Runoff on rooted trees

We introduce an idealised model for overland flow generated by rain falling on a hill-slope. Our prime motivation is to show how the coalescence of runoff streams promotes the total generation of runoff. We show that, for our model, as the rate of rainfall increases in relation to the soil infiltration rate, there is a distinct phase-change. For low rainfall (the subcritical case) only the bottom of the hill-slope contributes to the total overland runoff, while for high rainfall (the supercritical case) the whole slope contributes and the total runoff increases dramatically. We identify the critical point at which the phase-change occurs, and show how it depends on the degree of coalescence. When there is no stream coalescence the critical point occurs when the rainfall rate equals the average infiltration rate, but when we allow coalescence the critical point occurs when the rainfall rate is less than the average infiltration rate, and increasing the amount of coalescence increases the total expected runoff

Photonic Spiking Neural Networks with Highly Efficient Training Protocols for Ultrafast Neuromorphic Computing Systems

Photonic technologies offer great prospects for novel ultrafast, energy-efficient and hardware-friendly neuromorphic (brain-like) computing platforms. Moreover, neuromorphic photonic approaches based upon ubiquitous, technology-mature and low-cost Vertical-Cavity Surface Emitting Lasers (VCSELs) (devices found in fibre-optic transmitters, mobile phones, automotive sensors, etc.) are of particular interest. Given VCSELs have shown the ability to realise neuronal optical spiking responses (at ultrafast GHz rates), their use for spike-based information processing systems has been proposed. In this work, Spiking Neural Network (SNN) operation, based on a hardware-friendly photonic system of just one Vertical Cavity Surface Emitting Laser (VCSEL), is reported alongside a novel binary weight 'significance' training scheme that fully capitalises on the discrete nature of the optical spikes used by the SNN to process input information. The VCSEL-based photonic SNN is tested with a highly complex, multivariate, classification task (MADELON) before performance is compared using a traditional least-squares training method and the alternative novel binary weighting scheme. Excellent classification accuracies of >94% are reached by both training methods, exceeding the benchmark performance of the dataset in a fraction of processing time. The newly reported training scheme also dramatically reduces training set size requirements as well as the number of trained nodes (<1% of the total network node count). This VCSEL-based photonic SNN, in combination with the reported 'significance' weighting scheme, therefore grants ultrafast spike-based optical processing with highly reduced training requirements and hardware complexity for potential application in future neuromorphic systems and artificial intelligence applications

MaWGAN: a generative adversarial network to create synthetic data from datasets with missing data

The creation of synthetic data are important for a range of applications, for example, to anonymise sensitive datasets or to increase the volume of data in a dataset. When the target dataset has missing data, then it is common to just discard incomplete observations, even though this necessarily means some loss of information. However, when the proportion of missing data are large, discarding incomplete observations may not leave enough data to accurately estimate their joint distribution. Thus, there is a need for data synthesis methods capable of using datasets with missing data, to improve accuracy and, in more extreme cases, to make data synthesis possible. To achieve this, we propose a novel generative adversarial network (GAN) called MaWGAN (for masked Wasserstein GAN), which creates synthetic data directly from datasets with missing values. As with existing GAN approaches, the MaWGAN synthetic data generator generates samples from the full joint distribution. We introduce a novel methodology for comparing the generator output with the original data that does not require us to discard incomplete observations, based on a modification of the Wasserstein distance and easily implemented using masks generated from the pattern of missing data in the original dataset. Numerical experiments are used to demonstrate the superior performance of MaWGAN compared to (a) discarding incomplete observations before using a GAN, and (b) imputing missing values (using the GAIN algorithm) before using a GA

GHz rate neuromorphic photonic spiking neural network with a single Vertical-Cavity Surface-Emitting Laser (VCSEL)

Vertical-Cavity Surface-Emitting Lasers (VCSELs) are highly promising devices for the construction of neuro- morphic photonic information processing systems, due to their numerous desirable properties such as low power consumption, high modulation speed, and compactness. Of particular interest is the ability of VCSELs to exhibit neuron-like spiking responses at ultrafast sub-nanosecond rates; thus offering great prospects for high-speed light-enabled spike-based processors. Recent works have shown spiking VCSELs are capable of pattern recognition and image processing problems, but additionally, VCSELs have been used as nonlinear elements in photonic reservoir comput- ing (RC) implementations, yielding state of the art operation. This work introduces and experimentally demonstrates for the first time a new GHz-rate photonic spiking neural network (SNN) built with a single VCSEL neuron. The reported system effectively implements a photonic VCSEL-based spiking reser- voir computer, and demonstrates its successful application to a complex nonlinear classification task. Importantly, the proposed system benefits from a highly hardware-friendly, inexpensive realization (a single VCSEL device and off-the-shelf fibre-optic components), for high-speed (GHz-rate inputs) and low-power (sub-mW optical input power) photonic operation. These results open new pathways towards future neuromorphic photonic spike- based processing systems based upon VCSELs (or other laser types) for novel ultrafast machine learning and AI hardware

Interconnected VCSEL-based photonic synapses for neuromorphic processsing architectures

Pairs of interconnected brain-inspired photonic synapses (connected in-parallel and in-series) are developed using Vertical Cavity Surface Emitting Lasers (VCSELs). We discuss the operation of each configuration and demonstrate their capability to perform different spike-based processing tasks including information encoding, temporal filtering, and Multiply-and-Accumulate (MAC) operations

Photonic neuromorphic computing with vertical cavity surface emitting lasers

Photonic approaches emulating the powerful computational capabilities of the brain are receiving increasing research interest for radically new paradigms in ultrafast information processing and Artificial Intelligence (AI). In this talk, I will review our research on neuromorphic photonic systems built with artificial optical neurons based upon Vertical-Cavity Surface Emitting Lasers (VCSELs). These are ubiquitous light-emitting optical devices found in mobile phones, supermarket barcode scanners, automotive sensors, optical transceivers in data centres, etc. Hence, there is great potential in adding intelligence and novel processing capabilities in key-enabling VCSELs for a wide range of novel technological developments. Our research has shown that a rich variety of neuronal computational features (e.g. spiking activation/inhibition) can be reproduced optically in VCSELs at ultrafast sub-nanosecond speeds (up to 9 orders of magnitude faster than the millisecond timescales in cortical neurons) [1-3]. During the talk I will describe how we capitalise on the ultrafast neural-like behaviours elicited in VCSELs to develop novel photonic spike-based processing systems for use in strategic applications (e.g. pattern recognition, image processing) and neuronal circuit emulation at ultrafast speeds [1-3]. This talk will also introduce our recent work on laser-based, Recurrent and Spiking Neural Networks (RNNs and SNNs) for novel VCSEL-based photonic Reservoir Computing (RC) systems, yielding excellent performance across complex computing tasks at ultrafast rates [4]. Finally, this talk will review our recent work on neuromorphic systems merging in the same platform VCSELs with key-enabling Resonant Tunnelling Diodes (RTDs), for novel ultrafast, low power spiking optoelectronic artificial neuronal models, towards future chip-scale SNN implementations of light-enabled brain-inspired computing and AI hardware [5]