  Coded distributed computation has become common practice for performing
gradient descent on large datasets to mitigate stragglers and other faults.
This paper proposes a novel algorithm that encodes the partial derivatives
themselves and furthermore optimizes the codes by performing lossy compression
on the derivative codewords by maximizing the information contained in the
codewords while minimizing the information between the codewords. The utility
of this application of coding theory is a geometrical consequence of the
observed fact in optimization research that noise is tolerable, sometimes even
helpful, in gradient descent based learning algorithms since it helps avoid
overfitting and local minima. This stands in contrast with much current
conventional work on distributed coded computation which focuses on recovering
all of the data from the workers. A second further contribution is that the
low-weight nature of the coding scheme allows for asynchronous gradient updates
since the code can be iteratively decoded; i.e., a worker's task can
immediately be updated into the larger gradient. The directional derivative is
always a linear function of the direction vectors; thus, our framework is
robust since it can apply linear coding techniques to general machine learning
frameworks such as deep neural networks.
