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arXiv · 2512.23410

High-Dimensional Search, Low-Dimensional Solution: Decoupling Optimization from Representation

Yusuf Kalyoncuoglu·Ratmir Miftachov
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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"

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Yusuf Kalyoncuoglu, Ratmir Miftachov. 2025-12-29. High-Dimensional Search, Low-Dimensional Solution: Decoupling Optimization from Representation. https://arxiv.org/abs/2512.23410

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