arXiv Machine Learning By Samuel Larson

The Rank the Task Demands: A Causal Rank Law for Matrix Memories Trained on Group Composition

Read the original on arXiv Machine Learning →

arXiv:2609. 12259v1 Announce Type: new Abstract: Matrix-valued memories make rank the natural budget of a learned representation: the number of independent directions a state spans bounds what it can bind, compose, and track.

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arXiv Machine Learning
Aug 20

Score the Algebra, Not the Span: Dimension Reduction for Transfer Operator Models of Dynamical Systems

The paper proposes a new dimension‑reduction strategy for transfer‑operator models of dynamical systems that focuses on scoring the σ‑algebra generated by coordinates rather than the operator’s spectral span. By using a χ²‑divergence criterion between embedded present and future states, the method guarantees that twice the intrinsic system dimension suffices to capture the full operator spectrum, even for systems with weakly interacting components that would otherwise require exponentially many modes. Experiments on benchmark systems show that this algebraic approach recovers masked components missed by rank‑based methods and enables accurate prediction of those components from few labels.

By Mark Kozdoba, Shie Mannor
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)