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A Random Walk in 10 Dimensions (2021)


The geometry of random walks in high dimensions provides the power behind deep learning and may be the secret to intelligence.

For these reasons, as physics students today are being increasingly exposed to the challenges and problems of high-dimensional dynamics, it is important to build tools they can use to give them an intuitive feeling for the highly unintuitive behavior of systems in high-D. In even higher dimensions, the percolation threshold decreases roughly inversely with the dimensionality, and mountain peaks become extremely rare and play virtually no part in walks about the landscape. Therefore, despite the insanely large number of adjustable parameters, general solutions, that are meaningful and predictive, can be found by adding random walks around the objective landscape as a partial strategy in combination with gradient descent.

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