Exact Backpropagation in Binary Weighted Networks with Group Weight Transformations

Quantization based model compression serves as high performing and fast approach for inference that yields highly compressed models compared to their full-precision floating point counterparts. The most extreme quantization is a 1-bit representation of parameters such that they have only two possible values, typically -1(0) or +1. Models that constrain the weights to binary values enable efficient implementation of the ubiquitous dot product by additions only without requiring floating point multiplications which is beneficial for resources constrained inference. The main contribution of this work is the introduction of a method to smooth the combinatorial problem of determining a binary vector of weights to minimize the expected loss for a given objective by means of empirical risk minimization with backpropagation. This is achieved by approximating a multivariate binary state over the weights utilizing a deterministic and differentiable transformation of real-valued continuous parameters. The proposed method adds little overhead in training, can be readily applied without any substantial modifications to the original architecture, does not introduce additional saturating non-linearities or auxiliary losses, and does not prohibit applying other methods for binarizing the activations. It is demonstrated that contrary to common assertions made in the literature, binary weighted networks can train well with the same standard optimization techniques and similar hyperparameters settings as their full-precision counterparts, namely momentum SGD with large learning rates and $L_2$ regularization. The source code is publicly available at https://bitbucket.org/YanivShu/binary_weighted_networks_public