Near-Exponential Convergence Rates for kNN Classification
problem Convergence rates for kNN classification
method Introducing Boltzmann margin
result First near-exponential convergence rates for kNN classification
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48 results for “Boltzmann margin”
RBMs model binary interactions with hidden node activation effects.
problem Understanding how RBM hidden node activation affects binary variable distributions.
method Investigated RBM marginal distributions with different hidden node activation functions.
result Found exact expressions for RBM marginals as interacting binary variables.
The recent book by T. Piketty (Capital in the Twenty-First Century) promoted the important issue of wealth inequality. In the last twenty years, physicists and mathematicians developed models to derive the wealth distribution using discrete and continuous stochastic processes (random exchange models) as well as related…
A new method estimates protein evolutionary fields and couplings from alignments.
problem Estimating evolutionary fields and couplings from protein sequence alignments.
method Boltzmann machine with parallel, persistent Markov chain Monte Carlo method.
result Improved precision in predicting contact residue pairs.
Boltzmann machines (BMs) are appealing candidates for powerful priors in variational autoencoders (VAEs), as they are capable of capturing nontrivial and multi-modal distributions over discrete variables. However, non-differentiability of the discrete units prohibits using the reparameterization trick, essential for lo…
A Kronecker product model is the set of visible marginal probability distributions of an exponential family whose sufficient statistics matrix factorizes as a Kronecker product of two matrices, one for the visible variables and one for the hidden variables. We estimate the dimension of these models by the maximum rank …
Transferable Boltzmann Generators learn to sample unseen molecules efficiently.
problem Generating equilibrium samples of molecular systems.
method Boltzmann Generators using normalizing flows to learn transformations.
result Transferable Boltzmann Generators can predict zero-shot Boltzmann distributions for unseen molecules.
Latent truth discovery, LTD for short, refers to the problem of aggregating ltiple claims from various sources in order to estimate the plausibility of atements about entities. In the absence of a ground truth, this problem is highly challenging, when some sources provide conflicting claims and others no claims at all.…
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.
The paper proposes a probabilistic autoencoder for discovering causal directions between variables.
problem Finding the causal direction between two associated variables.
method Building an autoencoder of the joint distribution and maximizing its estimation capacity relative to marginal distributions.
result The higher estimation capacity is consistent with the unconstrained choice of a distribution representing the cause, while the lower capacity reflects the constraints imposed by the mechanism on the distribution of the effect.
Improves interpretability of anomaly scores in GBRBM-based detection.
problem Difficulty in setting a proper threshold for anomaly scores.
method Proposes a measure based on cumulative distribution and uses simulated annealing for evaluation.
result Established a guideline for setting the threshold using the interpretable measure.
We present transductive Boltzmann machines (TBMs), which firstly achieve transductive learning of the Gibbs distribution. While exact learning of the Gibbs distribution is impossible by the family of existing Boltzmann machines due to combinatorial explosion of the sample space, TBMs overcome the problem by adaptively …
The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a reparameterization of the Riemann-Theta Boltzmann machine modelling the original probability…
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.
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.
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.
New algorithm for learning RBMs with sparse latent variables.
problem Learning RBMs with sparse latent variables efficiently.
method Algorithm with time complexity O(n^(2^s+1)) for sparse RBMs.
result Improves learning time for RBMs with sparse latent variables.
A new method speeds up sampling of Boltzmann distribution in high-dimensional systems.
problem High computational cost of obtaining Jacobian of flow-based models in high dimensions.
method Flow perturbation method that incorporates stochastic perturbations and reweighting.
result Achieves unbiased sampling of Boltzmann distribution with orders of magnitude speedup.
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…
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.
PolarBM models complex-valued audio signals in polar coordinates, improving over conventional methods.
problem Discarding structural information in complex-valued problems simplifies models but loses important amplitude-phase relationships.
method Proposes PolarBM, a novel Boltzmann machine for complex-valued variables in polar coordinates, and LogPolarBM for logarithmic amplitude.
result PolarBM and LogPolarBM achieve superior modeling accuracy compared to conventional models, including deep neural networks.
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.
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.
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…
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.
