Publications

2021

• Analog Implementation of Approximate Derivative and Sigmoidal Function
  
  • Chabane Lylia Thiziri
  • Pham Dang-Kièn Germain
  • Desgreys Patricia
  , 2021.
• Further Study of 2-to-1 Mappings Over F 2 n
  
  • Li Kangquan
  • Mesnager Sihem
  • Qu Longjiang
  IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2021, 67 (6), pp.3486-3496. (10.1109/TIT.2021.3057094)
  DOI : 10.1109/TIT.2021.3057094
• Experimental Analysis of the Electromagnetic Instruction Skip Fault Model and Consequences for Software Countermeasures
  
  • Dutertre Jean-Max
  • Menu Alexandre
  • Potin Olivier
  • Rigaud Jean-Baptiste
  • Danger Jean-Luc
  Microelectronics Reliability, Elsevier, 2021. Microcontrollers storing valuable data or using security functions are vulnerable to fault injection attacks. Among the various types of faults, instruction skips induced at runtime proved to be effective against identification routines or encryption algorithms. Until recently, most research works assessed a fault model that consists in a single instruction skip, i.e. the ability to prevent one chosen instruction in a program from being executed. We question this fault model for EM fault injection on experimental basis and report the possibility to induce several consecutive instructions skips. Such an extended fault model proved to be effective against a duplication-based software countermeasure as our experiments revealed.
• Towards alignment strategies in human-agent interactions based on measures of lexical repetitions
  
  • Dubuisson Duplessis Guillaume
  • Langlet Caroline
  • Clavel Chloé
  • Landragin Frédéric
  Language Resources and Evaluation, Springer Verlag, 2021, 55 (2), pp.353-388. Alignment of communicative behaviour is an important feature of Human-Human interaction that directly affects the collaboration and the social connection of conversational partners. With the aim of improving virtual agent communicative capabilities, and in particular its strategies related to (lexical) verbal alignment, this article focuses on the alignment of linguistic productions of dialogue participants in task-oriented dialogues. We propose a new framework to quantify both the lexical alignment and the self-repetition behaviours of dialogue participants from dyadic dialogue transcripts. It involves easily computable measures based on repetition of lexical patterns automatically extracted via a sequential pattern mining approach. These measures allow the characterisation of the nature of these processes by addressing various informative aspects (10.1007/s10579-021-09532-w)
  DOI : 10.1007/s10579-021-09532-w
• Autonomous racecar control in head-to-head competition using Mixed-Integer Quadratic Programming
  
  • Li Nan
  • Goubault Eric
  • Pautet Laurent
  • Putot S.
  , 2021. This work deals with the control of an autonomous racecar that should perform the fastest lap time on a track, while in presence of an opponent vehicle. Controlling the vehicle at its physical limit while ensuring collision-freeness is a challenging problem. We propose a Nonlinear Model Predictive Control (NMPC) model under a minimum time objective, which integrates the opponent vehicle's trajectory as a collision-avoidance constraint. By using a curvilinear coordinates system, progress time can be set as a direct optimization objective. The approximation of vehicle's shape is proposed and collision-avoidance constraints can therefore be represented efficiently. A safe control strategy is finally generated by a method based on Mixed-Integer Quadratic Programming (MIQP). We perform several experiments on our prototype implementation and discuss its performance issues.
• Post-layout Security Evaluation Methodology Against Probing Attacks
  
  • Takarabt Sofiane
  • Guilley Sylvain
  • Souissi Youssef
  • Sauvage Laurent
  • Mathieu Yves
  , 2021, 379, pp.465-482. Probing attack is considered to be one of the most powerful attack used to break the security and extract confidential information from an embedded system. This attack requires different bespoke equipment’s and expertise. However, for the moment, there is no methodology to evaluate theoretically the security level of a design or circuit against this threat. It can be only realized by a real evaluation of a certified evaluation laboratory. For the design house, this evaluation can be expensive in term of time and money. In this paper, we introduce an innovative methodology that can be applied to evaluate the probing attack on any design at simulation level. Our method helps to extract the sensitive signals of a design, emulate different Focused Ions Beam technologies used for probing attacks, and evaluate the accessibility level of each signal. It can be used to evaluate precisely any probing attack on the target design at simulation level, hence reducing the cost and time to market of the design. This methodology can be applied for both ASIC and FPGA technology. A use-case on an AES-128 shows the efficiency of our methodology. It also helps to evaluate the efficiency of the active shield used as a countermeasure against probing attack. (10.1007/978-3-030-77424-0_37)
  DOI : 10.1007/978-3-030-77424-0_37
• On Some Associations Between Mathematical Morphology and Artificial Intelligence
  
