arXiv:2604. 14727v2 Announce Type: replace Abstract: To quantify the geometric capacity of transformers, we develop a tropical-geometric framework for analyzing the spatial partitions induced by conditioned self-attention.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2607. 22757v1 Announce Type: cross Abstract: We introduce Graded Large Language Models (GLLMs), an algebraic framework that equips the representation space of a transformer with a grading and propagates the induced weighted scalar action through embeddings, self-attention, and the training objective.
arXiv:2607. 20594v1 Announce Type: cross Abstract: When does a weight-tied looped transformer -- one block applied T times -- implement an actual algorithm?
arXiv:2602. 18849v2 Announce Type: replace-cross Abstract: We develop a sensitivity analysis for transformer attention in a geometry aligned with tokenwise computation.
arXiv:2607. 10677v1 Announce Type: new Abstract: Self-attention is a ubiquitous primitive in modern sequence models, yet its operator-level geometry is only partially understood.
arXiv:2605. 28983v2 Announce Type: replace-cross Abstract: In this paper, training a neural network is identified, exactly, as a search through Hamilton--Jacobi initial-value problems: each gradient step selects the initial data of a viscous Hamilton--Jacobi equation whose Hopf--Cole propagator best fits the observations; at inference, the input is the spatial point at which that solution is evaluated and the initial condition is already encoded in the weights.
arXiv:2608. 10869v1 Announce Type: new Abstract: Worst-case multiclass bounds do not become smaller when the best classifier is already nearly correct: what is missing is an optimistic rate, a guarantee whose fluctuation scales with the oracle risk itself.