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Deep neural networks (DNNs) generalize remarkably well without explicit regularization even in the strongly over-parametrized regime where classical learning theory would instead predict that they would severely overfit. While many…

Given an $n$-length input signal $\mbf{x}$, it is well known that its Discrete Fourier Transform (DFT), $\mbf{X}$, can be computed in $O(n \log n)$ complexity using a Fast Fourier Transform (FFT). If the spectrum $\mbf{X}$ is exactly…

We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…

We initiate the study of active learning polynomial threshold functions (PTFs). While traditional lower bounds imply that even univariate quadratics cannot be non-trivially actively learned, we show that allowing the learner basic access to…

In this paper we investigate k-submodular functions. This natural family of discrete functions includes submodular and bisubmodular functions as the special cases k = 1 and k = 2 respectively. In particular we generalize the known…

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled…

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…

Recently regular decision processes have been proposed as a well-behaved form of non-Markov decision process. Regular decision processes are characterised by a transition function and a reward function that depend on the whole history,…

The model of learning with \emph{local membership queries} interpolates between the PAC model and the membership queries model by allowing the learner to query the label of any example that is similar to an example in the training set. This…

In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…

We give an algorithm that learns arbitrary Boolean functions of $k$ arbitrary halfspaces over $\mathbb{R}^n$, in the challenging distribution-free Probably Approximately Correct (PAC) learning model, running in time $2^{\sqrt{n} \cdot (\log…

In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime…

We introduce a new model of membership query (MQ) learning, where the learning algorithm is restricted to query points that are \emph{close} to random examples drawn from the underlying distribution. The learning model is intermediate…

This paper proposes a new mean-field framework for over-parameterized deep neural networks (DNNs), which can be used to analyze neural network training. In this framework, a DNN is represented by probability measures and functions over its…

In this paper, exact rate of approximation of functions by linear means of Fourier series and Fourier integrals and corresponding $K$-functionals are expressed via special moduli of smoothness. . Introduction is given in $\S 1$. In $\S2$…

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning…

Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…

We study the number of queries needed to identify a monotone Boolean function $f:\{0,1\}^n \rightarrow \{0,1\}$. A query consists of a 0-1-sequence, and the answer is the value of $f$ on that sequence. It is well-known that the number of…

We proposes a novel method that enables Graph Neural Networks (GNNs) to solve SAT problems by leveraging a technique developed for applying GNNs to Mixed Integer Linear Programming (MILP). Specifically, k-CNF formulae are mapped into MILP…

We consider PAC learning of probability distributions (a.k.a. density estimation), where we are given an i.i.d. sample generated from an unknown target distribution, and want to output a distribution that is close to the target in total…