Hyperdimensional (HD) computing is an emerging paradigm for machine learning based on biologically plausible models of memory. HD computing represents data as random points with i.i.d. components in a high-dimensional, low-precision, space. These points are then used as input to learning algorithms. The i.i.d. and low-precision nature of HD representations accord naturally with highly parallel hardware like FPGAs and PIM architectures and HD computing has recently gained significant popularity in the hardware community [1]–[3]. Existing work on HD computing has focused primarily on learning linear functions over the encodings. However, much data of practical interest is nonlinear, meaning that linear methods may fail to capture important structure in the data. Our goal is to assess the utility of using nonlinear learning algorithms on HD representations of data. A complication arises because nonlinear models are generally more complex computationally than simple linear methods which are traditionally used with HD computing. In this work, we show how nonlinear learning on HD representations can be formulated as a sparse convex optimization problem using the Boolean Fourier transform. We additionally present results from a preliminary empirical study motivated by this formulation designed to assess the possible practical benefits of this approach.
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