We introduce a new method for training deep Boltzmann machines jointly. Prior methods require an initial learning pass that trains the deep Boltzmann machine greedily, one layer at a time, or do not perform well on classifi- cation tasks.
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48 results for “deep Boltzmann machines”
Boltzmann machines as two-dimensional tensor networkscond-mat.stat-mech
RBM and DBM are represented as 2D tensor networks, revealing their expressive power and efficiency.
problem Understanding and optimizing RBM and DBM models.
method Representing RBM and DBM as 2D tensor networks and developing an efficient tensor network contraction algorithm.
result The proposed algorithm for computing partition functions is more accurate than state-of-the-art methods.
We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as the visible layer. We show that, within certain parameter domains, deep Boltzmann…
This paper provides a tutorial on Boltzmann Machines and Deep Belief Networks.
problem Understanding and applying Boltzmann Machines and Deep Belief Networks.
method Explains the structures, conditional distributions, Gibbs sampling, training methods, and deep belief networks of RBMs.
result Comprehensive overview of RBMs and DBNs, useful in various fields.
Restricted Boltzmann Machines (RBM) are a neural network model used in deep learning.
problem Representing probability distributions with hidden variables.
method Mathematical analysis and geometric study of RBM structures.
result Geometry of probability distributions in RBM models.
Deep Boltzmann machines are in principle powerful models for extracting the hierarchical structure of data. Unfortunately, attempts to train layers jointly (without greedy layer-wise pretraining) have been largely unsuccessful. We propose a modification of the learning algorithm that initially recenters the output of t…
Since learning is typically very slow in Boltzmann machines, there is a need to restrict connections within hidden layers. However, the resulting states of hidden units exhibit statistical dependencies. Based on this observation, we propose using regularization upon the activation possibilities of hidden unit…
We introduce a Deep Boltzmann Machine model suitable for modeling and extracting latent semantic representations from a large unstructured collection of documents. We overcome the apparent difficulty of training a DBM with judicious parameter tying. This parameter tying enables an efficient pretraining algorithm and a …
A random energy approach to deep learningcond-mat.dis-nn
Deep learning depends on tuning layers near critical points.
problem Understanding how deep learning architectures depend on tuning parameters.
method Random energy approach to analyze statistical dependence in deep belief networks.
result Statistical dependence can propagate only if layers are tuned near critical points.
Improved training of RBMs using mode-assisted gradient updates.
problem Difficulty in training RBMs due to hard-to-compute gradients.
method Combining standard gradient updates with mode-assisted off-gradient direction.
result Mode training improves training speed and stability, reduces KL divergence.
Since 2006, deep learning (DL) has become a rapidly growing research direction, redefining state-of-the-art performances in a wide range of areas such as object recognition, image segmentation, speech recognition and machine translation. In modern manufacturing systems, data-driven machine health monitoring is gaining …
Much work has been done refining and characterizing the receptive fields learned by deep learning algorithms. A lot of this work has focused on the development of Gabor-like filters learned when enforcing sparsity constraints on a natural image dataset. Little work however has investigated how these filters might expan…
One conjecture in both deep learning and classical connectionist viewpoint is that the biological brain implements certain kinds of deep networks as its back-end. However, to our knowledge, a detailed correspondence has not yet been set up, which is important if we want to bridge between neuroscience and machine learni…
Deep learning approximates system moments from data.
problem Approximating moments of spatial probabilistic systems.
method Dynamic Boltzmann Distributions (DBDs) with deep Boltzmann machines (DBMs).
result Learned moment closures improve generalization over traditional methods.
Paper explores Monge-Ampère in deep learning and quantum geometry.
problem Understanding the Monge-Ampère equation in deep learning.
method Review of Boltzmann learning, connection to optimal transport, insights from quantum geometry, renormalization group flow.
result Space of covariance matrices in learning dynamics coincides with the CAH cone.
DBMs model Fitbit usage patterns revealing two distinct weekly usage habits.
problem Challenges in modeling activity tracker data due to unlabeled data.
method Deep Boltzmann Machines (DBMs) for unsupervised learning of weekly usage patterns.
result Two distinct weekly usage patterns identified: frequent Monday-Tuesday use and consistent weekly use.
