Gaspard Abel

Erkan Turan, Gaspard Abel, Maysam Behmanesh et al.

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 \emph{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 \emph{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.

Gaspard Abel, Eloi Campagne, Mohamed Benloughmari et al.

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.