6 accepted papers
Classical optimisation theory guarantees monotonic objective decrease for gradient descent (GD) when employed in a small step size, or "stable", regime. In contrast, gradient descent on neural networks is frequently performed in a large step size regime called the "edge of stability", in which the o…
Despite the empirical success of Low-Rank Adaptation (LoRA) in fine-tuning pre-trained models, there is little theoretical understanding of how first-order methods with carefully crafted initialization adapt models to new tasks. In this work, we take the first step towards bridging this gap by theor…
In this paper we present a new method for deformable NeRF that can directly use optical flow as supervision. We overcome the major challenge with respect to the computationally inefficiency of enforcing the flow constraints to the backward deformation field, used by deformable NeRFs. Specifically, w…
Characterizing the remarkable generalization properties of over-parameterized neural networks remains an open problem. A growing body of recent literature shows that the bias of stochastic gradient descent (SGD) and architecture choice implicitly leads to better generalization. In this paper, we sho…
We introduce a general theoretical framework, designed for the study of gradient optimisation of deep neural networks, that encompasses ubiquitous architecture choices including batch normalisation, weight normalisation and skip connections. Our framework determines the curvature and regularity pro…
We show that typical implicit regularization assumptions for deep neural networks (for regression) do not hold for coordinate-MLPs, a family of MLPs that are now ubiquitous in computer vision for representing high-frequency signals. Lack of such implicit bias disrupts smooth interpolations between t…