Convergent Stochastic Training of Attention and Understanding LoRA

• URL: http://arxiv.org/abs/2605.07959v1
• Date: Fri, 08 May 2026 16:22:08 GMT
• Title: Convergent Stochastic Training of Attention and Understanding LoRA
• Abstract summary: Transformers have revolutionized machine learning and deploying attention layers in the model is increasingly standard across a myriad of applications.<n>For large models, it is common to implement Low Rank Adaptation (LoRA), whereby a factorized parameterization of them is trained, to achieve a surprisingly beneficial accuracy-size tradeoff.<n>We prove that for any mild regularization, the empirical regression loss on a attention layer and LoRA on a shallow neural net induce Poincaré inequality for the corresponding Gibbs' measure.
• Score: 40.81245220414135
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Transformers have revolutionized machine learning and deploying attention layers in the model is increasingly standard across a myriad of applications. Further, for large models, it is common to implement Low Rank Adaptation (LoRA), whereby a factorized parameterization of them is trained, to achieve a surprisingly beneficial accuracy-size trade-off. In this work, via a unified framework we rigorously establish trainability of such models under stochastic methods. We prove that for any mild regularization, the empirical regression loss on a attention layer and LoRA on a shallow neural net, both induce Poincaré inequality for the corresponding Gibbs' measure. Then it follows via invoking recent results that a certain SDE, which mimics the SGD, minimizes the corresponding losses. In both the cases, our first-of-its-kind results of trainability on attention and nets, do not rely on any assumptions on the data or the size of the architecture.

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