Geometric perspectives on multi-input reservoir computing

A geometric framework for multi-input reservoir computing is developed. Channel-wise Gramians, principal angles, and a coupling index are used to characterise collapse, decoupling, and a nontrivial multimodal regime within a single recurrent system. Structured sparse input pathways are shown to realise this intermediate regime, and the analysis is extended to nonlinear tanh reservoirs through time-varying linearisations and local Gramians. CLIP-style contrastive experiments on synthetic paired features and on small paired data constructed from Flickr8k images by index alignment, together with a coupled chaotic benchmark based on two weakly interacting Lorenz systems, illustrate the three regimes. The results indicate that the nontrivial structured case yields a balanced internal multimodal geometry and competitive retrieval and multi-task prediction, while the proposed diagnostics provide an interpretable tool to analyse and design multi-input reservoir couplings.