arXiv AI By James Hazelden, Balaaji Reddy Nagireddy, Eric Shea-Brown

Fast Generalized Neural Tangent Kernel Statistics via Trace Estimation

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The paper presents efficient approximations for key statistics of the Neural Tangent Kernel (NTK) in finite-width neural networks using randomized trace estimation (Hutch++). It demonstrates that the NTK trace, Frobenius norm, effective rank, and alignment can be estimated with high accuracy via matrix-free products, leveraging the NTK’s positive-semidefinite structure to use one-sided estimators with forward or reverse-mode differentiation. Experiments on MLPs, GRUs, and a 410‑million‑parameter Transformer show orders‑of‑magnitude speedups and enable practical state‑space NTK diagnostics at large scales, including applications to RNN training and data‑scarce knowledge distillation.

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arXiv Machine Learning
Sep 17

Long-Context Demonstration Selection Using State Space Models

The paper addresses the challenge of selecting demonstrations for long-context language model queries, where transformer inference costs grow quadratically with sequence length. It proposes two algorithms that distill transformer behavior into state space models (SSMs) with linear inference time, partitioning transformer layers into groups and estimating separate SSMs for each. The distilled SSMs achieve less than 0.7% approximation error, and in downstream tasks they reduce FLOPs by 14.2× while improving accuracy by 6.48% compared to baseline methods.

By Ziniu Zhang, Zhenshuo Zhang, Ruoxuan Xiong, Gene Cooperman, Hongyang R. Zhang