Kernel method improves measuring computation in dynamical systems
Efficiently and Reliably Measuring Information Processing Capacity in Dynamical Systems via Kernels
Information Theory
Summary
Measuring how well systems process information is important but can be very slow and complicated using current methods. This paper introduces a new approach called Kernel-IPC that uses mathematical kernel techniques to efficiently measure a system’s ability to process information without complex calculations. The method can consider all possible patterns without cutting off at a certain complexity level. The authors tested it on artificial and quantum systems to show it works well.
What this means in practice
- •For quantum computing teams: Evaluate and compare quantum reservoir systems’ computational power more efficiently without degree-limited approximations.
- •For machine learning engineers: Assess information processing capabilities of recurrent neural networks using scalable kernel-based techniques.
Authors
Alessio Benavoli, Felix Binder, Cangxiong Chen
Abstract
Information Processing Capacity (IPC) is a powerful system-agnostic metric for quantifying a dynamical system's computational capability and is widely used in quantum reservoir computing. However, standard IPC suffers from severe computational limitations. Computing IPC involves estimating how well the system can reconstruct, via linear regression, an (in principle) infinite family of orthogonal polynomial functions of delayed inputs. In practice, this evaluation must be made finite, so we need only to consider polynomials up to a chosen maximum degree. Moreover, the computational complexity for computing IPC grows combinatorially with the considered maximum degree and delay. Here, we introduce Kernel-IPC (KIPC), a scalable framework that uses kernel methods to compute the total IPC without explicitly enumerating basis functions. This allows us to account for the full (infinite) basis (without degree truncation). We also provide a null-hypothesis test for statistically comparing the KIPC of two dynamical systems. We validate KIPC on an echo state network and demonstrate its utility for quantum reservoir computing on a disordered spin chain.