  The Boltzmann Machine (BM) is a neural network composed of stochastically
firing neurons that can learn complex probability distributions by adapting the
synaptic interactions between the neurons. BMs represent a very generic class
of stochastic neural networks that can be used for data clustering, generative
modelling and deep learning. A key drawback of software-based stochastic neural
networks is the required Monte Carlo sampling, which scales intractably with
the number of neurons. Here, we realize a physical implementation of a BM
directly in the stochastic spin dynamics of a gated ensemble of coupled cobalt
atoms on the surface of semiconducting black phosphorus. Implementing the
concept of orbital memory utilizing scanning tunnelling microscopy, we
demonstrate the bottom-up construction of atomic ensembles whose stochastic
current noise is defined by a reconfigurable multi-well energy landscape.
Exploiting the anisotropic behaviour of black phosphorus, we build ensembles of
atoms with two well-separated intrinsic time scales that represent neurons and
synapses. By characterizing the conditional steady-state distribution of the
neurons for given synaptic configurations, we illustrate that an ensemble can
represent many distinct probability distributions. By probing the intrinsic
synaptic dynamics, we reveal an autonomous reorganization of the synapses in
response to external electrical stimuli. This self-adaptive architecture paves
the way for on-chip learning directly in atomic-scale machine learning
hardware.
