Leveraging the manifold hypothesis for learning representations in deep neural networks

一旦从相关信息的正确、高级别表示开始，自动化智能决策就变得很容易。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水平表示(例如，数百万像素强度)开始的，在那里，任何与决策有关的潜在信息都被隐藏、严重扩散和扰乱。因此，一个根本的挑战是开发能够发现和利用数据中隐藏的统计规律的方法，以学习从低级别的表示产生有用的较高级别的表示。在这个研究项目中，我将利用这种统计规律的几何特征来开发能够提取有意义的表示的新技术。在这一目标上的重大进展可能是在阐明智力的关键机制之一方面的突破。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，这些基础科学和能力落后于谷歌搜索引擎、Siri智能个人代理或自动驾驶汽车等许多现代技术的成功。

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.