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The logic of bunched implications (BI), introduced by O'Hearn and Pym (1999), has attracted significant attention due to its elegant proof calculus, varied semantics, and close connections to the propositional fragment of separation logic.…

In a large, possibly infinite population, each subject is colored red with probability $p$, independently of the others. Then, a finite sub-population is selected, possibly as a function of the coloring. The imbalance in the sub-population…

Probability · Mathematics 2016-12-28 Erel Segal-Halevi , Avinatan Hassidim

In lifelong learning, tasks (or classes) to be learned arrive sequentially over time in arbitrary order. During training, knowledge from previous tasks can be captured and transferred to subsequent ones to improve sample efficiency. We…

Machine Learning · Computer Science 2022-03-02 Xinyuan Cao , Weiyang Liu , Santosh S. Vempala

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

Representation Theory · Mathematics 2019-11-19 Michael Bate , David I. Stewart

We give new, explicit and asymptotically sharp, lower bounds for dimensions of irreducible modular representations of finite symmetric groups.

Representation Theory · Mathematics 2019-09-10 Alexander Kleshchev , Lucia Morotti , Pham Huu Tiep

Approximate Bayesian inference on the basis of summary statistics is well-suited to complex problems for which the likelihood is either mathematically or computationally intractable. However the methods that use rejection suffer from the…

Computation · Statistics 2010-05-04 M. G. B. Blum , O. Francois

We study the problem of learning predictors that are robust to adversarial examples with respect to an unknown perturbation set, relying instead on interaction with an adversarial attacker or access to attack oracles, examining different…

Machine Learning · Computer Science 2021-02-04 Omar Montasser , Steve Hanneke , Nathan Srebro

In this thesis I develop a variety of techniques to train, evaluate, and sample from intractable and high dimensional probabilistic models. Abstract exceeds arXiv space limitations -- see PDF.

Machine Learning · Computer Science 2012-05-22 Jascha Sohl-Dickstein

Reweighting a distribution to minimize a distance to a target distribution is a powerful and flexible strategy for estimating a wide range of causal effects, but can be challenging in practice because optimal weights typically depend on…

Machine Learning · Statistics 2026-02-16 Oscar Clivio , Avi Feller , Chris Holmes

In order to deal with the curse of dimensionality in reinforcement learning (RL), it is common practice to make parametric assumptions where values or policies are functions of some low dimensional feature space. This work focuses on the…

Machine Learning · Computer Science 2020-07-23 Alekh Agarwal , Sham Kakade , Akshay Krishnamurthy , Wen Sun

Deep neural networks generalize well despite being heavily overparameterized, in apparent contradiction with classical learning theory based on uniform convergence over fixed hypothesis spaces. Uniform bounds over the entire parameter space…

Machine Learning · Statistics 2026-05-15 Hubert Leroux , Jean Marcus , Julien Roger

The canonical dimension is an invariant attached to admissible representations of p-adic reductive groups, which has only received significant attention in the case of mod-p representations. In the case of complex representations, the…

Representation Theory · Mathematics 2025-09-30 Mick Gielen

In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…

Machine Learning · Computer Science 2025-06-17 Sebastian Bordt , Eric Raidl , Ulrike von Luxburg

Rademacher complexity is often used to characterize the learnability of a hypothesis class and is known to be related to the class size. We leverage this observation and introduce a new technique for estimating the size of an arbitrary…

Machine Learning · Computer Science 2018-01-30 Jonathan Kuck , Ashish Sabharwal , Stefano Ermon

We study the *refuter* problems for proof complexity lower bounds. Suppose $\varphi$ is a hard tautology that does not admit any length-$s$ proof in some proof system $P$. In the corresponding refuter problem, we are given (query access to)…

Computational Complexity · Computer Science 2026-03-25 Jiawei Li , Yuhao Li , Hanlin Ren

We know from reinforcement learning theory that temporal difference learning can fail in certain cases. Sutton and Barto (2018) identify a deadly triad of function approximation, bootstrapping, and off-policy learning. When these three…

Artificial Intelligence · Computer Science 2018-12-07 Hado van Hasselt , Yotam Doron , Florian Strub , Matteo Hessel , Nicolas Sonnerat , Joseph Modayil

Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.

Analysis of PDEs · Mathematics 2022-08-08 Simon Eberle , Henrik Shahgholian , Georg S. Weiss

After four decades of research there still exists a Classification accuracy gap of about 20% between our best Unsupervisedly Learned Representations methods and the accuracy rates achieved by intelligent animals. It thus may well be that we…

Machine Learning · Computer Science 2025-05-30 Daniel N. Nissani

In this work we study the quantitative relation between the recursive teaching dimension (RTD) and the VC dimension (VCD) of concept classes of finite sizes. The RTD of a concept class $\mathcal C \subseteq \{0, 1\}^n$, introduced by Zilles…

Machine Learning · Computer Science 2017-02-21 Lunjia Hu , Ruihan Wu , Tianhong Li , Liwei Wang

We prove that the problem of deciding the consequence relation of the full Lambek calculus with weakening is complete for the class HAck of hyper-Ackermannian problems (i.e., level F_{\omega}^{\omega} of the ordinal-indexed hierarchy of…

Logic in Computer Science · Computer Science 2024-06-25 Vitor Greati , Revantha Ramanayake