12 accepted papers
It is a central challenge in deep learning to understand how neural networks learn representations. A leading approach is the Neural Feature Ansatz (NFA) (Radhakrishnan et al., 2024), a conjectured mechanism for how feature learning occurs. Although the NFA is empirically validated, it is an educate…
We study kernel regression with common rotation-invariant kernels on real datasets including CIFAR-5m, SVHN, and ImageNet. We give a theoretical framework that predicts learning curves (test risk vs. sample size) from only two measurements: the empirical data covariance matrix and an empirical polyn…
When a deep ReLU network is initialized with small weights, gradient descent (GD) is at first dominated by the saddle at the origin in parameter space. We study the so-called escape directions along which GD leaves the origin, which play a similar role as the eigenvectors of the Hessian for strict s…
What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dynamics of feature learning in two-layer networks trained from small initialization. Prior works have shown that gradient…
Self-supervised word embedding algorithms such as word2vec provide a minimal setting for studying representation learning in language modeling. We examine the quartic Taylor approximation of the word2vec loss around the origin, and we show that both the resulting training dynamics and the final perf…
We consider neural networks (NNs) where the final layer is down-scaled by a fixed hyperparameter $\gamma$. Recent work has identified $\gamma$ as controlling the strength of feature learning. As $\gamma$ increases, network evolution changes from "lazy" kernel dynamics to "rich" feature-learning dyn…
We study the cost of overfitting in noisy kernel ridge regression (KRR), which we define as the ratio between the test error of the interpolating ridgeless model and the test error of the optimally-tuned model. We take an ``agnostic'' view in the following sense: we consider the cost as a function o…
In our era of enormous neural networks, empirical progress has been driven by the philosophy that *more is better.* Recent deep learning practice has found repeatedly that larger model size, more data, and more computation (resulting in lower training loss) optimizing to near-interpolation improves…
We present a simple picture of the training process of self-supervised learning methods with dual deep networks. In our picture, these methods learn their high-dimensional embeddings one dimension at a time in a sequence of discrete, well-separated steps. We arrive at this picture via the study of a…
Despite impressive successes, deep reinforcement learning (RL) systems still fall short of human performance on generalization to new tasks and environments that differ from their training. As a benchmark tailored for studying RL generalization, we introduce Avalon, a set of tasks in which embodied…
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…
Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit many strange and potentially undesirable behaviors. Specificall…