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Cross-modal retrieval (CMR) aims to establish interaction between different modalities, among which supervised CMR is emerging due to its flexibility in learning semantic category discrimination. Despite the remarkable performance of previous supervised CMR methods, much of their success can be attributed to the well-annotated data. However, even for unimodal data, precise annotation is expensive and time-consuming, and it becomes more challenging with the multimodal scenario. In practice, massive multimodal data are collected from the Internet with coarse annotation, which inevitably introduces noisy labels. Training with such misleading labels would bring two key challenges -- enforcing the multimodal samples to \emph{align incorrect semantics} and \emph{widen the heterogeneous gap}, resulting in poor retrieval performance. To tackle these challenges, this work proposes UOT-RCL, a Unified framework based on Optimal Transport (OT) for Robust Cross-modal Retrieval. First, we propose a semantic alignment based on partial OT to progressively correct the noisy labels, where a novel cross-modal consistent cost function is designed to blend different modalities and provide precise transport cost. Second, to narrow the discrepancy in multi-modal data, an OT-based relation alignment is proposed to infer the semantic-level cross-modal matching. Both of these two components leverage the inherent correlation among multi-modal data to facilitate effective cost function. The experiments on three widely-used cross-modal retrieval datasets demonstrate that our UOT-RCL surpasses the state-of-the-art approaches and significantly improves the robustness against noisy labels.

Generative models are invaluable in many fields of science because of their ability to capture high-dimensional and complicated distributions, such as photo-realistic images, protein structures, and connectomes. How do we evaluate the samples these models generate? This work aims to provide an accessible entry point to understanding popular notions of statistical distances, requiring only foundational knowledge in mathematics and statistics. We focus on four commonly used notions of statistical distances representing different methodologies: Using low-dimensional projections (Sliced-Wasserstein; SW), obtaining a distance using classifiers (Classifier Two-Sample Tests; C2ST), using embeddings through kernels (Maximum Mean Discrepancy; MMD), or neural networks (Fr\'echet Inception Distance; FID). We highlight the intuition behind each distance and explain their merits, scalability, complexity, and pitfalls. To demonstrate how these distances are used in practice, we evaluate generative models from different scientific domains, namely a model of decision making and a model generating medical images. We showcase that distinct distances can give different results on similar data. Through this guide, we aim to help researchers to use, interpret, and evaluate statistical distances for generative models in science.

Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews reconstruction methods in inverse problems with learned forward operators that follow two different paradigms. The first one is completely agnostic to the forward operator and learns its restriction to the subspace spanned by the training data. The framework of regularisation by projection is then used to find a reconstruction. The second one uses a simplified model of the physics of the measurement process and only relies on the training data to learn a model correction. We present the theory of these two approaches and compare them numerically. A common theme emerges: both methods require, or at least benefit from, training data not only for the forward operator, but also for its adjoint.

The ultimate goal of Dataset Distillation is to synthesize a small synthetic dataset such that a model trained on this synthetic set will perform equally well as a model trained on the full, real dataset. Until now, no method of Dataset Distillation has reached this completely lossless goal, in part due to the fact that previous methods only remain effective when the total number of synthetic samples is extremely small. Since only so much information can be contained in such a small number of samples, it seems that to achieve truly loss dataset distillation, we must develop a distillation method that remains effective as the size of the synthetic dataset grows. In this work, we present such an algorithm and elucidate why existing methods fail to generate larger, high-quality synthetic sets. Current state-of-the-art methods rely on trajectory-matching, or optimizing the synthetic data to induce similar long-term training dynamics as the real data. We empirically find that the training stage of the trajectories we choose to match (i.e., early or late) greatly affects the effectiveness of the distilled dataset. Specifically, early trajectories (where the teacher network learns easy patterns) work well for a low-cardinality synthetic set since there are fewer examples wherein to distribute the necessary information. Conversely, late trajectories (where the teacher network learns hard patterns) provide better signals for larger synthetic sets since there are now enough samples to represent the necessary complex patterns. Based on our findings, we propose to align the difficulty of the generated patterns with the size of the synthetic dataset. In doing so, we successfully scale trajectory matching-based methods to larger synthetic datasets, achieving lossless dataset distillation for the very first time. Code and distilled datasets are available at //gzyaftermath.github.io/DATM.

