← Back to all news
Hugging Face Trending Papers

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

The paper addresses the limitations of spectral dimension reduction for dynamical systems composed of weakly interacting components, where standard rank‑based methods either require exponentially many modes or omit entire components (a phenomenon termed linear masking). It proposes scoring the σ‑algebra generated by coordinates instead of individual modes, using a χ²‑divergence criterion that guarantees an embedding with twice the intrinsic dimension captures the full operator spectrum. Experiments on benchmark systems show that this algebraic approach recovers masked components and enables accurate prediction from few labels, outperforming traditional rank‑based and VAMP methods.

Related stories

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
ragbenchmarks
More like this →
arXiv Machine Learning
Oct 12

A Categorical Atlas of Parameter-Efficient Fine-Tuning: Cones, Orbits, and Gauges

The paper presents a comprehensive framework for comparing parameter‑efficient fine‑tuning (PEFT) methods by treating each as a smooth map from a small parameter space into weight space, with a pretrained checkpoint as the base point. It identifies three key invariants—image near the base point, fibre dynamics, and base change—that explain expressivity, training dynamics, and initialization behavior. The authors prove numerous results about common PEFT techniques (e.g., LoRA, Householder adaptation) and classify 382 methods from 138 papers using seven coordinate descriptors.

By Xiaoyu Li, Zhizhou Sha, Chiwun Yang, Dai Shi
fine-tuningbenchmarks
More like this →
arXiv Machine Learning
Jul 30

Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules

arXiv:2605. 20440v2 Announce Type: replace Abstract: Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude.

By Paulina Hoyos, Shashanka Ubaru, Dongsung Huh, Vasileios Kalantzis, Kenneth L. Clarkson, Misha Kilmer, Haim Avron, Lior Horesh
More like this →