In 1870s, L. Boltzmann proved the famous -theorem for the Boltzmann equation in the kinetic theory of gas and gave the statistical interpretation of the thermodynamic entropy. In 2002, G. Perelman introduced the notion of -entropy and proved the -entropy formula for the Ricci flow. This plays a crucial role in…
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…
Boltzmann machines are powerful distributions that have been shown to be an effective prior over binary latent variables in variational autoencoders (VAEs). However, previous methods for training discrete VAEs have used the evidence lower bound and not the tighter importance-weighted bound. We propose two approaches fo…
A new sampler and temperature estimation method enable efficient learning of Boltzmann Machines.
problem Efficient learning of Boltzmann Machines (BMs) is challenging due to high training costs and difficulty in parallelization.
method Proposed a new Boltzmann sampler (Langevin SB, LSB) and an efficient method (Conditional Expectation Matching, CEM) for estimating inverse temperature.
result Established an efficient learning framework (Sampler-Adaptive Learning, SAL) for BMs with greater expressive power than Restricted Boltzmann Machines (RBMs).
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…
EDG generates Boltzmann samples from latent variables efficiently.
problem Sampling from complex energy functions in high dimensions.
method Combines variational autoencoders and diffusion models; uses a decoder and diffusion-based encoder.
result EDG outperforms existing methods in various sampling tasks.
BNEM improves Boltzmann sampler efficiency.
problem Generating IID samples from Boltzmann distributions efficiently.
method Bootstrapped Noised Energy Matching (NEM) combined with diffusion-based learning and bootstrapping.
result BNEM achieves state-of-the-art performance with improved robustness.
Inverse problem solved for relativistic Boltzmann equation on spacetime.
problem Determining spacetime from causal measurements.
method Using the nonlinearity of the Boltzmann equation to uniquely determine the spacetime.
result The spacetime is uniquely determined up to isometry in the causal set .
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.
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 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…
Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and luck and not of reason! 2. Data for property, automobile sales, marriages and job m…
In this paper, we build on the biquasiles and dual graph diagrams introduced in arXiv:1610.06969. We introduce \textit{biquasile Boltzmann weights} that enhance the previous knot coloring invariant defined in terms of finite biquasiles and provide examples differentiating links with the same counting invariant, demonst…
CG-BGs combine flow-based models with PMFs to sample large systems efficiently.
problem Sampling equilibrium molecular configurations from the Boltzmann distribution is challenging.
method Coarse-grained Boltzmann Generators (CG-BGs) use flow-based models and learned PMFs for efficient sampling.
result CG-BGs provide a practical route for sampling larger molecular systems efficiently.
Value function estimation is an important task in reinforcement learning, i.e., prediction. The Boltzmann softmax operator is a natural value estimator and can provide several benefits. However, it does not satisfy the non-expansion property, and its direct use may fail to converge even in value iteration. In this pape…
Advanced Mean Field Theory of Restricted Boltzmann Machinecond-mat.stat-mech
Learning in restricted Boltzmann machine is typically hard due to the computation of gradients of log-likelihood function. To describe the network state statistics of the restricted Boltzmann machine, we develop an advanced mean field theory based on the Bethe approximation. Our theory provides an efficient message pas…
The restricted Boltzmann machine is a network of stochastic units with undirected interactions between pairs of visible and hidden units. This model was popularized as a building block of deep learning architectures and has continued to play an important role in applied and theoretical machine learning. Restricted Bolt…
The Boltzmann machine provides a useful framework to learn highly complex, multimodal and multiscale data distributions that occur in the real world. The default method to learn its parameters consists of minimizing the Kullback-Leibler (KL) divergence from training samples to the Boltzmann model. We propose in this wo…
We propose a method to decrease the number of hidden units of the restricted Boltzmann machine while avoiding decrease of the performance measured by the Kullback-Leibler divergence. Then, we demonstrate our algorithm by using numerical simulations.
In emissions trading, the initial allocation of permits is an intractable issue because it needs to be essentially fair to the participating countries. There are many ways to distribute a given total amount of emissions permits among countries, but the existing distribution methods, such as auctioning and grandfatherin…
New geometric perspective for optimal learning on hexagonal structures.
problem Optimal learning process on hexagonal structures.
method Local trivial fibrations and Ceva's theorem.
result Learning can be defined on hexagonal structures.
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…
In recent work, Boltzmann and Fokker-Planck equations were derived for the "Yard-Sale Model" of asset exchange. For the version of the model without redistribution, it was conjectured, based on numerical evidence, that the time-asymptotic state of the model was oligarchy -- complete concentration of wealth by a single …