Understanding how performance scales jointly with model size and data is a central problem in modern machine learning. Existing theoretical works on scaling laws typically describe generalization as a function of data or compute, often in fixed-feature or infinite-width regimes and for online SGD. Here, we instead study how generalization scales with the number of trainable parameters and the number of samples in a feature-learning model. We analyze $\ell_2$-regularized empirical test error minimization in a quadratic two-layer network in a finite-sample setting with structured data. This setting allows for an explicit characterization of the generalization error as a function of the number of samples, model width, and regularization. Our results reveal a phase diagram with distinct scaling regimes as the number of parameters varies. In particular, the generalization error follows data-dependent power laws controlled by the spectral structure of the target. We further characterize the transitions between regimes, including the onset of interpolation, and their impact on generalization.

Hyperparameter selection is a critical step in the deployment of modern artificial intelligence systems, given the need to tune degrees of freedom such as inference-time parameters, implementation-level settings, and thresholds driving decision rules. Despite its practical importance, hyperparameter selection is typically performed using best-effort empirical methods such as grid search or Bayesian optimization, which provide no formal statistical guarantees on reliability or safety. This monograph presents a unified statistical framework for reliable hyperparameter selection, centered on the learn-then-test (LTT) paradigm, which formulates the problem as multiple hypothesis testing over a candidate set of hyperparameters. The framework enables the selection of hyperparameters that provably satisfy application-specific reliability requirements -- such as bounds on average risk, quantile risk, or information-theoretic constraints -- with explicit, finite-sample control of error probabilities. The supporting statistical machinery, namely p-values, e-values, and concentration inequalities, is developed from first principles in a dedicated appendix.

In this paper, we address the problem of cost-sensitive hyperparameter optimization (HPO) built upon freeze-thaw Bayesian optimization (BO). Specifically, we assume a scenario where users want to early-stop the HPO process when the expected performance improvement is not satisfactory with respect to the additional computational cost. Motivated by this scenario, we introduce utility in the freezethaw framework, a function describing the trade-off between the cost and performance that can be estimated from the user's preference data. This utility function, combined with our novel acquisition function and stopping criterion, allows us to dynamically continue training the configuration that we expect to maximally improve the utility in the future, and also automatically stop the HPO process around the maximum utility. Further, we improve the sample efficiency of existing freezethaw methods with transfer learning to develop a specialized surrogate model for the cost-sensitive HPO problem. We validate our algorithm on established multifidelity HPO benchmarks and show that it outperforms all the previous freezethaw BO and transfer-BO baselines we consider, while achieving a significantly better trade-off between the cost and performance. Our code is publicly available at https://github.com/db-Lee/CFBO.

Recent advances in graph machine learning have shifted to data-centric paradigms, driven by two emerging research fields: (1) Federated graph learning (FGL) facilitates multi-client collaboration but struggles with data and task heterogeneity, resulting in limited practicality; (2) Graph foundation model (GFM) enables desirable domain generalization but is typically confined to single-machine training, neglecting the potential of cross-silo data and computational resources. It is evident that these two paradigms are complementary, and their integration offers substantial advantages. Motivated by this, we present a pioneering study about the federated graph foundation model (FedGFM), a novel decentralized GFM training paradigm. Despite the promising vision of FedGFM, knowledge entanglement has emerged as a critical challenge, where multi-domain knowledge is encoded into indistinguishable representations, thereby limiting downstream adaptation. To this end, we propose FedGFM+, an effective FedGFM framework with two key modules to mitigate knowledge entanglement in a dual-pronged manner.

Recently, reasoning-based MLLMs have achieved a degree of success in generating long-form textual reasoning chains. However, they still struggle with complex tasks that necessitate dynamic and iterative focusing on and revisiting of visual regions to achieve precise grounding of textual reasoning in visual evidence. We introduce VLM-R3 (Visual Language Model with Region Recognition and Reasoning), a framework that equips an MLLM with the ability to (i) decide when additional visual evidence is needed, (ii) determine where to ground within the image, and (iii) seamlessly weave the relevant sub-image content back into an interleaved chain-of-thought. The core of our method is Region-Conditioned Reinforcement Policy Optimization (R-GRPO), a training paradigm that rewards the model for selecting informative regions, formulating appropriate transformations (e.g.

