Figure 3. Hierarchical generative neural networks.

(A) Deep Boltzmann Machines (DBMs) are deep neural networks of symmetrically coupled stochastic neurons organized in a hierarchy of multiple layers. The DBM learns a hierarchical generative model of the input (e.g., sensory) data presented on the "visible layer". "Hidden layers" contain neurons that encode latent causes of the data: when trained on images (here, handwritten digits) they become tuned to visual features that are increasingly more complex in deeper layers (examples of receptive fields of individual neurons are shown in the right panels [130]). Learning is unsupervised (i.e., it does not require external teaching or reward signal): its objective is to learn a probability distribution that approximates the true probability distribution of the training data. Recurrent connections convey the information sampled from the upper layers downstream to generate data on the visible layer, in a top-down fashion. The divergence between real input and its top-down reconstruction drives the change of connection weights during learning, using Hebbian rules. After learning, recurrent interactions support stochastic inference that leads to denoising, completion or "filling in" of ambiguous (or missing) inputs, in the same sensory modality or in different modalities if the architecture is multimodal (e.g., learns visual and linguistic inputs). Discriminative tasks (here, digit classification) can be learned by adding a layer of neurons representing the class labels. During learning, the model acquires "generic priors": here, prototypical digit shapes that abstract away from many input details [57,130]. (B) After learning, sampling can be conditioned by the class labels to generate prototypical digit shapes "spontaneously", i.e., in the absence of sensor inputs.