Scalable Digital Architecture of a Liquid State Machine

Liquid State Machine (LSM) is an adaptive neural computational model with rich dynamics to process spatio-temporal inputs. These machines are extremely fast in learning because the goal-oriented training is moved to the output layer, unlike conventional recurrent neural networks. The capability to multiplex at the output layer for multiple tasks makes LSM a powerful intelligent engine. These properties are desirable in several machine learning applications such as speech recognition, anomaly detection, user identification etc. Scalable hardware architectures for spatio-temporal signal processing algorithms like LSMs are energy efficient compared to the software implementations. These designs can also naturally adapt to dierent temporal streams of inputs. Early literature shows few behavioral models of LSM. However, they cannot process real time data either due to their hardware complexity or xed design approach. In this thesis, a scalable digital architecture of an LSM is proposed. A key feature of the architecture is a digital liquid that exploits spatial locality and is capable of processing real time data. The quality of the proposed LSM is analyzed using kernel quality, separation property of the liquid and Lyapunov exponent. When realized using TSMC 65nm technology node, the total power dissipation of the liquid layer, with 60 neurons, is 55.7 mW with an area requirement of 2 mm^2. The proposed model is validated for two benchmark. In the case of an epileptic seizure detection an average accuracy of 84% is observed. For user identification/authentication using gait an average accuracy of 98.65% is achieved

Photonic neuromorphic information processing and reservoir computing

Photonic neuromorphic computing is attracting tremendous research interest now, catalyzed in no small part by the rise of deep learning in many applications. In this paper, we will review some of the exciting work that has been going in this area and then focus on one particular technology, namely, photonic reservoir computing

Dynamical Systems in Spiking Neuromorphic Hardware

Dynamical systems are universal computers. They can perceive stimuli, remember, learn from feedback, plan sequences of actions, and coordinate complex behavioural responses. The Neural Engineering Framework (NEF) provides a general recipe to formulate models of such systems as coupled sets of nonlinear differential equations and compile them onto recurrently connected spiking neural networks – akin to a programming language for spiking models of computation. The Nengo software ecosystem supports the NEF and compiles such models onto neuromorphic hardware. In this thesis, we analyze the theory driving the success of the NEF, and expose several core principles underpinning its correctness, scalability, completeness, robustness, and extensibility. We also derive novel theoretical extensions to the framework that enable it to far more effectively leverage a wide variety of dynamics in digital hardware, and to exploit the device-level physics in analog hardware. At the same time, we propose a novel set of spiking algorithms that recruit an optimal nonlinear encoding of time, which we call the Delay Network (DN). Backpropagation across stacked layers of DNs dramatically outperforms stacked Long Short-Term Memory (LSTM) networks—a state-of-the-art deep recurrent architecture—in accuracy and training time, on a continuous-time memory task, and a chaotic time-series prediction benchmark. The basic component of this network is shown to function on state-of-the-art spiking neuromorphic hardware including Braindrop and Loihi. This implementation approaches the energy-efficiency of the human brain in the former case, and the precision of conventional computation in the latter case

Synaptic rewiring in neuromorphic VLSI for topographic map formation

A generalised model of biological topographic map development is presented which combines both weight plasticity and the formation and elimination of synapses (synaptic rewiring) as well as both activity-dependent and -independent processes. The question of whether an activity-dependent process can refine a mapping created by an activity-independent process is investigated using a statistical approach to analysingmapping quality. The model is then implemented in custom mixed-signal VLSI. Novel aspects of this implementation include: (1) a distributed and locally reprogrammable address-event receiver, with which large axonal fan-out does not reduce channel capacity; (2) an analogue current-mode circuit for Euclidean distance calculation which is suitable for operation across multiple chips; (3) slow probabilistic synaptic rewiring driven by (pseudo-)random noise; (4) the application of a very-low-current design technique to improving the stability of weights stored on capacitors; (5) exploiting transistor non-ideality to implement partially weightdependent spike-timing-dependent plasticity; (6) the use of the non-linear capacitance of MOSCAP devices to compensate for other non-linearities. The performance of the chip is characterised and it is shown that the fabricated chips are capable of implementing the model, resulting in biologically relevant behaviours such as activity-dependent reduction of the spatial variance of receptive fields. Complementing a fast synaptic weight change mechanism with a slow synapse rewiring mechanism is suggested as a method of increasing the stability of learned patterns

Structure, Dynamics and Self-Organization in Recurrent Neural Networks: From Machine Learning to Theoretical Neuroscience

