Gaspard Abel

The emergence of online social platforms, such as social networks and social media, has drastically affected the way people apprehend the information flows to which they are exposed. In such platforms, various information cascades spreading among users is the main force creating complex dynamics of opinion formation, each user being characterized by their own behavior adoption mechanism. Moreover, the spread of multiple pieces of information or beliefs in a networked population is rarely uncorrelated. In this paper, we introduce the Mixture of Interacting Cascades (MIC), a model of marked multidimensional Hawkes processes with the capacity to model jointly non-trivial interaction between cascades and users. We emphasize on the interplay between information cascades and user activity, and use a mixture of temporal point processes to build a coupled user/cascade point process model. Experiments on synthetic and real data highlight the benefits of this approach and demonstrate that MIC achieves superior performance to existing methods in modeling the spread of information cascades. Finally, we demonstrate how MIC can provide, through its learned parameters, insightful bi-layered visualizations of real social network activity data.

Graph Neural Networks (GNNs) learn node representations through iterative network-based message-passing. While powerful, deep GNNs suffer from oversmoothing, where node features converge to a homogeneous, non-informative state. We re-frame this problem of representational collapse from a bifurcation theory perspective, characterizing oversmoothing as convergence to a stable “homogeneous fixed point.” Our central contribution is the theoretical discovery that this undesired stability can be broken by replacing standard monotone activations (e.g., ReLU) with a class of functions. Using Lyapunov-Schmidt reduction, we analytically prove that this substitution induces a bifurcation that destabilizes the homogeneous state and creates a new pair of stable, non-homogeneous patterns that provably resist oversmoothing. Our theory predicts a precise, nontrivial scaling law for the amplitude of these emergent patterns, which we quantitatively validate in experiments. Finally, we demonstrate the practical utility of our theory by deriving a closed-form, bifurcation-aware initialization and showing its utility in real benchmark experiments.

Motivated by scenarios of epidemic competition, as well as how social contagions spread at the level of individuals, this work considers the competition between two conflicting node states that spread over a social graph according to a generic diffusion process. For this setting, we introduce the Generalized Largest Reduction in Infectious Edges (gLRIE), which is a dynamic resource allocation strategy that favors the preferred state against the other. Our analysis assumes a generic continuous-time SIS-like (Susceptible-Infectious-Susceptible) diffusion model that allows for: arbitrary node transition rate functions for nodes to change state, and competition between the healthy (positive) and infected (negative) states, which are both diffusive at the same time, yet mutually exclusive at each node. The strategy follows a minimum-risk-maximum-gain principle, and its features are particularly relevant for social contagion phenomena. In accordance with the LRIE strategy that we generalize, we show that in this context the gLRIE strategy remains a greedy solution for the minimization of the number of infected network nodes over time. Ultimately, simulations are employed to compare the proposed strategy with other existing alternatives, demonstrating that gLRIE exhibits superior performance across a spectrum of scenarios, including a realistic counter-contagion campaign in a small well-monitored community.

Curriculum Learning (CL) is a meta-learning paradigm that trains a model by feeding the data instances incrementally according to a schedule, which is based on difficulty progression. Defining meaningful difficulty assessment measures is crucial and most usually the main bottleneck for effective learning, while also in many cases the employed heuristics are only application-specific. In this work, we propose the Dual-Criterion Curriculum Learning (DCCL) framework that combines two views of assessing instance-wise difficulty: a loss-based criterion is complemented by a density-based criterion learned in the data representation space. Essentially, DCCL calibrates training-based evidence (loss) under the consideration that data sparseness amplifies the learning difficulty. As a testbed, we choose the time-series forecasting task. We evaluate our framework on multivariate time-series benchmarks under standard One-Pass and Baby-Steps training schedules. Empirical results show the interest of density-based and hybrid dual-criterion curricula over loss-only baselines and standard non-CL training in this setting.

This paper investigates the effect of asynchrony in agents' updates in the emergence of algorithmic collusion. We present a continuous-time model for algorithmic collusion in which two firms use Q-learning algorithms to set prices asynchronously in a Bertrand duopoly. The firms update their prices at times dictated by a Poisson clock. By controlling the extent of agents' asynchrony, we run extensive numerical experiments with three specifications of the algorithm to investigate the emergence of algorithmic collusion. The strength of collusion is measured by a standard collusion index, as well as by automatically detecting the reward-punishment schemes. This is done by recording a large number of algorithms' reactions to unilateral price cuts and comparing them with the reactions of untrained algorithms. Our findings indicate that asynchrony hampers collusion, especially when the algorithms are stateless. When they condition on their competitor's previous prices, the sensitivity of algorithmic collusion to asynchrony varies depending on the type of information they have access to. The implications of these results for the regulation of algorithmic pricing are discussed.

What are the inductive biases of a Transformer architecture? Existing theory on how the forward pass shapes representations either considers whether Transformers escape from rank collapse or demonstrates that self-attention drives tokens toward cluster patterns. The latter view arises from an elegant dynamical systems perspective, but relies on simplified architectural assumptions, and does not ex-plain the rich structures observed in practice. This leaves a major open question:when a full Transformer escapes rank collapse, how does it structure token representations? Using pattern-formation theory, we show that the dynamical view of Transformers can account for Positional Encoding, Multi-Head Attention, and Output-Value geometry. We demonstrate that a full Transformer architecture imposes an inductive prior by selectively amplifying a rich set of previously unreported patterns, including traveling or rotating waves among others. We characterize the role of each architectural component in controlling which pattern is amplified, which ones stabilize, compete, or coexist. Finally, we show that these structures can act as a controllable dynamical prior that facilitates learning. By choosing both task-aligned positional encoding and weight initialization, we demonstrate improved data efficiency and accelerated optimization on controlled sequence tasks and with ConViT on CIFAR-10.