Empirical Echo State Capacity Floors in Multimodal Liquid State Machines

This preprint delivers the first systematic, cross-modal empirical demonstration that Liquid State Machines (LSMs) operating at the commonly assumed neuromorphic scale of **N = 256** units exhibit a hard functional capacity floor: they are incapable of outperforming simple temporal baselines across biologically realistic sensory modalities. Using a rigorous dual-baseline protocol — (BL1) single-frame random projection and (BL5) 5-frame mean-pooling — we evaluated un-tuned LSMs (non-linear leaky integrators, τₘ = 15 ms, spectral radius α ∈ 0. 50, 0. 99) on three independent, modality-specific benchmarks under controlled noise regimes (0. 0–0. 30): • **V1 Visual** – frame-by-frame 2D Gabor classification • **A1 Auditory** – theta-gamma nested sequence discrimination • **S1 Haptic** – continuous beta-band force trajectory regression Across 5 identically-seeded macroscopic trials per condition, the N = 256 reservoir produced **zero statistically significant performance gain** over the naive temporal mean-pooling baseline (gap ≤ 0 everywhere, p > 0. 10). While qualitative α preferences differed by task (stable α ≈ 0. 60 for smooth regression; higher chaos for categorical tasks), the quantitative echo-state capacity was universally exhausted — the reservoir could not preserve more distinguishable temporal trajectories than a simple moving average. **Core Conclusion: ** Near-critical reservoir advantages do not emerge unconditionally below a structural scale threshold. We establish an **empirical minimum specification of N ≥ 1024** for any spatial topology relying on reservoir mechanics in neuromorphic or continuous-time implementations. **Relation to Prior Work** This capacity-floor result supplies the critical scaling invariant required to justify the liquid-dynamics substrate employed throughout the RDLNN architecture. It directly constrains the reservoir dimensions used in the multi-module system presented in: **Biologically-Constrained Modular Active Inference: A Functional Architecture from Trace to Gating** and is mechanistically enabled by the module-specific β-parameterisation proven necessary in: **Dual-Component Eligibility Traces: Structural Necessity of β-Parameterisation in Modular Neuromorphic Systems** All three works instantiate core components of the unified neural substrate previously released as: **NeuroForge: A Unified Neural Substrate for Scalable Biological AI** (https: //doi. org/10. 5281/zenodo. 17622945) **This paper forms part of a series. The integrated architecture paper "Biologically-Constrained Modular Active Inference: A Functional Architecture from Trace to Gating (RDLNN v1. 0) " is available at https: //doi. org/10. 5281/zenodo. 19186955 **This paper forms part of a series. The "Dual-Component Eligibility Traces: Structural Necessity of β-Parameterisation in Modular Neuromorphic Systems" at https: //doi. org/10. 5281/zenodo. 19189919 **Additional Notes for Zenodo: ** • Preprint (March 2026) – fully reproducible with dual-baseline protocol, seeded trials, noise sweeps, and statistical reporting. • Figure 1 (A1 accuracy curves showing LSM ≤ BL5 across all α and noise levels) included in the PDF. • Provides the grounded architectural floor specification for reservoir layers in any biologically-constrained neuromorphic blueprint. This work closes a critical gap between theoretical reservoir universality and practical neuromorphic deployment by proving that macroscopic dimension scaling is not optional but a hard prerequisite for liquid-state computational advantage.