Stochastic learning dynamics based on Langevin or Levy stochastic differential equations (SDEs) in deep neural networks control the variance of noise by varying the size of the mini-batch or directly those of injecting noise. Since the noise variance affects the approximation performance, the design of the additive noise is significant in SDE-based learning and practical implementation. In this paper, we propose an alternative stochastic descent learning equation based on quantized optimization for non-convex objective functions, adopting a stochastic analysis perspective. The proposed method employs a quantized optimization approach that utilizes Langevin SDE dynamics, allowing for controllable noise with an identical distribution without the need for additive noise or adjusting the mini-batch size. Numerical experiments demonstrate the effectiveness of the proposed algorithm on vanilla convolution neural network(CNN) models and the ResNet-50 architecture across various data sets. Furthermore, we provide a simple PyTorch implementation of the proposed algorithm.

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