Inverse problems are ubiquitous in science, engineering, and medicine, in particular for problems where observations provide only indirect or incomplete information about a system [1]. Inverse problems are central in a wide range of applications such as flow field reconstruction [2, 3, 4], data assimilation [5], medical imaging [6, 7], and parameters estimation of material properties [8, 9, 10]. A particularly challenging class of inverse problems arises when the forward model is governed by ordinary differential equations (ODEs) or partial differential equations (PDEs) [11]. Incorporating physical knowledge through this approach reduces the space of possible solutions, avoiding the need for arbitrary regularization as is often the case in inverse problems [12, 13, 14]. However, this approach can suffer from the high dimensionality of the problem, stiffness, noisy measurements, and sensitivity to parameters. In particular, quantifying the uncertainties of solutions is challenging with standard techniques for inverse PDE problems such as Bayesian inference [15, 14], variational methods [16], ensemble Kalman methods [17], and adjoint-based optimization [18], which can be limited with issues of scalability, robustness, and computational cost. In parallel, operator learning approaches based on DeepONets [19], Fourier neural operators [20], and graph neural networks [21, 22] have been extended to inverse problems and uncertainty quantification [23, 24, 25]. Similar Bayesian techniques rely on training data to build prior knowledge [26]. However, the application of these operator learning techniques to large-scale problems is limited by the cost of their training and the difficulty of generating sufficient high-fidelity data.

We propose the first parameter-free decentralized online learning algorithms with network regret guarantees, which achieve sublinear regret without requiring hyperparameter tuning. This family of algorithms connects multi-agent coin-betting and decentralized online learning via gossip steps. To enable our decentralized analysis, we introduce a novel "betting function" formulation for coin-betting that simplifies the multi-agent regret analysis. Our analysis shows sublinear network regret bounds and is validated through experiments on synthetic and real datasets. This family of algorithms is applicable to distributed sensing, decentralized optimization, and collaborative ML applications.

Modern face recognition models achieve high overall accuracy but continue to exhibit systematic biases that disproportionately affect certain subpopulations. Conventional bias evaluation frameworks rely on labeled attributes to form subpopulations, which are expensive to obtain and limited to predefined categories. We introduce Latent Feature Alignment (LFA), an attribute-label-free algorithm that uses latent directions to identify subpopulations. This yields two main benefits over standard clustering: (i) semantically coherent grouping, where faces sharing common attributes are grouped together more reliably than by proximity-based methods, and (ii) discovery of interpretable directions, which correspond to semantic attributes such as age, ethnicity, or attire. Across four state-of-the-art recognition models (ArcFace, CosFace, ElasticFace, PartialFC) and two benchmarks (RFW, CelebA), LFA consistently outperforms k-means and nearest-neighbor search in intra-group semantic coherence, while uncovering interpretable latent directions aligned with demographic and contextual attributes. These results position LFA as a practical method for representation auditing of face recognition models, enabling practitioners to identify and interpret biased subpopulations without predefined attribute annotations.

The concept of knowledge distillation (KD) describes the training of a student model from a teacher model and is a widely adopted technique in deep learning. However, it is still not clear how and why distillation works. Previous studies focus on two central aspects of distillation: model size, and generalisation. In this work we study distillation in a third dimension: dataset size. We present a suite of experiments across a wide range of datasets, tasks and neural architectures, demonstrating that the effect of distillation is not only preserved but amplified in low-data regimes. We call this newly discovered property the data efficiency of distillation. Equipped with this new perspective, we test the predictive power of existing theories of KD as we vary the dataset size. Our results disprove the hypothesis that distillation can be understood as label smoothing, and provide further evidence in support of the dark knowledge hypothesis. Finally, we analyse the impact of modelling factors such as the objective, scale and relative number of samples on the observed phenomenon. Ultimately, this work reveals that the dataset size may be a fundamental but overlooked variable in the mechanisms underpinning distillation.

Bayesian optimisation (BO) is a standard approach for sample-efficient global optimisation of expensive black-box functions, yet its scalability to high dimensions remains challenging. Here, we investigate nonlinear dimensionality reduction techniques that reduce the problem to a sequence of low-dimensional Latent-Space BO (LSBO). While early LSBO methods used (linear) random projections (Wang et al., 2013), building on Grosnit et al. (2021), we employ Variational Autoencoders (VAEs) for LSBO, focusing on deep metric loss for structured latent manifolds and VAE retraining to adapt the encoder-decoder to newly sampled regions. We propose some changes in their implementation, originally designed for tasks such as molecule generation, and reformulate the algorithm for broader optimisation purposes. We then couple LSBO with Sequential Domain Reduction (SDR) directly in the latent space (SDR-LSBO), yielding an algorithm that narrows the latent search domains as evidence accumulates. Implemented in a GPU-accelerated BoTorch stack with Matern-5/2 Gaussian process surrogates, our numerical results show improved optimisation quality across benchmark tasks and that structured latent manifolds improve BO performance. Additionally, we compare random embeddings and VAEs as two mechanisms for dimensionality reduction, showing that the latter outperforms the former. To the best of our knowledge, this is the first study to combine SDR with VAE-based LSBO, and our analysis clarifies design choices for metric shaping and retraining that are critical for scalable latent space BO. For reproducibility, our source code is available at https://github.com/L-Lok/Nonlinear-Dimensionality-Reduction-Techniques-for-Bayesian-Optimization.git.