Large Language Models (LLMs) deployed in real-world settings increasingly face the need to unlearn sensitive, outdated, or proprietary information. Existing unlearning methods typically formulate forgetting and retention as a regularized trade-off, combining both objectives into a single scalarized loss. This often leads to unstable optimization and degraded performance on retained data, especially under aggressive forgetting. We propose a new formulation of LLM unlearning as a constrained optimization problem: forgetting is enforced via a novel logit-margin flattening loss that explicitly drives the output distribution toward uniformity on a designated forget set, while retention is preserved through a hard constraint on a separate retain set. Compared to entropy-based objectives, our loss is softmaxfree, numerically stable, and maintains non-vanishing gradients, enabling more efficient and robust optimization. We solve the constrained problem using a scalable primal-dual algorithm that exposes the trade-off between forgetting and retention through the dynamics of the dual variable, all without any extra computational overhead. Evaluations on the TOFU and MUSE benchmarks across diverse LLM architectures demonstrate that our approach consistently matches or exceeds stateof-the-art baselines, effectively removing targeted information while preserving downstream utility.

Real-world datasets collected from sensors or human inputs are prone to noise and errors, posing significant challenges for applying offline reinforcement learning (RL). While existing methods have made progress in addressing corrupted actions and rewards, they remain insufficient for handling corruption in high-dimensional state spaces and for cases where multiple elements in the dataset are corrupted simultaneously. Diffusion models, known for their strong denoising capabilities, offer a promising direction for this problem--but their tendency to overfit noisy samples limits their direct applicability. To overcome this, we propose Ambient Diffusion-Guided Dataset Recovery (ADG), a novel approach that pioneers the use of diffusion models to tackle data corruption in offline RL. First, we introduce Ambient Denoising Diffusion Probabilistic Models (DDPM) from approximated distributions, which enable learning on partially corrupted datasets with theoretical guarantees.

Despite progress in Large Vision-Language Models (LVLMs), their capacity for visual reasoning is often limited by the binding problem: the failure to reliably associate perceptual features with their correct visual referents.

Knowledge distillation (KD) is a vital technique for deploying deep neural networks (DNNs) on resource-constrained devices by transferring knowledge from large teacher models to lightweight student models. While teacher models from third-party platforms may undergo security verification (e.g., backdoor detection), we uncover a novel and critical threat: distillation-conditional backdoor attacks (DCBAs). DCBA injects dormant and undetectable backdoors into teacher models, which become activated in student models via the KD process, even with clean distillation datasets. While the direct extension of existing methods is ineffective for DCBA, we implement this attack by formulating it as a bilevel optimization problem and proposing a simple yet effective method (i.e., SCAR). Specifically, the inner optimization simulates the KD process by optimizing a surrogate student model, while the outer optimization leverages outputs from this surrogate to optimize the teacher model for implanting the conditional backdoor.

While unmanned aerial vehicles (UAVs) offer wide-area, high-altitude coverage for anomaly detection, they face challenges such as dynamic viewpoints, scale variations, and complex scenes. Existing datasets and methods, mainly designed for fixed ground-level views, struggle to adapt to these conditions, leading to significant performance drops in drone-view scenarios. To bridge this gap, we introduce A2Seek (Aerial Anomaly Seek), a large-scale, reasoning-centric benchmark dataset for aerial anomaly understanding. This dataset covers various scenarios and environmental conditions, providing high-resolution real-world aerial videos with detailed annotations, including anomaly categories, frame-level timestamps, region-level bounding boxes, and natural language explanations for causal reasoning. Building on this dataset, we propose A2Seek-R1, a novel reasoning framework that generalizes R1-style strategies to aerial anomaly understanding, enabling a deeper understanding of "Where" anomalies occur and "Why" they happen in aerial frames.