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.

RBMs were initially proposed under the name Harmonium by Paul Smolensky in 1986, and rose to prominence after Geoffrey Hinton and collaborators used fast learning algorithms for them in the mid-2000s. RBMs have found applications in dimensionality reduction, classification, collaborative filtering, feature learning, topic modelling, immunology, and even many‑body quantum mechanics.

They can be trained in either supervised or unsupervised ways, depending on the task.^{[citation needed]}

As their name implies, RBMs are a variant of Boltzmann machines, with the restriction that their neurons must form a bipartite graph:

By contrast, "unrestricted" Boltzmann machines may have connections between hidden units. This restriction allows for more efficient training algorithms than are available for the general class of Boltzmann machines, in particular the gradient-based contrastive divergence algorithm.

Restricted Boltzmann machines can also be used in deep learning networks. In particular, deep belief networks can be formed by "stacking" RBMs and optionally fine-tuning the resulting deep network with gradient descent and backpropagation.

The standard type of RBM has binary-valued (Boolean) hidden and visible units, and consists of a matrix of weights ${\displaystyle W}$ of size ${\displaystyle m\times n}$. Each weight element ${\displaystyle (w_{i,j})}$ of the matrix is associated with the connection between the visible (input) unit ${\displaystyle v_{i}}$ and the hidden unit ${\displaystyle h_{j}}$. In addition, there are bias weights (offsets) ${\displaystyle a_{i}}$ for ${\displaystyle v_{i}}$ and ${\displaystyle b_{j}}$ for ${\displaystyle h_{j}}$. Given the weights and biases, the energy of a configuration (pair of Boolean vectors) (v,h) is defined as

or, in matrix notation,