  • Bloch Isabelle
  • Blusseau Samy
  • Pino Pérez Ramón
  • Puybareau Élodie
  • Tochon Guillaume
  , 2021, 12708, pp.457-469. This paper aims at providing an overview of the use of mathematical morphology, in its algebraic setting, in several fields of artificial intelligence (AI). Three domains of AI will be covered. In the first domain, mathematical morphology operators will be expressed in some logics (propositional, modal, description logics) to answer typical questions in knowledge representation and reasoning, such as revision, fusion, explanatory relations, satisfying usual postulates. In the second domain, spatial reasoning will benefit from spatial relations modeled using fuzzy sets and morphological operators, with applications in model-based image understanding. In the third domain, interactions between mathematical morphology and deep learning will be detailed. Morphological neural networks were introduced as an alternative to classical architectures, yielding a new geometry in decision surfaces. Deep networks were also trained to learn morphological operators and pipelines, and morphological algorithms were used as companion tools to machine learning, for pre/post processing or even regularization purposes. These ideas have known a large resurgence in the last few years and new ones are emerging. (10.1007/978-3-030-76657-3_33)
  DOI : 10.1007/978-3-030-76657-3_33
• A Compact Inverted-F Antenna covering 2.4-4.8 GHz and its Miniaturization Driven by Surrogate Model
  
  • Du Jinxin
  • Roblin Christophe
  • Yang Xue-Xia
  , 2021, pp.1-3. (10.1109/ICMMT52847.2021.9618637)
  DOI : 10.1109/ICMMT52847.2021.9618637
• Apprentissage profond pour la segmentation et la détection automatique en imagerie multi-modale : application à l'oncologie hépatique
  
  • Couteaux Vincent
  , 2021. Pour caractériser les lésions hépatiques, les radiologues s’appuient sur plusieurs images acquises selon différentes modalités (différentes séquences IRM, tomodensitométrie, etc.) car celles-ci donnent des informations complémentaires. En outre, les outils automatiques de segmentation et de détection leur sont d’une grande aide pour la caractérisation des lésions, le suivi de la maladie ou la planification d’interventions. A l’heure où l’apprentissage profond domine l’état de l’art dans tous les domaines liés au traitement de l’image médicale, cette thèse vise à étudier comment ces méthodes peuvent relever certains défis liés à l’analyse d’images multi-modales, en s’articulant autour de trois axes : la segmentation automatique du foie, l’interprétabilité des réseaux de segmentation et la détection de lésions hépatiques. La segmentation multi-modale dans un contexte où les images sont appariées mais pas recalées entre elles est un problème peu abordé dans la littérature. Je propose une comparaison de stratégies d’apprentissage proposées pour des problèmes voisins, ainsi qu’une méthode pour intégrer une contrainte de similarité des prédictions à l’apprentissage. L’interprétabilité en apprentissage automatique est un champ de recherche jeune aux enjeux particulièrement importants en traitement de l’image médicale, mais qui jusqu’alors s’était concentré sur les réseaux de classification d’images naturelles. Je propose une méthode permettant d’interpréter les réseaux de segmentation d’images médicales. Enfin, je présente un travail préliminaire sur une méthode de détection de lésions hépatiques dans des paires d’images de modalités différentes.
• Touch without Touching: Overcoming Social Distancing in Semi-Intimate Relationships with SansTouch
  
  • Zhang Zhuoming
  • Alvina Jessalyn
  • Héron Robin
  • Safin Stéphane
  • Detienne Françoise
  • Lecolinet Eric
  , 2021, pp.1-13. Social distancing may force people to restrict social touch practices. Our survey (N=136) highlighted substantial social touch breakdowns during the COVID-19 pandemic for semi-intimate relationships (e.g., friends, colleagues), with handshakes being the most reduced, and frustrations at having to re-establish social touch habits. We then designed SansTouch, a multi-modal hand sleeve used together along with a smartphone to enable mediated hand-to-hand interactions such as handshakes or holding hands. To invoke the mediated touch, users synchronously mimic the hand position as in real life while holding SansTouch. Users can feel the touch sensation in real time without touching. Participants from our observational study (N=12) quickly adopted the hand-to-hand interactions of SansTouch for exchanging greetings face-to-face with colleagues and reported stronger preferences towards using SansTouch as opposed to mid-air gestures (e.g., waving). We discuss design implications, including the trade-offs of multi-modality for touch devices in face-to-face communication. (10.1145/3411764.3445612)
  DOI : 10.1145/3411764.3445612
• Detection of State Transitions in Network elements: On-box demo
  
