Recursive Feature Machines (RFMs) are a class of kernel machines that utilize the Average Gradient Outer Product (AGOP) as a mechanism for feature learning. They have been shown to effectively replicate the learning dynamics and feature representations of Feedforward Neural Networks (FNNs) across various settings. However, despite comparable capacity for feature learning and the similarities in the features they acquire, RFMs exhibit significantly lower performance than neural networks in certain data-corrupted scenarios. In this work, we investigate these limitations in mathematical problems. As a solution, we introduce a remarkably effective transformation applied to the training labels which promotes learning in noisy, complexly represented, and class-imbalanced data. This simple yet powerful adjustment enables RFMs to close the performance gap with FNNs and, in some cases, even surpass them.
Neural network verification and data privacy are inherently in tension: verification demands full access to model parameters and input data, yet both are increasingly restricted by privacy regulations and intellectual property constraints. This tension has left robustness verific…
Symmetry is everywhere in nature and society. Geometric deep learning exploits symmetries in data to improve the performance and efficiency of deep learning systems. In this paper, we extend geometric deep learning to utilize richer symmetry structures. Specifically, we develop o…
The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error. However, the uniqueness of such neural network representations is not guaranteed, ra…
Understanding how performance scales jointly with model size and data is a central problem in modern machine learning. Existing theoretical works on scaling laws typically describe generalization as a function of data or compute, often in fixed-feature or infinite-width regimes a…
The application of graph data in numerous disciplines raises the need for gathering and analyzing huge volumes of data, some of which is private and sensitive. The non-Euclidean nature of the graph data makes the analysis computationally challenging, leading to the use of Graph N…
Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when ge…