A New Parallel Algorithm for Sinkhorn Word-Movers Distance and Its Performance on PIUMA and Xeon CPU
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The Word Movers Distance (WMD) measures the semantic dissimilarity between two text documents by computing the cost of optimally moving all words of a source/query document to the most similar words of a target document. Computing WMD between two documents is costly because it requires solving an O(V^3log(V)) optimization problem where V is the number of unique words in the document. Fortunately, WMD can be framed as an Earth Mover's Distance (EMD) for which the algorithmic complexity can be reduced to O(V^2) by adding an entropy penalty to the optimization problem and solving it using the Sinkhorn-Knopp algorithm. Additionally, the computation can be made highly parallel by adopting a batching approach, i.e., computing the WMD of a single query document against multiple target documents at once. Sinkhorn WMD is a key kernel used in many ML/NLP applications. and usually gets implemented in Python. However, a straightforward Python implementation may leave significant performance on the table even though it may internally call optimized C++ BLAS routines. We present a new sparse Parallel Algorithm for Sinkhorn-Knopp Word-movers Distance to compute the semantic distance of one document to many other documents by adopting the O(V^2) EMD algorithm. We algorithmically transform O(V^2) dense compute-heavy EMD version into an equivalent sparse one using new fused SDDMM-SpMM (sparse selection of dense-dense matrix-, sparse-dense matrix-multiplication) kernels. We implemented and optimized this algorithm for two very different architectures – the new Intel Programmable Integrated Unified Memory Architecture (PIUMA) and Intel Xeon CPUs. We show that we were able to reach close to peak performance on both platforms.
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