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Diagram of a restricted Boltzmann machine with three visible units and four hidden units (no bias units) A restricted Boltzmann machine (RBM) (also called a restricted Sherrington–Kirkpatrick model with external field or restricted stochastic Ising–Lenz–Little model) is a generative stochastic artificial neural network that can learn a probability distribution over its set of inputs.
The elements of the spatial weight matrix are determined by setting = for all connected pairs of nodes with all the other elements set to 0. This makes the spatial weight matrix equivalent to the adjacency matrix of the corresponding network. It is common [2] to row-normalize the matrix ,
In statistical mechanics, multiplicity (also called statistical weight) refers to the number of microstates corresponding to a particular macrostate of a thermodynamic system. [1]
The Lattice Boltzmann methods for solids (LBMS) are a set of methods for solving partial differential equations (PDE) in solid mechanics. The methods use a discretization of the Boltzmann equation(BM), and their use is known as the lattice Boltzmann methods for solids. LBMS methods are categorized by their reliance on: Vectorial distributions [1]
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A graphical representation of a Boltzmann machine with a few weights labeled. Each undirected edge represents dependency and is weighted with weight . In this example there are 3 hidden units (blue) and 4 visible units (white). This is not a restricted Boltzmann machine.
A vertex model is a type of statistical mechanics model in which the Boltzmann weights are associated with a vertex in the model (representing an atom or particle). [1] [2] This contrasts with a nearest-neighbour model, such as the Ising model, in which the energy, and thus the Boltzmann weight of a statistical microstate is attributed to the bonds connecting two neighbouring particles.
IRLS can be used for ℓ 1 minimization and smoothed ℓ p minimization, p < 1, in compressed sensing problems. It has been proved that the algorithm has a linear rate of convergence for ℓ 1 norm and superlinear for ℓ t with t < 1, under the restricted isometry property, which is generally a sufficient condition for sparse solutions.