2,407 research outputs found
On the Challenges of Physical Implementations of RBMs
Restricted Boltzmann machines (RBMs) are powerful machine learning models,
but learning and some kinds of inference in the model require sampling-based
approximations, which, in classical digital computers, are implemented using
expensive MCMC. Physical computation offers the opportunity to reduce the cost
of sampling by building physical systems whose natural dynamics correspond to
drawing samples from the desired RBM distribution. Such a system avoids the
burn-in and mixing cost of a Markov chain. However, hardware implementations of
this variety usually entail limitations such as low-precision and limited range
of the parameters and restrictions on the size and topology of the RBM. We
conduct software simulations to determine how harmful each of these
restrictions is. Our simulations are designed to reproduce aspects of the
D-Wave quantum computer, but the issues we investigate arise in most forms of
physical computation
Metric-Free Natural Gradient for Joint-Training of Boltzmann Machines
This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for
training Boltzmann Machines. Similar in spirit to the Hessian-Free method of
Martens [8], our algorithm belongs to the family of truncated Newton methods
and exploits an efficient matrix-vector product to avoid explicitely storing
the natural gradient metric . This metric is shown to be the expected second
derivative of the log-partition function (under the model distribution), or
equivalently, the variance of the vector of partial derivatives of the energy
function. We evaluate our method on the task of joint-training a 3-layer Deep
Boltzmann Machine and show that MFNG does indeed have faster per-epoch
convergence compared to Stochastic Maximum Likelihood with centering, though
wall-clock performance is currently not competitive
Conditional Restricted Boltzmann Machines for Structured Output Prediction
Conditional Restricted Boltzmann Machines (CRBMs) are rich probabilistic
models that have recently been applied to a wide range of problems, including
collaborative filtering, classification, and modeling motion capture data.
While much progress has been made in training non-conditional RBMs, these
algorithms are not applicable to conditional models and there has been almost
no work on training and generating predictions from conditional RBMs for
structured output problems. We first argue that standard Contrastive
Divergence-based learning may not be suitable for training CRBMs. We then
identify two distinct types of structured output prediction problems and
propose an improved learning algorithm for each. The first problem type is one
where the output space has arbitrary structure but the set of likely output
configurations is relatively small, such as in multi-label classification. The
second problem is one where the output space is arbitrarily structured but
where the output space variability is much greater, such as in image denoising
or pixel labeling. We show that the new learning algorithms can work much
better than Contrastive Divergence on both types of problems
A Deterministic and Generalized Framework for Unsupervised Learning with Restricted Boltzmann Machines
Restricted Boltzmann machines (RBMs) are energy-based neural-networks which
are commonly used as the building blocks for deep architectures neural
architectures. In this work, we derive a deterministic framework for the
training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer
(TAP) mean-field approximation of widely-connected systems with weak
interactions coming from spin-glass theory. While the TAP approach has been
extensively studied for fully-visible binary spin systems, our construction is
generalized to latent-variable models, as well as to arbitrarily distributed
real-valued spin systems with bounded support. In our numerical experiments, we
demonstrate the effective deterministic training of our proposed models and are
able to show interesting features of unsupervised learning which could not be
directly observed with sampling. Additionally, we demonstrate how to utilize
our TAP-based framework for leveraging trained RBMs as joint priors in
denoising problems
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