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Reservoir computing advances the intriguing idea that a nonlinear recurrent neural circuit—the reservoir—can encode spatio-temporal input signals to enable efficient ways to perform tasks like classification or regression. However, recently the idea of a monolithic reservoir network that simultaneously buffers input signals and expands them into nonlinear features has been challenged. A representation scheme in which memory buffer and expansion into higher-order polynomial features can be configured separately has been shown to significantly outperform traditional reservoir computing in prediction of multivariate time-series. Here we propose a configurable neuromorphic representation scheme that provides competitive performance on prediction, but with significantly better scaling properties than directly materializing higher-order features as in prior work. Our approach combines the use of randomized representations from traditional reservoir computing with mathematical principles for approximating polynomial kernels via such representations. While the memory buffer can be realized with standard reservoir networks, computing higher-order features requires networks of ‘Sigma-Pi’ neurons, i.e., neurons that enable both summation as well as multiplication of inputs. Finally, we provide an implementation of the memory buffer and Sigma-Pi networks on Loihi 2, an existing neuromorphic hardware platform. 

We apply deep learning to daytime satellite imagery to predict changes in income and population at high spatial resolution in US data. For grid cells with lateral dimensions of 1.2 km and 2.4 km (where the average US county has dimension of 51.9 km), our model predictions achieve R 2 values of 0.85 to 0.91 in levels, which far exceed the accuracy of existing models, and 0.32 to 0.46 in decadal changes, which have no counterpart in the literature and are 3–4 times larger than for commonly used nighttime lights. Our network has wide application for analyzing localized shocks. (JEL C45, R11, R23) 

Hyperdimensional (HD) computing is a set of neurally inspired methods for obtaining highdimensional, low-precision, distributed representations of data. These representations can be combined with simple, neurally plausible algorithms to effect a variety of information processing tasks. HD computing has recently garnered significant interest from the computer hardware community as an energy-efficient, low-latency, and noise-robust tool for solving learning problems. In this review, we present a unified treatment of the theoretical foundations of HD computing with a focus on the suitability of representations for learning.