  • Foroughi Parisa
  • Shao Wenqin
  • Brockners Frank
  • Kuriakose Anil
  • Rougier Jean-Louis
  , 2021, pp.724-725. Modern network devices like routers offer thousands of operational counters. All of them could be important for network monitoring, though their high number makes this process infeasible, often resulting in only a small subset of the counters to be considered for further interpretation and processing. This demo paper showcases the practical use of an unsupervised multivariate online detector, DESTIN [1], which could assist an operator in automatically monitoring all or at least a very large number of counters and exploring inter-dependencies between them to further the operator's understanding of the state of the network. DESTIN can detect changes in the network without any need for predefined KPIs on the router itself.
• DESTIN: Detecting State Transitions in Network elements
  
  • Foroughi Parisa
  • Shao Wenqin
  • Brockners Frank
  • Rougier Jean-Louis
  , 2021, pp.161-169. Operators are interested in gaining a comprehensive assessment of their network elements and tracking operational changes. Commonly, this assessment is achieved by performing regular checks of different operational counters and defining expert rules from known root causes. The common approach requires the maintenance of a regularly updated set of rules and only goes as far as the operator's pre-gained knowledge of the system. In this paper, a broader set of counters (not limited to the handpicked Key Performance Indicators (KPIs)) is explored with an unsupervised approach. The goal is to leverage the dependencies between the counters in order to discover complex state changes that might have otherwise slipped the operator's view. This paper proposes DESTIN, a multivariate unsupervised change detection for high dimensional time-series data of originally low effective dimension, which provides near real-time state assessment of network device. The efficiency of the method is demonstrated on an experimental test-bed.
• Improved CRL Distribution point for Cooperative Intelligent Transportation Systems
  
  • Serhrouchni Ahmed
  • Adja Elloh Yves Christian
  , 2021. The Cooperative Intelligent Transportation Systems (C-ITS) are already part of our daily life, and their adoption is exponentially increasing, especially with the rise of smart cities concept. However, the security of these infrastructures remains a critical and significant challenge to meet. The Public key infrastructure (PKI) using certificates is the most popular solution to address security issues. The vehicles are identified by a lot of pseudonyms certificates, which must be revoked when the vehicle becomes misbehaving or faulty. The use of multiple certificates introduces new critical problems on services, like the certificate revocation verification. The revocation management is critical for a PKI, even worse in vehicular communications, where there are long revocation lists to process. All nodes of a network must be aware of all pairs’ revocation status as soon as possible to prevent the revoked nodes from unauthorized activities in the network. The revocation is still an open challenge that is starting to attract a lot of attention from researchers. In this paper, we propose a new scalable and reliable approach for revocation lists dissemination called improved certificate distribution point system (ICRLDP). Our plan proposes a trade-off between vehicle privacy and security.
• Synthetic images as a regularity prior for image restoration neural networks
  
  • Achddou Raphaël
  • Gousseau Yann
  • Ladjal Saïd
  , 2021. Deep neural networks have recently surpassed other image restoration methods which rely on hand-crafted priors. However, such networks usually require large databases and need to be retrained for each new modality. In this paper, we show that we can reach nearoptimal performances by training them on a synthetic dataset made of realizations of a dead leaves model, both for image denoising and superresolution. The simplicity of this model makes it possible to create large databases with only a few parameters. We also show that training a network with a mix of natural and synthetic images does not affect results on natural images while improving the results on dead leaves images, which are classically used for evaluating the preservation of textures. We thoroughly describe the image model and its implementation, before giving experimental results.
• Manifold learning via tangent space alignment for accelerated dynamic MR imaging with highly undersampled (k,t)-data
  
