Local Stability and Gaussian Smoothing of Quantized Neural Networks

2026-07-22 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Mathematics & Computational Sciences · Depth: Expert, quick

Summary

Local Stability and Gaussian Smoothing of Quantized Neural Networks investigates Gaussian averaging as a smooth surrogate for quantized neural models. The research establishes a local dimension-dependent bound on "|f-g|" under conditions of bounded local oscillation, thereby linking Gaussian smoothing to the stability analysis of discontinuous networks. The authors compute closed-form Gaussian averages for both the rectified linear unit (ReLU) and sign activation functions. This mechanism is demonstrated on a high-dimensional binary perceptron, where layer-preactivation aggregation, utilizing an explicit quantization-noise surrogate, produces the Gaussian envelope. This envelope is subsequently employed for inference-side smoothing and for generating training-side smooth surrogate gradients, enhancing the understanding and application of quantized neural networks.

Key takeaway

For Machine Learning Engineers optimizing quantized neural networks, this research provides a robust method to enhance model stability and gradient estimation. By integrating Gaussian averaging and its closed-form solutions for activation functions like ReLU and sign, you can achieve smoother inference and more effective training with surrogate gradients. Consider applying layer-preactivation aggregation with a quantization-noise surrogate to improve the reliability and performance of your quantized models.

Key insights

Gaussian averaging offers a smooth surrogate for quantized neural networks, enhancing stability analysis and enabling smooth surrogate gradients.

Principles

• Bounded local oscillation bounds "|f-g|".
• Gaussian averaging improves network stability.
• Quantization noise surrogate creates Gaussian envelope.

Method

Compute closed-form Gaussian averages for ReLU and sign activations. Use layer-preactivation aggregation with a quantization-noise surrogate to generate a Gaussian envelope for inference-side smoothing and training-side smooth surrogate gradients in quantized networks.

In practice

• Apply Gaussian averaging for quantized model stability.
• Use closed-form averages for ReLU/sign functions.
• Implement Gaussian envelopes for inference smoothing.

Topics

• Quantized Neural Networks
• Gaussian Smoothing
• Model Stability
• Surrogate Gradients
• ReLU Activation
• Binary Perceptron

Best for: Research Scientist, AI Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.