Memristive-Friendly Hadamard Reservoir Computing: Structured, Multiplier-Free Recurrences at Scale

Reservoir Computing (RC) designs Recurrent Neural Networks around a fixed, i.e., untrained, recurrent layer, and is a natural candidate for neuromorphic hardware. Memristive-friendly reservoirs derive the neuron dynamics from memristive-device kinetics, but still rely on dense recurrent matrices, which are expensive to realize physically. In this paper, we replace the dense matrix with a structured orthogonal operator, built from sign diagonals, a permutation, and a fast Walsh-Hadamard transform. The operator is multiplier-free, requires $O(N)$ parameters and $O(N\log N)$ operations per step, and is never materialized as a matrix. We instantiate it in a standard and in a memristive-friendly Echo State Network, with one binary input connection per unit. Our mathematical analysis shows that exact orthogonality yields an echo state condition that is tight in the recurrent scaling, and a noise response that is predictable at design time. Moreover, the operator mixes the whole state in a single application. Experiments on twenty classification and seven regression benchmarks, at reservoir sizes up to $N = 8192$, show that the structured models match dense orthogonal reservoirs, and achieve better mean performance than the cycle reservoir by a margin that widens with size. Furthermore, we time the recurrent step on three hardware platforms, where it is up to $50\times$ faster than a dense product and $10^4\times$ smaller in memory. Finally, we ablate the operator and measure the response to noise, quantization, device mismatch and discrete faults.

Nanoparticle Networks for Neuromorphic Computing

Physical computing leverages complex dynamical systems for energy-efficient data processing. In this work, we present a neuromorphic architecture based on metallic nanoparticles interconnected by molecular junctions on a $\text{SiO}_2$/Si substrate. We demonstrate that surrounding static control electrodes transform this nanoparticle network from a passive reservoir into a tunable nonlinear dynamical system. By analyzing how these electrodes route simple one-dimensional voltage inputs into multidimensional signal responses, we establish three core design rules to maximize computational performance. First, operating near the system's cutoff frequency achieves an optimal balance between nonlinear charge tunneling and linear capacitive memory. Second, tuning the underlying $\text{SiO}_2$ thickness sets the electrostatic screening length and dictates the memory type. Thick oxide layers reduce the screening length, causing networks larger than this length to transition into a persistent, non-volatile-like regime. Conversely, networks smaller than the screening length exhibit only fading memory. Third, introducing structural disorder via heterogeneous molecular junctions overcomes inherent limits on expressivity. While a network's computational expressivity scales with its physical size, it is ultimately capped by the screening length. Breaking internal spatial symmetries with localized disorder bypasses this saturation, allowing control voltages to independently manipulate specific signal amplitudes and phases, universally maximizing performance for dynamic neuromorphic applications.