{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/additive-noise-annealing-and-approximation","title":"Additive Noise Annealing and Approximation Properties of Quantized Neural Networks","arxiv_id":"1905.10452","date":"2019-05-24","proceeding":null,"authors":["Matteo Spallanzani","Lukas Cavigelli","Gian Paolo Leonardi","Marko Bertogna","Luca Benini"],"abstract":"We present a theoretical and experimental investigation of the quantization problem for artificial neural networks. We provide a mathematical definition of quantized neural networks and analyze their approximation capabilities, showing in particular that any Lipschitz-continuous map defined on a hypercube can be uniformly approximated by a quantized neural network. We then focus on the regularization effect of additive noise on the arguments of multi-step functions inherent to the quantization of continuous variables. In particular, when the expectation operator is applied to a non-differentiable multi-step random function, and if the underlying probability density is differentiable (in either classical or weak sense), then a differentiable function is retrieved, with explicit bounds on its Lipschitz constant. Based on these results, we propose a novel gradient-based training algorithm for quantized neural networks that generalizes the straight-through estimator, acting on noise applied to the network's parameters. We evaluate our algorithm on the CIFAR-10 and ImageNet image classification benchmarks, showing state-of-the-art performance on AlexNet and MobileNetV2 for ternary networks.","url_abs":"https://arxiv.org/abs/1905.10452v1","url_pdf":"https://arxiv.org/pdf/1905.10452v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"additive-noise-annealing-and-approximation","repo_url":"https://github.com/spallanzanimatteo/QuantLab","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"image-classification","task_name":"Image Classification"},{"task_slug":"quantization","task_name":"Quantization"},{"task_slug":"image-classification","task_name":"image-classification"}],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"depthwise-convolution","method_name":"Depthwise Convolution"},{"method_slug":"depthwise-separable-convolution","method_name":"Depthwise Separable Convolution"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"grouped-convolution","method_name":"Grouped Convolution"},{"method_slug":"inverted-residual-block","method_name":"Inverted Residual Block"},{"method_slug":"local-response-normalization","method_name":"Local Response Normalization"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"pointwise-convolution","method_name":"Pointwise Convolution"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}