10 accepted papers
Conditioning unconditional diffusion models typically requires either retraining with conditional inputs or per-step gradient computations (e.g., classifier-based guidance), both of which incur substantial computational overhead. We present a general recipe for efficiently steering unconditional dif…
Modern machine learning paradigms, such as deep learning, occur in or close to the interpolation regime, wherein the number of model parameters is much larger than the number of data samples. In this work, we propose a regularity condition within the interpolation regime which endows the stochastic…
We consider the problem of optimization of deep learning models with smooth activation functions. While there exist influential results on the problem from the ``near initialization'' perspective, we shed considerable new light on the problem. In particular, we make two key technical contributions f…
Modern neural networks often have great expressive power and can be trained to overfit the training data, while still achieving a good test performance. This phenomenon is referred to as “benign overfitting”. Recently, there emerges a line of works studying “benign overfitting” from the theoretical…
The practical success of overparameterized neural networks has motivated the recent scientific study of \emph{interpolating methods}-- learning methods which are able fit their training data perfectly. Empirically, certain interpolating methods can fit noisy training data without catastrophically ba…
In this paper we show that feedforward neural networks corresponding to arbitrary directed acyclic graphs undergo transition to linearity as their ``width'' approaches infinity. The width of these general networks is characterized by the minimum in-degree of their neurons, except for the input and f…
Wide neural networks with linear output layer have been shown to be near-linear, and to have near-constant neural tangent kernel (NTK), in a region containing the optimization path of gradient descent. These findings seem counter-intuitive since in general neural networks are highly complex models.…
This paper explores the generalization loss of linear regression in variably parameterized families of models, both under-parameterized and over-parameterized. We show that the generalization curve can have an arbitrary number of peaks, and moreover, the locations of those peaks can be explicitly co…
Modern machine learning systems such as deep neural networks are often highly over-parameterized so that they can fit the noisy training data exactly, yet they can still achieve small test errors in practice. In this paper, we study this "benign overfitting" phenomenon of the maximum margin classifi…
The goal of this work is to shed light on the remarkable phenomenon of "transition to linearity" of certain neural networks as their width approaches infinity. We show that the "transition to linearity'' of the model and, equivalently, constancy of the (neural) tangent kernel (NTK) result from the s…