Brain-inspired learning in physical hardware has enormous potential to learn fast at minimal energy expenditure. One of the characteristics of biological learning systems is their ability to learn in the presence of various noise sources. Inspired by this observation, we introduce a novel noise-based learning approach for physical systems implementing multi-layer neural networks. Simulation results show that our approach allows for effective learning whose performance approaches that of the conventional effective yet energy-costly backpropagation algorithm. Using a spintronics hardware implementation, we demonstrate experimentally that learning can be achieved in a small network composed of physical stochastic magnetic tunnel junctions. These results provide a path towards efficient learning in general physical systems which embraces rather than mitigates the noise inherent in physical devices.

Extending Moore's law by augmenting complementary-metal-oxide semiconductor (CMOS) transistors with emerging nanotechnologies (X) has become increasingly important. Accelerating Monte Carlo algorithms that rely on random sampling with such CMOS+X technologies could have significant impact on a large number of fields from probabilistic machine learning, optimization to quantum simulation. In this paper, we show the combination of stochastic magnetic tunnel junction (sMTJ)-based probabilistic bits (p-bits) with versatile Field Programmable Gate Arrays (FPGA) to design a CMOS + X (X = sMTJ) prototype. Our approach enables high-quality true randomness that is essential for Monte Carlo based probabilistic sampling and learning. Our heterogeneous computer successfully performs probabilistic inference and asynchronous Boltzmann learning, despite device-to-device variations in sMTJs. A comprehensive comparison using a CMOS predictive process design kit (PDK) reveals that compact sMTJ-based p-bits replace 10,000 transistors while dissipating two orders of magnitude of less energy (2 fJ per random bit), compared to digital CMOS p-bits. Scaled and integrated versions of our CMOS + stochastic nanomagnet approach can significantly advance probabilistic computing and its applications in various domains by providing massively parallel and truly random numbers with extremely high throughput and energy-efficiency.