Related papers: A note on sample complexity of learning binary out…

The rapid advancement of models based on artificial intelligence demands innovative monitoring techniques which can operate in real time with low computational costs. In machine learning, especially if we consider artificial neural networks…

Q-learning with function approximation could diverge in the off-policy setting and the target network is a powerful technique to address this issue. In this manuscript, we examine the sample complexity of the associated target Q-learning…

The fundamental theorem of statistical learning states that binary PAC learning is governed by a single parameter -- the Vapnik-Chervonenkis (VC) dimension -- which determines both learnability and sample complexity. Extending this to…

We investigate the sample complexity of networks with bounds on the magnitude of its weights. In particular, we consider the class \[ H=\left\{W_t\circ\rho\circ \ldots\circ\rho\circ W_{1} :W_1,\ldots,W_{t-1}\in M_{d, d}, W_t\in…

It is well-known that the robustness of artificial neural networks (ANNs) is important for their wide ranges of applications. In this paper, we focus on the robustness of the classification ability of a spiking neural network which receives…

It is becoming increasingly important to understand the vulnerability of machine learning models to adversarial attacks. One of the fundamental problems in adversarial machine learning is to quantify how much training data is needed in the…

Guiding the design of neural networks is of great importance to save enormous resources consumed on empirical decisions of architectural parameters. This paper constructs shallow sigmoid-type neural networks that achieve 100% accuracy in…

Statistical learning theory provides bounds on the necessary number of training samples needed to reach a prescribed accuracy in a learning problem formulated over a given target class. This accuracy is typically measured in terms of a…

In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…

We give a polynomial-time algorithm for learning neural networks with one layer of sigmoids feeding into any Lipschitz, monotone activation function (e.g., sigmoid or ReLU). We make no assumptions on the structure of the network, and the…

A large set of signals can sometimes be described sparsely using a dictionary, that is, every element can be represented as a linear combination of few elements from the dictionary. Algorithms for various signal processing applications,…

Training a neural network (NN) typically relies on some type of curve-following method, such as gradient descent (GD) (and stochastic gradient descent (SGD)), ADADELTA, ADAM or limited memory algorithms. Convergence for these algorithms…

We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this…

We study the sample complexity of learning one-hidden-layer convolutional neural networks (CNNs) with non-overlapping filters. We propose a novel algorithm called approximate gradient descent for training CNNs, and show that, with high…

A fundamental problem in adversarial machine learning is to quantify how much training data is needed in the presence of evasion attacks. In this paper we address this issue within the framework of PAC learning, focusing on the class of…

Semi-supervised node classification is a foundational task in graph machine learning, yet state-of-the-art Graph Neural Networks (GNNs) are hindered by significant computational overhead and reliance on strong homophily assumptions.…

Artificial neural networks (ANNs) require tremendous amount of data to train on. However, in classification models, most data features are often similar which can lead to increase in training time without significant improvement in the…

The phenomena of Spectral Bias, where the higher frequency components of a function being learnt in a feedforward Artificial Neural Network (ANN) are seen to converge more slowly than the lower frequencies, is observed ubiquitously across…

Graphical models capture relations between entities in a wide range of applications including social networks, biology, and natural language processing, among others. Graph neural networks (GNN) are neural models that operate over graphs,…

We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…