1,963 research outputs found
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
Network Plasticity as Bayesian Inference
General results from statistical learning theory suggest to understand not
only brain computations, but also brain plasticity as probabilistic inference.
But a model for that has been missing. We propose that inherently stochastic
features of synaptic plasticity and spine motility enable cortical networks of
neurons to carry out probabilistic inference by sampling from a posterior
distribution of network configurations. This model provides a viable
alternative to existing models that propose convergence of parameters to
maximum likelihood values. It explains how priors on weight distributions and
connection probabilities can be merged optimally with learned experience, how
cortical networks can generalize learned information so well to novel
experiences, and how they can compensate continuously for unforeseen
disturbances of the network. The resulting new theory of network plasticity
explains from a functional perspective a number of experimental data on
stochastic aspects of synaptic plasticity that previously appeared to be quite
puzzling.Comment: 33 pages, 5 figures, the supplement is available on the author's web
page http://www.igi.tugraz.at/kappe
Deep learning systems as complex networks
Thanks to the availability of large scale digital datasets and massive
amounts of computational power, deep learning algorithms can learn
representations of data by exploiting multiple levels of abstraction. These
machine learning methods have greatly improved the state-of-the-art in many
challenging cognitive tasks, such as visual object recognition, speech
processing, natural language understanding and automatic translation. In
particular, one class of deep learning models, known as deep belief networks,
can discover intricate statistical structure in large data sets in a completely
unsupervised fashion, by learning a generative model of the data using
Hebbian-like learning mechanisms. Although these self-organizing systems can be
conveniently formalized within the framework of statistical mechanics, their
internal functioning remains opaque, because their emergent dynamics cannot be
solved analytically. In this article we propose to study deep belief networks
using techniques commonly employed in the study of complex networks, in order
to gain some insights into the structural and functional properties of the
computational graph resulting from the learning process.Comment: 20 pages, 9 figure
Stochasticity from function -- why the Bayesian brain may need no noise
An increasing body of evidence suggests that the trial-to-trial variability
of spiking activity in the brain is not mere noise, but rather the reflection
of a sampling-based encoding scheme for probabilistic computing. Since the
precise statistical properties of neural activity are important in this
context, many models assume an ad-hoc source of well-behaved, explicit noise,
either on the input or on the output side of single neuron dynamics, most often
assuming an independent Poisson process in either case. However, these
assumptions are somewhat problematic: neighboring neurons tend to share
receptive fields, rendering both their input and their output correlated; at
the same time, neurons are known to behave largely deterministically, as a
function of their membrane potential and conductance. We suggest that spiking
neural networks may, in fact, have no need for noise to perform sampling-based
Bayesian inference. We study analytically the effect of auto- and
cross-correlations in functionally Bayesian spiking networks and demonstrate
how their effect translates to synaptic interaction strengths, rendering them
controllable through synaptic plasticity. This allows even small ensembles of
interconnected deterministic spiking networks to simultaneously and
co-dependently shape their output activity through learning, enabling them to
perform complex Bayesian computation without any need for noise, which we
demonstrate in silico, both in classical simulation and in neuromorphic
emulation. These results close a gap between the abstract models and the
biology of functionally Bayesian spiking networks, effectively reducing the
architectural constraints imposed on physical neural substrates required to
perform probabilistic computing, be they biological or artificial
Accelerated physical emulation of Bayesian inference in spiking neural networks
The massively parallel nature of biological information processing plays an
important role for its superiority to human-engineered computing devices. In
particular, it may hold the key to overcoming the von Neumann bottleneck that
limits contemporary computer architectures. Physical-model neuromorphic devices
seek to replicate not only this inherent parallelism, but also aspects of its
microscopic dynamics in analog circuits emulating neurons and synapses.
However, these machines require network models that are not only adept at
solving particular tasks, but that can also cope with the inherent
imperfections of analog substrates. We present a spiking network model that
performs Bayesian inference through sampling on the BrainScaleS neuromorphic
platform, where we use it for generative and discriminative computations on
visual data. By illustrating its functionality on this platform, we implicitly
demonstrate its robustness to various substrate-specific distortive effects, as
well as its accelerated capability for computation. These results showcase the
advantages of brain-inspired physical computation and provide important
building blocks for large-scale neuromorphic applications.Comment: This preprint has been published 2019 November 14. Please cite as:
Kungl A. F. et al. (2019) Accelerated Physical Emulation of Bayesian
Inference in Spiking Neural Networks. Front. Neurosci. 13:1201. doi:
10.3389/fnins.2019.0120
State-space model with deep learning for functional dynamics estimation in resting-state fMRI
Studies on resting-state functional Magnetic Resonance Imaging (rs-fMRI) have shown that different brain regions still actively interact with each other while a subject is at rest, and such functional interaction is not stationary but changes over time. In terms of a large-scale brain network, in this paper, we focus on time-varying patterns of functional networks, i.e., functional dynamics, inherent in rs-fMRI, which is one of the emerging issues along with the network modelling. Specifically, we propose a novel methodological architecture that combines deep learning and state-space modelling, and apply it to rs-fMRI based Mild Cognitive Impairment (MCI) diagnosis. We first devise a Deep Auto-Encoder (DAE) to discover hierarchical non-linear functional relations among regions, by which we transform the regional features into an embedding space, whose bases are complex functional networks. Given the embedded functional features, we then use a Hidden Markov Model (HMM) to estimate dynamic characteristics of functional networks inherent in rs-fMRI via internal states, which are unobservable but can be inferred from observations statistically. By building a generative model with an HMM, we estimate the likelihood of the input features of rs-fMRI as belonging to the corresponding status, i.e., MCI or normal healthy control, based on which we identify the clinical label of a testing subject. In order to validate the effectiveness of the proposed method, we performed experiments on two different datasets and compared with state-of-the-art methods in the literature. We also analyzed the functional networks learned by DAE, estimated the functional connectivities by decoding hidden states in HMM, and investigated the estimated functional connectivities by means of a graph-theoretic approach
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