Armand Kassaï Koupaï, Lise Le Boudec, Patrick Gallinari
We introduce ECHO, a transformer-operator framework for generating million-point PDE trajectories. While existing neural operators (NOs) have shown promise for solving partial differential equations, they remain limited in practice due to poor scalability on dense grids, error accumulation during dynamic unrolling, and task-specific design. ECHO addresses these challenges through three key innovations. (i) It employs a hierarchical convolutional encode-decode architecture that achieves a 100 $\times$ spatio-temporal compression while preserving fidelity on mesh points. (ii) It incorporates a training and adaptation strategy that enables high-resolution PDE solution generation from sparse input grids. (iii) It adopts a generative modeling paradigm that learns complete trajectory segments, mitigating long-horizon error drift. The training strategy decouples representation learning from downstream task supervision, allowing the model to tackle multiple tasks such as trajectory generation, forward and inverse problems, and interpolation. The generative model further supports both conditional and unconditional generation. We demonstrate state-of-the-art performance on million-point simulations across diverse PDE systems featuring complex geometries, high-frequency dynamics, and long-term horizons.
Louis Castres Saint Martin, Clement Calauzenes, Alain Rakotomamonjy, Patrick Gallinari
Next-item prediction is inherently ambiguous: a single interaction history often admits multiple plausible continuations across distinct catalogue regions. Standard sequential recommenders compress these alternatives into a single prediction, conflating user intents. We introduce COllapse-resistant Multiple hyPOThesis lEarning (COMPOTE), a multi-hypothesis transformer trained with an annealed objective that transitions from uniform supervision to a winner-takes-all assignment. This mechanism forces hypotheses to specialize into distinct catalogue regions, while inference relies on an efficient, normalizer-free max-similarity rule. Theoretically, we show that in the population case, the optimal solutions partition the conditional next-item distribution according to a max-entropy quantization principle, while pooled scores preserve the Bayes-optimal ranking. We also prove a generalization bound scaling logarithmically with the number of hypotheses. Across three Amazon Reviews 2023 benchmarks, COMPOTE outperforms strong ID-based, generative, and multi-interest baselines using item IDs alone. Matched-capacity ablations confirm that performance gains stem directly from the annealed objective, preventing the head collapse observed in conventional multi-head architectures, rather than added capacity, ensembling, or routing.
Louis Castres Saint Martin, Alain Rakotomamonjy, Patrick Gallinari
A user history can admit multiple plausible next interactions, yet conventional sequential recommenders produce a single deterministic ranking. While diffusion models offer a natural way to sample alternative continuations, we show that existing target-item diffusion recommenders often suffer from severe sampling collapse, producing nearly identical outputs across independent draws. We identify two ubiquitous design choices that promote this collapse: joint learning of the latent space and denoiser, and in-trajectory supervision via discrete losses. To address these failure modes, we introduce DARTS (Diverse and Accurate Recommendation Through Sampling), a three-stage latent diffusion framework that explicitly decouples representation learning, generative modeling, and discrete ranking by learning and freezing the latent space before diffusion training and postponing ranking supervision to the final decoding stage. We further characterize sampling diversity using complementary measures of variation before and after decoding, and use posterior-predictive aggregation to exploit this diversity at inference. Across three Amazon Reviews 2023 categories, DARTS preserves substantially greater sampling diversity while outperforming strong sequential, generative-retrieval, and diffusion baselines by 7-12% on standard ranking metrics. Aggregating multiple samples further improves ranking accuracy at a fixed slate size.