An energy-based model (EBM) learns a function that assigns one number, the energy, to every configuration of the variables it cares about. Configurations that fit the data, such as a realistic image or a correct answer paired with its question, get low energy; everything else gets high energy. Making a prediction means searching for the lowest-energy answer given what you already know.
The appeal is freedom. A normal probabilistic model must make its probabilities add up to one, which requires summing over every possible configuration, a quantity called the partition function that is often impossible to compute. An EBM only has to rank configurations, so it can use any neural network as its energy function. When probabilities are needed, energies can be turned into them, with lower energy meaning exponentially more likely.
Training
Learning has two halves: push the energy down on real data and push it up on wrong or made-up configurations. The hard part is finding good “wrong” examples to push up. Classic approaches draw them with MCMC sampling; others use margin-based loss functions against the most tempting wrong answer. LeCun and colleagues framed many familiar models, including some discriminative classifiers, as special cases of this recipe.
Family tree
Hopfield networks and Boltzmann machines are early EBMs: they define an energy over the states of their units and settle into low-energy states. Modern EBMs use deep networks as the energy function; Du and Mordatch scaled MCMC-based training to generate ImageNet images.
The catch
Generating a sample means running a long search or sampling chain rather than a single forward pass, and training can be unstable. That cost is the main reason EBMs remain a research topic more than a production tool.