# Stochastic Learning Equation using Monotone Increasing Resolution of Quantization

arXiv: https://arxiv.org/abs/2112.13006 · HTML: https://mlsanity.com/paper/2112.13006/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 17 references that are in the map.
- First posted on arXiv 24 Dec 2021.

## Builds on (most cited first, 4 of 4)

- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Quantized Neural Networks: Training Neural Networks with Low Precision Weights and Activations](https://mlsanity.com/paper/1609.07061/) (2016)
- [QSGD: Communication-Efficient SGD via Gradient Quantization and Encoding](https://mlsanity.com/paper/1610.02132/) (2016)

## Abstract (arXiv)

In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense and uniform distribution, we can regard the quantization error as i.i.d. white noise. Based on this, we show that the learning equation with monotonically increasing quantization resolution converges weakly as the distribution viewpoint. The analysis of this paper shows that global optimization is possible for a domain that satisfies the Lipschitz condition instead of local convergence properties such as the Hessian constraint of the objective function.