Collaborative Research: RI: Medium: Lie group representation learning for vision

协作研究：RI：中：视觉的李群表示学习

• 批准号: 2313150
• 负责人: Nina Miolane
• 金额: $ 50万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-10-01 至 2026-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2313150&HistoricalAwards=false
• 关键词: Collaborative; Research; RI; Medium; Lie

The quest to build intelligent machines capable of sensing, understanding and acting in their environment presents one of the great scientific challenges of our time. Despite recent advances in artificial intelligence (AI), the realization of robust, autonomous vision systems that understand and interact with the physical world remains elusive. Mathematically, vision requires understanding the relationships among an immense variety of object shapes, each subject to an immense variety of geometric and lighting transformations, leading to an explosion of possible visual scenes. This project aims to break through this barrier by developing a mathematically grounded computational theory of vision that will enable a new class of neural network learning algorithms to parse visual scenes into their constituent objects and transformations, thereby enabling computers to better represent the world around them. The results and computational tools arising from this research will be disseminated to the scientific community and general public through courses, seminars, hackathons, and open-source software contributed to the Geomstats library.The premise of this project is that the current limitations of AI and computer vision can be addressed with an appropriate mathematical framework, Lie theory, that models the hierarchical structure of natural transformations in the visual world. The investigators will develop generalizations of foundational signal processing transforms through explicit Lie group operations encoded in learnable G-Modules (Group-Modules). These modules directly tackle the combinatoric explosion in vision by factorizing images into shapes and their underlying transformations. Specifically, the team will develop G-modules that learn group-equivariant representations of the transformations contained in natural images (Aim 1), robust representations of shape by collapsing group orbits only with respect to specific transformations (Aim 2), and disentangling of transformation and shape via factorization (Aim 3). The modules are assembled into hierarchical architectures that can learn complex representations of transformations and shapes (Aim 4). Together, these aims provide a new paradigm that grounds existing models of vision and gives a set of guiding principles for the design of future deep learning architectures with enhanced abilities to sense and understand the world.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.

建立能够在环境中传感，理解和行动的智能机器的追求提出了我们这个时代的巨大科学挑战之一。尽管人工智能（AI）最近取得了进步，但理解和与物理世界互动的强大，自主愿景系统的实现仍然难以捉摸。从数学上讲，视觉需要了解各种物体形状之间的关系，每个对象形状都受到各种几何和照明转换的影响，从而导致可能的视觉场景爆炸。该项目旨在通过开发数学上扎根的视觉计算理论来打破这一障碍，该计算理论将使新的神经网络学习算法能够将视觉场景解析为其组成对象和转换，从而使计算机能够更好地代表周围的世界。 The results and computational tools arising from this research will be disseminated to the scientific community and general public through courses, seminars, hackathons, and open-source software contributed to the Geomstats library.The premise of this project is that the current limitations of AI and computer vision can be addressed with an appropriate mathematical framework, Lie theory, that models the hierarchical structure of natural transformations in the visual world. 研究人员将通过在可学习的G模型（组模型）中编码的明确谎言组操作来开发基础信号处理转换的概括。 这些模块通过将图像分解为形状及其基本转换，直接解决视觉中的组合爆炸。 具体而言，团队将开发G模型，以学习自然图像中包含的转换的群体等级表示（AIM 1），仅通过对特定转换（AIM 2）崩溃的组轨道来形状的鲁棒表示，以及通过分解分解的转换和形状（AIM 3）。这些模块被组装成层次结构，可以学习转换和形状的复杂表示形式（AIM 4）。这些目标共同提供了一种新的范式，以现有的愿景模型为基础，并为未来的深度学习体系结构设计提供了一系列指导原则，具有增强的感知和理解世界的能力。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力和更广泛影响的评估来进行评估的审查审查审查的审查批评，这是值得的。