We present a layered Boltzmann machine (BM) that can better exploit the advantages of a distributed representation. It is widely believed that deep BMs (DBMs) have far greater representational power than its shallow counterpart, restricted Boltzmann machines (RBMs). However, this expectation on the supremacy of DBMs ov…
Deep Learning the Ising Model Near Criticalitycond-mat.dis-nn
Deep networks outperform shallow ones in Ising model near criticality.
problem Comparing deep vs shallow neural networks for Ising model.
method Trained deep and shallow Boltzmann machines on Ising system data.
result Accuracy depends only on first hidden layer size, not network depth.
End-to-end training of DBMs with improved gradient estimation.
problem Biased gradient estimation in DBMs, especially with high-dimensional states.
method Unbiased contrastive divergence using MH coupling and local mode initialization.
result End-to-end training of DBMs without greedy pretraining, achieving FID score of 10.33 for MNIST.
Conditional probabilities modeled using Riemann-Theta Boltzmann Machines.
problem Modeling conditional probabilities in Boltzmann machines.
method Deriving conditional density functions from Riemann-Theta Boltzmann machines.
result Conditional densities can be directly inferred from Riemann-Theta 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 g…
Deep neural network improves DNA methylation data analysis.
problem Analyzing highly dimensional DNA methylation data with bounded support.
method Designing a deep neural network composed of stacked binary restricted Boltzmann machines.
result Deep features learned by the neural network perform best in cluster analysis of breast cancer DNA methylation data.
TBMs learn Gibbs distribution adaptively from data.
problem Combinatorial explosion in Boltzmann machines.
method Adaptive construction of minimum required sample space.
result TBMs outperform other Boltzmann machines in efficiency and effectiveness.
Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their success is the existence of efficient and practical stochastic algorithms, such a…
Deep Temperingcs.LG
Restricted Boltzmann Machines (RBMs) are one of the fundamental building blocks of deep learning. Approximate maximum likelihood training of RBMs typically necessitates sampling from these models. In many training scenarios, computationally efficient Gibbs sampling procedures are crippled by poor mixing. In this work w…
A new machine learning model uses score matching to estimate probability densities efficiently.
problem Estimating probability density functions is challenging.
method Introduced a product Jacobi-Theta Boltzmann machine (pJTBM) and used score matching for efficient fitting.
result The pJTBM can fit probability densities more efficiently than the RTBM using score matching.
New method uses RBM flows to find critical temperatures in Ising models.
problem Detecting critical temperatures in RBM flows without model topology information.
method Iterative sampling from RBM mapped on Ising model temperature space using a neural network thermometer.
result Flow of RBM trained on Ising spin configurations approaches critical temperature around .
We introduce a new method for training deep Boltzmann machines jointly. Prior methods of training DBMs require an initial learning pass that trains the model greedily, one layer at a time, or do not perform well on classification tasks. In our approach, we train all layers of the DBM simultaneously, using a novel train…
D-Wave computers struggle with sampling Boltzmann distributions efficiently.
problem Sampling Boltzmann distributions efficiently on D-Wave computers.
method Exploring various obstacles and remaining difficulties.
result Challenges remain in using D-Wave computers for efficient sampling.
Can Boltzmann Machines Discover Cluster Updates ?physics.comp-ph
Boltzmann machines are physics informed generative models with wide applications in machine learning. They can learn the probability distribution from an input dataset and generate new samples accordingly. Applying them back to physics, the Boltzmann machines are ideal recommender systems to accelerate Monte Carlo simu…
Neural Boltzmann Machines improve on CRBMs for modeling data.
problem Limited expressivity of CRBMs with noisy data.
method Convert CRBM parameters to neural networks.
result NBMs can approximate data likelihood better.
Quantum Boltzmann Machines trained on quantum annealers produce noisy synthetic data.
problem Training quantum Boltzmann machines on quantum annealers for financial data generation.
method Used D-Wave Advantage 4.1 quantum annealer to train QBMs and compare with classical RBMs.
result Quantum Boltzmann Machines trained on quantum annealers are noisier and less effective than classical RBMs.
