A preprint presents VALG, an agentic system designed to help with research in machine learning theory, where a learning procedure is formalised through elements such as the data model, training protocol, oracle access, loss, metric and randomness. The authors frame theorem-proving in this setting as an open problem the system aims to address, and the paper is a revised cross-listing on arXiv.
A newly updated arXiv monograph examines the relationship between two kernel-based machine learning traditions: probabilistic modeling with Gaussian processes and non-probabilistic methods built on reproducing kernel Hilbert spaces. The work lays out the mathematical connections and equivalences between the two approaches, providing a unified theoretical treatment of positive definite kernel techniques.
A new machine learning theory paper on arXiv examines how a learner can predict elements of a sequence when the oracle supplying feedback may misreport outcomes. The authors frame the task as a repeated interaction in which the environment picks an outcome from a finite alphabet and the learner must commit to a probability distribution without reliable ground truth. The work analyzes what prediction performance can still be guaranteed in this adversarial setting.
A new machine learning theory paper establishes a 'diagonal saturation principle' for modal inverse problems. When truncation noise is isotropic, the optimal diagonal Tikhonov regularizer takes a closed-form power-law shape whose exponent is fixed entirely by the prior. The authors argue this explains why learned regularization converges on an analytic solution rather than a data-dependent one.
A new arXiv paper in machine learning theory settles the gap-entropy conjecture, an open problem in best-arm identification for multi-armed bandits. The proof covers the fixed-confidence setting with independent unit-variance Gaussian arms, means bounded in [0,1], and a single optimal arm. The result confirms that the entropy of suboptimality gaps governs the sample complexity needed to identify the best arm.