Geometric perspectives on multi-input reservoir computing

Area of Science:

• Computational neuroscience
• Machine learning
• Complex systems

Background:

• Reservoir computing models complex dynamics using recurrent neural networks.
• Multi-input systems offer richer data processing but pose design challenges.
• Characterizing internal system dynamics is crucial for optimizing performance.

Purpose of the Study:

• Develop a geometric framework to analyze multi-input reservoir computing.
• Identify and characterize distinct operational regimes within recurrent systems.
• Investigate how structured input pathways influence system dynamics and performance.

Main Methods:

• Utilized channel-wise Gramians, principal angles, and a coupling index for geometric analysis.
• Extended analysis to nonlinear reservoirs via time-varying linearizations and local Gramians.
• Employed CLIP-style contrastive experiments and a coupled chaotic benchmark for validation.

Main Results:

• Characterized three regimes: collapse, decoupling, and a nontrivial multimodal regime.
• Demonstrated that structured sparse input pathways realize the intermediate multimodal regime.
• Showcased balanced internal multimodal geometry and competitive retrieval/prediction in the structured case.

Conclusions:

• The developed geometric framework provides interpretable diagnostics for multi-input reservoir couplings.
• Structured input pathways are key to achieving a balanced multimodal internal geometry.
• The findings offer insights for designing and analyzing advanced reservoir computing systems.