# High-dimensional Optimization with Low Rank Tensor Sampling and Local Search

arXiv: https://arxiv.org/abs/2505.12383 · HTML: https://mlsanity.com/paper/2505.12383/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 May 2025.

## Built on by (most cited first, 1 of 1)

- [CrystalFormer-CSP: Thinking Fast and Slow for Crystal Structure Prediction](https://mlsanity.com/paper/2512.18251/) (2025)

## Abstract (arXiv)

We present a novel method called TESALOCS (TEnsor SAmpling and LOCal Search) for multidimensional optimization, combining the strengths of gradient-free discrete methods and gradient-based approaches. The discrete optimization in our method is based on low-rank tensor techniques, which, thanks to their low-parameter representation, enable efficient optimization of high-dimensional problems. For the second part, i.e., local search, any effective gradient-based method can be used, whether existing (such as quasi-Newton methods) or any other developed in the future. Our approach addresses the limitations of gradient-based methods, such as getting stuck in local optima; the limitations of discrete methods, which cannot be directly applied to continuous functions; and limitations of gradient-free methods that require large computational budgets. Note that we are not limited to a single type of low-rank tensor decomposition for discrete optimization, but for illustrative purposes, we consider a specific efficient low-rank tensor train decomposition. For 20 challenging 100-dimensional functions, we demonstrate that our method can significantly outperform results obtained with gradient-based methods like Conjugate Gradient, BFGS, SLSQP, and other methods, improving them by orders of magnitude with the same computing budget.