104 research outputs found
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
Contrastive Learning for Lifted Networks
In this work we address supervised learning of neural networks via lifted
network formulations. Lifted networks are interesting because they allow
training on massively parallel hardware and assign energy models to
discriminatively trained neural networks. We demonstrate that the training
methods for lifted networks proposed in the literature have significant
limitations and show how to use a contrastive loss to address those
limitations. We demonstrate that this contrastive training approximates
back-propagation in theory and in practice and that it is superior to the
training objective regularly used for lifted networks.Comment: 9 pages, BMVC 201
Contrastive Hebbian Learning with Random Feedback Weights
Neural networks are commonly trained to make predictions through learning
algorithms. Contrastive Hebbian learning, which is a powerful rule inspired by
gradient backpropagation, is based on Hebb's rule and the contrastive
divergence algorithm. It operates in two phases, the forward (or free) phase,
where the data are fed to the network, and a backward (or clamped) phase, where
the target signals are clamped to the output layer of the network and the
feedback signals are transformed through the transpose synaptic weight
matrices. This implies symmetries at the synaptic level, for which there is no
evidence in the brain. In this work, we propose a new variant of the algorithm,
called random contrastive Hebbian learning, which does not rely on any synaptic
weights symmetries. Instead, it uses random matrices to transform the feedback
signals during the clamped phase, and the neural dynamics are described by
first order non-linear differential equations. The algorithm is experimentally
verified by solving a Boolean logic task, classification tasks (handwritten
digits and letters), and an autoencoding task. This article also shows how the
parameters affect learning, especially the random matrices. We use the
pseudospectra analysis to investigate further how random matrices impact the
learning process. Finally, we discuss the biological plausibility of the
proposed algorithm, and how it can give rise to better computational models for
learning
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
Bidirectional Learning in Recurrent Neural Networks Using Equilibrium Propagation
Neurobiologically-plausible learning algorithms for recurrent neural networks that can perform supervised learning are a neglected area of study. Equilibrium propagation is a recent synthesis of several ideas in biological and artificial neural network research that uses a continuous-time, energy-based neural model with a local learning rule. However, despite dealing with recurrent networks, equilibrium propagation has only been applied to discriminative categorization tasks. This thesis generalizes equilibrium propagation to bidirectional learning with asymmetric weights. Simultaneously learning the discriminative as well as generative transformations for a set of data points and their corresponding category labels, bidirectional equilibrium propagation utilizes recurrence and weight asymmetry to share related but non-identical representations within the network. Experiments on an artificial dataset demonstrate the ability to learn both transformations, as well as the ability for asymmetric-weight networks to generalize their discriminative training to the untrained generative task
Backpropagation at the Infinitesimal Inference Limit of Energy-Based Models: Unifying Predictive Coding, Equilibrium Propagation, and Contrastive Hebbian Learning
How the brain performs credit assignment is a fundamental unsolved problem in
neuroscience. Many `biologically plausible' algorithms have been proposed,
which compute gradients that approximate those computed by backpropagation
(BP), and which operate in ways that more closely satisfy the constraints
imposed by neural circuitry. Many such algorithms utilize the framework of
energy-based models (EBMs), in which all free variables in the model are
optimized to minimize a global energy function. However, in the literature,
these algorithms exist in isolation and no unified theory exists linking them
together. Here, we provide a comprehensive theory of the conditions under which
EBMs can approximate BP, which lets us unify many of the BP approximation
results in the literature (namely, predictive coding, equilibrium propagation,
and contrastive Hebbian learning) and demonstrate that their approximation to
BP arises from a simple and general mathematical property of EBMs at free-phase
equilibrium. This property can then be exploited in different ways with
different energy functions, and these specific choices yield a family of
BP-approximating algorithms, which both includes the known results in the
literature and can be used to derive new ones.Comment: 31/05/22 initial upload; 22/06/22 change corresponding author;
03/08/22 revision
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