Distributed Representations Enable Robust Multi-Timescale Symbolic Computation in Neuromorphic Hardware

TL;DR

The paper addresses the challenge of robust multi-timescale computation with recurrent spiking networks by embedding deterministic finite automata into RSNN dynamics using high-dimensional distributed representations from vector symbolic architectures. It introduces a one-shot learning scheme where each DFA state is stored as a fixed-point attractor via autoassociative terms and transitions are implemented as superimposed heteroassociative terms bound to input hypervectors; masking acts as an unbinding operation to trigger transitions. The approach is validated across simulations with noisy weights, a closed-loop memristive crossbar hardware setup, and a large-scale Loihi 2 implementation, showing scalability and robustness without heavy hardware-specific tuning. Capacity analyses reveal quadratic scaling with network size, confirming that distributed representations provide a robust, hardware-friendly abstraction for embedding symbolic computation in neuromorphic hardware, potentially enabling cross-platform cognitive algorithms.

Abstract

Programming recurrent spiking neural networks (RSNNs) to robustly perform multi-timescale computation remains a difficult challenge. To address this, we describe a single-shot weight learning scheme to embed robust multi-timescale dynamics into attractor-based RSNNs, by exploiting the properties of high-dimensional distributed representations. We embed finite state machines into the RSNN dynamics by superimposing a symmetric autoassociative weight matrix and asymmetric transition terms, which are each formed by the vector binding of an input and heteroassociative outer-products between states. Our approach is validated through simulations with highly nonideal weights; an experimental closed-loop memristive hardware setup; and on Loihi 2, where it scales seamlessly to large state machines. This work introduces a scalable approach to embed robust symbolic computation through recurrent dynamics into neuromorphic hardware, without requiring parameter fine-tuning or significant platform-specific optimisation. Moreover, it demonstrates that distributed symbolic representations serve as a highly capable representation-invariant language for cognitive algorithms in neuromorphic hardware.

Figures (15)

• Figure 1: An RSNN performing a walk on a 23-state DFA, using noisy 1-bit weights. a) The embedded DFA. If a binary number is input most-significant-bit first, the final state indicates the result of the input $\mathrm{mod} \: \: 23$. b) The symbolic input to the RSNN. c) The input vector to the RSNN at any time, which each masks out half of the neurons therein. Each different input $s$ corresponds to a different hypervector $\mathbf{\bm{s}}$. Only the first 64 neurons are shown. d) A spike raster plot of activity within the RSNN. When the input to the network is constant, the network stabilises in an attractor state. When the input changes, some blocks are masked out or revealed, which may cause transitions to a new attractor state. The block-WTA mechanism ensures that only one neuron is persistently active in each block. e) The kernel-filtered mean firing rate of the neurons active in the attractor states $\mathbf{\bm{q}}_0, \ldots , \mathbf{\bm{q}}_{22}$, as well as the transition-facilitating bridge states $\mathbf{\bm{b}}_0, \ldots , \mathbf{\bm{b}}_{22}$. The bridge states are represented by dashed lines and coloured the same as their corresponding $q$ attractor states. We here serially input the number 68 in binary format, and the RSNN correctly halts in the $q_{22}$ state. f) The same RSNN is given different sequences of inputs, and the RSNN performs the correct walk between attractor states in all cases.
• Figure 2: The simulated RSNN with an irregular input timing scheme. a) The symbolic input to the network. Inputs were given for between 200ms and 1000ms. b) The corresponding input hypervector masking the neurons. c) A raster plot of spike activity in the RSNN. d) The mean firing rate of the neurons in each attractor state. The network is not reliant on an exact input timing scheme to perform the correct sequence of transitions. There is however still a minimum duration for which an input (or lack thereof) must be given, determined by the synaptic time constant.
• Figure 3: The closed-loop experimental setup for running the RSNN using the 4K RRAM system. a) A simplified schematic of the 64-neuron RSNN. b) The physical RRAM measurement system, containing an FPGA board, three DAC boards, and one ADC board. c) The scheme of running the closed-loop experiment in which the LIF neurons are simulated on a PC. The FPGA board receives the control commands from the PC and operates all word-, source- and bit lines (WLs, SLs, BLs) of the RRAM chip in parallel. At each time step ($t_n$), the spikes generated by the neurons are sent to the synapse array on WLs, which are represented by voltage pulses. Meanwhile, a 0.2V read voltage is applied to the SLs. The postsynaptic currents ($I_{t_n}$) produced by the RRAM cells accumulate on each BL, and the readout results are returned to the PC through the ADCs and FPGA.
• Figure 4: A 4-state DFA embedded into an RSNN using a memristive crossbar with 64$\times$64 RRAM devices as the synaptic weights. The DFA is described by $q_0 \overset{s}{\rightarrow} q_1 \overset{s}{\rightarrow} q_2 \overset{s}{\rightarrow} q_3 \overset{s}{\rightarrow} q_0$ for a single input $s$. a) The ternary weight matrix to be written to the RRAM crossbar, and a histogram of the values. b) Readout currents from each of the 64$\times$64 RRAM devices after programming, and separate histograms for each of the ternary weight values. There is notable mismatch between the measured currents and the ideal values; a row of faulty devices giving almost no current; and devices giving anomalously large currents. c) The masking input to the network. d) A spike raster plot of the neurons within the RSNN. Due to the size constraints introduced by the crossbar, we chose the attractor hypervectors $\mathbf{\bm{q}}$ to be orthogonal rather than random. e) Measured postsynaptic current readings from whenever a neuron in the second block spiked, chosen for the prominence of trial-to-trial current variation. The weights between neurons in the same block were programmed to the lowest weight, hence the horizontal band of low currents. At some times, multiple neurons fired within the same time step (labelled by $\ast$). f) The mean firing rates of the neurons in each attractor state. Despite the considerable nonidealities present, the RSNN performs the correct walk between attractor states.
• Figure 5: The 23-state DFA on Intel's asynchronous digital neuromorphic research chip, Loihi 2. a) The input symbol to the network at any time, and b) the corresponding input vectors, which mask the network activity. c) A spike raster plot of the first 64 neurons. The shunting-inhibition WTA mechanism ensures that only one neuron in every block may spike at once (see Methods). d) Kernel firing-rate estimates of each $q$ and $b$ state, choosing arbitrarily that 1 time step on Loihi represents 1ms. The sequence of inputs given corresponds to the binary representation of the number 92. The RSNN halts in the $q_0$ state, indicating correctly that 92 is divisible by 23. e) For all sequences of inputs, the correct walk between attractor states is performed.