In this video from Uber AI Labs, researchers Chunyuan Li and Jason Yosinski describe their ICLR 2018 paper "Measuring the Intrinsic Dimension of Objective Landscapes". The research, performed with co-authors Heerad Farkhoor and Rosanne Liu, develops intrinsic dimension as a fundamental property of neural networks. Intrinsic dimension quantifies the complexity of a model in a manner decoupled from its raw parameter count, and the paper provides a simple way of measuring this dimension using random projections. Many problems have smaller intrinsic dimension than one might suspect. By using intrinsic dimension to compare across problem domains, one may 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.
The attendant blog post: Measuring the Intrinsic Dimension of Objective Landscapes
Measuring the Intrinsic Dimension of Objective Landscapes by Chunyuan Li, Heerad Farkhoor, Rosanne Liu, Jason Yosinski
Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.
Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.