2,181 research outputs found
Searching for collective behavior in a network of real neurons
Maximum entropy models are the least structured probability distributions
that exactly reproduce a chosen set of statistics measured in an interacting
network. Here we use this principle to construct probabilistic models which
describe the correlated spiking activity of populations of up to 120 neurons in
the salamander retina as it responds to natural movies. Already in groups as
small as 10 neurons, interactions between spikes can no longer be regarded as
small perturbations in an otherwise independent system; for 40 or more neurons
pairwise interactions need to be supplemented by a global interaction that
controls the distribution of synchrony in the population. Here we show that
such "K-pairwise" models--being systematic extensions of the previously used
pairwise Ising models--provide an excellent account of the data. We explore the
properties of the neural vocabulary by: 1) estimating its entropy, which
constrains the population's capacity to represent visual information; 2)
classifying activity patterns into a small set of metastable collective modes;
3) showing that the neural codeword ensembles are extremely inhomogenous; 4)
demonstrating that the state of individual neurons is highly predictable from
the rest of the population, allowing the capacity for error correction.Comment: 24 pages, 19 figure
Stimulus-dependent maximum entropy models of neural population codes
Neural populations encode information about their stimulus in a collective
fashion, by joint activity patterns of spiking and silence. A full account of
this mapping from stimulus to neural activity is given by the conditional
probability distribution over neural codewords given the sensory input. To be
able to infer a model for this distribution from large-scale neural recordings,
we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal
extension of the canonical linear-nonlinear model of a single neuron, to a
pairwise-coupled neural population. The model is able to capture the
single-cell response properties as well as the correlations in neural spiking
due to shared stimulus and due to effective neuron-to-neuron connections. Here
we show that in a population of 100 retinal ganglion cells in the salamander
retina responding to temporal white-noise stimuli, dependencies between cells
play an important encoding role. As a result, the SDME model gives a more
accurate account of single cell responses and in particular outperforms
uncoupled models in reproducing the distributions of codewords emitted in
response to a stimulus. We show how the SDME model, in conjunction with static
maximum entropy models of population vocabulary, can be used to estimate
information-theoretic quantities like surprise and information transmission in
a neural population.Comment: 11 pages, 7 figure
The Computational Structure of Spike Trains
Neurons perform computations, and convey the results of those computations
through the statistical structure of their output spike trains. Here we present
a practical method, grounded in the information-theoretic analysis of
prediction, for inferring a minimal representation of that structure and for
characterizing its complexity. Starting from spike trains, our approach finds
their causal state models (CSMs), the minimal hidden Markov models or
stochastic automata capable of generating statistically identical time series.
We then use these CSMs to objectively quantify both the generalizable structure
and the idiosyncratic randomness of the spike train. Specifically, we show that
the expected algorithmic information content (the information needed to
describe the spike train exactly) can be split into three parts describing (1)
the time-invariant structure (complexity) of the minimal spike-generating
process, which describes the spike train statistically; (2) the randomness
(internal entropy rate) of the minimal spike-generating process; and (3) a
residual pure noise term not described by the minimal spike-generating process.
We use CSMs to approximate each of these quantities. The CSMs are inferred
nonparametrically from the data, making only mild regularity assumptions, via
the causal state splitting reconstruction algorithm. The methods presented here
complement more traditional spike train analyses by describing not only spiking
probability and spike train entropy, but also the complexity of a spike train's
structure. We demonstrate our approach using both simulated spike trains and
experimental data recorded in rat barrel cortex during vibrissa stimulation.Comment: Somewhat different format from journal version but same conten
Supervised Parameter Estimation of Neuron Populations from Multiple Firing Events
The firing dynamics of biological neurons in mathematical models is often
determined by the model's parameters, representing the neurons' underlying
properties. The parameter estimation problem seeks to recover those parameters
of a single neuron or a neuron population from their responses to external
stimuli and interactions between themselves. Most common methods for tackling
this problem in the literature use some mechanistic models in conjunction with
either a simulation-based or solution-based optimization scheme. In this paper,
we study an automatic approach of learning the parameters of neuron populations
from a training set consisting of pairs of spiking series and parameter labels
via supervised learning. Unlike previous work, this automatic learning does not
require additional simulations at inference time nor expert knowledge in
deriving an analytical solution or in constructing some approximate models. We
simulate many neuronal populations with different parameter settings using a
stochastic neuron model. Using that data, we train a variety of supervised
machine learning models, including convolutional and deep neural networks,
random forest, and support vector regression. We then compare their performance
against classical approaches including a genetic search, Bayesian sequential
estimation, and a random walk approximate model. The supervised models almost
always outperform the classical methods in parameter estimation and spike
reconstruction errors, and computation expense. Convolutional neural network,
in particular, is the best among all models across all metrics. The supervised
models can also generalize to out-of-distribution data to a certain extent.Comment: 31 page
Advancing models of the visual system using biologically plausible unsupervised spiking neural networks
Spikes are thought to provide a fundamental unit of computation in the nervous system. The retina is known to use the relative timing of spikes to encode visual input, whereas primary visual cortex (V1) exhibits sparse and irregular spiking activity – but what do these different spiking patterns represent about sensory stimuli? To address this question, I set out to model the retina and V1 using a biologically-realistic spiking neural network (SNN), exploring the idea that temporal prediction underlies the sensory transformation of natural inputs.
Firstly, I trained a recurrently-connected SNN of excitatory and inhibitory units to predict the sensory future in natural movies under metabolic-like constraints. This network exhibited V1-like spike statistics, simple and complex cell-like tuning, and - advancing prior studies - key physiological and tuning differences between excitatory and inhibitory neurons.
Secondly, I modified this spiking network to model the retina to explore its role in visual processing. I found the model optimized for efficient prediction to capture retina-like receptive fields and - in contrast to previous studies - various retinal phenomena, such as latency coding, response omissions, and motion-tuning properties. Notably, the temporal prediction model also more accurately predicts retinal ganglion cell responses to natural images and movies across various animal species.
Lastly, I developed a new method to accelerate the simulation and training of SNNs, obtaining a 10-50 times speedup, with performance on a par with the standard training approach on supervised classification benchmarks and for fitting electrophysiological recordings of cortical neurons.
The retina and V1 models lay the foundation for developing normative models of increasing biological realism and link sensory processing to spiking activity, suggesting that temporal prediction is an underlying function of visual processing. This is complemented by a new approach to drastically accelerate computational research using SNNs
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