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Denoising score matching plays a pivotal role in the performance of diffusion-based generative models. However, the empirical optimal score--the exact solution to the denoising score matching--leads to memorization, where generated samples…

Learning rate schedulers have shown great success in speeding up the convergence of learning algorithms in practice. However, their convergence to a minimum has not been proven theoretically. This difficulty mainly arises from the fact…

We generalize the notion of average Lipschitz smoothness proposed by Ashlagi et al. (COLT 2021) by extending it to H\"older smoothness. This measure of the "effective smoothness" of a function is sensitive to the underlying distribution and…

To improve the robustness of deep classifiers against adversarial perturbations, many approaches have been proposed, such as designing new architectures with better robustness properties (e.g., Lipschitz-capped networks), or modifying the…

Training deep neural networks typically relies on backpropagating high dimensional error signals a computationally intensive process with little evidence supporting its implementation in the brain. However, since most tasks involve…

The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…

ShuffleNet is a state-of-the-art light weight convolutional neural network architecture. Its basic operations include group, channel-wise convolution and channel shuffling. However, channel shuffling is manually designed empirically.…

This paper is motivated by structured sparsity for deep neural network training. We study a weighted group L0-norm constraint, and present the projection and normal cone of this set. Using randomized smoothing, we develop zeroth and…

Representations are fundamental to artificial intelligence. The performance of a learning system depends on the type of representation used for representing the data. Typically, these representations are hand-engineered using domain…

Techniques known as Nonlinear Set Membership prediction, Kinky Inference or Lipschitz Interpolation are fast and numerically robust approaches to nonparametric machine learning that have been proposed to be utilised in the context of system…

The success of deep learning relies on the availability of large-scale annotated data sets, the acquisition of which can be costly, requiring expert domain knowledge. Semi-supervised learning (SSL) mitigates this challenge by exploiting the…

Hierarchical neural networks are exponentially more efficient than their corresponding "shallow" counterpart with the same expressive power, but involve huge number of parameters and require tedious amounts of training. Our main idea is to…

This paper analyzes a new regularized learning scheme for high dimensional partially linear support vector machine. The proposed approach consists of an empirical risk and the Lasso-type penalty for linear part, as well as the standard…

We prove that, for the fundamental regression task of learning a single neuron, training a one-hidden layer ReLU network of any width by gradient flow from a small initialisation converges to zero loss and is implicitly biased to minimise…

Ability of deep networks to extract high level features and of recurrent networks to perform time-series inference have been studied. In view of universality of one hidden layer network at approximating functions under weak constraints, the…

Structured stochastic multi-armed bandits provide accelerated regret rates over the standard unstructured bandit problems. Most structured bandits, however, assume the knowledge of the structural parameter such as Lipschitz continuity,…

Operator learning based on neural operators has emerged as a promising paradigm for the data-driven approximation of operators, mapping between infinite-dimensional Banach spaces. Despite significant empirical progress, our theoretical…

Generalising well in supervised learning tasks relies on correctly extrapolating the training data to a large region of the input space. One way to achieve this is to constrain the predictions to be invariant to transformations on the input…

Bayesian methods for learning Gaussian graphical models offer a principled framework for quantifying model uncertainty and incorporating prior knowledge. However, their scalability is constrained by the computational cost of jointly…

Backpropagation with gradient descent is a common optimization strategy employed by most neural network architectures in machine learning. However, finding optimal hyperparameters to guide training has proven challenging. While it is widely…