Measuring the Intrinsic Dimension of Objective Landscapes
In our paper, Measuring the Intrinsic Dimension of Objective Landscapes, to be presented at ICLR 2018, we contribute to this ongoing effort by developing a simple way of measuring a fundamental network property known as intrinsic dimension. In the paper, we develop intrinsic dimension as a quantification of the complexity of a model in a manner decoupled from its raw parameter count, and we provide a simple way of measuring this dimension using random projections. We find that many problems have smaller intrinsic dimension than one might suspect.
By using intrinsic dimension to compare across problem domains, we measure, for example, that solving the inverted pendulum problem is about 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10.