MIQCQP reformulation of the ReLU neural networks Lipschitz constant estimation problem

It is well established that to ensure or certify the robustness of a neural network, its Lipschitz constant plays a prominent role. However, its calculation is NP-hard. In this note, by taking into account activation regions at each layer as new constraints, we propose new quadratically constrained MIP formulations for the neural network Lipschitz estimation problem. The solutions of these problems give lower bounds and upper bounds of the Lipschitz constant and we detail conditions when they coincide with the exact Lipschitz constant.

Sentiment analysis in Tourism: Fine-tuning BERT or sentence embeddings concatenation?

Undoubtedly that the Bidirectional Encoder representations from Transformers is the most powerful technique in making Natural Language Processing tasks such as Named Entity Recognition, Question & Answers or Sentiment Analysis, however, the use of traditional techniques remains a major potential for the improvement of recent models, in particular word tokenization techniques and embeddings, but also the improvement of neural network architectures which are now the core of each architecture. recent. In this paper, we conduct a comparative study between Fine-Tuning the Bidirectional Encoder Representations from Transformers and a method of concatenating two embeddings to boost the performance of a stacked Bidirectional Long Short-Term Memory-Bidirectional Gated Recurrent Units model; these two approaches are applied in the context of sentiment analysis of shopping places in Morocco. A search for the best learning rate was made at the level of the two approaches, and a comparison of the best optimizers was made for each sentence embedding combination with regard to the second approach.

Robust SVM Optimization in Banach spaces

We address the issue of binary classification in Banach spaces in presence of uncertainty. We show that a number of results from classical support vector machines theory can be appropriately generalised to their robust counterpart in Banach spaces. These include the Representer Theorem, strong duality for the associated Optimization problem as well as their geometric interpretation. Furthermore, we propose a game theoretic interpretation by expressing a Nash equilibrium problem formulation for the more general problem of finding the closest points in two closed convex sets when the underlying space is reflexive and smooth.