Learning to process with spikes and to localise pulses

Abstract

In the last few decades, deep learning with artificial neural networks (ANNs) has emerged as one of the most widely used techniques in tasks such as classification and regression, achieving competitive results and in some cases even surpassing human-level performance. Nonetheless, as ANN architectures are optimised towards empirical results and departed from their biological precursors, how exactly human brains process information using these short electrical pulses called spikes remains a mystery. Hence, in this thesis, we explore the problem of learning to process with spikes and to localise pulses. We first consider spiking neural networks (SNNs), a type of ANN that more closely mimic biological neural networks in that neurons communicate with one another using spikes. This unique architecture allows us to look into the role of heterogeneity in learning. Since it is conjectured that the information is encoded by the timing of spikes, we are particularly interested in the heterogeneity of time constants of neurons. We then trained SNNs for classification tasks on a range of visual and auditory neuromorphic datasets, which contain streams of events (spike times) instead of the conventional frame-based data, and show that the overall performance is improved by allowing the neurons to have different time constants, especially on tasks with richer temporal structure. We also find that the learned time constants are distributed similarly to those experimentally observed in some mammalian cells. Besides, we demonstrate that learning with heterogeneity improves robustness against hyperparameter mistuning. These results suggest that heterogeneity may be more than the byproduct of noisy processes and perhaps serves a key role in learning in changing environments, yet heterogeneity has been overlooked in basic artificial models. While neuromorphic datasets, which are often captured by neuromorphic devices that closely model the corresponding biological systems, have enabled us to explore the more biologically plausible SNNs, there still exists a gap in understanding how spike times encode information in actual biological neural networks like human brains, as such data is difficult to acquire due to the trade-off between the timing precision and the number of cells simultaneously recorded electrically. Instead, what we usually obtain is the low-rate discrete samples of trains of filtered spikes. Hence, in the second part of the thesis, we focus on a different type of problem involving pulses, that is to retrieve the precise pulse locations from these low-rate samples. We make use of the finite rate of innovation (FRI) sampling theory, which states that perfect reconstruction is possible for classes of continuous non-bandlimited signals that have a small number of free parameters. However, existing FRI methods break down under very noisy conditions due to the so-called subspace swap event. Thus, we present two novel model-based learning architectures: Deep Unfolded Projected Wirtinger Gradient Descent (Deep Unfolded PWGD) and FRI Encoder-Decoder Network (FRIED-Net). The former is based on the existing iterative denoising algorithm for subspace-based methods, while the latter models directly the relationship between the samples and the locations of the pulses using an autoencoder-like network. Using a stream of K Diracs as an example, we show that both algorithms are able to overcome the breakdown inherent in the existing subspace-based methods. Moreover, we extend our FRIED-Net framework beyond conventional FRI methods by considering when the shape is unknown. We show that the pulse shape can be learned using backpropagation. This coincides with the application of spike detection from real-world calcium imaging data, where we achieve competitive results. Finally, we explore beyond canonical FRI signals and demonstrate that FRIED-Net is able to reconstruct streams of pulses with different shapes.Open Acces