 episodes
• Scaling Laws — 5× in this paper · explained in 4 episodes
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• Hultman numbers, polygon gluings and matrix integrals
• Layer Normalization
• Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation
• Griffin: Mixing Gated Linear Recurrences with Local Attention for Efficient Language Models
• Dynamical Isometry and a Mean Field Theory of LSTMs and GRUs
• Mamba: Linear-Time Sequence Modeling with Selective State Spaces
• Efficiently Modeling Long Sequences with Structured State Spaces
• Finite Depth and Width Corrections to the Neural Tangent Kernel
• Gaussian Process Behaviour in Wide Deep Neural Networks
• Deep Information Propagation
• Scaling Limits of Wide Neural Networks with Weight Sharing: Gaussian Process Behavior, Gradient Independence, and Neural Tangent Kernel Derivation
• Tensor Programs II: Neural Tangent Kernel for Any Architecture
• Tensor Programs III: Neural Matrix Laws

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