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…
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48 results for “Boltzmann weights”
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…
In this work an iterative algorithm based on unsupervised learning is presented, specifically on a Restricted Boltzmann Machine (RBM) to solve a perfect matching problem on a bipartite weighted graph. Iteratively is calculated the weights and the bias parameters that maximize the energy funct…
New method models aptamer libraries as Boltzmann-weighted graph ensembles for better affinity predictions.
problem Anomalous candidates in SELEX datasets obscure true aptamer-ligand affinity.
method Boltzmann graph ensemble embeddings for thermodynamically parameterized exponential-family random graphs.
result Proposed embedding enables robust community detection and subgraph-level explanations for aptamer ligand affinity.
New method for initializing RBM weights without datasets.
problem No dataset-free weight-initialization for RBMs.
method Statistical mechanical analysis to derive Gaussian distribution with optimized standard deviation.
result Optimal weight initialization improves learning efficiency in RBMs.
New invariants for RNA foldings and stuck links defined.
problem Defining invariants for RNA foldings and stuck links.
method Assigning Boltzmann weights at classical and stuck crossings.
result Explicit computations of new invariants provided.
EWFM trains continuous flows with only energy evaluations, improving sample quality with fewer computations.
problem Efficiently sampling from complex, high-dimensional Boltzmann distributions using only energy evaluations.
method Energy-Weighted Flow Matching (EWFM) using importance sampling and iterative/annealed training.
result Improved sample quality with up to 3 orders of magnitude fewer energy evaluations compared to existing methods.
We study Generalised Restricted Boltzmann Machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as Generalised Hopfield models. We underline the role of the r…
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
We show that the visible sector probability density function of the Riemann-Theta Boltzmann machine corresponds to a gaussian mixture model consisting of an infinite number of component multi-variate gaussians. The weights of the mixture are given by a discrete multi-variate gaussian over the hidden state space. This a…
Conditional restricted Boltzmann machines are undirected stochastic neural networks with a layer of input and output units connected bipartitely to a layer of hidden units. These networks define models of conditional probability distributions on the states of the output units given the states of the input units, parame…
Maximum Likelihood Estimation (MLE) is the bread and butter of system inference for stochastic systems. In some generality, MLE will converge to the correct model in the infinite data limit. In the context of physical approaches to system inference, such as Boltzmann machines, MLE requires the arduous computation of pa…
The autoregressive neural network architecture of the Boltzmann distribution of pairwise interacting spins systemscond-mat.dis-nn
This work maps Boltzmann distributions to ARNNs for better physics-based model approximations.
problem Approximating Boltzmann distributions of binary systems.
method Exact mapping of Boltzmann distribution to autoregressive neural network architecture.
result New ARNN architectures derived from physical models show superior performance.
Enhanced coloring invariant distinguishes folded molecular chain topologies.
problem Apparent indistinguishability of folded chain topologies using current coloring invariants.
method Introduced Boltzmann weights to improve the resolving power of quandle colorings.
result Improved resolution in distinguishing folded chain topologies.
Efficient and Unbiased Sampling from Boltzmann Distributions via Variance-Tuned Diffusion Modelscs.LG
VT-DIS improves sampling from Boltzmann distributions with minimal overhead.
problem Bias in Monte Carlo estimates from score-based diffusion models.
method Variance-Tuned Diffusion Importance Sampling (VT-DIS) adapts noise covariance to correct bias.
result VT-DIS achieves effective sample sizes of 80%, 35%, and 3.5% on benchmarks, using less computational budget.
We propose a particularly structured Boltzmann machine, which we refer to as a dynamic Boltzmann machine (DyBM), as a stochastic model of a multi-dimensional time-series. The DyBM can have infinitely many layers of units but allows exact and efficient inference and learning when its parameters have a proposed structure…
Learning algorithms for energy based Boltzmann architectures that rely on gradient descent are in general computationally prohibitive, typically due to the exponential number of terms involved in computing the partition function. In this way one has to resort to approximation schemes for the evaluation of the gradient.…
Variational mean-field theory for training restricted Boltzmann machines with binary synapsesstat.ML
Unsupervised learning requiring only raw data is not only a fundamental function of the cerebral cortex, but also a foundation for a next generation of artificial neural networks. However, a unified theoretical framework to treat sensory inputs, synapses and neural activity together is still lacking. The computational …
Extracting automatically the complex set of features composing real high-dimensional data is crucial for achieving high performance in machine--learning tasks. Restricted Boltzmann Machines (RBM) are empirically known to be efficient for this purpose, and to be able to generate distributed and graded representations of…
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.
Hardware-accelerated RBM solves large combinatorial problems and integer factorization.
problem Solving large combinatorial optimization and integer factorization problems.
method Logically synthesized RBM architecture, hardware acceleration, and efficient training methods.
result Hardware-accelerated RBM factorizes 16-bit numbers with 10000x speed and 32x power improvements.
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.
A softmax operator applied to a set of values acts somewhat like the maximization function and somewhat like an average. In sequential decision making, softmax is often used in settings where it is necessary to maximize utility but also to hedge against problems that arise from putting all of one's weight behind a sing…
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.
New invariants for virtual knots and links defined via quiver representations.
problem Defining new invariants for virtual knots and links.
method Quiver representations associated to virtual biquandles and rings.
result New polynomial invariants for virtual knots and links.
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.
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.
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…
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…
Flow AIS Bootstrap improves flow training by generating samples in hard-to-reach regions.
problem Training flows with high variance and mode-seeking behavior.
method Augment flows with AIS and minimize -divergence with .
result FAB learns Boltzmann distribution of alanine dipeptide without MD samples.
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.
In this letter, we propose enhanced factored three way restricted Boltzmann machines (EFTW-RBMs) for speech detection. The proposed model incorporates conditional feature learning by multiplying the dynamical state of the third unit, which allows a modulation over the visible-hidden node pairs. Instead of stacking prev…
Improved sampling efficiency for molecular systems using path gradients after Flow Matching.
problem Improving sampling efficiency for complex molecular systems.
method Hybrid approach combining Flow Matching and path gradients.
result Up to a threefold increase in sampling efficiency for molecular systems.
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…
Phase Diagram of Restricted Boltzmann Machines and Generalised Hopfield Networks with Arbitrary Priorscond-mat.dis-nn
Restricted Boltzmann Machines are described by the Gibbs measure of a bipartite spin glass, which in turn corresponds to the one of a generalised Hopfield network. This equivalence allows us to characterise the state of these systems in terms of retrieval capabilities, both at low and high load. We study the paramagnet…
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 .