Context-Controlled Linear Mappings Using Binary Sign Flips and Fast Walsh–Hadamard Transforms 1. Generating a constrained binary context The first component constructs a binary context vector from analog control signals and fixed Gaussian random vectors. Begin with analog signals, for example random projections of the input. Associate each signal with a fixed random vector whose components are sampled from a Gaussian distribution. Multiply each random vector by its corresponding analog signal and sum the weighted vectors. Binarize the resulting vector into +1 and -1 values. The result is a binary context that controls the signs of selected input dimensions. This construction provides a way to restrict the binary context space. Although an m-dimensional binary vector has 2ⁿ possible patterns in principle, a low-dimensional analog control process will reach only a subset of them. The context mechanism can therefore introduce useful variation without necessarily exposing the trainable map...