# Schr"odinger's FP: Dynamic Adaptation of Floating-Point Containers for Deep Learning Training

arXiv: https://arxiv.org/abs/2204.13666 · HTML: https://mlsanity.com/paper/2204.13666/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 42 references that are in the map.
- First posted on arXiv 28 Apr 2022.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [MobileNetV2: Inverted Residuals and Linear Bottlenecks](https://mlsanity.com/paper/1801.04381/) (2018)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Deep Learning Recommendation Model for Personalization and Recommendation Systems](https://mlsanity.com/paper/1906.00091/) (2019)
- [EIE: Efficient Inference Engine on Compressed Deep Neural Network](https://mlsanity.com/paper/1602.01528/) (2016)
- [A Study of BFLOAT16 for Deep Learning Training](https://mlsanity.com/paper/1905.12322/) (2019)
- [Training Deep Neural Networks with 8-bit Floating Point Numbers](https://mlsanity.com/paper/1812.08011/) (2018)
- [Mixed Precision Quantization of ConvNets via Differentiable Neural Architecture Search](https://mlsanity.com/paper/1812.00090/) (2018)
- [Mixed Precision Training of Convolutional Neural Networks using Integer Operations](https://mlsanity.com/paper/1802.00930/) (2018)
- [Flexpoint: An Adaptive Numerical Format for Efficient Training of Deep Neural Networks](https://mlsanity.com/paper/1711.02213/) (2017)
- [Training DNNs with Hybrid Block Floating Point](https://mlsanity.com/paper/1804.01526/) (2018)
- [BSQ: Exploring Bit-Level Sparsity for Mixed-Precision Neural Network Quantization](https://mlsanity.com/paper/2102.10462/) (2021)
- [FAST: DNN Training Under Variable Precision Block Floating Point with Stochastic Rounding](https://mlsanity.com/paper/2110.15456/) (2021)
- [BitPruning: Learning Bitlengths for Aggressive and Accurate Quantization](https://mlsanity.com/paper/2002.03090/) (2020)
- [FPRaker: A Processing Element For Accelerating Neural Network Training](https://mlsanity.com/paper/2010.08065/) (2020)

## Built on by (most cited first, 1 of 1)

- [Just-in-time Quantization with Processing-In-Memory for Efficient ML Training](https://mlsanity.com/paper/2311.05034/) (2023)

## Abstract (arXiv)

The transfer of tensors from/to memory during neural network training dominates time and energy. To improve energy efficiency and performance, research has been exploring ways to use narrower data representations. So far, these attempts relied on user-directed trial-and-error to achieve convergence. We present methods that relieve users from this responsibility. Our methods dynamically adjust the size and format of the floating-point containers used for activations and weights during training, achieving adaptivity across three dimensions: i) which datatype to use, ii) on which tensor, and iii) how it changes over time. The different meanings and distributions of exponent and mantissas lead us to tailored approaches for each. We present two lossy pairs of methods to eliminate as many mantissa and exponent bits as possible without affecting accuracy. Quantum Mantissa and Quantum Exponent are machine learning compression methods that tap into the gradient descent algorithm to learn the minimal mantissa and exponent bitlengths on a per-layer granularity. They automatically learn that many tensors can use just 1 or 2 mantissa bits and 3 or 4 exponent bits. Overall, the two machine learning methods reduce the footprint by 4.74×. Alternatively, BitWave observes changes in the loss function during training to adjust mantissa and exponent bitlengths network-wide, yielding a 3.19× reduction in footprint. Finally, we present an optional method, Gecko, to exploit the naturally emerging, lop-sided exponent distribution to losslessly compress resulting exponents from Quantum Exponent or BitWave and, on average, improve compression rates to 5.64× and 4.56×.