Related papers: Complexity theoretic limitations on learning DNF's

We analyze two Natural Language Inference data sets with respect to their linguistic features. The goal is to identify those syntactic and semantic properties that are particularly hard to comprehend for a machine learning model. To this…

We provide a general framework for computing lower-bounds on the sample complexity of recovering the underlying graphs of Ising models, given i.i.d samples. While there have been recent results for specific graph classes, these involve…

This paper focuses on understanding how the generalization error scales with the amount of the training data for deep neural networks (DNNs). Existing techniques in statistical learning require computation of capacity measures, such as VC…

Can deep neural networks learn to solve any task, and in particular problems of high complexity? This question attracts a lot of interest, with recent works tackling computationally hard tasks such as the traveling salesman problem and…

Standard evaluations of deep learning models for semantics using naturalistic corpora are limited in what they can tell us about the fidelity of the learned representations, because the corpora rarely come with good measures of semantic…

The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…

Query evaluation over probabilistic databases is known to be intractable in many cases, even in data complexity, i.e., when the query is fixed. Although some restrictions of the queries [19] and instances [4] have been proposed to lower the…

While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose clauses are chosen uniformly from among…

Rubinfeld & Vasilyan recently introduced the framework of testable learning as an extension of the classical agnostic model. It relaxes distributional assumptions which are difficult to verify by conditions that can be checked efficiently…

The study of graph products is a major research topic and typically concerns the term $f(G*H)$, e.g., to show that $f(G*H)=f(G)f(H)$. In this paper, we study graph products in a non-standard form $f(R[G*H]$ where $R$ is a "reduction", a…

Machine learning models are vulnerable to Adversarial Examples: minor perturbations to input samples intended to deliberately cause misclassification. Current defenses against adversarial examples, especially for Deep Neural Networks (DNN),…

Neural Networks (NNs) are vulnerable to adversarial examples. Such inputs differ only slightly from their benign counterparts yet provoke misclassifications of the attacked NNs. The required perturbations to craft the examples are often…

We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show…

Statistical learning theory chiefly studies restricted hypothesis classes, particularly those with finite Vapnik-Chervonenkis (VC) dimension. The fundamental quantity of interest is the sample complexity: the number of samples required to…

In this paper, we consider the problem of replicable realizable PAC learning. We construct a particularly hard learning problem and show a sample complexity lower bound with a close to $(\log|H|)^{3/2}$ dependence on the size of the…

Deep Neural Networks (DNNs) have shown substantial success in various applications but remain vulnerable to adversarial attacks. This study aims to identify and isolate the components of two different adversarial training techniques that…

Despite recent advances in Natural Language Processing (NLP), hierarchical discourse parsing in the framework of Rhetorical Structure Theory remains challenging, and our understanding of the reasons for this are as yet limited. In this…

Deep neural networks (DNN) are increasingly being used to perform algorithm-selection in combinatorial optimisation domains, particularly as they accommodate input representations which avoid designing and calculating features. Mounting…