  • Djebra Y.
  • Bloch Isabelle
  • El Fakhri Georges
  • Ma Chao
  , 2021.
• Nearest Neighbour Based Estimates of Gradients: Sharp Nonasymptotic Bounds and Applications
  
  • Clémençon Stéphan
  • Ausset Guillaume
  • Portier François
  , 2021, 130, pp.1-12. Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory. We consider here the classical regression setup, where a real valued square integrable r.v. Y is to be predicted upon observing a (possibly high dimensional) random vector X by means of a predictive function f (X) as accurately as possible in the meansquared sense and study a nearest-neighbourbased pointwise estimate of the gradient of the optimal predictive function, the regression function m(x) = E[Y | X = x]. Under classical smoothness conditions combined with the assumption that the tails of Y − m(X) are sub-Gaussian, we prove nonasymptotic bounds improving upon those obtained for alternative estimation methods. Beyond the novel theoretical results established, several illustrative numerical experiments have been carried out. The latter provide strong empirical evidence that the estimation method proposed here performs very well for various statistical problems involving gradient estimation, namely dimensionality reduction, stochastic gradient descent optimization and disentanglement quantification.
• Investigation of PVT-Aware STT-MRAM Sensing Circuits for Low-VDD Scenario
  
  • Bian Zhongjian
  • Hong Xiaofeng
  • Guo Yanan
  • Naviner Lirida
  • Ge Wei
  • Cai Hao
  Micromachines, MDPI, 2021, 12 (5), pp.551. Spintronic based embedded magnetic random access memory (eMRAM) is becoming a foundry validated solution for the next-generation nonvolatile memory applications. The hybrid complementary metal-oxide-semiconductor (CMOS)/magnetic tunnel junction (MTJ) integration has been selected as a proper candidate for energy harvesting, area-constraint and energy-efficiency Internet of Things (IoT) systems-on-chips. Multi-VDD (low supply voltage) techniques were adopted to minimize energy dissipation in MRAM, at the cost of reduced writing/sensing speed and margin. Meanwhile, yield can be severely affected due to variations in process parameters. In this work, we conduct a thorough analysis of MRAM sensing margin and yield. We propose a current-mode sensing amplifier (CSA) named 1D high-sensing 1D margin, high 1D speed and 1D stability (HMSS-SA) with reconfigured reference path and pre-charge transistor. Process-voltage-temperature (PVT) aware analysis is performed based on an MTJ compact model and an industrial 28 nm CMOS technology, explicitly considering low-voltage (0.7 V), low tunneling magnetoresistance (TMR) (50%) and high temperature (85 °C) scenario as the worst sensing case. A case study takes a brief look at sensing circuits, which is applied to in-memory bit-wise computing. Simulation results indicate that the proposed high-sensing margin, high speed and stability sensing-sensing amplifier (HMSS-SA) achieves remarkable performance up to 2.5 GHz sensing frequency. At 0.65 V supply voltage, it can achieve 1 GHz operation frequency with only 0.3% failure rate. (10.3390/mi12050551)
  DOI : 10.3390/mi12050551
• A survey of in-spin transfer torque MRAM computing
  
  • Cai Hao
  • Liu Bo
  • Chen Juntong
  • Naviner Lirida
  • Zhou Yongliang
  • Wang Zhen
  • Yang Jun
  Science China Information Sciences, Springer, 2021, 64 (6), pp.160402. In traditional von Neumann computing architectures, the essential transfer of data between the processor and memory hierarchies limits the computational efficiency of next-generation system-on-a-chip. The emerging in-memory computing (IMC) approach addresses this issue and facilitates the movement of significant data and rapid computations. Among the different memory types, intrinsic energy efficiency is demonstrated by in-magnetic random access memory (MRAM) computing with a low-power spintronic magnetic tunnel junction device and hybrid integration at an advanced complementary metal-oxide semiconductor node. This study reviews state-of-the-art techniques for managing IMC with an emphasis on spin-transfer torque-MRAM computing via design schemes at the bit-cell, circuit, and system levels. In addition, this study presents effective design techniques and potential challenges and demonstrates the existing limitations of in-MRAM computing and potential methods for overcoming these issues. This study also considers the design technology co-optimization from the IMC perspective. (10.1007/s11432-021-3220-0)
  DOI : 10.1007/s11432-021-3220-0
• Chaos Bandwidth in Mid-infrared Quantum Cascade Photonic Devices with Interband and Intersubband Transitions
  
