{"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/inrank-incremental-low-rank-learning","title":"InRank: Incremental Low-Rank Learning","arxiv_id":"2306.11250","date":"2023-06-20","proceeding":null,"authors":["Jiawei Zhao","Yifei Zhang","Beidi Chen","Florian Schäfer","Anima Anandkumar"],"abstract":"The theory of greedy low-rank learning (GLRL) aims to explain the impressive generalization capabilities of deep learning. It proves that stochastic gradient-based training implicitly regularizes neural networks towards low-rank solutions through a gradual increase of the rank during training. However, there is a gap between theory and practice since GLRL requires an infinitesimal initialization of the weights, which is not practical due to the fact that it is a saddle point. In this work, we remove the assumption of infinitesimal initialization by focusing on cumulative weight updates. We prove the cumulative weight updates follow an incremental low-rank trajectory for arbitrary orthogonal initialization of weights in a three-layer linear network. Empirically, we demonstrate that our theory holds on a broad range of neural networks (e.g., transformers) and standard training algorithms (e.g., SGD, Adam). However, existing training algorithms do not exploit the low-rank property to improve computational efficiency as the networks are not parameterized in low-rank. To remedy this, we design a new training algorithm Incremental Low-Rank Learning (InRank), which explicitly expresses cumulative weight updates as low-rank matrices while incrementally augmenting their ranks during training. We evaluate InRank on GPT-2, and our results indicate that InRank achieves comparable prediction performance as the full-rank counterpart while requiring at most 33% of the total ranks throughout training. We also propose an efficient version of InRank that achieves a reduction of 37% in total training time and 36% in model size when training GPT-medium on WikiText-103 from scratch.","url_abs":"https://arxiv.org/abs/2306.11250v2","url_pdf":"https://arxiv.org/pdf/2306.11250v2.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":"inrank-incremental-low-rank-learning","repo_url":"https://github.com/jiaweizzhao/inrank","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"}],"methods":[{"method_slug":"adam","method_name":"Adam"},{"method_slug":"attention","method_name":"Attention"},{"method_slug":"attention-dropout","method_name":"Attention Dropout"},{"method_slug":"bpe","method_name":"BPE"},{"method_slug":"cosine-annealing","method_name":"Cosine Annealing"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"discriminative-fine-tuning","method_name":"Discriminative Fine-Tuning"},{"method_slug":"dropout","method_name":"Dropout"},{"method_slug":"gpt-2","method_name":"GPT-2"},{"method_slug":"layer-normalization","method_name":"Layer Normalization"},{"method_slug":"linear-layer","method_name":"Linear Layer"},{"method_slug":"linear-warmup-with-cosine-annealing","method_name":"Linear Warmup With Cosine Annealing"},{"method_slug":"multi-head-attention","method_name":"Multi-Head Attention"},{"method_slug":"residual-connection","method_name":"Residual Connection"},{"method_slug":"sgd","method_name":"SGD"},{"method_slug":"softmax","method_name":"Softmax"},{"method_slug":"weight-decay","method_name":"Weight Decay"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2306.11250","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}