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Flexpoint: An Adaptive Numerical Format for Efficient Training of Deep Neural Networks (1711.02213v2)

Published 6 Nov 2017 in cs.LG, cs.NA, and stat.ML

Abstract: Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neural networks in low bit-width remains a challenging problem. Here we present the Flexpoint data format, aiming at a complete replacement of 32-bit floating point format training and inference, designed to support modern deep network topologies without modifications. Flexpoint tensors have a shared exponent that is dynamically adjusted to minimize overflows and maximize available dynamic range. We validate Flexpoint by training AlexNet, a deep residual network and a generative adversarial network, using a simulator implemented with the neon deep learning framework. We demonstrate that 16-bit Flexpoint closely matches 32-bit floating point in training all three models, without any need for tuning of model hyperparameters. Our results suggest Flexpoint as a promising numerical format for future hardware for training and inference.

Evaluation of Mixed Precision in Deep Learning Architectures

The presented paper provides an extensive empirical evaluation of mixed precision arithmetic in the context of deep learning model training. Leveraging advancements in floating-point precision technology, specifically float16 (F16) and bfloat16 (BF16), the paper investigates their impact on model performance, convergence rate, and computational efficiency compared to traditional IEEE 754 single precision (float32 or F32) representations.

Research Context and Methodology

Recent developments have allowed deep learning practitioners to explore lower precision formats, like F16, which promise improved computational throughput and reduced memory usage without significantly degrading the model's convergence or final accuracy. The paper systematically compares training performance across AlexNet and ResNet architectures with different precision settings: float32, float16, and a mixed-precision strategy combining both float32 and float16.

The benchmarking experiments involve training ResNet on the CIFAR-10 dataset using varying epochs, while AlexNet evaluations focus on transformation efficiency over specified epochs. Additionally, a complementary paper explores generative adversarial networks (GANs) using WGAN architecture, where FID scores assess model quality across precision types.

Key Findings and Numerical Results

One of the primary empirical insights is that mixed precision offers significant reductions in memory footprint and computational load while maintaining a competitive error rate. The training process showed distinct improvements in computation time with negligible loss in model accuracy when trained with F16 or mixed precision. Notably, in AlexNet training, mixed precision demonstrated faster convergence at early phases, with mean values indicating efficient utilization of computing resources.

For the ResNet model, the investigations revealed that float16, when used in conjunction with dynamic loss scaling techniques, mitigates the accuracy issues commonly associated with lower precision. This approach ensures gradient scaling prevents underflow, thereby stabilizing training while accelerating computational throughput.

In the WGAN evaluation, float16 maintained competitive FID scores compared to float32, suggesting that generative models do not suffer significant quality degradation from lower precision representations. These results underscore a potential paradigm shift in GAN training efficiency, as mixed precision arithmetic can significantly reduce the time-to-solution.

Implications and Future Work

The paper's findings suggest that adopting mixed precision techniques could be transformative for deep learning research and applications, especially in resource-constrained environments or large-scale deployment scenarios. By optimizing precision types for specific computational tasks, significant resource savings can be achieved without compromising model performance or convergence stability. As hardware manufacturers increasingly support mixed precision operations at the processor and accelerator level, there is a foreseeable trend towards such optimizations becoming the standard practice.

Future research directions should further explore precision-specific optimizations in various neural network architectures and develop more robust adaptive scaling techniques tailored to different deep learning tasks. Moreover, comparative analyses involving larger, more complex datasets and additional model types (e.g., transformers) could provide deeper insights into the universal applicability of these findings across the AI landscape.

In conclusion, this paper contributes to the growing evidence validating mixed precision arithmetic as a practical, efficient alternative to full-precision training in deep learning, offering both theoretical and practical benefits that align with current trends in AI hardware and software development.

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Authors (14)
  1. Urs Köster (7 papers)
  2. Tristan J. Webb (2 papers)
  3. Xin Wang (1306 papers)
  4. Marcel Nassar (17 papers)
  5. Arjun K. Bansal (4 papers)
  6. William H. Constable (1 paper)
  7. Scott Gray (11 papers)
  8. Stewart Hall (1 paper)
  9. Luke Hornof (1 paper)
  10. Amir Khosrowshahi (6 papers)
  11. Carey Kloss (1 paper)
  12. Ruby J. Pai (1 paper)
  13. Naveen Rao (1 paper)
  14. Oğuz H. Elibol (1 paper)
Citations (255)