716 research outputs found
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
Stochastic firing rate models
We review a recent approach to the mean-field limits in neural networks that
takes into account the stochastic nature of input current and the uncertainty
in synaptic coupling. This approach was proved to be a rigorous limit of the
network equations in a general setting, and we express here the results in a
more customary and simpler framework. We propose a heuristic argument to derive
these equations providing a more intuitive understanding of their origin. These
equations are characterized by a strong coupling between the different moments
of the solutions. We analyse the equations, present an algorithm to simulate
the solutions of these mean-field equations, and investigate numerically the
equations. In particular, we build a bridge between these equations and
Sompolinsky and collaborators approach (1988, 1990), and show how the coupling
between the mean and the covariance function deviates from customary
approaches
Self-sustained irregular activity in an ensemble of neural oscillators
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the
presence of a mean-field coupling and a dispersion of their natural
frequencies. In spite of the analogies with the Kuramoto setup, a much richer
scenario is observed. The "synchronised phase", which emerges upon increasing
the coupling strength, is characterized by highly-irregular fluctuations: a
time-series analysis reveals that the dynamics of the order parameter is indeed
high-dimensional. The complex dynamics appears to be the result of the
non-perturbative action of a suitably shaped phase-response curve. Such
mechanism differs from the often invoked balance between excitation and
inhibition and might provide an alternative basis to account for the
self-sustained brain activity in the resting state. The potential interest of
this dynamical regime is further strengthened by its (microscopic) linear
stability, which makes it quite suited for computational tasks. The overall
study has been performed by combining analytical and numerical studies,
starting from the linear stability analysis of the asynchronous regime, to
include the Fourier analysis of the Kuramoto order parameter, the computation
of various types of Lyapunov exponents, and a microscopic study of the
inter-spike intervals.Comment: 11 pages, 10 figure
A topological data analysis based classification method for multiple measurements
HR was partly supported by a collaboration agreement between the University of Aberdeen and EPFL. WC was partially supported by VR 2014-04770 and Wallenberg AI, Autonomous System and Software Program (WASP) funded by Knut and Alice Wallenberg Foundation, Göran Gustafsson Stiftelse. JT is fully funded by the Wenner-Gren Foundation. JH is partially supported by VR K825930053. RR is partially supported by MultipleMS. The collaboration agreement between EPFL and University of Aberdeen played a role in the design of the neuron spiking analysis and in providing the data required, i.e. the neuronal network and the spiking activity. Open access funding provided by Karolinska Institute.Peer reviewedPublisher PD
Contributions to statistical analysis methods for neural spiking activity
With the technical advances in neuroscience experiments in the past few decades, we have seen a massive expansion in our ability to record neural activity. These advances enable neuroscientists to analyze more complex neural coding and communication properties, and at the same time, raise new challenges for analyzing neural spiking data, which keeps growing in scale, dimension, and complexity.
This thesis proposes several new statistical methods that advance statistical analysis approaches for neural spiking data, including sequential Monte Carlo (SMC) methods for efficient estimation of neural dynamics from membrane potential threshold crossings, state-space models using multimodal observation processes, and goodness-of-fit analysis methods for neural marked point process models.
In a first project, we derive a set of iterative formulas that enable us to simulate trajectories from stochastic, dynamic neural spiking models that are consistent with a set of spike time observations. We develop a SMC method to simultaneously estimate the parameters of the model and the unobserved dynamic variables from spike train data. We investigate the performance of this approach on a leaky integrate-and-fire model.
In another project, we define a semi-latent state-space model to estimate information related to the phenomenon of hippocampal replay. Replay is a recently discovered phenomenon where patterns of hippocampal spiking activity that typically occur during exploration of an environment are reactivated when an animal is at rest. This reactivation is accompanied by high frequency oscillations in hippocampal local field potentials. However, methods to define replay mathematically remain undeveloped. In this project, we construct a novel state-space model that enables us to identify whether replay is occurring, and if so to estimate the movement trajectories consistent with the observed neural activity, and to categorize the content of each event. The state-space model integrates information from the spiking activity from the hippocampal population, the rhythms in the local field potential, and the rat's movement behavior.
Finally, we develop a new, general time-rescaling theorem for marked point processes, and use this to develop a general goodness-of-fit framework for neural population spiking models. We investigate this approach through simulation and a real data application
Training deep neural density estimators to identify mechanistic models of neural dynamics
Mechanistic modeling in neuroscience aims to explain observed phenomena in terms of underlying causes. However, determining which model parameters agree with complex and stochastic neural data presents a significant challenge. We address this challenge with a machine learning tool which uses deep neural density estimators-- trained using model simulations-- to carry out Bayesian inference and retrieve the full space of parameters compatible with raw data or selected data features. Our method is scalable in parameters and data features, and can rapidly analyze new data after initial training. We demonstrate the power and flexibility of our approach on receptive fields, ion channels, and Hodgkin-Huxley models. We also characterize the space of circuit configurations giving rise to rhythmic activity in the crustacean stomatogastric ganglion, and use these results to derive hypotheses for underlying compensation mechanisms. Our approach will help close the gap between data-driven and theory-driven models of neural dynamics
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
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Single Biological Neurons as Temporally Precise Spatio-Temporal Pattern Recognizers
This PhD thesis is focused on the central idea that single neurons in the
brain should be regarded as temporally precise and highly complex
spatio-temporal pattern recognizers. This is opposed to the prevalent view of
biological neurons as simple and mainly spatial pattern recognizers by most
neuroscientists today. In this thesis, I will attempt to demonstrate that this
is an important distinction, predominantly because the above-mentioned
computational properties of single neurons have far-reaching implications with
respect to the various brain circuits that neurons compose, and on how
information is encoded by neuronal activity in the brain. Namely, that these
particular "low-level" details at the single neuron level have substantial
system-wide ramifications. In the introduction we will highlight the main
components that comprise a neural microcircuit that can perform useful
computations and illustrate the inter-dependence of these components from a
system perspective. In chapter 1 we discuss the great complexity of the
spatio-temporal input-output relationship of cortical neurons that are the
result of morphological structure and biophysical properties of the neuron. In
chapter 2 we demonstrate that single neurons can generate temporally precise
output patterns in response to specific spatio-temporal input patterns with a
very simple biologically plausible learning rule. In chapter 3, we use the
differentiable deep network analog of a realistic cortical neuron as a tool to
approximate the gradient of the output of the neuron with respect to its input
and use this capability in an attempt to teach the neuron to perform nonlinear
XOR operation. In chapter 4 we expand chapter 3 to describe extension of our
ideas to neuronal networks composed of many realistic biological spiking
neurons that represent either small microcircuits or entire brain regions
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