Palestras

Vivemos um tempo em que as IAG estão resolvendo problemas matemáticos que estavam em aberto há muito tempo. E isso ocorre numa velocidade impressionante. Matemáticos se perguntam sobre qual será o papel dos seres humanos nesse futuro que se avizinha. Estudantes se perguntam se vale a pena começar uma carreira em Matemática nesse momento. Vamos refletir sobre  essas questões e o papel da Matemática na sociedade do hoje e de amanhã.

Data e horário: 01/10, às 9h 

This talk presents several regularization methods for deep learning that share a common origin: a notion of intrinsic dimension rooted in Gromov's metric measure geometry.

The approach rests on the observable diameter, which measures how much of the geometry of a metric measure space remains visible under real-valued observation; the intrinsic dimension of a set of points, or of the representation a network forms of them, is read off from its concentration behaviour. It requires neither an underlying manifold nor a metric of a particular form, and it can be computed for data sets and network representations alike.

From this one quantity we derive regularizers at three stages of the learning process. At the level of the data, it selects features by their resilience to the curse of dimensionality. At the level of the model, it prunes the components of an overparameterized network that contribute nothing to the intrinsic dimension of its representations. At the level of training, applied layer by layer, it regularizes the representations themselves. We present these methods as instances of a single geometric principle, discuss what distinguishes them in practice, and argue that where the complexity of a problem resides determines which of them to use.

This is joint work with Friedrich Martin Schneider and Vladimir Pestov.

Data e horário: 02/10, às 14h