arXiv:2607. 18817v1 Announce Type: cross Abstract: Algebraic statistics characterizes statistical models through polynomial constraints, but it has mainly been used for analytically specified model classes.
arXiv:2609.23774v1 Announce Type: new Abstract: Probabilistic inference is generally only tractable in low-treewidth graphical models, limiting its effective applicability in high-treewidth settings....
arXiv:2606. 19366v1 Announce Type: cross Abstract: Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain.
arXiv:2410. 06329v4 Announce Type: replace-cross Abstract: Obtaining a reliable estimate of the joint probability mass function (PMF) of a set of random variables from observed data is a significant objective in statistical signal processing and machine learning.
Large language models (LLMs) are built from structured high-dimensional objects such as token representations, weights, adaptation updates, caches, and activations, whose multilinear structure is unde...
The paper establishes tight pseudo-dimension bounds for data-driven multiple hyper‑parameter tuning with structured loss functions. By refining upper bounds through real algebraic geometry and analyzing invariant connected sign cells, the authors avoid over‑counting and achieve sharper sample complexities. A multi‑regime lower‑bound framework demonstrates that these upper bounds are tight, and the approach is extended to general bi‑level validation‑loss tuning and broader semi‑algebraic applications.
Ensuring model reliability in Explainable AI requires a global assessment of the hypothesis space. We propose a formal framework for the exhaustive analysis of optimal and near-optimal decision trees, called Algebraic Decision Tree Counting (ADTC).
arXiv:2605. 11644v3 Announce Type: replace-cross Abstract: Positive data can show that two tuple occurrences share a successful sentence context without certifying that they are safely interchangeable.
arXiv:2608. 08118v1 Announce Type: new Abstract: There are several methods for searching for graphs with prescribed properties, such as SAT solvers and specialized generators.
Lifted inference algorithms scale probabilistic inference by exploiting indistinguishable objects, but real‑world data often yields only approximately commutative factors. The paper introduces ε‑commutativity, a relaxation that tolerates small deviations from exact invariance, and shows how it can be used to build lifted models and perform inference with provable error bounds. Empirical results confirm that queries remain accurate while runtime is reduced.
arXiv:2607. 12443v1 Announce Type: cross Abstract: Motivated by the power of large language models, there has been renewed interest in the Gold-Angluin model of language identification in the limit, with an eye toward variants of the model that might overcome the negative results for its original formulation.
arXiv:2606. 04176v1 Announce Type: new Abstract: We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar.
arXiv:2607. 18883v1 Announce Type: cross Abstract: A central aim of unsupervised learning is to uncover latent factors that explain dependencies among observations.