At a first glance, artificial neural networks, with engineered learning algorithms and carefully chosen nonlinearities, are nothing like the complicated self-organized spiking neural networks studied by theoretical neuroscientists. Yet, both adapt to their inputs, keep information from the past in their state space and are able of learning, implying that some information processing principles should be common to both. In this thesis we study those principles by incorporating notions of systems theory, statistical physics and graph theory into artificial neural networks and theoretical neuroscience models. % TO DO: What is different in this thesis? -> classical signal processing with complex systems on top The starting point for this thesis is \ac{RC}, a learning paradigm used both in machine learning\cite{jaeger2004harnessing} and in theoretical neuroscience\cite{maass2002real}. A neural network in \ac{RC} consists of two parts, a reservoir – a directed and weighted network of neurons that projects the input time series onto a high dimensional space – and a readout which is trained to read the state of the neurons in the reservoir and combine them linearly to give the desired output. In classical \ac{RC}, the reservoir is randomly initialized and left untrained, which alleviates the training costs in comparison to other recurrent neural networks. However, this lack of training implies that reservoirs are not adapted to specific tasks and thus their performance is often lower than that of other neural networks. Our contribution has been to show how knowledge about a task can be integrated into the reservoir architecture, so that reservoirs can be tailored to specific problems without training. We do this design by identifying two features that are useful for machine learning: the memory of the reservoir and its power spectra. First we show that the correlations between neurons limit the capacity of the reservoir to retain traces of previous inputs, and demonstrate that those correlations are controlled by moduli of the eigenvalues of the adjacency matrix of the reservoir. Second, we prove that when the reservoir resonates at the frequencies that are present on the desired output signal, the performance of the readout increases. Knowing the features of the reservoir dynamics that we need, the next question is how to impose them. The simplest way to design a network with that resonates at a certain frequency is by adding cycles, which act as feedback loops, but this also induces correlations and hence memory modifications. To disentangle the frequencies and the memory design, we studied how the addition of cycles modifies the eigenvalues in the adjacency matrix of the network. Surprisingly, the shape of the eigenvalues is quite beautiful \cite{aceituno2019universal} and can be characterized using random matrix theory tools. Combining this knowledge with our result relating eigenvalues and correlations, we designed an heuristic that tailors reservoirs to specific tasks and showed that it improves upon state of the art \ac{RC} in three different machine learning tasks. Although this idea works in the machine learning version of \ac{RC}, there is one fundamental problem when we try to translate to the world of theoretical neuroscience: the proposed frequency adaptation requires prior knowledge of the task, which might not be plausible in a biological neural network. Therefore the following questions are whether those resonances can emerge by unsupervised learning, and which kind of learning rules would be required. Remarkably, these resonances can be induced by the well-known Spike Time-Dependent Plasticity (STDP) combined with homeostatic mechanisms. We show this by deriving two self-consistent equations: one where the activity of every neuron can be calculated from its synaptic weights and its external inputs and a second one where the synaptic weights can be obtained from the neural activity. By considering spatio-temporal symmetries in our inputs we obtained two families of solutions to those equations where a periodic input is enhanced by the neural network after STDP. This approach shows that periodic and quasiperiodic inputs can induce resonances that agree with the aforementioned \ac{RC} theory. Those results, although rigorous, are expressed on a language of statistical physics and cannot be easily tested or verified in real, scarce data. To make them more accessible to the neuroscience community we showed that latency reduction, a well-known effect of STDP\cite{song2000competitive} which has been experimentally observed \cite{mehta2000experience}, generates neural codes that agree with the self-consistency equations and their solutions. In particular, this analysis shows that metabolic efficiency, synchronization and predictions can emerge from that same phenomena of latency reduction, thus closing the loop with our original machine learning problem. To summarize, this thesis exposes principles of learning recurrent neural networks that are consistent with adaptation in the nervous system and also improve current machine learning methods. This is done by leveraging features of the dynamics of recurrent neural networks such as resonances and correlations in machine learning problems, then imposing the required dynamics into reservoir computing through control theory notions such as feedback loops and spectral analysis. Then we assessed the plausibility of such adaptation in biological networks, deriving solutions from self-organizing processes that are biologically plausible and align with the machine learning prescriptions. Finally, we relate those processes to learning rules in biological neurons, showing how small local adaptations of the spike times can lead to neural codes that are efficient and can be interpreted in machine learning terms