  • Spitz O
  • Wu J
  • Didier P
  • Díaz-Thomas D A
  • Cerutti Laurent
  • Baranov A. N. N
  • Maisons G
  • Carras M
  • Wong C.-W
  • Grillot F
  , 2021. We experimentally display temporal chaotic waveforms in the mid-infrared domain with two different types of semiconductor lasers. The generated high-dimensional non-linear dynamics are of prime interest for private communications and physical random number generation.
• An InP Reflective SOA-EAM for 10 Gb/s Colorless Multi-IFoF/mmWave Fiber-Wireless Uplink in 5G Networks
  
  • Atra Kebede
  • Ruggeri Eugenio
  • Cerulo Giancarlo
  • Provost Jean-Guy
  • Mekhazni Karim
  • Vagionas Christos
  • Garreau Alexandre
  • Pommereau Frederic
  • Gomez Carmen
  • Fortin Catherine
  • Paret Jean-François
  • Wilk Arnaud
  • Ware Cédric
  • Erasme Didier
  • Mallecot Franck
  • Miliou Amalia
  • Achouche Mohand
  , 2021. We experimentally present a 10-Gb/s Fiber Wireless IFoF/V-band uplink of four 625Mbaud 16QAM signals with a linear, high-power monolithically integrated reflective electroabsorption modulator with semiconductor optical amplifier for 5G mmWave fronthaul networks.
• FingerMapper: Enabling Arm Interaction in Confined Spaces for Virtual Reality through Finger Mappings
  
  • Tseng Wen-Jie
  • Huron Samuel
  • Lecolinet Eric
  • Gugenheimer Jan
  , 2021. As Virtual Reality (VR) headsets become more mobile, people can interact in public spaces with applications often requiring large arm movements. However, using these open gestures is often uncomfortable and sometimes impossible in confined and public spaces (e.g., commuting in a bus). We present FingerMapper, a mapping technique that maps small and energy-efficient finger motions onto virtual arms so that users have less physical motions while maintaining presence and partially virtual body ownership. FingerMapper works as an alternative function while the environment is not allowed for full arm interaction and enables users to interact inside a small physical, but larger virtual space. We present one example application, FingerSaber that allows the user to perform the large arm swinging movement using FingerMapper. (10.1145/3411763.3451573)
  DOI : 10.1145/3411763.3451573
• Blockchain Performance Benchmarking: a VCG Auction Smart Contract Use Case for Ethereum and Tezos (Short Paper)
  
  • Massoni Sguerra Lucas
  • Jouvelot Pierre
  • Gallego Arias Emilio Jesús
  • Memmi Gérard
  • Coelho Fabien
  , 2021. The second generation of blockchains introduces the notion of "smart contract" to decentralized ledgers, but with each new blockchain system comes di erent consensus mechanisms or di erent approaches on how to assess the cost of computation inside the chain, both aspects that a ect the e ciency of the systems as a decentralized computer. We present an experimental comparison of two blockchain systems, namely Ethereum and Tezos, from the perspective of smart contracts, centered around the same implementation of a VCG for Sponsored Search auction algorithm, respectively encoded in Solidity and SmartPy. Our analysis shows the feasibility of implementing an algorithm for sponsored search in such an environment while providing information on how useful these systems can be for this type of smart contracts.
• Computer-aided diagnosis methods for cervical cancer screening on liquid-based Pap smears using convolutional neural networks : design, optimization and interpretability
  
