{"ID":2882794,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.09787","arxiv_id":"2508.09787","title":"Prototype Training with Dual Pseudo-Inverse and Optimized Hidden Activations","abstract":"We present Proto-PINV+H, a fast training paradigm that combines closed-form weight computation with gradient-based optimisation of a small set of synthetic inputs, soft labels, and-crucially-hidden activations. At each iteration we recompute all weight matrices in closed form via two (or more) ridge-regularised pseudo-inverse solves, while updating only the prototypes with Adam. The trainable degrees of freedom are thus shifted from weight space to data/activation space. On MNIST (60k train, 10k test) and Fashion-MNIST (60k train, 10k test), our method reaches 97.8% and 89.3% test accuracy on the official 10k test sets, respectively, in 3.9s--4.5s using approximately 130k trainable parameters and only 250 epochs on an RTX 5060 (16GB). We provide a multi-layer extension (optimised activations at each hidden stage), learnable ridge parameters, optional PCA/PLS projections, and theory linking the condition number of prototype matrices to generalisation. The approach yields favourable accuracy--speed--size trade-offs against ELM, random-feature ridge, and shallow MLPs trained by back-propagation.","short_abstract":"We present Proto-PINV+H, a fast training paradigm that combines closed-form weight computation with gradient-based optimisation of a small set of synthetic inputs, soft labels, and-crucially-hidden activations. At each iteration we recompute all weight matrices in closed form via two (or more) ridge-regularised pseudo-...","url_abs":"https://arxiv.org/abs/2508.09787","url_pdf":"https://arxiv.org/pdf/2508.09787v1","authors":"[\"Mauro Tucci\"]","published":"2025-08-13T13:13:32Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}