I am starting a CIFRE PhD program with Yann Ollivier. My research interests are Artificial Intelligence, Deep Learning, Reinforcment Learning, Information Theory, Kolmogorov Complexity and Solomonoff's induction theory, Learning Theory, Bayesian Statistics, ...
Publications ans Preprints
(2018) Blier, L. and Ollivier, Y. : Do deep learning models have too many parameters? An information theory viewpoint, submitted
Deep learning models often have more parameters than observations, and still perform well. This is sometimes described as a paradox. In this work, we show experimentally that despite their huge number of parameters, deep neural networks can compress the data losslessly even when taking the cost of encoding the parameters into account. Such a compression viewpoint originally motivated the use of variational methods in neural networks. However, we show that these variational methods provide surprisingly poor compression bounds, despite being explicitly built to minimize such bounds. This might explain the relatively poor practical performance of variational methods in deep learning. Better encoding methods, imported from the Minimum Description Length (MDL) toolbox, yield much better compression values on deep networks, corroborating the hypothesis that good compression on the training set correlates with good test performance.
For a more detailed presentation of this work, with an introduction to Kolmogorov Complexity theory and Solomonoff's induction theory, you can also read my Master Thesis : Universal Compression Bounds and Deep Learning