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We study the implicit bias of gradient flow (i.e., gradient descent with infinitesimal step size) on linear neural network training. We propose a tensor formulation of neural networks that includes fully-connected, diagonal, and…

We present an algorithm that learns representations which explicitly compensate for domain mismatch and which can be efficiently realized as linear classifiers. Specifically, we form a linear transformation that maps features from the…

This paper considers a distributed adaptive optimization problem, where all agents only have access to their local cost functions with a common unknown parameter, whereas they mean to collaboratively estimate the true parameter and find the…

Gradient-based meta-learning techniques are both widely applicable and proficient at solving challenging few-shot learning and fast adaptation problems. However, they have practical difficulties when operating on high-dimensional parameter…

We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…

The non-stationary nature of image characteristics calls for adaptive processing, based on the local image content. We propose a simple and flexible method to learn local tuning of parameters in adaptive image processing: we extract simple…

We study gradient-based data attribution, aiming to identify which training examples most influence a given output. Existing methods for this task either treat network parameters uniformly or rely on implicit weighting derived from Hessian…

The paper presents a dynamic solution method for dynamic minimum parametric networks flow. The solution method solves the problem for a special parametric dynamic network with linear lower bound functions of a single parameter. Instead…

Natural gradient descent is a principled method for adapting the parameters of a statistical model on-line using an underlying Riemannian parameter space to redefine the direction of steepest descent. The algorithm is examined via methods…

We propose a new method for parameter learning in Bayesian networks with qualitative influences. This method extends our previous work from networks of binary variables to networks of discrete variables with ordered values. The specified…

We introduce a new embarrassingly parallel parameter learning algorithm for Markov random fields with untied parameters which is efficient for a large class of practical models. Our algorithm parallelizes naturally over cliques and, for…

When optimizing over-parameterized models, such as deep neural networks, a large set of parameters can achieve zero training error. In such cases, the choice of the optimization algorithm and its respective hyper-parameters introduces…

Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…

This is a sequel to our paper `On the kernel learning problem'. We identify a canonical choice of Riemannian gradient flow, to find the stationary points in the kernel learning problem. In the presence of Gaussian noise variables, this flow…

Enhancing the efficiency of high-quality image generation using Diffusion Models (DMs) is a significant challenge due to the iterative nature of the process. Flow Matching (FM) is emerging as a powerful generative modeling paradigm based on…

Learning rules -- prescriptions for updating model parameters to improve performance -- are typically assumed rather than derived. Why do some learning rules work better than others, and under what assumptions can a given rule be considered…

Learning from small amounts of labeled data is a challenge in the area of deep learning. This is currently addressed by Transfer Learning where one learns the small data set as a transfer task from a larger source dataset. Transfer Learning…

We propose an inexact optimization algorithm on Riemannian manifolds, motivated by quadratic discrimination tasks in high-dimensional, low-sample-size (HDLSS) imaging settings. In such applications, gradient evaluations are often biased due…

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the fidelity weight and weights within the kernel of the nonlocal operator. In both cases we…

This paper introduces the sigma flow model for the prediction of structured labelings of data observed on Riemannian manifolds, including Euclidean image domains as special case. The approach combines the Laplace-Beltrami framework for…