Waves and symbols in neuromorphic hardware: from analog signal processing to digital computing on the same computational substrate

TL;DR

This work addresses bridging analog signal processing and discrete symbol computation on a single neuromorphic substrate. It develops a mixed-feedback framework using recurrent spiking neural networks (rSNNs) to smoothly transition between analog processing and digital, symbolic operations, and provides both theoretical (dominant eigenstructure, monotone-system concepts) and hardware-backed validation. A key contribution is showing a pitchfork bifurcation controlled by a single parameter $\alpha$ that governs the analog-to-digital switch, with experimental demonstrations on sWTA hardware and a mixed-feedback neuromorphic processor. The findings demonstrate robust, low-power multifunctionality suitable for edge devices, and offer a path to graded symbolic representations on neuromorphic substrates even in the presence of device mismatch and noise.

Abstract

Neural systems use the same underlying computational substrate to carry out analog filtering and signal processing operations, as well as discrete symbol manipulation and digital computation. Inspired by the computational principles of canonical cortical microcircuits, we propose a framework for using recurrent spiking neural networks to seamlessly and robustly switch between analog signal processing and categorical and discrete computation. We provide theoretical analysis and practical neural network design tools to formally determine the conditions for inducing this switch. We demonstrate the robustness of this framework experimentally with hardware soft Winner-Take-All and mixed-feedback recurrent spiking neural networks, implemented by appropriately configuring the analog neuron and synapse circuits of a mixed-signal neuromorphic processor chip.

Figures (5)

• Figure 1: Recurrent Spiking Neural Network (rSNN) architectures. (\ref{['fig:sRNNnet']}) Generic mixed-feedback rSNN with input layer, recurrent pool of excitatory and inhibitory spiking neurons, and readout units that encode continuous time varying outputs; (\ref{['fig:position-wta']}) Specific rSNN architecture in which excitatory and inhibitory neurons have been arranged to form a sWTA network. Recurrent excitatory and inhibitory connections are shown only for one cluster.
• Figure 2: sWTA response properties measured from the neuromorphic chip. The different input signals are encoded as Poisson spike trains with constant firing rates (dots in black dashed lines). The mean firing rates of each cluster and their standard deviation are plotted as a solid line with vertical bars in blue. The shaded bars represent the average firing rate of each neuron in the network (inhibitory neurons not shown). In the top row, the network operates in analog signal processing mode. In the bottom row, the same network with the same inputs but different (higher) gain operates in the categorization mode.
• Figure 3: Faithful input representation ($\alpha=0.02$). First, two inputs A and B (blue and orange) are presented as 200Hz Poisson spike trains through either excitatory or inhibitory synapses (the excitatory inputs are highlighted with the coloured shading on the raster plot, inhibitory ones are omitted for clarity). The next two inputs are also A and B, but the firing rates are reduced to 100Hz. The last two inputs C and D (green and red) are orthogonal to the clusters. The thick gray trace in the top panel represents the network-averaged mean firing rate. The lower panel shows the alignment index traces $\rho_1(t) ... \rho_4(t)$ (coloured).
• Figure 4: Emergence of categorical representations ($\alpha = 0.1$). Symbols A and B are robustly preserved by the network, even in the case of lower amplitudes of input rates, while symbols C and D do not lead to a persistent state switch after the stimulus is removed.
• Figure 5: Empirical rSNN bifurcation diagram computed using mean firing rates and by projecting the resulting population vector of steady-state rates onto the dominant eigenvector ${\bf v}_{max}$. The colours indicate different initial conditions before the rate estimation is taken: stimulus A (blue), stimulus B (orange) or only background DC input (black). Each rate estimation was performed after the removal of the stimulus.