(193c) When Have Two Networks Learned the Same Task? Data-Driven Transformations between System Representations

If several networks are trained on the same data set and for the same task, differences in the hyperparameters, weight initialization, and the stochastic nature of the training procedure can and will lead to different intrinsic representations. After successful training on such a task, each artificial neural network will have its own intrinsic representation of the input data set, tailored to the specific task. The interpolation and, especially, the generalization ability of each network heavily depends on this representation. Here, we show a way in which multiple intrinsic representations (encoded in multiple “equivalent” networks trained on the same task) can be analyzed and transformed into each other.

We employ manifold learning with Diffusion Maps [1] to extract intrinsic representations. Then, we construct data-driven transformations between the activations of the different networks, extract regions in the input space where the different representations are topologically equivalent (here, the transformation succeeds) as well as areas where representations cannot be mapped to each other (here, we obtain singularities in the transformation). In the event that the network outputs cannot be transformed to each other, we observe that the internal layer network activations provide a richer picture.

Transforming representations through manifold learning techniques [2] is a powerful tool: finding regions in the input space where these transformations break down (i.e. finding the singularities of the mapping) allows us to usefully compare the generalization capabilities of different networks.

[1] R. R. Coifman and S. Lafon. "Diffusion maps." Applied and Computational Harmonic Analysis, 2006.

[2] A. Singer, & R. R. Coifman. "Non-linear independent component analysis with diffusion maps." Applied and Computational Harmonic Analysis, 2008.