Gradient Boosting within a Single Attention Layer

Transformer attention computes a single softmax-weighted average over values -- a one-pass estimate that cannot correct its own errors. We introduce \emph{gradient-boosted attention}, which applies the principle of gradient boosting \emph{within} a single attention layer: a second attention pass, with its own learned projections, attends to the prediction error of the first and applies a gated correction. Under a squared reconstruction objective, the construction maps onto Friedman's gradient boosting machine, with each attention pass as a base learner and the per-dimension gate as the shrinkage parameter. We show that a single Hopfield-style update erases all query information orthogonal to the stored-pattern subspace, and that further iteration under local contraction can collapse distinct queries in the same region to the same fixed point. We also show that separate projections for the correction pass can recover residual information inaccessible to the shared-projection approach of Tukey's twicing. On a 10M-token subset of WikiText-103, gradient-boosted attention achieves a test perplexity of $67.9$ compared to $72.2$ for standard attention, $69.6$ for Twicing Attention, and $69.0$ for a parameter-matched wider baseline, with two rounds capturing most of the benefit.

Improving Out-of-Distribution Data Handling and Corruption Resistance via Modern Hopfield Networks

This study explores the potential of Modern Hopfield Networks (MHN) in improving the ability of computer vision models to handle out-of-distribution data. While current computer vision models can generalize to unseen samples from the same distribution, they are susceptible to minor perturbations such as blurring, which limits their effectiveness in real-world applications. We suggest integrating MHN into the baseline models to enhance their robustness. This integration can be implemented during the test time for any model and combined with any adversarial defense method. Our research shows that the proposed integration consistently improves model performance on the MNIST-C dataset, achieving a state-of-the-art increase of 13.84% in average corruption accuracy, a 57.49% decrease in mean Corruption Error (mCE), and a 60.61% decrease in relative mCE compared to the baseline model. Additionally, we investigate the capability of MHN to converge to the original non-corrupted data. Notably, our method does not require test-time adaptation or augmentation with corruptions, underscoring its practical viability for real-world deployment. (Source code publicly available at: https://github.com/salehsargolzaee/Hopfield-integrated-test)