1,060 research outputs found
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
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
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
Counting to Ten with Two Fingers: Compressed Counting with Spiking Neurons
We consider the task of measuring time with probabilistic threshold gates implemented by bio-inspired spiking neurons. In the model of spiking neural networks, network evolves in discrete rounds, where in each round, neurons fire in pulses in response to a sufficiently high membrane potential. This potential is induced by spikes from neighboring neurons that fired in the previous round, which can have either an excitatory or inhibitory effect.
Discovering the underlying mechanisms by which the brain perceives the duration of time is one of the largest open enigma in computational neuro-science. To gain a better algorithmic understanding onto these processes, we introduce the neural timer problem. In this problem, one is given a time parameter t, an input neuron x, and an output neuron y. It is then required to design a minimum sized neural network (measured by the number of auxiliary neurons) in which every spike from x in a given round i, makes the output y fire for the subsequent t consecutive rounds.
We first consider a deterministic implementation of a neural timer and show that Theta(log t) (deterministic) threshold gates are both sufficient and necessary. This raised the question of whether randomness can be leveraged to reduce the number of neurons. We answer this question in the affirmative by considering neural timers with spiking neurons where the neuron y is required to fire for t consecutive rounds with probability at least 1-delta, and should stop firing after at most 2t rounds with probability 1-delta for some input parameter delta in (0,1). Our key result is a construction of a neural timer with O(log log 1/delta) spiking neurons. Interestingly, this construction uses only one spiking neuron, while the remaining neurons can be deterministic threshold gates. We complement this construction with a matching lower bound of Omega(min{log log 1/delta, log t}) neurons. This provides the first separation between deterministic and randomized constructions in the setting of spiking neural networks.
Finally, we demonstrate the usefulness of compressed counting networks for synchronizing neural networks. In the spirit of distributed synchronizers [Awerbuch-Peleg, FOCS\u2790], we provide a general transformation (or simulation) that can take any synchronized network solution and simulate it in an asynchronous setting (where edges have arbitrary response latencies) while incurring a small overhead w.r.t the number of neurons and computation time
Learning First-to-Spike Policies for Neuromorphic Control Using Policy Gradients
Artificial Neural Networks (ANNs) are currently being used as function
approximators in many state-of-the-art Reinforcement Learning (RL) algorithms.
Spiking Neural Networks (SNNs) have been shown to drastically reduce the energy
consumption of ANNs by encoding information in sparse temporal binary spike
streams, hence emulating the communication mechanism of biological neurons. Due
to their low energy consumption, SNNs are considered to be important candidates
as co-processors to be implemented in mobile devices. In this work, the use of
SNNs as stochastic policies is explored under an energy-efficient
first-to-spike action rule, whereby the action taken by the RL agent is
determined by the occurrence of the first spike among the output neurons. A
policy gradient-based algorithm is derived considering a Generalized Linear
Model (GLM) for spiking neurons. Experimental results demonstrate the
capability of online trained SNNs as stochastic policies to gracefully trade
energy consumption, as measured by the number of spikes, and control
performance. Significant gains are shown as compared to the standard approach
of converting an offline trained ANN into an SNN.Comment: Submitted for conference publicatio
Spiking Neural Networks for Inference and Learning: A Memristor-based Design Perspective
On metrics of density and power efficiency, neuromorphic technologies have
the potential to surpass mainstream computing technologies in tasks where
real-time functionality, adaptability, and autonomy are essential. While
algorithmic advances in neuromorphic computing are proceeding successfully, the
potential of memristors to improve neuromorphic computing have not yet born
fruit, primarily because they are often used as a drop-in replacement to
conventional memory. However, interdisciplinary approaches anchored in machine
learning theory suggest that multifactor plasticity rules matching neural and
synaptic dynamics to the device capabilities can take better advantage of
memristor dynamics and its stochasticity. Furthermore, such plasticity rules
generally show much higher performance than that of classical Spike Time
Dependent Plasticity (STDP) rules. This chapter reviews the recent development
in learning with spiking neural network models and their possible
implementation with memristor-based hardware
Spiking neurons with short-term synaptic plasticity form superior generative networks
Spiking networks that perform probabilistic inference have been proposed both
as models of cortical computation and as candidates for solving problems in
machine learning. However, the evidence for spike-based computation being in
any way superior to non-spiking alternatives remains scarce. We propose that
short-term plasticity can provide spiking networks with distinct computational
advantages compared to their classical counterparts. In this work, we use
networks of leaky integrate-and-fire neurons that are trained to perform both
discriminative and generative tasks in their forward and backward information
processing paths, respectively. During training, the energy landscape
associated with their dynamics becomes highly diverse, with deep attractor
basins separated by high barriers. Classical algorithms solve this problem by
employing various tempering techniques, which are both computationally
demanding and require global state updates. We demonstrate how similar results
can be achieved in spiking networks endowed with local short-term synaptic
plasticity. Additionally, we discuss how these networks can even outperform
tempering-based approaches when the training data is imbalanced. We thereby
show how biologically inspired, local, spike-triggered synaptic dynamics based
simply on a limited pool of synaptic resources can allow spiking networks to
outperform their non-spiking relatives.Comment: corrected typo in abstrac
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