82 citations · 246 across the 15 of their papers we have counts for
7 papers · 1 filter
There Will Be a Scientific Theory of Deep Learning
Jamie Simon, Daniel Kunin, Alexander Atanasov +11
In this paper, we make the case that a scientific theory of deep learning is emerging. By this we mean a theory which characterizes important properties and statistics of the train…
How Feature Learning Can Improve Neural Scaling Laws
Blake Bordelon, Alexander Atanasov, Cengiz Pehlevan
We develop a solvable model of neural scaling laws beyond the kernel limit. Theoretical analysis of this model shows how performance scales with model size, training time, and the…
Risk and cross validation in ridge regression with correlated samples
Alexander Atanasov, Jacob A. Zavatone-Veth, Cengiz Pehlevan
Recent years have seen substantial advances in our understanding of high-dimensional ridge regression, but existing theories assume that training examples are independent. By lever…
Scaling and renormalization in high-dimensional regression
Alexander Atanasov, Jacob A. Zavatone-Veth, Cengiz Pehlevan
From benign overfitting in overparameterized models to rich power-law scalings in performance, simple ridge regression displays surprising behaviors sometimes thought to be limited…
A Dynamical Model of Neural Scaling Laws
Blake Bordelon, Alexander Atanasov, Cengiz Pehlevan
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is k…
The Onset of Variance-Limited Behavior for Networks in the Lazy and Rich Regimes
Alexander Atanasov, Blake Bordelon, Sabarish Sainathan +1
For small training set sizes , the generalization error of wide neural networks is well-approximated by the error of an infinite width neural network (NN), either in the kernel…
Neural Networks as Kernel Learners: The Silent Alignment Effect
Alexander Atanasov, Blake Bordelon, Cengiz Pehlevan
Neural networks in the lazy training regime converge to kernel machines. Can neural networks in the rich feature learning regime learn a kernel machine with a data-dependent kernel…