Addressing the large distribution gap between training and testing data has long been a challenge in machine learning, giving rise to fields such as transfer learning and domain adaptation. Recently, Continuous Domain Adaptation (CDA) has emerged as an effective technique, closing this gap by utilizing a series of intermediate domains. This paper contributes a novel CDA method, W-MPOT, which rigorously addresses the domain ordering and error accumulation problems overlooked by previous studies. Specifically, we construct a transfer curriculum over the source and intermediate domains based on Wasserstein distance, motivated by theoretical analysis of CDA. Then we transfer the source model to the target domain through multiple valid paths in the curriculum using a modified version of continuous optimal transport. A bidirectional path consistency constraint is introduced to mitigate the impact of accumulated mapping errors during continuous transfer. We extensively evaluate W-MPOT on multiple datasets, achieving up to 54.1\% accuracy improvement on multi-session Alzheimer MR image classification and 94.7\% MSE reduction on battery capacity estimation.

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses the $f$-DRO, Wasserstein-DRO, and spectral/$L$-risk formulations used in practice. We present Drago, a stochastic primal-dual algorithm that achieves a state-of-the-art linear convergence rate on strongly convex-strongly concave DRO problems. The method combines both randomized and cyclic components with mini-batching, which effectively handles the unique asymmetric nature of the primal and dual problems in DRO. We support our theoretical results with numerical benchmarks in classification and regression.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh corresponds to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at \url{//github.com/yuyudeep/hcmt}.

State estimation is a crucial component for the successful implementation of robotic systems, relying on sensors such as cameras, LiDAR, and IMUs. However, in real-world scenarios, the performance of these sensors is degraded by challenging environments, e.g. adverse weather conditions and low-light scenarios. The emerging 4D imaging radar technology is capable of providing robust perception in adverse conditions. Despite its potential, challenges remain for indoor settings where noisy radar data does not present clear geometric features. Moreover, disparities in radar data resolution and field of view (FOV) can lead to inaccurate measurements. While prior research has explored radar-inertial odometry based on Doppler velocity information, challenges remain for the estimation of 3D motion because of the discrepancy in the FOV and resolution of the radar sensor. In this paper, we address Doppler velocity measurement uncertainties. We present a method to optimize body frame velocity while managing Doppler velocity uncertainty. Based on our observations, we propose a dual imaging radar configuration to mitigate the challenge of discrepancy in radar data. To attain high-precision 3D state estimation, we introduce a strategy that seamlessly integrates radar data with a consumer-grade IMU sensor using fixed-lag smoothing optimization. Finally, we evaluate our approach using real-world 3D motion data.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.

Federated Learning (FL) is a decentralized machine-learning paradigm, in which a global server iteratively averages the model parameters of local users without accessing their data. User heterogeneity has imposed significant challenges to FL, which can incur drifted global models that are slow to converge. Knowledge Distillation has recently emerged to tackle this issue, by refining the server model using aggregated knowledge from heterogeneous users, other than directly averaging their model parameters. This approach, however, depends on a proxy dataset, making it impractical unless such a prerequisite is satisfied. Moreover, the ensemble knowledge is not fully utilized to guide local model learning, which may in turn affect the quality of the aggregated model. Inspired by the prior art, we propose a data-free knowledge distillation} approach to address heterogeneous FL, where the server learns a lightweight generator to ensemble user information in a data-free manner, which is then broadcasted to users, regulating local training using the learned knowledge as an inductive bias. Empirical studies powered by theoretical implications show that, our approach facilitates FL with better generalization performance using fewer communication rounds, compared with the state-of-the-art.