While high-dimensional embedding vectors are being increasingly employed in various tasks like Retrieval-Augmented Generation and Recommendation Systems, popular dimensionality reduction (DR) methods such as PCA and UMAP have rarely been adopted for accelerating the retrieval process due to their inability of preserving the nearest neighbor (NN) relationship among vectors. Empowered by neural networks' optimization capability and the bounding effect of Rayleigh quotient, we propose a Regularized Auto-Encoder (RAE) for k-NN preserving dimensionality reduction. RAE constrains the network parameter variation through regularization terms, adjusting singular values to control embedding magnitude changes during reduction, thus preserving k-NN relationships. We provide a rigorous mathematical analysis demonstrating that regularization establishes an upper bound on the norm distortion rate of transformed vectors, thereby offering provable guarantees for k-NN preservation. With modest training overhead, RAE achieves superior k-NN recall compared to existing DR approaches while maintaining fast retrieval efficiency. V ector embeddings have become the cornerstone of modern AI systems, enabling sophisticated semantic understanding across diverse domains including Information Retrieval (Zhu et al. (2023)), Recommendation Systems (Zhao et al. (2024)), and Retrieval-Augmented Generation (RAG) pipelines (Gao et al. (2023)).

Time series foundation models (TSFMs) have emerged as a powerful paradigm for time series analysis, driven by large-scale pretraining on diverse data corpora. However, time series inherently exhibit heterogeneous information density over time, influenced by system states and signal complexity, presenting significant modeling challenges especially in a zero-shot scenario. Current TSFMs rely on non-adaptive processing pipelines that fail to capture this dynamic nature. For example, common tokenization strategies such as fixed-size patching enforce rigid observational granularity, limiting their ability to adapt to varying information densities. Similarly, conventional positional encodings impose a uniform temporal scale, making it difficult to model diverse periodicities and trends across series. To overcome these limitations, we propose Kairos, a flexible TSFM framework that integrates a dynamic patching tokenizer and an instance-adaptive positional embedding. Kairos adaptively selects tokenization granularity and tailors positional encodings to the unique characteristics of each time series instance. Trained on a large-scale Predictability-Stratified Time Series (PreSTS) corpus comprising over 300 billion time points and adopting a multi-patch prediction strategy in the inference stage, Kairos achieves superior performance with much fewer parameters on two common zero-shot benchmarks, GIFT-Eval and the Time-Series-Library benchmark, consistently outperforming established methods across diverse tasks. The project page is at https://foundation-model-research.github.io/Kairos .

Ensuring power grid resilience requires the timely and unsupervised detection of anomalies in synchrophasor data streams. We introduce T-BiGAN, a novel framework that integrates window-attention Transformers within a bidirectional Generative Adversarial Network (BiGAN) to address this challenge. Its self-attention encoder-decoder architecture captures complex spatio-temporal dependencies across the grid, while a joint discriminator enforces cycle consistency to align the learned latent space with the true data distribution. Anomalies are flagged in real-time using an adaptive score that combines reconstruction error, latent space drift, and discriminator confidence. Evaluated on a realistic hardware-in-the-loop PMU benchmark, T-BiGAN achieves an ROC-AUC of 0.95 and an average precision of 0.996, significantly outperforming leading supervised and unsupervised methods. It shows particular strength in detecting subtle frequency and voltage deviations, demonstrating its practical value for live, wide-area monitoring without relying on manually labeled fault data.

Black-box optimization (BBO) addresses problems where objectives are accessible only through costly queries without gradients or explicit structure. Classical derivative-free methods -- line search, direct search, and model-based solvers such as Bayesian optimization -- form the backbone of BBO, yet often struggle in high-dimensional, noisy, or mixed-integer settings. Recent advances use machine learning (ML) and reinforcement learning (RL) to enhance BBO: ML provides expressive surrogates, adaptive updates, meta-learning portfolios, and generative models, while RL enables dynamic operator configuration, robustness, and meta-optimization across tasks. This paper surveys these developments, covering representative algorithms such as NNs with the modular model-based optimization framework (mlrMBO), zeroth-order adaptive momentum methods (ZO-AdaMM), automated BBO (ABBO), distributed block-wise optimization (DiBB), partition-based Bayesian optimization (SPBOpt), the transformer-based optimizer (B2Opt), diffusion-model-based BBO, surrogate-assisted RL for differential evolution (Surr-RLDE), robust BBO (RBO), coordinate-ascent model-based optimization with relative entropy (CAS-MORE), log-barrier stochastic gradient descent (LB-SGD), policy improvement with black-box (PIBB), and offline Q-learning with Mamba backbones (Q-Mamba). We also review benchmark efforts such as the NeurIPS 2020 BBO Challenge and the MetaBox framework. Overall, we highlight how ML and RL transform classical inexact solvers into more scalable, robust, and adaptive frameworks for real-world optimization.

