98,191 research outputs found
A three-threshold learning rule approaches the maximal capacity of recurrent neural networks
Understanding the theoretical foundations of how memories are encoded and
retrieved in neural populations is a central challenge in neuroscience. A
popular theoretical scenario for modeling memory function is the attractor
neural network scenario, whose prototype is the Hopfield model. The model has a
poor storage capacity, compared with the capacity achieved with perceptron
learning algorithms. Here, by transforming the perceptron learning rule, we
present an online learning rule for a recurrent neural network that achieves
near-maximal storage capacity without an explicit supervisory error signal,
relying only upon locally accessible information. The fully-connected network
consists of excitatory binary neurons with plastic recurrent connections and
non-plastic inhibitory feedback stabilizing the network dynamics; the memory
patterns are presented online as strong afferent currents, producing a bimodal
distribution for the neuron synaptic inputs. Synapses corresponding to active
inputs are modified as a function of the value of the local fields with respect
to three thresholds. Above the highest threshold, and below the lowest
threshold, no plasticity occurs. In between these two thresholds,
potentiation/depression occurs when the local field is above/below an
intermediate threshold. We simulated and analyzed a network of binary neurons
implementing this rule and measured its storage capacity for different sizes of
the basins of attraction. The storage capacity obtained through numerical
simulations is shown to be close to the value predicted by analytical
calculations. We also measured the dependence of capacity on the strength of
external inputs. Finally, we quantified the statistics of the resulting
synaptic connectivity matrix, and found that both the fraction of zero weight
synapses and the degree of symmetry of the weight matrix increase with the
number of stored patterns.Comment: 24 pages, 10 figures, to be published in PLOS Computational Biolog
STDP in Recurrent Neuronal Networks
Recent results about spike-timing-dependent plasticity (STDP) in recurrently connected neurons are reviewed, with a focus on the relationship between the weight dynamics and the emergence of network structure. In particular, the evolution of synaptic weights in the two cases of incoming connections for a single neuron and recurrent connections are compared and contrasted. A theoretical framework is used that is based upon Poisson neurons with a temporally inhomogeneous firing rate and the asymptotic distribution of weights generated by the learning dynamics. Different network configurations examined in recent studies are discussed and an overview of the current understanding of STDP in recurrently connected neuronal networks is presented
Low Tensor Rank Learning of Neural Dynamics
Learning relies on coordinated synaptic changes in recurrently connected
populations of neurons. Therefore, understanding the collective evolution of
synaptic connectivity over learning is a key challenge in neuroscience and
machine learning. In particular, recent work has shown that the weight matrices
of task-trained RNNs are typically low rank, but how this low rank structure
unfolds over learning is unknown. To address this, we investigate the rank of
the 3-tensor formed by the weight matrices throughout learning. By fitting RNNs
of varying rank to large-scale neural recordings during a motor learning task,
we find that the inferred weights are low-tensor-rank and therefore evolve over
a fixed low-dimensional subspace throughout the entire course of learning. We
next validate the observation of low-tensor-rank learning on an RNN trained to
solve the same task by performing a low-tensor-rank decomposition directly on
the ground truth weights, and by showing that the method we applied to the data
faithfully recovers this low rank structure. Finally, we present a set of
mathematical results bounding the matrix and tensor ranks of gradient descent
learning dynamics which show that low-tensor-rank weights emerge naturally in
RNNs trained to solve low-dimensional tasks. Taken together, our findings
provide novel constraints on the evolution of population connectivity over
learning in both biological and artificial neural networks, and enable reverse
engineering of learning-induced changes in recurrent network dynamics from
large-scale neural recordings.Comment: The last two authors contributed equall
Gradient-trained Weights in Wide Neural Networks Align Layerwise to Error-scaled Input Correlations
Recent works have examined how deep neural networks, which can solve a
variety of difficult problems, incorporate the statistics of training data to
achieve their success. However, existing results have been established only in
limited settings. In this work, we derive the layerwise weight dynamics of
infinite-width neural networks with nonlinear activations trained by gradient
descent. We show theoretically that weight updates are aligned with input
correlations from intermediate layers weighted by error, and demonstrate
empirically that the result also holds in finite-width wide networks. The
alignment result allows us to formulate backpropagation-free learning rules,
named Align-zero and Align-ada, that theoretically achieve the same alignment
as backpropagation. Finally, we test these learning rules on benchmark problems
in feedforward and recurrent neural networks and demonstrate, in wide networks,
comparable performance to backpropagation.Comment: 22 pages, 11 figure
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