1,295 research outputs found
Direct Feedback Alignment with Sparse Connections for Local Learning
Recent advances in deep neural networks (DNNs) owe their success to training
algorithms that use backpropagation and gradient-descent. Backpropagation,
while highly effective on von Neumann architectures, becomes inefficient when
scaling to large networks. Commonly referred to as the weight transport
problem, each neuron's dependence on the weights and errors located deeper in
the network require exhaustive data movement which presents a key problem in
enhancing the performance and energy-efficiency of machine-learning hardware.
In this work, we propose a bio-plausible alternative to backpropagation drawing
from advances in feedback alignment algorithms in which the error computation
at a single synapse reduces to the product of three scalar values. Using a
sparse feedback matrix, we show that a neuron needs only a fraction of the
information previously used by the feedback alignment algorithms. Consequently,
memory and compute can be partitioned and distributed whichever way produces
the most efficient forward pass so long as a single error can be delivered to
each neuron. Our results show orders of magnitude improvement in data movement
and improvement in multiply-and-accumulate operations over
backpropagation. Like previous work, we observe that any variant of feedback
alignment suffers significant losses in classification accuracy on deep
convolutional neural networks. By transferring trained convolutional layers and
training the fully connected layers using direct feedback alignment, we
demonstrate that direct feedback alignment can obtain results competitive with
backpropagation. Furthermore, we observe that using an extremely sparse
feedback matrix, rather than a dense one, results in a small accuracy drop
while yielding hardware advantages. All the code and results are available
under https://github.com/bcrafton/ssdfa.Comment: 15 pages, 8 figure
H∞ Optimality Criteria for LMS and Backpropagation
We have recently shown that the widely known LMS algorithm
is an H∞ optimal estimator. The H∞ criterion has been
introduced, initially in the control theory literature, as
a means to ensure robust performance in the face of
model uncertainties and lack of statistical information
on the exogenous signals. We extend here our analysis to the nonlinear setting often encountered in neural networks,
and show that the backpropagation algorithm is locally
H∞ optimal. This fact provides a theoretical justification of the widely observed excellent robustness properties
of the LMS and backpropagation algorithms. We further
discuss some implications of these results
Neural Network Gradient Hamiltonian Monte Carlo
Hamiltonian Monte Carlo is a widely used algorithm for sampling from
posterior distributions of complex Bayesian models. It can efficiently explore
high-dimensional parameter spaces guided by simulated Hamiltonian flows.
However, the algorithm requires repeated gradient calculations, and these
computations become increasingly burdensome as data sets scale. We present a
method to substantially reduce the computation burden by using a neural network
to approximate the gradient. First, we prove that the proposed method still
maintains convergence to the true distribution though the approximated gradient
no longer comes from a Hamiltonian system. Second, we conduct experiments on
synthetic examples and real data sets to validate the proposed method
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