Title: Scalable Neural Methods for Reasoning With a Symbolic Knowledge   Base. Abstract: We describe a novel way of representing a symbolic knowledge base (KB) called a sparse-matrix reified KB.  This representation enables neural modules that are fully differentiable, faithful to the original semantics of the KB, expressive enough to model multi-hop inferences, and scalable enough to use with realistically large KBs. The sparse-matrix reified KB can be distributed across multiple GPUs, can scale to tens of millions of entities and facts, and is orders of magnitude faster than naive sparse-matrix implementations.  The reified KB enables very simple end-to-end architectures to obtain competitive performance on several benchmarks representing two families of tasks: KB completion, and learning semantic parsers from denotations.