Prospective Messaging: Learning in Networks with Communication Delays

TL;DR

The paper tackles the problem of inter-neuron communication delays hindering learning in continuous-time neural networks (CTNNs) and neuromorphic hardware. It introduces prospective messaging (PM), a neuron-local delay-compensation strategy that predicts future signals from past observations, implemented in two forms: linear extrapolation and neural-network-based PM, within Latent Equilibrium (LE) networks. Empirical results on Fourier synthesis and autoregressive video prediction show that PM restores learning performance across diverse delays, architectures, and tasks, with NN-based PM providing robustness at the cost of higher memory and computation. The work offers a general, biologically plausible approach to scaling delay-prone CTNNs and informs future developments in neuromorphic computing and online learning under communication constraints.

Abstract

Inter-neuron communication delays are ubiquitous in physically realized neural networks such as biological neural circuits and neuromorphic hardware. These delays have significant and often disruptive consequences on network dynamics during training and inference. It is therefore essential that communication delays be accounted for, both in computational models of biological neural networks and in large-scale neuromorphic systems. Nonetheless, communication delays have yet to be comprehensively addressed in either domain. In this paper, we first show that delays prevent state-of-the-art continuous-time neural networks called Latent Equilibrium (LE) networks from learning even simple tasks despite significant overparameterization. We then propose to compensate for communication delays by predicting future signals based on currently available ones. This conceptually straightforward approach, which we call prospective messaging (PM), uses only neuron-local information, and is flexible in terms of memory and computation requirements. We demonstrate that incorporating PM into delayed LE networks prevents reaction lags, and facilitates successful learning on Fourier synthesis and autoregressive video prediction tasks.

Figures (13)

• Figure 1: A three-neuron circuit with delayed forward (blue) and backward (red) signals. Synapses are depicted as a coupling of an axon terminal and dendritic spine .
• Figure 2: (a) Signals propagating through a minimal three-neuron linear network with delays $\delta$. Arrows indicate the transmission of signals between variables being computed continuously through time. Each variable is local to one neuron, indicated by colouring. Red arrows emphasize two signals that converge on $w_1$ in order to compute the gradient with respect to that weight. (b) Gradient dynamics of weight $w_1$. Without delay, gradients converge to the loss minimizers, whereas gradients in the network with delays experience strong oscillations.
• Figure 3: Transmission of signals to neuron $j$ as hidden (a) and output (b) neuron in an LE network, for the computation of three states: activation and parameter velocities $\dot{u}_{j}(t)$ and $\dot{W}_{ji}(t)$, and error $e_j(t)$. The presynaptic neuron $i$ influences the activation dynamics of neuron $j$ and errors flow back from post-synaptic neuron $k$ or loss node $\mathcal{L}$. Weights are considered local to post-synaptic neurons. Dashed lines represent signals which we consider not to be local to the relevant value being computed, and are therefore delayed. In order to distinguish them from abstract signals (shown as arrows), synaptic connections are depicted as a coupling of an axon terminal and dendritic spine .
• Figure 4: Without PM, LE networks with 10-step delays cannot learn the simple two-componet Fourier synthesis task, despite significant overparameterization.
• Figure 5: Fourier synthesis of two sine waves. Predictions produced by LE without PM (orange), with LE-NN (blue) and with LE-Ex (green), and undelayed LE without PM (purple). (a) Final 1000 time steps of test period with 5-step communication delays. (b) When delays are increased from 5-steps to 10-steps, linear extrapolation induces high frequency oscillations.