eXmY: A Data Type and Technique for Arbitrary Bit Precision Quantization

Abstract: eXmY is a novel data type for quantization of ML models. It supports both arbitrary bit widths and arbitrary integer and floating point formats. For example, it seamlessly supports 3, 5, 6, 7, 9 bit formats. For a specific bit width, say 7, it defines all possible formats e.g. e0m6, e1m5, e2m4, e3m3, e4m2, e5m1 and e6m0. For non-power of two bit widths e.g. 5, 6, 7, we created a novel encoding and decoding scheme which achieves perfect compression, byte addressability and is amenable to sharding and vector processing. We implemented libraries for emulation, encoding and decoding tensors and checkpoints in C++, TensorFlow, JAX and PAX. For optimal performance, the codecs use SIMD instructions on CPUs and vector instructions on TPUs and GPUs. eXmY is also a technique and exploits the statistical distribution of exponents in tensors. It can be used to quantize weights, static and dynamic activations, gradients, master weights and optimizer state. It can reduce memory (CPU DRAM and accelerator HBM), network and disk storage and transfers. It can increase multi tenancy and accelerate compute. eXmY has been deployed in production for almost 2 years.