Optimal Transport (OT) has attracted significant interest in the machine learning community, not only for its ability to define meaningful distances between probability distributions - such as the Wasserstein distance - but also for its formulation of OT plans. Its computational complexity remains a bottleneck, though, and slicing techniques have been developed to scale OT to large datasets. Recently, a novel slicing scheme, dubbed min-SWGG, lifts a single one-dimensional plan back to the original multidimensional space, finally selecting the slice that yields the lowest Wasserstein distance as an approximation of the full OT plan. Despite its computational and theoretical advantages, min-SWGG inherits typical limitations of slicing methods: (i) the number of required slices grows exponentially with the data dimension, and (ii) it is constrained to linear projections. Here, we reformulate min-SWGG as a bilevel optimization problem and propose a differentiable approximation scheme to efficiently identify the optimal slice, even in high-dimensional settings. We furthermore define its generalized extension for accommodating to data living on manifolds. Finally, we demonstrate the practical value of our approach in various applications, including gradient flows on manifolds and highdimensional spaces, as well as a novel sliced OT-based conditional flow matching for image generation - where fast computation of transport plans is essential.

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We consider the problem of how many samples from a Gaussian multi-index model are required to weakly reconstruct the relevant index subspace. Despite its increasing popularity as a testbed for investigating the computational complexity of neural networks, results beyond the single-index setting remain elusive. In this work, we introduce spectral algorithms based on the linearization of a message passing scheme tailored to this problem. Our main contribution is to show that the proposed methods achieve the optimal reconstruction threshold. Leveraging a high-dimensional characterization of the algorithms, we show that above the critical threshold the leading eigenvector correlates with the relevant index subspace, a phenomenon reminiscent of the Baik-Ben Arous-Peche (BBP) transition in spiked models arising in random matrix theory.

This adaptive mechanism adjusts the resolution of the predictions over both time and space, yielding refined regret bounds in terms of local regularity. Consequently, in heterogeneous environments, our adaptive guarantees can significantly surpass those obtained by standard global methods.

Communication between agents often constitutes a major computational bottleneck in distributed learning. One of the most common mitigation strategies is to compress the information exchanged, thereby reducing communication overhead. To counteract the degradation in convergence associated with compressed communication, error feedback schemes--most notably EF and EF21--were introduced. In this work, we provide a tight analysis of both of these methods. Specifically, we find the Lyapunov function that yields the best possible convergence rate for each method--with matching lower bounds.

Federated learning (FL) is now recognized as a key framework for communicationefficient collaborative learning. Most theoretical and empirical studies, however, rely on the assumption that clients have access to pre-collected data sets, with limited investigation into scenarios where clients continuously collect data. In many real-world applications, particularly when data is generated by physical or biological processes, client data streams are often modeled by non-stationary Markov processes.

Intent classification models have made a significant progress in recent years. However, previous studies primarily focus on high-resource language datasets, which results in a gap for low-resource languages and for regions with high rates of illiteracy, where languages are more spoken than read or written. This is the case in Senegal, for example, where Wolof is spoken by around 90% of the population, while the national illiteracy rate remains at of 42%. Wolof is actually spoken by more than 10 million people in West African region. To address these limitations, we introduce the Wolof Banking Speech Intent Classification Dataset (WolBanking77), for academic research in intent classification.

Point Cloud Few-Shot Semantic Segmentation (PC-FSS) aims to segment unknown categories in query samples using only a small number of annotated support samples. However, scene complexity and insufficient representation of local geometric structures pose significant challenges to PC-FSS. To address these issues, we propose a novel pre-training-free Visual Introspective Prototype Segmentation network (VIP-Seg). Specifically, we design a Visual Introspective Prototype (VIP) module that employs a multi-step reasoning approach to tackle intra-class diversity and domain gaps between support and query sets. The VIP module consists of a Prototype Enhancement Module (PEM) and a Prototype Difference Module (PDM), which work alternately to progressively refine prototypes. The PEM enhances prototype discriminability and reduces intra-class diversity, while the PDM learns common representations from the differences between query and support features, effectively eliminating semantic inconsistencies caused by domain gaps. To further reduce intra-class diversity and enhance point discriminative ability, we propose a Dynamic Power Convolution (DyPowerConv) that leverages learnable power functions to effectively capture local geometric structures and detailed features of point clouds. Extensive experiments on S3DIS and ScanNet demonstrate that our proposed VIP-Seg significantly outperforms current state-of-the-art methods, proving its effectiveness in PC-FSS tasks.

The Schrödinger Bridge (SB) problem has become a fundamental tool in computational optimal transport and generative modeling. To address this problem, ideal methods such as Iterative Proportional Fitting and Iterative Markovian Fitting (IMF) have been proposed--alongside practical approximations like Diffusion Schrödinger Bridge and its Matching (DSBM) variant. While previous work have established asymptotic convergence guarantees for IMF, a quantitative, nonasymptotic understanding remains unknown. In this paper, we provide the first non-asymptotic exponential convergence guarantees for IMF under mild structural assumptions on the reference measure and marginal distributions, assuming a sufficiently large time horizon. Our results encompass two key regimes: one where the marginals are log-concave, and another where they are weakly log-concave. The analysis relies on new contraction results for the Markovian projection operator and paves the way to theoretical guarantees for DSBM.

We consider a common case of the combinatorial semi-bandit problem, the m-set semi-bandit, where the learner exactly selects m arms from the total d arms. In the adversarial setting, the best regret bound, known to be O( nmd) for time horizon n, is achieved by the well-known Follow-the-Regularized-Leader (FTRL) policy. However, this requires to explicitly compute the arm-selection probabilities via optimizing problems at each time step and sample according to them. This problem can be avoided by the Follow-the-Perturbed-Leader (FTPL) policy, which simply pulls the m arms that rank among the m smallest (estimated) loss with random perturbation. In this paper, we show that FTPL with a Fréchet perturbation also enjoys the near optimal regret bound O( nm( p dlog(d) + m5/6)) in the adversarial setting and approaches best-of-both-world regret bounds, i.e., achieves a logarithmic regret for the stochastic setting. Moreover, our lower bounds show that the extra factors are unavoidable with our approach; any improvement would require a fundamentally different and more challenging method.