Hypergraph cycle method enhances detection of planted signals in noisy data
Hypergraph cycle enumeration for efficient inference of planted k-XOR with smooth trade-off
Data Structures and Algorithms
Summary
Detecting hidden patterns in complex noisy data can be hard. The authors developed a new method called hypergraph cycle enumeration (HCE) that helps find and recover specific hidden signals in complex datasets involving many relationships at once. They showed that this method works about as well as existing advanced techniques, sometimes better, and can be sped up using quantum computing. However, other quantum methods still have advantages in certain tough situations.
What this means in practice
- •For data security teams: Improve algorithms that decode encrypted information in the presence of noise by applying efficient signal recovery methods.
- •For quantum algorithm developers: Use the HCE framework combined with quantum walks to accelerate inference tasks on noisy hypergraphs.
Authors
Arman Babakhani, Enrico Fontana, Junhyung Lyle Kim, Shouvanik Chakrabarti, Ruslan Shaydulin
Abstract
We introduce hypergraph cycle enumeration (HCE), a simple spectral framework for detecting and recovering planted signals in noisy hypergraph inference problems. We study HCE on one representative problem from this class, namely planted noisy k-XOR, also known as sparse Learning Parity with Noise (LPN). Both theoretically and empirically, HCE achieves comparable recovery behavior to Kikuchi method, matching Kikuchi hierarchy. We identify parameter regimes where HCE outperforms Kikuchi method, showing that neither algorithm is universally better. We also show a subquadratic quantum speedup for HCE by replacing one of the algorithm's steps with a quantum walk. Our classical and quantum algorithms do not refute the quartic quantum speedup of quantum Kikuchi method, which remains valid for the practically relevant regime of large size and high noise strength.