{"id":1153510,"date":"2025-11-03T16:00:15","date_gmt":"2025-11-04T00:00:15","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=1153510"},"modified":"2025-11-03T16:00:15","modified_gmt":"2025-11-04T00:00:15","slug":"pzo-pseudo-zeroth-order-algorithm-for-training-deep-neural-networks","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/pzo-pseudo-zeroth-order-algorithm-for-training-deep-neural-networks\/","title":{"rendered":"PZO: Pseudo-Zeroth-Order Algorithm for Training Deep Neural Networks"},"content":{"rendered":"<p>Zeroth-order Optimization (ZO) has received wide attention in machine learning, especially when computing full gradient is expensive or even impossible. Recently, ZO has emerged as an important paradigm for memory-efficient fine-tuning of large language models (LLMs), circumventing the memory overhead of backpropagation. However, existing ZO gradient estimators exhibit dimension-dependent variance scaling as\u00a0<span style=\"font-size: 1rem;\">[equation], leading to dimension-dependent convergence rates which is prohibitive for large-scale LLM parameters. To address this problem, we present a Pseudo-Zeroth-Order (PZO) framework for optimizing composite objective functions, especially large-scale models: [equation], where <em>h<\/em> represents complex, high-dimensional representations and [equation]\u00a0is a task-specific loss. While existing zeroth-order methods estimate gradients with final loss functions, our PZO algorithm estimate the Jacobian matrix of [equation]\u00a0with the model output [equation], and the gradient of the loss function on model output [equation]. Moreover, we apply exponential moving average on Jacobian estimators to reduce the variance. Experimental results demonstrate that PZO outperforms MeZO and MeZO-SVRG in classification, multiple choice and generation tasks in both full-parameter and PEFT fine-tuning settings by boosting convergence in the early stages of training. With the sliding window technique, our PZO only introduced a small dimension-independent memory overhead, which enables efficient scaling of the model size.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Zeroth-order Optimization (ZO) has received wide attention in machine learning, especially when computing full gradient is expensive or even impossible. Recently, ZO has emerged as an important paradigm for memory-efficient fine-tuning of large language models (LLMs), circumventing the memory overhead of backpropagation. However, existing ZO gradient estimators exhibit dimension-dependent variance scaling as\u00a0[equation], leading to dimension-dependent [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"NeurIPS 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