arXiv AI

Linear Algebra Foundations of Efficient Attention: A Phase Reversal in Rank Collapse Under SVD Compression

Hugging Face Trending Papers
Jul 15

Transforming Rank: How Architecture Navigates the Spectral Pathologies of Depth

We investigate how each component of the Transformer feedforward block architecture design determines how much rank survives across depth at initialization. We reinterpret skip connections and normalization, long understood as controlling magnitude, as mechanisms for preserving gradient rank across depth, since the very matrix multiplications and nonlinear activations that make the network expressive also reduce the rank.

arXiv Machine Learning
Sep 4

The Gradient Does Not See Rank: Rank-Indifference in Matrix-CODI on ProsQA

The paper investigates whether the rank of latent matrices in matrix‑chain‑of‑thought (Matrix‑CODI) models influences performance on reasoning tasks. Across multiple training regimes on ProsQA and GSM8K‑Aug, rank‑k projection ablations show flat accuracy curves, indicating that truncating the latent matrix to low rank does not hurt performance. Experiments with various readout architectures—bilinear, bilinear‑plus‑GELU, SVD‑augmented, and quadratic—confirm that rank‑indifference persists even for nonlinear readouts, and a linear probe on the latent matrix underperforms a raw pretrained hidden state.

By Samuel Larson (Pebble ML)