Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networks

Networks of spiking neurons underpin the extraordinary information-processing capabilities of the brain and have emerged as pillar models in neuromorphic intelligence. Despite extensive research on spiking neural networks (SNNs), most are established on deterministic models. Integrating noise into SNNs leads to biophysically more realistic neural dynamics and may benefit model performance. This work presents the noisy spiking neural network (NSNN) and the noise-driven learning rule (NDL) by introducing a spiking neuron model incorporating noisy neuronal dynamics. Our approach shows how noise may act as a resource for computation and learning and theoretically provides a framework for general SNNs. Moreover, NDL provides an insightful biological rationale for surrogate gradients. By incorporating various SNN architectures and algorithms, we show that our approach exhibits competitive performance and improved robustness against challenging perturbations than deterministic SNNs. Additionally, we demonstrate the utility of the NSNN model for neural coding studies. Overall, NSNN offers a powerful, flexible, and easy-to-use tool for machine learning practitioners and computational neuroscience researchers.Comment: Fixed the bug in the BBL file generated with bibliography management progra

Energy-Efficient Visual Search by Eye Movement and Low-Latency Spiking Neural Network

Human vision incorporates non-uniform resolution retina, efficient eye movement strategy, and spiking neural network (SNN) to balance the requirements in visual field size, visual resolution, energy cost, and inference latency. These properties have inspired interest in developing human-like computer vision. However, existing models haven't fully incorporated the three features of human vision, and their learned eye movement strategies haven't been compared with human's strategy, making the models' behavior difficult to interpret. Here, we carry out experiments to examine human visual search behaviors and establish the first SNN-based visual search model. The model combines an artificial retina with spiking feature extraction, memory, and saccade decision modules, and it employs population coding for fast and efficient saccade decisions. The model can learn either a human-like or a near-optimal fixation strategy, outperform humans in search speed and accuracy, and achieve high energy efficiency through short saccade decision latency and sparse activation. It also suggests that the human search strategy is suboptimal in terms of search speed. Our work connects modeling of vision in neuroscience and machine learning and sheds light on developing more energy-efficient computer vision algorithms

Geometry and dimensionality reduction of feature spaces in primary visual cortex

Some geometric properties of the wavelet analysis performed by visual neurons are discussed and compared with experimental data. In particular, several relationships between the cortical morphologies and the parametric dependencies of extracted features are formalized and considered from a harmonic analysis point of view

Biologically Inspired Spatial Representation

In this thesis I explore a biologically inspired method of encoding continuous space within a population of neurons. This method provides an extension to the Semantic Pointer Architecture (SPA) to encompass Semantic Pointers with real-valued spatial content in addition to symbol-like representations. I demonstrate how these Spatial Semantic Pointers (SSPs) can be used to generate cognitive maps containing objects at various locations. A series of operations are defined that can retrieve objects or locations from the encoded map as well as manipulate the contents of the memory. These capabilities are all implemented by a network of spiking neurons. I explore the topology of the SSP vector space and show how it preserves metric information while compressing all coordinates to unit length vectors. This allows a limitless spatial extent to be represented in a finite region. Neurons encoding space represented in this manner have firing fields similar to entorhinal grid cells. Beyond constructing biologically plausible models of spatial cognition, SSPs are applied to the domain of machine learning. I demonstrate how replacing traditional spatial encoding mechanisms with SSPs can improve performance on networks trained to compute a navigational policy. In addition, SSPs are also effective for training a network to localize within an environment based on sensor measurements as well as perform path integration. To demonstrate a practical, integrated system using SSPs, I combine a goal driven navigational policy with the localization network and cognitive map representation to produce an agent that can navigate to semantically defined goals. In addition to spatial tasks, the SSP encoding is applied to a more general class of machine learning problems involving arbitrary continuous signals. Results on a collection of 122 benchmark datasets across a variety of domains indicate that neural networks trained with SSP encoding outperform commonly used methods for the majority of the datasets. Overall, the experiments in this thesis demonstrate the importance of exploring new kinds of representations within neural networks and how they shape the kinds of functions that can be effectively computed. They provide an example of how insights regarding how the brain may encode information can inspire new ways of designing artificial neural networks

