Neural networks have demonstrably achieved stateof-the art accuracy using low-bitlength integer quantization, yielding both execution time and energy benefits on existing hardware designs that support short bitlengths. However, the question of finding the minimum bitlength for a desired accuracy remains open. We introduce a training method for minimizing inference bitlength at any granularity while maintaining accuracy. Furthermore, we propose a regularizer that penalizes large bitlength representations throughout the architecture and show how it can be modified to minimize other quantifiable criteria, such as number of operations or memory footprint. We demonstrate that our method learns thrifty representations while maintaining accuracy. With ImageNet, the method produces an average per layer bitlength of 4.13 and 3.76 bits on AlexNet and ResNet18 respectively, remaining within 2.0% and 0.5% of the baseline TOP-1 accuracy.

No abstract

No abstract

We present FPRaker, a processing element for composing training accelerators. FPRaker processes several floatingpoint multiply-accumulation operations concurrently and accumulates their result into a higher precision accumulator. FPRaker boosts performance and energy efficiency during training by taking advantage of the values that naturally appear during training. It processes the significand of the operands of each multiply-accumulate as a series of signed powers of two. The conversion to this form is done on-the-fly. This exposes ineffectual work that can be skipped: values when encoded have few terms and some of them can be discarded as they would fall outside the range of the accumulator given the limited precision of floatingpoint. FPRaker also takes advantage of spatial correlation in values across channels and uses delta-encoding off-chip to reduce memory footprint and bandwidth. We demonstrate that FPRaker can be used to compose an accelerator for training and that it can improve performance and energy efficiency compared to using optimized bit-parallel floating-point units under isocompute area constraints. We also demonstrate that FPRaker delivers additional benefits when training incorporates pruning and quantization. Finally, we show that FPRaker naturally amplifies performance with training methods that use a different precision per layer.

No abstract