The role of architectural and learning constraints in neural network models: A case study on visual space coding

The recent “deep learning revolution” in artificial neural networks had strong impact and widespread deployment for engineering applications, but the use of deep learning for neurocomputational modeling has been so far limited. In this article we argue that unsupervised deep learning represents an important step forward for improving neurocomputational models of perception and cognition, because it emphasizes the role of generative learning as opposed to discriminative (supervised) learning. As a case study, we present a series of simulations investigating the emergence of neural coding of visual space for sensorimotor transformations. We compare different network architectures commonly used as building blocks for unsupervised deep learning by systematically testing the type of receptive fields and gain modulation developed by the hidden neurons. In particular, we compare Restricted Boltzmann Machines (RBMs), which are stochastic, generative networks with bidirectional connections trained using contrastive divergence, with autoencoders, which are deterministic networks trained using error backpropagation. For both learning architectures we also explore the role of sparse coding, which has been identified as a fundamental principle of neural computation. The unsupervised models are then compared with supervised, feed-forward networks that learn an explicit mapping between different spatial reference frames. Our simulations show that both architectural and learning constraints strongly influenced the emergent coding of visual space in terms of distribution of tuning functions at the level of single neurons. Unsupervised models, and particularly RBMs, were found to more closely adhere to neurophysiological data from single-cell recordings in the primate parietal cortex. These results provide new insights into how basic properties of artificial neural networks might be relevant for modeling neural information processing in biological systems

Statistical Physics and Representations in Real and Artificial Neural Networks

This document presents the material of two lectures on statistical physics and neural representations, delivered by one of us (R.M.) at the Fundamental Problems in Statistical Physics XIV summer school in July 2017. In a first part, we consider the neural representations of space (maps) in the hippocampus. We introduce an extension of the Hopfield model, able to store multiple spatial maps as continuous, finite-dimensional attractors. The phase diagram and dynamical properties of the model are analyzed. We then show how spatial representations can be dynamically decoded using an effective Ising model capturing the correlation structure in the neural data, and compare applications to data obtained from hippocampal multi-electrode recordings and by (sub)sampling our attractor model. In a second part, we focus on the problem of learning data representations in machine learning, in particular with artificial neural networks. We start by introducing data representations through some illustrations. We then analyze two important algorithms, Principal Component Analysis and Restricted Boltzmann Machines, with tools from statistical physics

Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware

Visual scene recognition with biologically relevant generative models

This research focuses on developing visual object categorization methodologies that are based on machine learning techniques and biologically inspired generative models of visual scene recognition. Modelling the statistical variability in visual patterns, in the space of features extracted from them by an appropriate low level signal processing technique, is an important matter of investigation for both humans and machines. To study this problem, we have examined in detail two recent probabilistic models of vision: a simple multivariate Gaussian model as suggested by (Karklin & Lewicki, 2009) and a restricted Boltzmann machine (RBM) proposed by (Hinton, 2002). Both the models have been widely used for visual object classification and scene analysis tasks before. This research highlights that these models on their own are not plausible enough to perform the classification task, and suggests Fisher kernel as a means of inducing discrimination into these models for classification power. Our empirical results on standard benchmark data sets reveal that the classification performance of these generative models could be significantly boosted near to the state of the art performance, by drawing a Fisher kernel from compact generative models that computes the data labels in a fraction of total computation time. We compare the proposed technique with other distance based and kernel based classifiers to show how computationally efficient the Fisher kernels are. To the best of our knowledge, Fisher kernel has not been drawn from the RBM before, so the work presented in the thesis is novel in terms of its idea and application to vision problem

Phase synchrony facilitates binding and segmentation of natural images in a coupled neural oscillator network

Synchronization has been suggested as a mechanism of binding distributed feature representations facilitating segmentation of visual stimuli. Here we investigate this concept based on unsupervised learning using natural visual stimuli. We simulate dual-variable neural oscillators with separate activation and phase variables. The binding of a set of neurons is coded by synchronized phase variables. The network of tangential synchronizing connections learned from the induced activations exhibits small-world properties and allows binding even over larger distances. We evaluate the resulting dynamic phase maps using segmentation masks labeled by human experts. Our simulation results show a continuously increasing phase synchrony between neurons within the labeled segmentation masks. The evaluation of the network dynamics shows that the synchrony between network nodes establishes a relational coding of the natural image inputs. This demonstrates that the concept of binding by synchrony is applicable in the context of unsupervised learning using natural visual stimuli

NASA JSC neural network survey results

A survey of Artificial Neural Systems in support of NASA's (Johnson Space Center) Automatic Perception for Mission Planning and Flight Control Research Program was conducted. Several of the world's leading researchers contributed papers containing their most recent results on artificial neural systems. These papers were broken into categories and descriptive accounts of the results make up a large part of this report. Also included is material on sources of information on artificial neural systems such as books, technical reports, software tools, etc

Neural Dynamics as Sampling: A Model for Stochastic Computation in Recurrent Networks of Spiking Neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons

Statistical modelling of neuronal population activity: from data analysis to network function

The term statistical modelling refers to a number of abstract models designed to reproduce and understand the statistical properties of the activity of neuronal networks at the population level. Large-scale recordings by multielectrode arrays (MEAs) have now made possible to scale their use to larger groups of neurons. The initial step in this work focused on improving the data analysis pipeline that leads from the experimental protocol used in dense MEA recordings to a clean dataset of sorted spike times, to be used in model training. In collaboration with experimentalists, I contributed to developing a fast and scalable algorithm for spike sorting, which is based on action potential shapes and on the estimated location for the spike. Using the resulting datasets, I investigated the use of restricted Boltzmann machines in the analysis of neural data, finding that they can be used as a tool in the detection of neural ensembles or low-dimensional activity subspaces. I further studied the physical properties of RBMs fitted to neural activity, finding they exhibit signatures of criticality, as observed before in similar models. I discussed possible connections between this phenomenon and the \dynamical" criticality often observed in neuronal networks that exhibit emergent behaviour. Finally, I applied what I found about the structure of the parameter space in statistical models to the discovery of a learning rule that helps long-term storage of previously learned memories in Hopfield networks during sequential learning tasks. Overall, this work aimed to contribute to the computational tools used for analysing and modelling large neuronal populations, on different levels: starting from raw experimental recordings and gradually proceeding towards theoretical aspects