{"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/cbp-backpropagation-with-constraint-on-weight","title":"CBP: Backpropagation with constraint on weight precision using a pseudo-Lagrange multiplier method","arxiv_id":"2110.02550","date":"2021-10-06","proceeding":"NeurIPS 2021 12","authors":["Guhyun Kim","Doo Seok Jeong"],"abstract":"Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often required to alleviate prohibitive workloads on hardware. Despite the remarkable success of backpropagation, the algorithm itself is not capable of considering such constraints unless additional algorithms are applied simultaneously. To address this issue, we propose the constrained backpropagation (CBP) algorithm based on a pseudo-Lagrange multiplier method to obtain the optimal set of weights that satisfy a given set of constraints. The defining characteristic of the proposed CBP algorithm is the utilization of a Lagrangian function (loss function plus constraint function) as its objective function. We considered various types of constraints--binary, ternary, one-bit shift, and two-bit shift weight constraints. As a post-training method, CBP applied to AlexNet, ResNet-18, ResNet-50, and GoogLeNet on ImageNet, which were pre-trained using the conventional backpropagation. For all cases, the proposed algorithm outperforms the state-of-the-art methods on ImageNet, e.g., 66.6%, 74.4%, and 64.0% top-1 accuracy for ResNet-18, ResNet-50, and GoogLeNet with binary weights, respectively. This highlights CBP as a learning algorithm to address diverse constraints with the minimal performance loss by employing appropriate constraint functions.","url_abs":"https://arxiv.org/abs/2110.02550v2","url_pdf":"https://arxiv.org/pdf/2110.02550v2.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":"cbp-backpropagation-with-constraint-on-weight","repo_url":"https://github.com/dooseokjeong/cbp","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"auxiliary-classifier","method_name":"Auxiliary Classifier"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"inception-module","method_name":"Inception Module"},{"method_slug":"local-response-normalization","method_name":"Local Response Normalization"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"softmax","method_name":"Softmax"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2110.02550","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2110.02550"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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