Tensor Programs IVb: Adaptive Optimization in the Infinite-Width Limit
Going beyond stochastic gradient descent (SGD), what new phenomena emerge in wide neural networks trained by adaptive optimizers like Adam? Here we show: The same dichotomy between feature learning and kernel behaviors (as in SGD) holds for general optimizers as well, including Adam -- albeit with a nonlinear notion of "kernel." We derive the corresponding "neural tangent" and "maximal update" limits for any architecture. Two foundational advances underlie the above results: 1) A new Tensor Program language, NEXORT, that can express how adaptive optimizers process gradients into updates. 2) The introduction of bra-ket notation to drastically simplify expressions and calculations in Tensor Programs. This work summarizes and generalizes all previous results in the Tensor Programs series of papers.
Code (0)
등록된 구현이 없습니다.
Methods 이 논문이 사용한 방법론
Similar Papers 제목 키워드 기반
Tensor Programs IIb: Architectural Universality of Neural Tangent Kernel Training Dynamics
Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their …
Quantitative Gaussian-Process limits of Tensor Programs
We study the infinite-width Gaussian-process limit of random neural networks through the lens of tensor programs, and we provide a quantitative convergence theory in Wasserstein distance. Our main result gives explicit f…
Feature Learning in Infinite-Width Neural Networks
As its width tends to infinity, a deep neural network's behavior under gradient descent can become simplified and predictable (e.g. given by the Neural Tangent Kernel (NTK)), if it is parametrized appropriately (e.g. the…
Few-Shot LearningTransfer LearningTensor Programs VI: Feature Learning in Infinite-Depth Neural Networks
By classifying infinite-width neural networks and identifying the *optimal* limit, Tensor Programs IV and V demonstrated a universal way, called $\mu$P, for *widthwise hyperparameter transfer*, i.e., predicting optimal h…
DiversityEfficient Computation of Deep Nonlinear Infinite-Width Neural Networks that Learn Features
While a popular limit of infinite-width neural networks, the Neural Tangent Kernel (NTK) often exhibits performance gaps from finite-width neural networks on standard datasets, due to lack of feature learning. Although t…