Seminar

Cette thèse explore l’application des réseaux de neurones à impulsions (Spiking Neural Networks, SNNs) pour les communications sans fil dans le contexte de l’Internet des Objets (IoT), où la gestion de l’énergie constitue un défi majeur. Les Wake-up Radios (WuRs) sont des dispositifs qui permettent aux nœuds IoT de rester en veille avec une consommation d’énergie minimale, en ne s’activant que lors de la réception de signaux spécifiques. Cette étude propose l’utilisation des SNNs comme WuR, le réseau de neurones étant chargé de reconnaître des séquences d’activation spécifiques dans un flux de bits, permettant ainsi l’activation du nœud concerné. Une contribution majeure de cette thèse est l’introduction du modèle “Saturating Leaky Integrate and Fire” (SLIF), qui incorpore un phénomène bio-inspiré appelé “Saturation Synaptique” pour créer un filtre temporel sensible aux intervalles entre impulsions (Inter-Spike Timing). L’étude approfondit les paramètres du modèle SLIF, explore différentes topologies de réseaux, et démontre la pertinence de cette approche pour la reconnaissance de séquences temporelles analogiques. Les résultats établissent les bases pour l’utilisation des réseaux neuromorphiques dans les dispositifs IoT à très faible consommation d’énergie, offrant des perspectives prometteuses pour la conception de WuRs capables de traiter des signaux temporels de manière efficace et économe en énergie.

Detecting active users in a non-orthogonal multiple access (NOMA) network poses a significant challenge for 5G/6G applications. Traditional algorithms tackling this task, relying on classical processors, have to make a compromise between performance and complexity. However, a quantum computing based strategy called quantum annealing (QA) can mitigate this trade-off. In this paper, we first propose a mapping between the AUD searching problem and the identification of the ground state of an Ising Hamiltonian. Then, we compare the execution times of our QA approach for several code domain multiple access (CDMA) scenarios. We evaluate the impact of the cross-correlation properties of the chosen codes in a NOMA network for detecting the active user’s set.

Federated Learning (FL) enables multiple entities with local datasets to collaboratively train machine learning models without requiring data centralization. Most existing FL approaches assume that local datasets are either pre-collected or sampled I.I.D from an unknown distribution. However, this assumption can be too limiting in many scenarios, such as crowd sensing, where sensors continuously collect user data, or model-free reinforcement learning, where agents interact with an evolving environment and train their policy to maximize the reward. In this work, we relax the I.I.D. assumption by modeling each client’s data as coming from an ergodic Markov chain, which converges to their local distribution. We then analyze the sample and communication complexity of two classical FL algorithms—Minibatch SGD and Local SGD. Our findings show that, under this Markovian framework, both algorithms achieve linear speedup with respect to the number of clients, and their communication complexities are unchanged, given that they perform more local computation.

Covert communication, also known as communication with low probability of detection, refers to a scenario where a legitimate receiver and a eavesdropper share the same channel while the sender wishes to prevent the eavesdropper from guessing whether a communication is ongoing or not. In this scenario, the transmitter and receiver share a secret key which gives the receiver the advantage needed in order to decode. It can be shown that the maximum message length that can be transmitted reliably and covertly scales like the square root of the number of channel uses. In this work, we extend previous results for Gaussian channels and study the fundamental limits of covert communications over general memoryless additive-noise channels. Under mild integrability assumptions, we find a general upper bound on the square-root scaling constant. Furthermore, we show that under some additional assumptions, this upper bound is tight. We also provide upper bounds on the length of the secret key required to achieve the optimal scaling.

Many optimization problems are inherently multi-objective. To address them, we formalize Jacobian descent (JD), a direct generalization of gradient descent for vector-valued functions. Each step of this algorithm relies on a Jacobian matrix consisting of one gradient per objective. The aggregator, responsible for reducing this matrix into an update vector, characterizes JD. While the multi-task learning literature already contains a variety of aggregators, they often lack some natural properties. In particular, the update should not conflict with any objective and should scale proportionally to the norm of each gradient. We propose a new aggregator specifically designed to satisfy this. Emphasizing conflict between objectives, we then highlight direct applications for our methods. Most notably, we introduce instance-wise risk minimization (IWRM), a learning paradigm in which the loss of each training example is considered a separate objective. On simple image classification tasks, IWRM exhibits promising results compared to the direct minimization of the average loss. The performance of our aggregator in those experiments also corroborates our theoretical findings. Lastly, as speed is the main limitation of JD, we provide a path towards a more efficient implementation.

In a brief but important 1974 paper, L. R. Welch gave a family of bounds on the maximum modulus of inner products between distinct vectors in a set of m unit vectors in an n-dimensional space. It was noted that these bounds have implications in the design of sequences having desirable correlation properties for multichannel communication systems. Over the years, motivated by several applications, sets that attain the Welch bound have been sought after. On the other hand, mutually unbiased bases (MUBs) are a primitive used in quantum information processing. From a mathematical standpoint, the existence and construction of maximal sets of MUBs in all dimensions pose important open questions. Maximal sets of MUBs turn out to be the same objects as complex projective 2-designs. This talk will discuss these various mathematical objects in connection to sets that attain the Welch bounds.