Zero-th Order Algorithm for Softmax Attention Optimization
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Abstract (arXiv)
Large language models (LLMs) have brought about significant transformations in human society. Among the crucial computations in LLMs, the softmax unit holds great importance. Its helps the model generating a probability distribution on potential subsequent words or phrases, considering a series of input words. By utilizing this distribution, the model selects the most probable next word or phrase, based on the assigned probabilities. The softmax unit assumes a vital function in LLM training as it facilitates learning from data through the adjustment of neural network weights and biases. With the development of the size of LLMs, computing the gradient becomes expensive. However, Zero-th Order method can approximately compute the gradient with only forward passes. In this paper, we present a Zero-th Order algorithm specifically tailored for Softmax optimization. We demonstrate the convergence of our algorithm, highlighting its effectiveness in efficiently computing gradients for large-scale LLMs. By leveraging the Zeroth-Order method, our work contributes to the advancement of optimization techniques in the context of complex language models.
Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 36 of its 52 references that are in the map. First posted on arXiv 17 Jul 2023.
Builds on
36 of 52 references.
References · 36
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- 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 526
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- 2023Fast Attention Requires Bounded Entriescited by 102
- 2023How Do Transformers Learn Topic Structure: Towards a Mechanistic Understandingcited by 85
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Citing papers per year: 2023: 5; 2024: 6; 2025: 5.
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- 2024Conv-Basis: A New Paradigm for Efficient Attention Inference and Gradient Computation in Transformerscited by 32
- 2023A Fast Optimization View: Reformulating Single Layer Attention in LLM Based on Tensor and SVM Trick, and Solving It in Matrix Multiplication Timecited by 30
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Modelscited by 30
- 2023How to Protect Copyright Data in Optimization of Large Language Models?cited by 26
- 2024The Computational Limits of State-Space Models and Mamba via the Lens of Circuit Complexitycited by 21
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- 2024Exploring the Frontiers of Softmax: Provable Optimization, Applications in Diffusion Model, and Beyondcited by 15
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- 2025Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decodingcited by 2
- 2024Binary Hypothesis Testing for Softmax Models and Leverage Score Modelscited by 1
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- 2025Towards Sampling Data Structures for Tensor Products in Turnstile Streams4 Oct 2025
- 2025Do LLMs trust AI regulation? Emerging behaviour of game-theoretic LLM agents11 Apr 2025
- 2025Time and Memory Trade-off of KV-Cache Compression in Tensor Transformer Decoding14 Mar 2025
- 2025Scaling Law Phenomena Across Regression Paradigms: Multiple and Kernel Approaches3 Mar 2025
- 2025Bilevel ZOFO: Efficient LLM Fine-Tuning and Meta-Training5 Feb 2025
- 2024The Computational Limits of State-Space Models and Mamba via the Lens of Circuit Complexity9 Dec 2024
- 2024Binary Hypothesis Testing for Softmax Models and Leverage Score Models9 May 2024
- 2024Conv-Basis: A New Paradigm for Efficient Attention Inference and Gradient Computation in Transformers8 May 2024
- 2024Exploring the Frontiers of Softmax: Provable Optimization, Applications in Diffusion Model, and Beyond6 May 2024
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Models7 Feb 2024
- 2024Enhancing Stochastic Gradient Descent: A Unified Framework and Novel Acceleration Methods for Faster Convergence2 Feb 2024
- 2023Unmasking Transformers: A Theoretical Approach to Data Recovery via Attention Weights19 Oct 2023
4 more
- 2023Why Softmax Attention Outperforms Linear Attention18 Oct 2023
- 2023A Fast Optimization View: Reformulating Single Layer Attention in LLM Based on Tensor and SVM Trick, and Solving It in Matrix Multiplication Time14 Sep 2023
- 2023How to Protect Copyright Data in Optimization of Large Language Models?23 Aug 2023
- 2023Convergence of Two-Layer Regression with Nonlinear Units16 Aug 2023
- 2024Conv-Basis: A New Paradigm for Efficient Attention Inference and Gradient Computation in Transformerscited by 32
- 2023A Fast Optimization View: Reformulating Single Layer Attention in LLM Based on Tensor and SVM Trick, and Solving It in Matrix Multiplication Timecited by 30
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Modelscited by 30
- 2023How to Protect Copyright Data in Optimization of Large Language Models?cited by 26
- 2023Why Softmax Attention Outperforms Linear Attentioncited by 15
- 2023Unmasking Transformers: A Theoretical Approach to Data Recovery via Attention Weightscited by 11
- 2023Convergence of Two-Layer Regression with Nonlinear Unitscited by 6
- 2025Bilevel ZOFO: Efficient LLM Fine-Tuning and Meta-Trainingcited by 5
- 2025Scaling Law Phenomena Across Regression Paradigms: Multiple and Kernel Approachescited by 4
- 2024Binary Hypothesis Testing for Softmax Models and Leverage Score Modelscited by 1
- 2025Towards Sampling Data Structures for Tensor Products in Turnstile Streamscited by 1
- 2024Enhancing Stochastic Gradient Descent: A Unified Framework and Novel Acceleration Methods for Faster Convergencecited by 0
- 2025Towards Sampling Data Structures for Tensor Products in Turnstile Streams4 Oct 2025
- 2025Scaling Law Phenomena Across Regression Paradigms: Multiple and Kernel Approaches3 Mar 2025
- 2025Bilevel ZOFO: Efficient LLM Fine-Tuning and Meta-Training5 Feb 2025
- 2024Binary Hypothesis Testing for Softmax Models and Leverage Score Models9 May 2024
- 2024Conv-Basis: A New Paradigm for Efficient Attention Inference and Gradient Computation in Transformers8 May 2024
- 2024The Fine-Grained Complexity of Gradient Computation for Training Large Language Models7 Feb 2024
- 2024Enhancing Stochastic Gradient Descent: A Unified Framework and Novel Acceleration Methods for Faster Convergence2 Feb 2024
- 2023Unmasking Transformers: A Theoretical Approach to Data Recovery via Attention Weights19 Oct 2023
- 2023Why Softmax Attention Outperforms Linear Attention18 Oct 2023
- 2023A Fast Optimization View: Reformulating Single Layer Attention in LLM Based on Tensor and SVM Trick, and Solving It in Matrix Multiplication Time14 Sep 2023
- 2023How to Protect Copyright Data in Optimization of Large Language Models?23 Aug 2023
- 2023Convergence of Two-Layer Regression with Nonlinear Units16 Aug 2023