## Table of Contents

Different kind of positions are available. Feel free to contact me if you are interested in or if you have any questions. Moreover, feel free to also get in touch if you want to work with on nice other topics related to my research interests.

## 1 Master internship

The following topics are proposed for funded internship positions. Most of them can also be extended by a funded PhD position.

- Prediction of genetic traits with deep neural networks: how to consider epistasis ?, in collaboration with Philippe Nghe of ESPCI
- Adversarial attacks in the light of stability of ResNets in collaboration with Laurent Meunier
- Neural ODE
- Stability and robustness of Deep Learning models to process video from thermal cameras in collaboration with foxstream
- Dynamic topic models: from text to physics

## 2 PhD position

### 2.1 Stability and robustness of Deep Learning models to process video from thermal cameras (CIFRE)

The PhD position is funded by Foxstream, a software company, founded in 2004, that specializes in real-time automated processing of video content analysis. The PhD thesis is a collaboration with Dauphine Université (the MILES team of the LAMSADE) with a join supervision (Quentin Barthélemy from Foxstream and Alexandre Allauzen from MILES).

For a couple of decades, Deep Learning (DL) added a huge boost to the already rapidly developing field of computer vision. While for some kind of data and tasks, DL is the most successful approach, this is not the case for all applications. For instance, the analysis of video streams generated by thermal cameras is still a research challenge because of the long range perimeter and the associated geometrical issues, along with the frequent calibration change. Therefore, the stability and robustness of DL models must be better characterized and improved. The goal of the PhD is to design a Deep architecture that can explicitely deal with these peculiarities, along with providing theoritical guarantees on the stability of the prediction and the underlying invariances.

The recent work of [1,2] proposes an interesting mathematical tool to charaterize the stability and the generalization capacity of convolutional network. This paper is important to better explain the lack of robustness of the DL models to some kind of examples like adversarial ones [3].

The PhD student will be host in Paris (France)in Dauphine Université and frequent meeting will be scheduled to ensure a tight collaboration with the team at Foxstream. The PhD can start in January 2021 and the position is open until it is filled.

Requirements:

- Outstanding master's degree (or an equivalent university degree) in

computer science or another related disciplines (as e.g. mathematics, information sciences, computer engineering, etc.).

- Proficiency in machine learning, computer vision, or signal

processing. - Fluency in spoken and written English is required.

Application: To apply, please email alexandre.allauzen [at] dauphine.psl.eu with:

- a curriculum vitae, with contact of 2 or more referees
- a cover letter
- a research outcome (e.g. master thesis and/or published papers) of

the candidate

- a transcript of grades

[1] Understanding Deep Convolutional Networks, S. Mallat, in Phil. Trans. R. Soc. A., 2016.

[2] A. Bietti and J. Mairal, Group Invariance, Stability to Deformations,and Complexity of Deep Convolutional Representations, in JMLR 2019. http://www.jmlr.org/papers/volume20/18-190/18-190.pdf

[3] Szegedy et al, Intriguing properties of neural networks, https://arxiv.org/abs/1312.6199, 2013

### 2.2 Machine Learning and Physics (ANR Funded position)

The position will start as soon as possible, and the subject is under construction. It will be funded by the ANR project called Speed. Contact me if you are interested in.

The interaction between machine learning and Physics has transformed the methodology in many research areas. Simulations of complex physical systems provide an illustration of such recent de- velopment. While computer simulations are invaluable tools for scientific discovery and forecasting systems, the cost of accurate simulations limits in many cases their applicability and the capacity to explore a wide range of physical parameters or to quantify uncertainty in the prediction. In the last decades, data-driven approaches have offered an efficient workaround. For instance a deep-learning model can be learned to emulate the physical model. Then, its computational efficiency makes it an efficient proxy that can be integrated in a forecasting system or a control loop. Depending on your skills different tracks can be explored.

#### 2.2.1 Noisy, scarce and partial observation

In modern machine learning, the cornerstone is to let the model learn its own representation of the process from data observation. While, for many applications, data are readily available (computer vision, natural language processing, . . . ), some requirements are not met in the case of complex physical systems. Without loss of generality, let us consider the example of a turbulent flow field or the prediction of the sea surface temperature. The corresponding dataset is really small and scarce compared with usual machine learning applications. More importantly, the state cannot be fully observed in many situations and the data acquisition step often introduces noise.

The issues raised by noisy and scarce dataset are not new in the machine learning domain and there is, for instance, a long history of research in the field of generative models and how to represent high dimensional datasets in a compressed mathematical model. However, in the context of Physics, we can leverage some important properties like symmetries and invariances to address these challenges.

#### 2.2.2 Training algorithm to enforce physical properties

In some cases, a mathematical model for the system at hand is available, for instance: dynamical systems such as the Lorentz (63 and 93) attractors, Kuramoto-Sivashinsky and Kardar-Parisi-Zhang. With these case studies, this step includes the important definitions of the physical properties we want to introduce in the machine learning models.

Two approaches can be considered:

: the loss function optimized during the training process can be augmented with tailored regularization terms. As an example, optimal transport-based (OT) loss definitions are often more relevant for physical systems featuring significant structure. This will be made computationaly tractable with the convolutional Wasserstein flavor of OT, e.g., see this paper.**Physical regularization**: the second approach relies on the recent adversarial learning trend to guide the model during the training process toward solutions that exhibit the desired properties. Early efforts are reported in this paper where the solution and the test functions in the weak formulation of high-dimensional linear and nonlinear PDE problems are parameterized as a primal and adversarial networks respectively.**Adversarial training**

#### 2.2.3 Neural Ordinary Differential Equations

The relationship between neural networks and differential equations has been studied in several recent works Lu et al. (2018); Chen et al. (2018). In particular, the very efficient neural architecture ResNet (or Residual Network), He et al. (2016), can be interpreted as discretized ordinary differential equations. This kind of architectures leads to a very large number of parameters. Hence, while the idea is really appealing in our context, architectures like ResNet are suitable for applications beyond our scope, where the data availability is not an issue. Pushing the discretization step towards its limit of zero, along with parameters tying, have given rise to a new family of models called Neural Ordinary Differential Equations (or Neural ODEs). In these recent papers and their extension, Dupont et al. (2019), the experimental setup mainly relies on conventional datasets used in image classification (MNIST or CIFAR10). Preliminary work on this new type of neural networks has demonstrated its parameter efficiency for supervised learning task which can be of a great importance in our case.