New method trains Boltzmann machines without supervision.
problem Training unsupervised learning models.
method Mixed binary quadratic feasibility problem formulation.
result Theory validated on XOR patterns.
CAP-BM learns complex-valued data's amplitude and phase distributions.
problem Learning from complex-valued data with amplitude variation.
method Complex Amplitude-Phase Boltzmann machine (CAP-BM) with Gibbs sampling.
result Necessity of amplitude-amplitude coupling term in CAP-BM.
We propose a relaxation-based approximate inference algorithm that samples near-MAP configurations of a binary pairwise Markov random field. We experiment on MAP inference tasks in several restricted Boltzmann machines. We also use our underlying sampler to estimate the log-partition function of restricted Boltzmann ma…
Improved discrete VAEs using relaxed Boltzmann priors for better performance.
problem Training discrete VAEs with tighter importance-weighted bounds.
method Two approaches for relaxing Boltzmann machines to continuous distributions, based on generalized overlapping transformations and the Gaussian integral trick.
result These relaxations outperform previous discrete VAEs with Boltzmann priors on MNIST and OMNIGLOT datasets.
Reduced hidden units in RBM without performance loss.
problem Maintaining performance with fewer hidden units in RBM.
method Proposed algorithm to decrease hidden units while keeping performance constant.
result Demonstrated through numerical simulations that fewer hidden units can be used without performance degradation.
Large-scale automated meta-analysis of neuroimaging data has recently established itself as an important tool in advancing our understanding of human brain function. This research has been pioneered by NeuroSynth, a database collecting both brain activation coordinates and associated text across a large cohort of neuro…
We improve recently published results about resources of Restricted Boltzmann Machines (RBM) and Deep Belief Networks (DBN) required to make them Universal Approximators. We show that any distribution p on the set of binary vectors of length n can be arbitrarily well approximated by an RBM with k-1 hidden units, where …
Image denoising based on a probabilistic model of local image patches has been employed by various researchers, and recently a deep (denoising) autoencoder has been proposed by Burger et al. [2012] and Xie et al. [2012] as a good model for this. In this paper, we propose that another popular family of models in the fie…
Introduces a Boltzmann machine with Riemann-Theta functions for continuous and discrete states.
problem Modeling continuous and discrete states in neural networks.
method Develops a Boltzmann machine with continuous visible and discrete hidden states, solving probability density and conditional expectation analytically.
result Derives a novel parametric density function involving Riemann-Theta functions and uses it as an activation function in a feedforward neural network.
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In th…
Graph clustering improved using Boltzmann machine heuristics.
problem Graph clustering to form densely connected clusters.
method Two mathematical programming formulations, two variations of Boltzmann machine heuristic.
result Boltzmann machine provides superior solutions and faster computation times.
The Riemann-Theta Boltzmann machine's visible sector is sampled using a discrete multi-variate Gaussian.
problem Sampling the visible sector of the Riemann-Theta Boltzmann machine.
method Discrete multi-variate Gaussian over the hidden state space.
result The visible sector probability density function is an infinite mixture of multi-variate Gaussians.
Empirical Bayes method for Boltzmann machines avoids computational hardness.
problem Estimating hyperparameters of Boltzmann machines with intractable integrations.
method Replica method and Plefka expansion to avoid integrations.
result Simple and fast algorithm with a bias in estimates.
We propose an expectation-maximization-like(EMlike) method to train Boltzmann machine with unconstrained connectivity. It adopts Monte Carlo approximation in the E-step, and replaces the intractable likelihood objective with efficiently computed objectives or directly approximates the gradient of likelihood objective i…
BEAMs use adversarial training to improve RBM performance.
problem Likelihood-based training fails to penalize high-probability regions.
method Adversarial training against RBM hidden layer activations.
result BEAMs outperform RBMs and GANs on benchmarks.
DO-EM framework for quantum models improves generative tasks.
problem Lack of Expectation-Maximization framework for density operators.
method Demonstrated inequality for density operators, derived DO-EM framework.
result DO-EM framework outperforms probabilistic models in generative tasks.