77 research outputs found
Semi-Supervised Generation with Cluster-aware Generative Models
Deep generative models trained with large amounts of unlabelled data have
proven to be powerful within the domain of unsupervised learning. Many real
life data sets contain a small amount of labelled data points, that are
typically disregarded when training generative models. We propose the
Cluster-aware Generative Model, that uses unlabelled information to infer a
latent representation that models the natural clustering of the data, and
additional labelled data points to refine this clustering. The generative
performances of the model significantly improve when labelled information is
exploited, obtaining a log-likelihood of -79.38 nats on permutation invariant
MNIST, while also achieving competitive semi-supervised classification
accuracies. The model can also be trained fully unsupervised, and still improve
the log-likelihood performance with respect to related methods
Reduce, Reuse, Recycle: Compositional Generation with Energy-Based Diffusion Models and MCMC
Since their introduction, diffusion models have quickly become the prevailing
approach to generative modeling in many domains. They can be interpreted as
learning the gradients of a time-varying sequence of log-probability density
functions. This interpretation has motivated classifier-based and
classifier-free guidance as methods for post-hoc control of diffusion models.
In this work, we build upon these ideas using the score-based interpretation of
diffusion models, and explore alternative ways to condition, modify, and reuse
diffusion models for tasks involving compositional generation and guidance. In
particular, we investigate why certain types of composition fail using current
techniques and present a number of solutions. We conclude that the sampler (not
the model) is responsible for this failure and propose new samplers, inspired
by MCMC, which enable successful compositional generation. Further, we propose
an energy-based parameterization of diffusion models which enables the use of
new compositional operators and more sophisticated, Metropolis-corrected
samplers. Intriguingly we find these samplers lead to notable improvements in
compositional generation across a wide set of problems such as
classifier-guided ImageNet modeling and compositional text-to-image generation.Comment: ICML 2023, Project Webpage:
https://energy-based-model.github.io/reduce-reuse-recycle
Concrete Score Matching: Generalized Score Matching for Discrete Data
Representing probability distributions by the gradient of their density
functions has proven effective in modeling a wide range of continuous data
modalities. However, this representation is not applicable in discrete domains
where the gradient is undefined. To this end, we propose an analogous score
function called the "Concrete score", a generalization of the (Stein) score for
discrete settings. Given a predefined neighborhood structure, the Concrete
score of any input is defined by the rate of change of the probabilities with
respect to local directional changes of the input. This formulation allows us
to recover the (Stein) score in continuous domains when measuring such changes
by the Euclidean distance, while using the Manhattan distance leads to our
novel score function in discrete domains. Finally, we introduce a new framework
to learn such scores from samples called Concrete Score Matching (CSM), and
propose an efficient training objective to scale our approach to high
dimensions. Empirically, we demonstrate the efficacy of CSM on density
estimation tasks on a mixture of synthetic, tabular, and high-dimensional image
datasets, and demonstrate that it performs favorably relative to existing
baselines for modeling discrete data.Comment: First two authors contributed equall
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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