How can agents navigate physical and abstract environments?

Many fundamental problems in various disciplines can be formulated as a navigating a complex environment. Neuroscientists and cognitive scientists, for example, hypothesize that the mind connects concepts by their relationships on an abstract map. Reasoning occurs by navigating this abstract, mental map. Many concepts can be formulated as abstract navigation. Programming languages—from computer science—and games—from economics—are equivalent to navigation in an abstract space—such as a graph.

Neural networks—in the context of deep learning—can solve complex tasks such as classifying real-world images and championing world-renowned Go players. Given the success of neural networks, I research how neural networks can navigate in complex, abstract settings. To study this question, I use differential geometry, statistics, and neuroscience.

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