TAB: Unified and Optimized Ternary, Binary, and Mixed-precision Neural Network Inference on the Edge

Abstract

Ternary Neural Networks (TNNs) and mixed-precision Ternary Binary Networks (TBNs) have demonstrated higher accuracy compared to Binary Neural Networks (BNNs) while providing fast, low-power and memory-efficient inference. Related works have improved the accuracy of TNNs and TBNs, but overlooked their optimizations on CPU and GPU platforms. First, there is no unified encoding for the binary and ternary values in TNNs and TBNs. Second, existing works store the 2-bit quantized data sequentially in 32/64-bit integers, resulting in bit-extraction overhead. Last, adopting standard 2-bit multiplications for ternary values leads to a complex computation pipeline, and efficient mixed-precision multiplication between ternary and binary values is unavailable. In this paper, we propose TAB as a unified and optimized inference method for ternary, binary and mixed-precision neural networks. TAB includes unified value representation, efficient data storage scheme, and novel bitwise dot product pipelines on CPU/GPU platforms. We adopt signed integers for consistent value representation across binary and ternary values. We introduce a bitwidth-last data format that stores the first and second bits of the ternary values separately to remove the bit extraction overhead. We design the ternary and binary bitwise dot product pipelines based on Gated-XOR using up to 40% fewer operations than State-Of-The-Art (SOTA) methods. Theoretical speedup analysis shows that our proposed TAB-TNN is 2.3 × fast as the SOTA ternary method RTN, 9.8 × fast as 8-bit integer quantization (INT8), and 39.4 × fast as 32-bit full-precision convolution (FP32). Experiment results on CPU and GPU platforms show that our TAB-TNN has achieved up to 34.6 × speedup and 16 × storage size reduction compared with FP32 layers. TBN, Binary-activation Ternary-weight Network (BTN) and BNN in TAB are up to 40.7 ×, 56.2 × and 72.2 × fast as FP32. TAB-TNN is up to 70.1% faster and 12.8% more power-efficient than RTN on Darknet-19 while keeping the same accuracy. TAB is open source as a PyTorch Extension 1 for easy integration with existing CNN models.

4.6-Bit Quantization for Fast and Accurate Neural Network Inference on CPUs

“…These instructions can noticeably speed up eightbit QNN inference [16]. Fast implementations are also available for ternary [17][18][19] and binary networks [18,20]. However, binary and ternary networks still suffer from accuracy loss compared to full-precision or eight-bit quantized networks with a similar number of parameters and architecture, which limits their suitability for certain tasks.…”

“…There are 21 pairs (N x , N w ) which satisfy ( 6): (255, 3), (127, 5), (85, 7), (63, 9), (51, 11), (43,13), (37,15), (31,17), (29,19), (25,21), (23,23) and symmetrical ones. If we compute the average bitwidth required to store x and w as (log 2 N x + log 2 N w )/2, we obtain values in the range 4.51-4.79.…”

An Empirical Study of Low Precision Quantization for TinyML

“…Quantization with lower precision can further reduce the memory consumption and computation. And ultra-low precision (1 or 2-bit) operations can often be computed efficiently with bit-wise arithmetic and thus achieving signification computation acceleration [28]. However, due to the large quantization noise, the benefits of low precision quantization often come at the cost of significant accuracy degradation.…”