Related papers: On the Sample Complexity of Two-Layer Networks: Li…
Research in computational deep learning has directed considerable efforts towards hardware-oriented optimisations for deep neural networks, via the simplification of the activation functions, or the quantization of both activations and…
We study non-convex empirical risk minimization for learning halfspaces and neural networks. For loss functions that are $L$-Lipschitz continuous, we present algorithms to learn halfspaces and multi-layer neural networks that achieve…
We consider the problem of active learning for single neuron models, also sometimes called ``ridge functions'', in the agnostic setting (under adversarial label noise). Such models have been shown to be broadly effective in modeling…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide…
A new non-linear variant of a quantitative extension of the uniform boundedness principle is used to show sharpness of error bounds for univariate approximation by sums of sigmoid and ReLU functions. Single hidden layer feedforward neural…
We provide several new results on the sample complexity of vector-valued linear predictors (parameterized by a matrix), and more generally neural networks. Focusing on size-independent bounds, where only the Frobenius norm distance of the…
We develop a minimax theory for operator learning, where the goal is to estimate an unknown operator between separable Hilbert spaces from finitely many noisy input-output samples. For uniformly bounded Lipschitz operators, we prove…
This paper considers the following question: how well can depth-two ReLU networks with randomly initialized bottom-level weights represent smooth functions? We give near-matching upper- and lower-bounds for $L_2$-approximation in terms of…
We study the sample complexity of learning ReLU neural networks from the point of view of generalization. Given norm constraints on the weight matrices, a common approach is to estimate the Rademacher complexity of the associated function…
We study the excess capacity of deep networks in the context of supervised classification. That is, given a capacity measure of the underlying hypothesis class - in our case, empirical Rademacher complexity - to what extent can we (a…
We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared $\ell_2$-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results…
Tight estimation of the Lipschitz constant for deep neural networks (DNNs) is useful in many applications ranging from robustness certification of classifiers to stability analysis of closed-loop systems with reinforcement learning…
Lipschitz continuity is a crucial functional property of any predictive model, that naturally governs its robustness, generalisation, as well as adversarial vulnerability. Contrary to other works that focus on obtaining tighter bounds and…
We prove some new results concerning the approximation rate of neural networks with general activation functions. Our first result concerns the rate of approximation of a two layer neural network with a polynomially-decaying non-sigmoidal…
We establish improved sample-complexity bounds for sample-based Lindbladian simulation based on the Wave Matrix Lindbladization (WML) algorithm. For a jump operator $L$ with dimension $d$, we derive an explicit non-asymptotic sample…
We study how the optimization landscape of a neural network deforms as a non-linear activation is introduced through a smooth homotopy. Working first in an abstract local setting - a smooth one-parameter family of objective functions…
Smooth activation functions are ubiquitous in modern deep learning, yet their theoretical advantages over non-smooth counterparts remain poorly understood. In this work, we study both approximation and statistical properties of neural…
This paper investigates the approximation properties of deep neural networks with piecewise-polynomial activation functions. We derive the required depth, width, and sparsity of a deep neural network to approximate any H\"{o}lder smooth…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…