This work introduces TapirXLA, a replacement for TensorFlow's XLA compiler that embeds recursive fork-join parallelism into XLA's low-level representation of code. Machinelearning applications rely on efficient parallel processing to achieve performance, and they employ a variety of technologies to improve performance, including compiler technology. But compilers in machine-learning frameworks lack a deep understanding of parallelism, causing them to lose performance by missing optimizations on parallel computation. This work studies how Tapir, a compiler intermediate representation (IR) that embeds parallelism into a mainstream compiler IR, can be incorporated into a compiler for machine learning to remedy this problem. TapirXLA modifies the XLA compiler in TensorFlow to employ the Tapir/LLVM compiler to optimize low-level parallel computation. TapirXLA encodes the parallelism within high-level TensorFlow operations using Tapir's representation of fork-join parallelism. TapirXLA also exposes to the compiler implementations of linear-algebra library routines whose parallel operations are encoded using Tapir's representation. We compared the performance of TensorFlow using TapirXLA against TensorFlow using an unmodified XLA compiler. On four neural-network benchmarks, TapirXLA speeds up the parallel running time of the network by a geometric-mean multiplicative factor of 30% to 100%, across four CPU architectures.