Black-box simulators are widely used in robotics, but optimizing their parameters remains challenging due to inaccessible likelihoods. Simulation-Based Inference (SBI) tackles this issue using simulation-driven approaches, estimating the posterior from offline real observations and forward simulations. However, in black-box scenarios, preparing observations that contain sufficient information for parameter estimation is difficult due to the unknown relationship between parameters and observations. In this work, we present Active Simulation-Based Inference (ASBI), a parameter estimation framework that uses robots to actively collect real-world online data to achieve accurate black-box simulator tuning. Our framework optimizes robot actions to collect informative observations by maximizing information gain, which is defined as the expected reduction in Shannon entropy between the posterior and the prior. While calculating information gain requires the likelihood, which is inaccessible in black-box simulators, our method solves this problem by leveraging Neural Posterior Estimation (NPE), which leverages a neural network to learn the posterior estimator. Three simulation experiments quantitatively verify that our method achieves accurate parameter estimation, with posteriors sharply concentrated around the true parameters. Moreover, we show a practical application using a real robot to estimate the simulation parameters of cubic particles corresponding to two real objects, beads and gravel, with a bucket pouring action.

This paper studies the generalization properties of a recently proposed kernel method, the Random Feature models with Learnable Activation Functions (RFLAF). By applying a data-dependent sampling scheme for generating features, we provide by far the sharpest bounds on the required number of features for learning RFLAF in both the regression and classification tasks. We provide a unified theorem that describes the complexity of the feature number $s$, and discuss the results for the plain sampling scheme and the data-dependent leverage weighted scheme. Through weighted sampling, the bound on $s$ in the MSE loss case is improved from $Ω(1/ε^2)$ to $\tildeΩ((1/ε)^{1/t})$ in general $(t\geq 1)$, and even to $Ω(1)$ when the Gram matrix has a finite rank. For the Lipschitz loss case, the bound is improved from $Ω(1/ε^2)$ to $\tildeΩ((1/ε^2)^{1/t})$. To learn the weighted RFLAF, we also propose an algorithm to find an approximate kernel and then apply the leverage weighted sampling. Empirical results show that the weighted RFLAF achieves the same performances with a significantly fewer number of features compared to the plainly sampled RFLAF, validating our theories and the effectiveness of this method.

Abstract--Single Positive Multi-Label Learning (SPMLL) addresses the challenging scenario where each training sample is annotated with only one positive label despite potentially belonging to multiple categories, making it difficult to capture complex label relationships and hierarchical structures. T o address these limitations, we propose the first hyperbolic classification framework for SPMLL that represents each label as a hyperbolic ball rather than a point or vector, enabling rich inter-label relationship modeling through geometric ball interactions. Our ball-based approach naturally captures multiple relationship types simultaneously: inclusion for hierarchical structures, overlap for co-occurrence patterns, and separation for semantic independence. Further, we introduce two key component innovations: a temperature-adaptive hyperbolic ball classifier and a physics-inspired double-well regularization that guides balls toward meaningful configurations. T o validate our approach, extensive experiments on four benchmark datasets (MS-COCO, PASCAL VOC, NUS-WIDE, CUB-200-2011) demonstrate competitive performance with superior interpretability compared to existing methods. Furthermore, statistical analysis reveals strong correlation between learned embeddings and real-world co-occurrence patterns, establishing hyperbolic geometry as a more robust paradigm for structured classification under incomplete supervision. Multi-label recognition (MLR) is a fundamental problem in domains such as computer vision, natural language processing, multimedia retrieval, and medical diagnosis.

We consider the minimisation problem of submodular functions and investigate the application of a zeroth-order method to this problem. The method is based on exploiting a Gaussian smoothing random oracle to estimate the smoothed function gradient. We prove the convergence of the algorithm to a global $ε$-approximate solution in the offline case and show that the algorithm is Hannan-consistent in the online case with respect to static regret. Moreover, we show that the algorithm achieves $O(\sqrt{NP_N^\ast})$ dynamic regret, where $N$ is the number of iterations and $P_N^\ast$ is the path length. The complexity analysis and hyperparameter selection are presented for all the cases. The theoretical results are illustrated via numerical examples.

The E-commerce advertising platforms typically sell commercial traffic through either second-price auction (SPA) or first-price auction (FPA). SPA was historically prevalent due to its dominant strategy incentive-compatible (DSIC) for bidders with quasi-linear utilities, especially when budgets are not a binding constraint, while FPA has gained more prominence for offering higher revenue potential to publishers and avoiding the possibility for discriminatory treatment in personalized reserve prices. Meanwhile, on the demand side, advertisers are increasingly adopting platform-wide marketing solutions akin to QuanZhanTui, shifting from spending budgets solely on commercial traffic to bidding on the entire traffic for the purpose of maximizing overall sales. For automated bidding systems, such a trend poses a critical challenge: determining optimal strategies across heterogeneous auction channels to fulfill diverse advertiser objectives, such as maximizing return (MaxReturn) or meeting target return on ad spend (TargetROAS). To overcome this challenge, this work makes two key contributions. First, we derive an efficient solution for optimal bidding under FPA channels, which takes into account the presence of organic traffic - traffic can be won for free. Second, we introduce a marginal cost alignment (MCA) strategy that provably secures bidding efficiency across heterogeneous auction mechanisms. To validate performance of our developed framework, we conduct comprehensive offline experiments on public datasets and large-scale online A/B testing, which demonstrate consistent improvements over existing methods.