12,284 research outputs found
Stochastic Digital Backpropagation
In this paper, we propose a novel detector for single-channel long-haul coherent optical communications, termed
stochastic digital backpropagation (SDBP), which takes into account noise from the optical amplifiers in addition to handling deterministic linear and nonlinear impairments. We discuss the design approach behind this detector, which is based on the maximum a posteriori (MAP) principle. As closed-form expressions of the MAP detector are not tractable for coherent optical transmission, we employ the framework of Bayesian graphical models, which allows a numerical evaluation of the proposed detector. Through simulations, we observe that by accounting for nonlinear signal–noise interactions, we achieve a significant improvement in system reach with SDBP over digital backpropagation (DBP) for systems with periodic inline
optical dispersion compensation. In uncompensated links with
high symbol rates, the performance difference in terms of system reach for SDBP over DBP is small. In the absence of noise, the proposed detector is equivalent to the well-known DBP detector
Stochastic Digital Backpropagation with Residual Memory Compensation
Stochastic digital backpropagation (SDBP) is an extension of digital
backpropagation (DBP) and is based on the maximum a posteriori principle. SDBP
takes into account noise from the optical amplifiers in addition to handling
deterministic linear and nonlinear impairments. The decisions in SDBP are taken
on a symbol-by-symbol (SBS) basis, ignoring any residual memory, which may be
present due to non-optimal processing in SDBP. In this paper, we extend SDBP to
account for memory between symbols. In particular, two different methods are
proposed: a Viterbi algorithm (VA) and a decision directed approach. Symbol
error rate (SER) for memory-based SDBP is significantly lower than the
previously proposed SBS-SDBP. For inline dispersion-managed links, the VA-SDBP
has up to 10 and 14 times lower SER than DBP for QPSK and 16-QAM, respectively.Comment: 7 pages, accepted to publication in 'Journal of Lightwave Technology
(JLT)
Improved Lower Bounds on Mutual Information Accounting for Nonlinear Signal-Noise Interaction
In fiber-optic communications, evaluation of mutual information (MI) is still
an open issue due to the unavailability of an exact and mathematically
tractable channel model. Traditionally, lower bounds on MI are computed by
approximating the (original) channel with an auxiliary forward channel. In this
paper, lower bounds are computed using an auxiliary backward channel, which has
not been previously considered in the context of fiber-optic communications.
Distributions obtained through two variations of the stochastic digital
backpropagation (SDBP) algorithm are used as auxiliary backward channels and
these bounds are compared with bounds obtained through the conventional digital
backpropagation (DBP). Through simulations, higher information rates were
achieved with SDBP, {which can be explained by the ability of SDBP to account
for nonlinear signal--noise interactionsComment: 8 pages, 5 figures, accepted for publication in Journal of Lightwave
Technolog
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
Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation
We introduce Equilibrium Propagation, a learning framework for energy-based
models. It involves only one kind of neural computation, performed in both the
first phase (when the prediction is made) and the second phase of training
(after the target or prediction error is revealed). Although this algorithm
computes the gradient of an objective function just like Backpropagation, it
does not need a special computation or circuit for the second phase, where
errors are implicitly propagated. Equilibrium Propagation shares similarities
with Contrastive Hebbian Learning and Contrastive Divergence while solving the
theoretical issues of both algorithms: our algorithm computes the gradient of a
well defined objective function. Because the objective function is defined in
terms of local perturbations, the second phase of Equilibrium Propagation
corresponds to only nudging the prediction (fixed point, or stationary
distribution) towards a configuration that reduces prediction error. In the
case of a recurrent multi-layer supervised network, the output units are
slightly nudged towards their target in the second phase, and the perturbation
introduced at the output layer propagates backward in the hidden layers. We
show that the signal 'back-propagated' during this second phase corresponds to
the propagation of error derivatives and encodes the gradient of the objective
function, when the synaptic update corresponds to a standard form of
spike-timing dependent plasticity. This work makes it more plausible that a
mechanism similar to Backpropagation could be implemented by brains, since
leaky integrator neural computation performs both inference and error
back-propagation in our model. The only local difference between the two phases
is whether synaptic changes are allowed or not
Hardware-efficient on-line learning through pipelined truncated-error backpropagation in binary-state networks
Artificial neural networks (ANNs) trained using backpropagation are powerful
learning architectures that have achieved state-of-the-art performance in
various benchmarks. Significant effort has been devoted to developing custom
silicon devices to accelerate inference in ANNs. Accelerating the training
phase, however, has attracted relatively little attention. In this paper, we
describe a hardware-efficient on-line learning technique for feedforward
multi-layer ANNs that is based on pipelined backpropagation. Learning is
performed in parallel with inference in the forward pass, removing the need for
an explicit backward pass and requiring no extra weight lookup. By using binary
state variables in the feedforward network and ternary errors in
truncated-error backpropagation, the need for any multiplications in the
forward and backward passes is removed, and memory requirements for the
pipelining are drastically reduced. Further reduction in addition operations
owing to the sparsity in the forward neural and backpropagating error signal
paths contributes to highly efficient hardware implementation. For
proof-of-concept validation, we demonstrate on-line learning of MNIST
handwritten digit classification on a Spartan 6 FPGA interfacing with an
external 1Gb DDR2 DRAM, that shows small degradation in test error performance
compared to an equivalently sized binary ANN trained off-line using standard
back-propagation and exact errors. Our results highlight an attractive synergy
between pipelined backpropagation and binary-state networks in substantially
reducing computation and memory requirements, making pipelined on-line learning
practical in deep networks.Comment: Now also consider 0/1 binary activations. Memory access statistics
reporte
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