{"ID":2824314,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.23410","arxiv_id":"2512.23410","title":"High-Dimensional Search, Low-Dimensional Solution: Decoupling Optimization from Representation","abstract":"State-of-the-art models rely on massive widths despite exhibiting low Intrinsic Dimension (ID). We posit that this redundancy serves the non-convex optimization search rather than the final representation. We validate this hypothesis by decoupling the solution geometry via data-independent random projections, demonstrating that ResNet, ViT, and BERT representations can be compressed by up to 16x with negligible performance degradation of around 1%. Notably, these oblivious projections achieve parity with PCA and learned baselines, confirming the solution manifold is intrinsically robust. These findings establish the foundation for Subspace-Native Distillation: a paradigm where student models target this intrinsic manifold directly, bypassing the high-dimensional optimization bottleneck to realize the vision of \"Train Big, Deploy Small\"","short_abstract":"State-of-the-art models rely on massive widths despite exhibiting low Intrinsic Dimension (ID). We posit that this redundancy serves the non-convex optimization search rather than the final representation. We validate this hypothesis by decoupling the solution geometry via data-independent random projections, demonstra...","url_abs":"https://arxiv.org/abs/2512.23410","url_pdf":"https://arxiv.org/pdf/2512.23410v2","authors":"[\"Yusuf Kalyoncuoglu\",\"Ratmir Miftachov\"]","published":"2025-12-29T12:13:15Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[]","has_code":false}