Leveraging the manifold hypothesis for learning representations in deep neural networks

一旦从正确的、高层次的相关信息表示开始，智能决策的自动化就很容易。但是感官输入，无论是生物的（例如眼睛和视神经或耳朵传递的信息）还是电子的（例如数码相机或录音），都是从一个非常大的低层次表示（例如数百万像素强度）开始的，其中任何潜在的相关信息都是隐藏的，非常分散和混乱的。因此，一个根本的挑战是开发能够发现和利用隐藏在数据中的统计特征的方法，以学习从低级别的数据中产生有用的高级别表示。在这项研究计划中，我将利用这种统计的几何特征，以开发新的技术，能够提取有意义的表示。在这一目标上取得重大进展，可以成为阐明情报的关键机制之一的突破。它将转化为更好的人工感知（视觉，听觉）系统，将人工智能能力提升到更接近人类的能力，并将算法的基础科学和能力提升到一个新的水平，这些算法是许多现代技术成功的基础，如谷歌搜索引擎，Siri智能个人代理或自动驾驶汽车。

Automating intelligent decision taking is easy once starting from the right, high-level representation of relevant information. But sensory input, whether biological (e.g. information relayed by eye and optic nerve, or ear) or electronic (e.g. digital camera or sound recording) start from a very large low-level representation (e.g. millions of pixel intensities) where any potentially relevant information for decision making is hidden, awfully diffuse and scrambled. A fundamental challenge is thus to develop approaches that are able to discover and exploit the hidden statistical regularities in data to learn to produce useful higher level representations from low level ones. In this research program I will leverage a geometric characterization of such statistical regularities in order to develop novel techniques able to extract meaningful representations. Significant progress on this objective could constitute a breakthrough in elucidating one of the key mechanisms of intelligence. It will translate into better artificial perception (vision, audition) systems, lift artificial intelligence capabilities closer to human capabilities, and take to the next level the fundamental science and capabilities of algorithm that underly many modern technological successes such as the Google search engine, the Siri intelligent personal agent, or the self-driving car.