Related papers: A Closed-Form Upper Bound for Admissible Learning-…

We present a simple picture of the training process of joint embedding self-supervised learning methods. We find that these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated…

The current definition of a Bayesian credible set cannot, in general, achieve an arbitrarily preassigned credible level. This drawback is particularly acute for classification problems, where there are only a finite number of achievable…

In this work, we develop a level-set subdifferential error bound condition aiming towards convergence rate analysis of a variable Bregman proximal gradient (VBPG) method for a broad class of nonsmooth and nonconvex optimization problems. It…

Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one…

This article addresses the challenge of validating the admission committee's decisions for undergraduate admissions. In recent years, the traditional review process has struggled to handle the overwhelmingly large amount of applicants'…

We consider an unconstrained continuous optimization problem where, in each iteration, gradient estimates may be arbitrarily corrupted with a probability greater than 1/2. Additionally, function value estimates may exhibit heavy-tailed…

We consider the problem of designing an adaptive sequence of questions that optimally classify a candidate's ability into one of several categories or discriminative grades. A candidate's ability is modeled as an unknown parameter, which,…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

We analyze sequences generated by interior point methods (IPMs) in convex and nonconvex settings. We prove that moving the primal feasibility at the same rate as the barrier parameter $\mu$ ensures the Lagrange multiplier sequence remains…

To better understand complexity in neural networks, we theoretically investigate the idealised phenomenon of lossless network compressibility, whereby an identical function can be implemented with fewer hidden units. In the setting of…

Identifying statistical regularities in solutions to some tasks in multi-task reinforcement learning can accelerate the learning of new tasks. Skill learning offers one way of identifying these regularities by decomposing pre-collected…

We consider a finite field model of the X-ray transform that integrates functions along lines in dimension 3, within the context of finite fields. The admissibility problem asks for minimal sets of lines for which the restricted transform…

The goal of few-shot learning is to generalize and achieve high performance on new unseen learning tasks, where each task has only a limited number of examples available. Gradient-based meta-learning attempts to address this challenging…

The belief revision field is opulent in new proposals and indigent in analyses of existing approaches. Much work hinge on postulates, employed as syntactic characterizations: some revision mechanism is equivalent to some properties.…

The problem of learning threshold functions is a fundamental one in machine learning. Classical learning theory implies sample complexity of $O(\xi^{-1} \log(1/\beta))$ (for generalization error $\xi$ with confidence $1-\beta$). The private…

We provide a framework to analyze the convergence of discretized kinetic Langevin dynamics for $M$-$\nabla$Lipschitz, $m$-convex potentials. Our approach gives convergence rates of $\mathcal{O}(m/M)$, with explicit stepsize restrictions,…

Uncertainty estimation in machine learning has traditionally focused on the prediction stage, aiming to quantify confidence in model outputs while treating learned representations as deterministic and reliable by default. In this work, we…

Developing foundational world models is a key research direction for embodied intelligence, with the ability to adapt to non-stationary environments being a crucial criterion. In this work, we introduce a new formalism, Hidden…

Testing under what conditions the product satisfies the desired properties is a fundamental problem in manufacturing industry. If the condition and the property are respectively regarded as the input and the output of a black-box function,…

This paper offers a new perspective on the limits of machine learning: the ceiling on progress is set not by model size or algorithm choice but by the information structure of the task itself. Code generation has progressed more reliably…