Optimal noise level for coding with tightly balanced networks of spiking neurons in the presence of transmission delays.

Neural circuits consist of many noisy, slow components, with individual neurons subject to ion channel noise, axonal propagation delays, and unreliable and slow synaptic transmission. This raises a fundamental question: how can reliable computation emerge from such unreliable components? A classic strategy is to simply average over a population of N weakly-coupled neurons to achieve errors that scale as [Formula: see text]. But more interestingly, recent work has introduced networks of leaky integrate-and-fire (LIF) neurons that achieve coding errors that scale superclassically as 1/N by combining the principles of predictive coding and fast and tight inhibitory-excitatory balance. However, spike transmission delays preclude such fast inhibition, and computational studies have observed that such delays can cause pathological synchronization that in turn destroys superclassical coding performance. Intriguingly, it has also been observed in simulations that noise can actually improve coding performance, and that there exists some optimal level of noise that minimizes coding error. However, we lack a quantitative theory that describes this fascinating interplay between delays, noise and neural coding performance in spiking networks. In this work, we elucidate the mechanisms underpinning this beneficial role of noise by deriving analytical expressions for coding error as a function of spike propagation delay and noise levels in predictive coding tight-balance networks of LIF neurons. Furthermore, we compute the minimal coding error and the associated optimal noise level, finding that they grow as power-laws with the delay. Our analysis reveals quantitatively how optimal levels of noise can rescue neural coding performance in spiking neural networks with delays by preventing the build up of pathological synchrony without overwhelming the overall spiking dynamics. This analysis can serve as a foundation for the further study of precise computation in the presence of noise and delays in efficient spiking neural circuits.

Optimised weight programming for analogue memory-based deep neural networks.

Analogue memory-based deep neural networks provide energy-efficiency and per-area throughput gains relative to state-of-the-art digital counterparts such as graphics processing units. Recent advances focus largely on hardware-aware algorithmic training and improvements to circuits, architectures, and memory devices. Optimal translation of software-trained weights into analogue hardware weights-given the plethora of complex memory non-idealities-represents an equally important task. We report a generalised computational framework that automates the crafting of complex weight programming strategies to minimise accuracy degradations during inference, particularly over time. The framework is agnostic to network structure and generalises well across recurrent, convolutional, and transformer neural networks. As a highly flexible numerical heuristic, the approach accommodates arbitrary device-level complexity, making it potentially relevant for a variety of analogue memories. By quantifying the limit of achievable inference accuracy, it also enables analogue memory-based deep neural network accelerators to reach their full inference potential.