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

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.

Data Selection Through Iterative Self-Filtering for Vision-Language Settings

The availability of large amounts of clean data is paramount to training neural networks. However, at large scales, manual oversight is impractical, resulting in sizeable datasets that can be very noisy. Attempts to mitigate this obstacle to producing performant vision-language models have so far involved heuristics, curated reference datasets, and using pre-trained models. Here we propose a novel, bootstrapped method in which a CLIP model is trained on an evolving, self-selected dataset. This evolving dataset constitutes a balance of filtered, highly probable clean samples as well as diverse samples from the entire distribution. Our proposed Self-Filtering method iterates between training the model and selecting a subsequently improved data mixture. Training on vision-language datasets filtered by the proposed approach improves downstream performance without the need for additional data or pre-trained models.