13 accepted papers
Transformer-based diffusion models have demonstrated remarkable performance at generating high-quality samples. However, our theoretical understanding of the reasons for this success remains limited. For instance, existing models are typically trained by minimizing a denoising objective, which is eq…
Diffusion models are widely used for image editing tasks. Existing editing methods often design a representation manipulation procedure by curating an edit direction in the text embedding or score space. However, such a procedure faces a key challenge: overestimating the edit strength harms visual c…
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…
Deep learning-based classifiers are known to be vulnerable to adversarial attacks. Existing methods for defending against such attacks require adding a defense mechanism or modifying the learning procedure (e.g., by adding adversarial examples). This paper shows that for certain data distributions o…
Among many mysteries behind the success of deep networks lies the exceptional discriminative power of their learned representations as manifested by the intriguing Neural Collapse (NC) phenomenon, where simple feature structures emerge at the last layer of a trained neural network. Prior works on th…
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…
The problem of generating a perpetual dynamic scene from a single view is an important problem with widespread applications in augmented and virtual reality, and robotics. However, since dynamic scenes regularly change over time, a key challenge is to ensure that different generated views be consist…
The implicit bias of gradient-based training algorithms has been considered mostly beneficial as it leads to trained networks that often generalize well. However, Frei et al. (2023) show that such implicit bias can harm adversarial robustness. Specifically, they show that if the data consists of clu…
This paper studies the problem of training a two-layer ReLU network for binary classification using gradient flow with small initialization. We consider a training dataset with well-separated input vectors: Any pair of input data with the same label are positively correlated, and any pair with diffe…
Recent theoretical analyses of the convergence of gradient descent (GD) to a global minimum for over-parametrized neural networks make strong assumptions on the step size (infinitesimal), the hidden-layer width (infinite), or the initialization (spectral, balanced). In this work, we relax these assu…
In this paper, we analyze the convergence of gradient flow on a multi-layer linear model with a loss function of the form $f(W_1W_2\cdots W_L)$. We show that when $f$ satisfies the gradient dominance property, proper weight initialization leads to exponential convergence of the gradient flow to a gl…
Neural networks trained via gradient descent with random initialization and without any regularization enjoy good generalization performance in practice despite being highly overparametrized. A promising direction to explain this phenomenon is to study how initialization and overparametrization affe…
A challenge of pan/tilt/zoom (PTZ) camera networks for efficient and flexible visual monitoring is automated active network reconfiguration in response to environmental stimuli. In this paper, given an event/activity distribution over a convex environment, we propose a new provably correct reactive…