Data Science: Boltzmann Machine (Definitions)

[Boltzmann machine (with learning):] "A net that adjusts its weights so that the equilibrium configuration of the net will solve a given problem, such as an encoder problem" (David H Ackley et al, "A learning algorithm for boltzmann machines", Cognitive Science Vol. 9 (1), 1985)

[Boltzmann machine (without learning):] "A class of neural networks used for solving constrained optimization problems. In a typical Boltzmann machine, the weights are fixed to represent the constraints of the problem and the function to be optimized. The net seeks the solution by changing the activations (either 1 or 0) of the units based on a probability distribution and the effect that the change would have on the energy function or consensus function for the net." (David H Ackley et al, "A learning algorithm for boltzmann machines", Cognitive Science Vol. 9 (1), 1985)

"neural-network model otherwise similar to a Hopfield network but having symmetric interconnects and stochastic processing elements. The input-output relation is optimized by adjusting the bistable values of its internal state variables one at a time, relating to a thermodynamically inspired rule, to reach a global optimum." (Teuvo Kohonen, "Self-Organizing Maps 3rd" Ed., 2001)

"A neural network model consisting of interacting binary units in which the probability of a unit being in the active state depends on its integrated synaptic inputs." (Terrence J Sejnowski, "The Deep Learning Revolution", 2018)

"An unsupervised network that maximizes the product of probabilities assigned to the elements of the training set." (Mário P Véstias, "Deep Learning on Edge: Challenges and Trends", 2020)

"Restricted Boltzmann machine (RBM) is an undirected graphical model that falls under deep learning algorithms. It plays an important role in dimensionality reduction, classification and regression. RBM is the basic block of Deep-Belief Networks. It is a shallow, two-layer neural networks. The first layer of the RBM is called the visible or input layer while the second is the hidden layer. In RBM the interconnections between visible units and hidden units are established using symmetric weights." (S Abirami & P Chitra, "The Digital Twin Paradigm for Smarter Systems and Environments: The Industry Use Cases", Advances in Computers, 2020)

"A deep Boltzmann machine (DBM) is a type of binary pairwise Markov random field (undirected probabilistic graphical model) with multiple layers of hidden random variables." (Udit Singhania & B. K. Tripathy, "Text-Based Image Retrieval Using Deep Learning",  2021) 

"A Boltzmann machine is a neural network of symmetrically connected nodes that make their own decisions whether to activate. Boltzmann machines use a straightforward stochastic learning algorithm to discover “interesting” features that represent complex patterns in the database." (DeepAI) [source]

"Boltzmann Machines is a type of neural network model that was inspired by the physical process of thermodynamics and statistical mechanics. [...] Full Boltzmann machines are impractical to train, which is one of the reasons why a limited form, called the restricted Boltzmann machine, is used." (Accenture)

"RBMs [Restricted Boltzmann Machines] are a type of probabilistic graphical model that can be interpreted as a stochastic artificial neural network. RBNs learn a representation of the data in an unsupervised manner. An RBN consists of visible and hidden layer, and connections between binary neurons in each of these layers. RBNs can be efficiently trained using Contrastive Divergence, an approximation of gradient descent." (Wild ML)