  • Pirovano Antoine
  , 2021. Cervical cancer is the second most important cancer for women after breast cancer. In 2012, the number of cases exceeded 500,000 worldwide, among which half turned to be deadly.Until today, primary cervical cancer screening is performed by a regular visual analysis of cells, sampled by pap-smear by cytopathologists under brightfield microscopy in pathology laboratories. In France, about 5 millions of cervical screening are performed each year and about 90% lead to a negative diagnosis (i.e. no pre-cancerous changes detected). Yet, these analyses under microscope are extremely tedious and time-consuming for cytotechnicians and can require the joint opinion of several experts. This process has an impact on the capacity to tackle this huge amount of cases and to avoid false negatives that are the main cause of treatment delay. The lack of automation and traceability of screening is thus becoming more critical as the number of cyto-pathologists decreases. In that respect, the integration of digital tools in pathology laboratories is becoming a real public health stake for patients and the privileged path for the improvement of these laboratories. Since 2012, deep learning methods have revolutionized the computer vision field, in particular thanks to convolutional neural networks that have been applied successfully to a wide range of applications among which biomedical imaging. Along with it, the whole slide imaging digitization process has opened the opportunity for new efficient computer-aided diagnosis methods and tools. In this thesis, after motivating the medical needs and introducing the state-of-the-art deep learning methods for image processing and understanding, we present our contribution to the field of computer vision tackling cervical cancer screening in the context of liquid-based cytology. Our first contribution consists in proposing a simple regularization constraint for classification model training in the context of ordinal regression tasks (i.e. ordered classes). We prove the advantage of our method on cervical cells classification using Herlev dataset. Furthermore, we propose to rely on explanations from gradient-based explanations to perform weakly-supervised localization and detection of abnormality. Finally, we show how we integrate these methods as a computer-aided tool that could be used to reduce the workload of cytopathologists.The second contribution focuses on whole slide classification and the interpretability of these pipelines. We present in detail the most popular approaches for whole slide classification relying on multiple instance learning, and improve the interpretability in a context of weakly-supervised learning through tile-level feature visualizations and a novel manner of computing explanations of heat-maps. Finally, we apply these methods for cervical cancer screening by using a weakly trained “abnormality” detector for region of interest sampling that guides the training.
• Design of ultra dense passive optical network to support high number of end users
  
  • Atra Kebede Tesema
  , 2021. In this thesis, we study reflective electroabsorption modulators (EAMs) monolithically integrated with semiconductor optical amplifiers (SOAs) to realize wavelength-independent (colorless) transmitters for low-cost access network applications that require dense deployment of optical transceivers. The devices are based on GaInAsP/InP multiple quantum-wells (MQWs), leveraging semi-insulating buried heterostructure (SI-BH) waveguide and butt-joint integration technologies. We analyze different design tradeoffs by considering three modulator lengths (80, 100 and 150 μm). After fabrication, we perform a complete performance analysis of our components in both static and dynamic modes. We obtain >17 dB SOA gain with a noise figure of about 4 dB. For the EAM, we achieve >33 GHz modulation bandwidth and up to 15 dB dynamic extinction ratio. The EAMs exhibit zero-chirp for reverse bias voltages in the range between −1.2 V and −1.5 V, depending on the operating wavelength. For C-band components, we demonstrate up to 16 km colorless trans-mission, over 15 nm, at 25 Gb/s using non-return-to-zero (NRZ) modulation format. With components working in the O-band, we per-form up to 50 Gb/s NRZ as well as PAM-4 transmissions without equalization. Finally, we perform a 10 Gb/s multi-channel V-band/IFoF transmission, achieving <11% error vector magnitude.
• La vie et l'oeuvre de Kolmogorov
  
  • Rioul Olivier
  CultureMath, ENS, 2021. Andreï Nikolaïevitch Kolmogorov est un mathématicien soviétique, l'un des plus grands mathématiciens du XXe siècle. Un esprit des plus brillants, profonds et originaux que le monde ait jamais connu. Que ce soit en probabilité, statistiques, analyse fonctionnelle, analyse spectrale, géométrie, théorie de l'approximation, logique intuitionniste, topologie algébrique, génétique, écologie, systèmes dynamiques, turbulence, mécanique classique, théorie de l'information, complexité algorithmique, pédagogie mathématique.. . il révolutionnait chaque sujet en l'abordant avec un regard étonnamment neuf et une perspective totalement originale. Ses idées, toujours d'une grande portée, paraissent dans des articles très courts : seulement quelques pages d'une profondeur, d'une perspicacité et d'une imagination stupéfiantes. Et sa bibliographie complète comporte plus de 500 publications. Il était admiré par ses collègues mathématiciens du monde entier pendant plus de 60 ans et donnait l'impression qu'il démontrait tous les théorèmes qu'il voulait. Il est surtout connu pour ses travaux sur la théorie des probabilités et particulièrement pour ses Grundbegriffe der Wahrscheinlichkeitsrechnung (« Fondements de la théorie des probabilités »), une modeste monographie de 60 pages paru en 1933. En reconstruisant rigoureusement toute la théorie des probabilités, ce petit ouvrage a totalement révolutionné la discipline à la fois scientifiquement et culturellement.