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Abstract We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs—even in the case of $$1$$-bit quantization—allow a high-accuracy approximation of the underlying kernels, and the approximation error decays at least polynomially fast as the dimension of the RFFs increases. We also show that the quantized RFFs can be further compressed, yielding an excellent trade-off between memory use and accuracy. Namely, the approximation error now decays exponentially as a function of the bits used. The quantization algorithms we propose are intended for digitizing RFFs without explicit knowledge of the application for which they will be used. Nevertheless, as we empirically show by testing the performance of our methods on several machine learning tasks, our method compares favourably with other state-of-the-art quantization methods. 

We propose a new computationally efficient method for quantizing the weights of pre- trained neural networks that is general enough to handle both multi-layer perceptrons and convolutional neural networks. Our method deterministically quantizes layers in an iterative fashion with no complicated re-training required. Specifically, we quantize each neuron, or hidden unit, using a greedy path-following algorithm. This simple algorithm is equivalent to running a dynamical system, which we prove is stable for quantizing a single-layer neural network (or, alternatively, for quantizing the first layer of a multi-layer network) when the training data are Gaussian. We show that under these assumptions, the quantization error decays with the width of the layer, i.e., its level of over-parametrization. We provide numerical experiments, on multi-layer networks, to illustrate the performance of our methods on MNIST and CIFAR10 data, as well as for quantizing the VGG16 network using ImageNet data.