Collaborative Research: SCH: Geometry and Topology for Interpretable and Reliable Deep Learning in Medical Imaging

深度学习模型正在为医疗保健、自动驾驶汽车和安全等安全关键型应用程序开发。它们令人印象深刻的表现有可能对人类生活产生深远影响。例如，医学成像中的深度神经网络(DNN)已被证明具有令人印象深刻的诊断能力，通常接近专业放射科医生。然而，深度学习没有进入标准的临床护理，主要是因为缺乏对模型为什么有效和为什么失败的理解。这个项目的目标是开发出使机器学习模型可解释和可靠的方法，从而弥合信任差距，使机器学习可翻译到临床。这个项目通过研究DNN的数学基础--特别是几何和拓扑学--来实现这一目标。基于这些数学基础，该项目将开发计算工具，以提高DNN的可解释性和可靠性。该项目开发的方法将广泛适用于使用深度学习的任何领域，包括医疗保健、安全、计算机视觉、自然语言处理等。深度神经网络的能力在于其隐层，网络在那里学习输入数据的内部表示。本研究项目围绕这样一个假设展开，即几何和拓扑学为分析DNN的内部表示提供了关键工具。这个项目的第一个目标是建立一个严格的数学和算法基础，用于描述神经网络内部表示的几何和拓扑，然后设计用于探索这些空间所需的几何和拓扑计算的高效算法。这个项目的下一个目标是应用这些工具来提高深度学习的可解释性。这将通过将模型的内部表示与可解释和可信的功能相链接，以及通过探索模型的内部表示的场景的交互式可视化来实现。该项目的下一个目标是模型可靠性，其中几何和拓扑将用于故障识别、缓解和预防。最后，该项目将在真实世界环境中测试开发的可靠和可解释的神经网络技术，以帮助专家肿瘤学家预测头颈部癌症的患者结果，例如，肿瘤是否会转移。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Deep learning models are being developed for safety-critical applications, such as health care, autonomous vehicles, and security. Their impressive performance has the potential to make profound impacts on human lives. For example, deep neural networks (DNNs) in medical imaging have been shown to have impressive diagnostic capabilities, often near that of expert radiologists. However, deep learning has not made it into standard clinical care, primarily due to a lack of understanding of why a model works and why it fails. The goal of this project is to develop methods for making machine learning models interpretable and reliable, and thus bridge the trust gap to make machine learning translatable to the clinic. This project achieves this goal through investigation of the mathematical foundations -- specifically the geometry and topology -- of DNNs. Based on these mathematical foundations, this project will develop computational tools that will improve the interpretability and reliability of DNNs. The methods developed in this project will be broadly applicable wherever deep learning is used, including health care, security, computer vision, natural language processing, etc.The power of a deep neural network lies in its hidden layers, where the network learns internal representations of input data. This research project centers around the hypothesis that geometry and topology provide critical tools for analyzing the internal representations of DNNs. The first goal of this project is to develop a rigorous mathematical and algorithmic foundation for describing the geometry and topology of a neural network's internal representations and then design efficient algorithms for geometric and topological computations necessary to explore these spaces. The next aim of this project is to apply these tools to improve the interpretability of deep learning. This will be done by linking a model's internal representation with interpretable and trusted features and by interactive visualization that explores the landscape of a model's internal representation. The next goal of this project focuses on model reliability, where geometry and topology will be used for failure identification, mitigation, and prevention. Finally, this project will test the developed techniques for reliable and interpretable neural networks in a real-world setting to aid expert oncologists in predicting patient outcomes in head and neck cancers, e.g., whether a tumor will metastasize.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.