Computational roles of cortico-cerebellar loops in temporal credit assignment

Animal survival depends on behavioural adaptation to the environment. This is thought to be enabled by plasticity in the neural circuit. However, the laws which govern neural plasticity are unclear. From a functional aspect, it is desirable to correctly identify, or assign “credit” for, the neurons or synapses responsible for the task decision and subsequent performance. In the biological circuit, the intricate, non-linear interactions involved in neural networks makes appropriately assigning credit to neurons highly challenging. In the temporal domain, this is known as the temporal credit assignment (TCA) problem. This Thesis considers the role the cerebellum – a powerful subcortical structure with strong error-guided plasticity rules – as a solution to TCA in the brain. In particular, I use artificial neural networks as a means to model and understand the mechanisms by which the cerebellum can support learning in the neocortex via the cortico-cerebellar loop. I introduce two distinct but compatible computational models of cortico-cerebellar interaction. The first model asserts that the cerebellum provides the neocortex predictive feedback, modeled in the form of error gradients, with respect to its current activity. This predictive feedback enables better credit assignment in the neocortex and effectively removes the lock between feedforward and feedback processing in cortical networks. This model captures observed long-term deficits associated with cerebellar dysfunction, namely cerebellar dysmetria, in both the motor and non-motor domain. Predictions are also made with respect to alignment of cortico-cerebellar activity during learning and the optimal task conditions for cerebellar contribution. The second model also looks at the role of the cerebellum in learning, but now considers its ability to instantaneously drive the cortex towards desired task dynamics. Unlike the first model, this model does not assume any local cortical plasticity need take place at all and task-directed learning can effectively be outsourced to the cerebellum. This model captures recent optogenetic studies in mice which show the cerebellum as a necessary component for the maintenance of desired cortical dynamics and ensuing behaviour. I also show that this driving input can eventually be used as a teaching signal for the cortical circuit, thereby conceptually unifying the two models. Overall, this Thesis explores the computational role of the cerebellum and cortico-cerebellar loops for task acquisition and maintenance in the brain

Evoked Patterns of Oscillatory Activity in Mean-Field Neuronal Networks

Oscillatory behaviors in populations of neurons are oberved in diverse contexts. In tasks involving working memory, a form of short-term memory, oscillations in different frequency bands have been shown to increase across varying spatial scales using recording methods such as EEG (electroencephalogram) and MEG (magnetoencephalogram). Such oscillatory activity has also been observed in the context of neural binding, where different features of objects that are perceived or recalled are associated with one another. These sets of data suggest that oscillatory dynamics may also play a key role in the maintenance and manipulation of items in working memory. Using similar recording techniques, including EEG and MEG, oscillatory neuronal activity has also been seen to occur when certain images that cause aversion and headaches in healthy human subjects or seizures in those with pattern-sensitive epilepsy are presented. The images most likely to cause such responses are those with dominant spatial frequencies near 3--5 cycles per degree, the same band of wavenumbers to which normal human vision exhibits the greatest contrast sensitivity. We model these oscillatory behaviors using mean-field, Wilson-Cowan-type neuronal networks. In the case of working memory and binding, we find that including the activity of certain long-lasting excitatory synapses in addition to the usual inhibitory and shorter-term excitatory synaptic activity allows for bistability between a low steady state and a high oscillatory state. By coupling several such populations together, both in-phase and out-of-phase oscillations arise, corresponding to distinct and bound items in working memory, respectively. We analyze the network's dynamics and dependence on biophysically relevant parameters using a combination of techniques, including numerical bifurcation analysis and weak coupling theory. In the case of spatially resonant responses to static simtuli, we employ Wilson-Cowan networks extended in one and two spatial dimensions. By placing the networks near Turing-Hopf bifurcations, we find they exhibit spatial resonances that compare well with empirical results. Using simulations, numerical bifurcation analysis, and perturbation theory, we characterize the observed dynamics and gain mathematical insight into the mechanisms that lead to these dynamics