Gaussian smoothing stabilizes quantized neural network training and inference
Researchers have formalized how Gaussian smoothing can stabilize quantized neural networks, a critical concern as model compression becomes standard practice. The work bridges discontinuous quantization effects with continuous approximations, deriving dimension-dependent bounds on approximation error and providing closed-form solutions for common activations like ReLU and sign functions. This addresses a fundamental challenge in deploying efficient models: quantization introduces sharp discontinuities that destabilize training and inference, but smooth surrogates enable both gradient-based optimization and robust inference-time smoothing. The findings matter for practitioners scaling models to edge devices and resource-constrained environments where quantization is non-negotiable.
Modelwire context
ExplainerThe paper's core contribution is dimension-dependent bounds on approximation error when replacing sharp quantization with Gaussian smoothing. This quantifies the trade-off between smoothness (which enables gradient flow) and fidelity to the original quantized function, filling a gap between empirical practice and formal guarantees.
This work sits alongside the entropy-stable learned finite volumes paper from earlier this week in a broader pattern: researchers are formalizing the structural constraints that matter more than learned parameters. Just as that work found that enforcing physical admissibility during design outweighed learned components, this paper shows that smoothing architecture (not just regularization) can provably stabilize quantized models. Both papers treat constraints as first-class design choices rather than post-hoc fixes. The Receptron work from the same batch also addresses quantization's practical endpoint (inference on microcontrollers), but this paper provides the theoretical scaffolding for why smoothing works there.
If practitioners report that Gaussian-smoothed quantized models trained with these bounds outperform standard quantization-aware training on mobile benchmarks (ImageNet-Mobile, CIFAR-10 with 4-bit weights) within the next two quarters, the theory has predictive power. If adoption remains confined to academic settings, the bounds may be too loose to guide real compression workflows.
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MentionsReLU · Gaussian smoothing · quantized neural networks · binary perceptron
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Modelwire summarizes, we don’t republish. arXiv cs.LG originally reported this story as “Local Stability and Gaussian Smoothing of Quantized Neural Networks”. The full content lives on arxiv.org. If you’re a publisher and want a different summarization policy for your work, see our takedown page.