763 research outputs found
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
Inherent Weight Normalization in Stochastic Neural Networks
Multiplicative stochasticity such as Dropout improves the robustness and
generalizability of deep neural networks. Here, we further demonstrate that
always-on multiplicative stochasticity combined with simple threshold neurons
are sufficient operations for deep neural networks. We call such models Neural
Sampling Machines (NSM). We find that the probability of activation of the NSM
exhibits a self-normalizing property that mirrors Weight Normalization, a
previously studied mechanism that fulfills many of the features of Batch
Normalization in an online fashion. The normalization of activities during
training speeds up convergence by preventing internal covariate shift caused by
changes in the input distribution. The always-on stochasticity of the NSM
confers the following advantages: the network is identical in the inference and
learning phases, making the NSM suitable for online learning, it can exploit
stochasticity inherent to a physical substrate such as analog non-volatile
memories for in-memory computing, and it is suitable for Monte Carlo sampling,
while requiring almost exclusively addition and comparison operations. We
demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and
event-based classification benchmarks (N-MNIST and DVS Gestures). Our results
show that NSMs perform comparably or better than conventional artificial neural
networks with the same architecture
Multi-Scale Information, Network, Causality, and Dynamics: Mathematical Computation and Bayesian Inference to Cognitive Neuroscience and Aging
The human brain is estimated to contain 100 billion or so neurons and 10 thousand times as many connections. Neurons never function in isolation: each of them is connected to 10, 000 others and they interact extensively every millisecond. Brain cells are organized into neural circuits often in a dynamic way, processing specific types of information and providing th
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
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