CIF: Small: Towards a Control Framework for Neural Generative Modeling

CIF：小：走向神经生成建模的控制框架

• 批准号: 2348624
• 负责人: Maxim Raginsky
• 金额: $ 60万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-03-01 至 2027-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2348624&HistoricalAwards=false
• 关键词: CIF; Small; Towards; Control; Framework

Generative machine learning are neural networks that are trained on input data so as to then generate new data with similar characteristics. In particular, generative machine learning has been used for the creation of images, and recent work has focused on diffusion-based neural networks driven by an image-to-image translation network trained to gradually remove noise. This project adopts control-theory methodologies to provide a theoretical framework for understanding diffusion-based generative machine learning. By framing the operation of diffusion models as an optimal control problem, the investigators seek to establish a foundational link to the domains of partial and stochastic differential equations with the aim to understand generative models in terms of their controllability, expressiveness, computational complexity, and robustness. In contrast to current diffusion models which rely heavily on empirical design with limited theoretical foundation, the project seeks to greatly improve training for generative networks at a reduced computational cost. Given the current widespread interest in generative models in numerous applications, the project has the potential to bridge multiple technical communities, particularly given its theoretical focus. The investigators also plan to include undergraduates in the research endeavors as well as to incorporate ethical and societal ramifications of generative machine learning in their educational activities.This project on a control framework for neural generative modeling will weave together several distinct intellectual strands in the novel context of generative modeling – namely, control of stochastic trajectories and ensembles, control of partial differential equations (PDEs), and classical theories of PDEs for multiscale image analysis. The research program is articulated around three major directions: (1) control of diffusion processes; (2) control in the space of densities; (3) control of image PDEs. The first direction will develop a first-principles framework for generative modeling by drawing on the techniques of optimal control of diffusion processes. The second direction will build on this framework to phrase generative modeling as a control problem in the space of probability densities, potentially bypassing explicit use of stochastic differential equations. This will connect the setting of generative modeling to the problem of optimal control of PDEs of Liouville type that describe the evolution of probability densities under the action of smooth flows. Finally, the third direction will expand the scope of this inquiry to the more general class of PDEs arising from the axioms of multiscale analysis in the context of image processing.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

通用机器学习是对输入数据训练的神经元网络，以便生成具有相似特征的新数据。特别是，通用机器学习已用于创建图像，最近的工作集中在基于扩散的神经元网络上，该网络是由图像到图像转换网络驱动的，该网络训练有素，该网络逐渐消除了噪声。该项目采用控制理论的方法来提供理论框架，以理解基于扩散的遗传机器学习。通过将差异模型作为最佳控制问题的操作构建，研究人员试图建立与部分和随机微分方程域的基础联系，目的是从其可控性，表现力，计算复杂性和鲁棒性方面理解通用模型。与当前的差异模型相反，这些模型在很大程度上依赖于具有有限的理论基础的经验设计，该项目旨在以降低的计算成本来对通用网络进行大量改进培训。鉴于当前对众多应用中通用模型的宽度兴趣，该项目有可能弥合多个技术社区，尤其是鉴于其理论重点。 The investigators also plan to include undergraduates in the research endeavors as well as to incorporate ethical and social ramifications of generic machine learning in their educational activities.This project on a control framework for neuronal generic modeling will weave together several distinct intelligent strands in the novel context of generic modeling – namely, control of stochastic trajectories and ensembles, control of partial differential equations (PDEs), and classical theories用于多尺度图像分析的PDE。该研究计划围绕三个主要方向阐明：（1）控制差异过程； （2）在密度的空间中控制； （3）对图像PDE的控制。第一个方向将通过借鉴对差异过程的最佳控制技术来开发通用建模的第一原理框架。第二个方向将基于此框架，将通用建模作为概率密度空间中的控制问题，可能绕开随机微分方程的明确使用。这将连接通用建模的设置与liouville类型PDE的最佳控制问题，该问题描述了在光滑流动的作用下概率密度的演变。最后，第三个方向将在图像处理的背景下，由多尺度分析的公理产生的更通用的PDE扩大范围。该奖项反映了NSF的法定任务，并被认为是通过基金会的知识分子优点和更广泛的影响审查标准来评估通过评估而被认为是珍贵的。