K-Inverse-RFM: A Modified RFM that Bridges the Gap to Neural Networks for Data-Corrupted Mathematical Tasks

Abstract: 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.