Quantum-inspired benchmark for Intrinsic Dimension Estimation

ICLR 2026 Conference Submission19488 Authors

Keywords: benchmark, intrinsic dimension estimation, quantum-inspired, manifold hypothesis

TL;DR: We propose a new benchmark for intrinsic dimension estimation techniques inspired from quantum information theory and demonstrate its advantages against existing benchmarks.

Abstract: Machine learning models can generalize well on real-world datasets. According to the manifold hypothesis, this is possible because datasets lie on a latent manifold with small intrinsic dimension (ID). There exist many methods for ID estimation (IDE), but their estimates vary substantially. This warrants benchmarking IDE methods on manifolds that are more complex than those in existing benchmarks. We propose a Quantum-Inspired Intrinsic-dimension Estimation (QuIIEst) benchmark consisting of infinite families of topologically non-trivial manifolds with known ID. Our benchmark stems from a quantum-optical method of embedding arbitrary homogeneous spaces while allowing for curvature modification and additive noise. The IDE methods tested were generally less accurate on QuIIEst manifolds than on existing benchmarks under identical resource allocation. We also observe minimal performance degradation with increasingly non-uniform curvature, underscoring the benchmark’s inherent difficulty.

Primary Area: datasets and benchmarks

Submission Number: 19488