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.

生成式机器学习是在输入数据上进行训练的神经网络，以便生成具有相似特征的新数据。特别是，生成式机器学习已被用于创建图像，最近的工作集中在基于扩散的神经网络上，该网络由经过训练的图像到图像转换网络驱动，以逐渐去除噪声。该项目采用控制理论方法，为理解基于扩散的生成机器学习提供理论框架。通过将扩散模型的操作框定为最优控制问题，研究人员试图建立与偏微分方程和随机微分方程域的基础联系，目的是从可控性、表达性、计算复杂性和鲁棒性方面理解生成模型。与目前严重依赖经验设计且理论基础有限的扩散模型相比，该项目旨在以更低的计算成本大大改善生成网络的训练。鉴于目前在许多应用中对生成模型的广泛兴趣，该项目有可能弥合多个技术社区，特别是考虑到其理论重点。研究人员还计划将本科生纳入研究工作，并将生成机器学习的伦理和社会影响纳入他们的教育活动中。这个关于神经生成建模控制框架的项目将在生成建模的新背景下编织几个不同的知识链-即随机轨迹和合奏的控制，偏微分方程（PDE）的控制，以及多尺度图像分析的PDE经典理论。研究计划围绕三个主要方向：（1）扩散过程的控制;（2）密度空间的控制;（3）图像偏微分方程的控制。第一个方向将通过借鉴扩散过程的最佳控制技术，开发生成建模的第一原理框架。第二个方向将建立在这个框架上，将生成建模作为概率密度空间中的控制问题，可能绕过显式使用随机微分方程。这将生成建模的设置连接到Liouville型偏微分方程的最优控制问题，该偏微分方程描述光滑流作用下概率密度的演化。最后，第三个方向将扩大调查范围，以更一般的类偏微分方程所产生的公理的多尺度分析的上下文中的imagecessition.This奖项反映了NSF的法定使命，并已被认为是值得的支持，通过评估使用基金会的智力价值和更广泛的影响审查标准。