NS-ATTENTION: Newton-Schulz Transformations of Attention Outputs in Vision Transformers

Newton-Schulz (NS) iteration has recently been used in the Muon optimizer to transform update matrices during the training of large language models. Motivated by its spectral effect, we investigate applying NS directly to Transformer attention representations. We introduce Newton-Schulz Attention (NS-Attn.), a parameter-free transformation applied to the output of each attention head. Each head output is arranged as a feature-by-token matrix and normalized by its Frobenius norm. We then apply a finite NS polynomial step and restore the original norm. The objective is to reduce spectral concentration and increase effective rank before standard head merging and output projection. Across ViT and Swin on CIFAR-10 and CIFAR-100, NS-Attn. improves final-epoch accuracy in all 12 matched-seed comparisons, with mean gains of 0.25--0.83 percentage points. ViT ablations show higher mean accuracy with one iteration than with two. Spectral analysis further shows reduced leading-eigenvalue concentration and increased effective rank. These gains incur additional inference latency.