Quantum processes, space-time representation and brain dynamics

The recent controversy of applicability of quantum formalism to brain dynamics has been critically analysed. The prerequisites for any type of quantum formalism or quantum field theory is to investigate whether the anatomical structure of brain permits any kind of smooth geometric notion like Hilbert structure or four dimensional Minkowskian structure for quantum field theory. The present understanding of brain function clearly denies any kind of space-time representation in Minkowskian sense. However, three dimensional space and one time can be assigned to the neuromanifold and the concept of probabilistic geometry is shown to be appropriate framework to understand the brain dynamics. The possibility of quantum structure is also discussed in this framework.Comment: Latex, 28 page

A Bayesian inference theory of attention: neuroscience and algorithms

The past four decades of research in visual neuroscience has generated a large and disparate body of literature on the role of attention [Itti et al., 2005]. Although several models have been developed to describe specific properties of attention, a theoretical framework that explains the computational role of attention and is consistent with all known effects is still needed. Recently, several authors have suggested that visual perception can be interpreted as a Bayesian inference process [Rao et al., 2002, Knill and Richards, 1996, Lee and Mumford, 2003]. Within this framework, topdown priors via cortical feedback help disambiguate noisy bottom-up sensory input signals. Building on earlier work by Rao [2005], we show that this Bayesian inference proposal can be extended to explain the role and predict the main properties of attention: namely to facilitate the recognition of objects in clutter. Visual recognition proceeds by estimating the posterior probabilities for objects and their locations within an image via an exchange of messages between ventral and parietal areas of the visual cortex. Within this framework, spatial attention is used to reduce the uncertainty in feature information; feature-based attention is used to reduce the uncertainty in location information. In conjunction, they are used to recognize objects in clutter. Here, we find that several key attentional phenomena such such as pop-out, multiplicative modulation and change in contrast response emerge naturally as a property of the network. We explain the idea in three stages. We start with developing a simplified model of attention in the brain identifying the primary areas involved and their interconnections. Secondly, we propose a Bayesian network where each node has direct neural correlates within our simplified biological model. Finally, we elucidate the properties of the resulting model, showing that the predictions are consistent with physiological and behavioral evidence

Natural-gradient learning for spiking neurons.

In many normative theories of synaptic plasticity, weight updates implicitly depend on the chosen parametrization of the weights. This problem relates, for example, to neuronal morphology: synapses which are functionally equivalent in terms of their impact on somatic firing can differ substantially in spine size due to their different positions along the dendritic tree. Classical theories based on Euclidean-gradient descent can easily lead to inconsistencies due to such parametrization dependence. The issues are solved in the framework of Riemannian geometry, in which we propose that plasticity instead follows natural-gradient descent. Under this hypothesis, we derive a synaptic learning rule for spiking neurons that couples functional efficiency with the explanation of several well-documented biological phenomena such as dendritic democracy, multiplicative scaling, and heterosynaptic plasticity. We therefore suggest that in its search for functional synaptic plasticity, evolution might have come up with its own version of natural-gradient descent

Natural-gradient learning for spiking neurons

In many normative theories of synaptic plasticity, weight updates implicitly depend on the chosen parametrization of the weights. This problem relates, for example, to neuronal morphology: synapses which are functionally equivalent in terms of their impact on somatic firing can differ substantially in spine size due to their different positions along the dendritic tree. Classical theories based on Euclidean gradient descent can easily lead to inconsistencies due to such parametrization dependence. The issues are solved in the framework of Riemannian geometry, in which we propose that plasticity instead follows natural gradient descent. Under this hypothesis, we derive a synaptic learning rule for spiking neurons that couples functional efficiency with the explanation of several well-documented biological phenomena such as dendritic democracy, multiplicative scaling and heterosynaptic plasticity. We therefore suggest that in its search for functional synaptic plasticity, evolution might have come up with its own version of natural gradient descent.Comment: Joint senior authorship: Walter M. Senn and Mihai A. Petrovic

Harnessing function from form: towards bio-inspired artificial intelligence in neuronal substrates

Despite the recent success of deep learning, the mammalian brain is still unrivaled when it comes to interpreting complex, high-dimensional data streams like visual, auditory and somatosensory stimuli. However, the underlying computational principles allowing the brain to deal with unreliable, high-dimensional and often incomplete data while having a power consumption on the order of a few watt are still mostly unknown. In this work, we investigate how specific functionalities emerge from simple structures observed in the mammalian cortex, and how these might be utilized in non-von Neumann devices like “neuromorphic hardware”. Firstly, we show that an ensemble of deterministic, spiking neural networks can be shaped by a simple, local learning rule to perform sampling-based Bayesian inference. This suggests a coding scheme where spikes (or “action potentials”) represent samples of a posterior distribution, constrained by sensory input, without the need for any source of stochasticity. Secondly, we introduce a top-down framework where neuronal and synaptic dynamics are derived using a least action principle and gradient-based minimization. Combined, neurosynaptic dynamics approximate real-time error backpropagation, mappable to mechanistic components of cortical networks, whose dynamics can again be described within the proposed framework. The presented models narrow the gap between well-defined, functional algorithms and their biophysical implementation, improving our understanding of the computational principles the brain might employ. Furthermore, such models are naturally translated to hardware mimicking the vastly parallel neural structure of the brain, promising a strongly accelerated and energy-efficient implementation of powerful learning and inference algorithms, which we demonstrate for the physical model system “BrainScaleS–1”

Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network

The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically

Understanding The Implications Of Neural Population Activity On Behavior

Learning how neural activity in the brain leads to the behavior we exhibit is one of the fundamental questions in Neuroscience. In this dissertation, several lines of work are presented to that use principles of neural coding to understand behavior. In one line of work, we formulate the efficient coding hypothesis in a non-traditional manner in order to test human perceptual sensitivity to complex visual textures. We find a striking agreement between how variable a particular texture signal is and how sensitive humans are to its presence. This reveals that the efficient coding hypothesis is still a guiding principle for neural organization beyond the sensory periphery, and that the nature of cortical constraints differs from the peripheral counterpart. In another line of work, we relate frequency discrimination acuity to neural responses from auditory cortex in mice. It has been previously observed that optogenetic manipulation of auditory cortex, in addition to changing neural responses, evokes changes in behavioral frequency discrimination. We are able to account for changes in frequency discrimination acuity on an individual basis by examining the Fisher information from the neural population with and without optogenetic manipulation. In the third line of work, we address the question of what a neural population should encode given that its inputs are responses from another group of neurons. Drawing inspiration from techniques in machine learning, we train Deep Belief Networks on fake retinal data and show the emergence of Garbor-like filters, reminiscent of responses in primary visual cortex. In the last line of work, we model the state of a cortical excitatory-inhibitory network during complex adaptive stimuli. Using a rate model with Wilson-Cowan dynamics, we demonstrate that simple non-linearities in the signal transferred from inhibitory to excitatory neurons can account for real neural recordings taken from auditory cortex. This work establishes and tests a variety of hypotheses that will be useful in helping to understand the relationship between neural activity and behavior as recorded neural populations continue to grow