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Register a new userAutomating Generation of Low Precision Deep Learning Operators
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State of the art deep learning models have made steady progress in the fields of computer vision and natural language processing, at the expense of growing model sizes and computational complexity. Deploying these models on low power and mobile devices poses a challenge due to their limited compute capabilities and strict energy budgets. One solution that has generated significant research interest is deploying highly quantized models that operate on low precision inputs and weights less than eight bits, trading off accuracy for performance. These models have a significantly reduced memory footprint (up to 32x reduction) and can replace multiply-accumulates with bitwise operations during compute intensive convolution and fully connected layers. Most deep learning frameworks rely on highly engineered linear algebra libraries such as ATLAS or Intels MKL to implement efficient deep learning operators. To date, none of the popular deep learning directly support low precision operators, partly due to a lack of optimized low precision libraries. In this paper we introduce a work flow to quickly generate high performance low precision deep learning operators for arbitrary precision that target multiple CPU architectures and include optimizations such as memory tiling and vectorization. We present an extensive case study on low power ARM Cortex-A53 CPU, and show how we can generate 1-bit, 2-bit convolutions with speedups up to 16x over an optimized 16-bit integer baseline and 2.3x better than handwritten implementations.
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Deep learning models typically use single-precision (FP32) floating point data types for representing activations and weights, but a slew of recent research work has shown that computations with reduced-precision data types (FP16, 16-bit integers, 8-bit integers or even 4- or 2-bit integers) are enough to achieve same accuracy as FP32 and are much more efficient. Therefore, we designed fbgemm, a high-performance kernel library, from ground up to perform high-performance quantized inference on current generation CPUs. fbgemm achieves efficiency by fusing common quantization operations with a high-performance gemm implementation and by shape- and size-specific kernel code generation at runtime. The library has been deployed at Facebook, where it delivers greater than 2x performance gains with respect to our current production baseline.
Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference - not training. Previous low-precision training algorithms suffered from a fundamental tradeoff: as the number of bits of precision is lowered, quantization noise is added to the model, which limits statistical accuracy. To address this issue, we describe a simple low-precision stochastic gradient descent variant called HALP. HALP converges at the same theoretical rate as full-precision algorithms despite the noise introduced by using low precision throughout execution. The key idea is to use SVRG to reduce gradient variance, and to combine this with a novel technique called bit centering to reduce quantization error. We show that on the CPU, HALP can run up to $4 times$ faster than full-precision SVRG and can match its convergence trajectory. We implemented HALP in TensorQuant, and show that it exceeds the validation performance of plain low-precision SGD on two deep learning tasks.
Why and how that deep learning works well on different tasks remains a mystery from a theoretical perspective. In this paper we draw a geometric picture of the deep learning system by finding its analogies with two existing geometric structures, the geometry of quantum computations and the geometry of the diffeomorphic template matching. In this framework, we give the geometric structures of different deep learning systems including convolutional neural networks, residual networks, recursive neural networks, recurrent neural networks and the equilibrium prapagation framework. We can also analysis the relationship between the geometrical structures and their performance of different networks in an algorithmic level so that the geometric framework may guide the design of the structures and algorithms of deep learning systems.
Crystal-structure phase mapping is a core, long-standing challenge in materials science that requires identifying crystal structures, or mixtures thereof, in synthesized materials. Materials science experts excel at solving simple systems but cannot solve complex systems, creating a major bottleneck in high-throughput materials discovery. Herein we show how to automate crystal-structure phase mapping. We formulate phase mapping as an unsupervised pattern demixing problem and describe how to solve it using Deep Reasoning Networks (DRNets). DRNets combine deep learning with constraint reasoning for incorporating scientific prior knowledge and consequently require only a modest amount of (unlabeled) data. DRNets compensate for the limited data by exploiting and magnifying the rich prior knowledge about the thermodynamic rules governing the mixtures of crystals with constraint reasoning seamlessly integrated into neural network optimization. DRNets are designed with an interpretable latent space for encoding prior-knowledge domain constraints and seamlessly integrate constraint reasoning into neural network optimization. DRNets surpass previous approaches on crystal-structure phase mapping, unraveling the Bi-Cu-V oxide phase diagram, and aiding the discovery of solar-fuels materials.
Training of large-scale deep neural networks is often constrained by the available computational resources. We study the effect of limited precision data representation and computation on neural network training. Within the context of low-precision fixed-point computations, we observe the rounding scheme to play a crucial role in determining the networks behavior during training. Our results show that deep networks can be trained using only 16-bit wide fixed-point number representation when using stochastic rounding, and incur little to no degradation in the classification accuracy. We also demonstrate an energy-efficient hardware accelerator that implements low-precision fixed-point arithmetic with stochastic rounding.
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