To evaluate the translational capabilities of foundation models, we develop a pathological concept learning approach focused on kidney cancer. By leveraging TNM staging guidelines and pathology reports, we build comprehensive pathological concepts for kidney cancer. Then, we extract deep features from whole slide images using foundation models, construct pathological graphs to capture spatial correlations, and trained graph neural networks to identify these concepts. Finally, we demonstrate the effectiveness of this approach in kidney cancer survival analysis, highlighting its explainability and fairness in identifying low- and high-risk patients. The source code has been released by https://github.com/shangqigao/RadioPath.

Molecular foundation models are rapidly advancing scientific discovery, but their unreliability on out-of-distribution (OOD) samples severely limits their application in high-stakes domains such as drug discovery and protein design. A critical failure mode is chemical hallucination, where models make high-confidence yet entirely incorrect predictions for unknown molecules. To address this challenge, we introduce Molecular Preference-Aligned Instance Ranking (Mole-PAIR), a simple, plug-and-play module that can be flexibly integrated with existing foundation models to improve their reliability on OOD data through cost-effective post-training. Specifically, our method formulates the OOD detection problem as a preference optimization over the estimated OOD affinity between in-distribution (ID) and OOD samples, achieving this goal through a pairwise learning objective. We show that this objective essentially optimizes AUROC, which measures how consistently ID and OOD samples are ranked by the model. Extensive experiments across five real-world molecular datasets demonstrate that our approach significantly improves the OOD detection capabilities of existing molecular foundation models, achieving up to 45.8%, 43.9%, and 24.3% improvements in AUROC under distribution shifts of size, scaffold, and assay, respectively.

Equation discovery provides a grey-box approach to system identification by uncovering governing dynamics directly from observed data. However, a persistent challenge lies in ensuring that identified models generalise across operating conditions rather than over-fitting to specific datasets. This work investigates this issue by applying a Bayesian relevance vector machine (RVM) within a multi-task learning (MTL) framework for simultaneous parameter identification across multiple datasets. In this formulation, responses from the same structure under different excitation levels are treated as related tasks that share model parameters but retain task-specific noise characteristics. A simulated single degree-of-freedom oscillator with linear and cubic stiffness provided the case study, with datasets generated under three excitation regimes. Standard single-task RVM models were able to reproduce system responses but often failed to recover the true governing terms when excitations insufficiently stimulated non-linear dynamics. By contrast, the MTL-RVM combined information across tasks, improving parameter recovery for weakly and moderately excited datasets, while maintaining strong performance under high excitation. These findings demonstrate that multi-task Bayesian inference can mitigate over-fitting and promote generalisation in equation discovery. The approach is particularly relevant to structural health monitoring, where varying load conditions reveal complementary aspects of system physics.

This paper introduces mixsemble, an ensemble method that adapts the Dawid-Skene model to aggregate predictions from multiple model-based clustering algorithms. Unlike traditional crowdsourcing, which relies on human labels, the framework models the outputs of clustering algorithms as noisy annotations. Experiments on both simulated and real-world datasets show that, although the mixsemble is not always the single top performer, it consistently approaches the best result and avoids poor outcomes. This robustness makes it a practical alternative when the true data structure is unknown, especially for non-expert users.

We introduce the Functional Competing Risk Net (FCRN), a unified deep-learning framework for discrete-time survival analysis under competing risks, which seamlessly integrates functional covariates and handles missing data within an end-to-end model. By combining a micro-network Basis Layer for functional data representation with a gradient-based imputation module, FCRN simultaneously learns to impute missing values and predict event-specific hazards. Evaluated on multiple simulated datasets and a real-world ICU case study using the MIMIC-IV and Cleveland Clinic datasets, FCRN demonstrates substantial improvements in prediction accuracy over random survival forests and traditional competing risks models. This approach advances prognostic modeling in critical care by more effectively capturing dynamic risk factors and static predictors while accommodating irregular and incomplete data.

We study active correlation clustering where pairwise similarities are not provided upfront and must be queried in a cost-efficient manner through active learning. Specifically, we focus on the cold-start scenario, where no true initial pairwise similarities are available for active learning. To address this challenge, we propose a coverage-aware method that encourages diversity early in the process. We demonstrate the effectiveness of our approach through several synthetic and real-world experiments.