We address the problem of looking into the water from the air, where we seek to remove image distortions caused by refractions at the water surface. Our approach is based on modeling the different water surface structures at various points in time, assuming the underlying image is constant. To this end, we propose a model that consists of two neural-field networks. The first network predicts the height of the water surface at each spatial position and time, and the second network predicts the image color at each position. Using both networks, we reconstruct the observed sequence of images and can therefore use unsupervised training. We show that using implicit neural representations with periodic activation functions (SIREN) leads to effective modeling of the surface height spatio-temporal signal and its derivative, as required for image reconstruction. Using both simulated and real data we show that our method outperforms the latest unsupervised image restoration approach. In addition, it provides an estimate of the water surface.

Binary (0-1) integer programming (BIP) is pivotal in scientific domains requiring discrete decision-making. As the advance of AI computing, recent works explore neural network-based solver for integer linear programming (ILP) problems. Yet, they lack scalability for tackling nonlinear challenges. To handle nonlinearities, state-of-the-art Branch-and-Cut solvers employ linear relaxations, leading to exponential growth in auxiliary variables and severe computation limitations. To overcome these limitations, we propose BIPNN, an unsupervised learning framework to solve BIP problems via hypergraph neural networks (HyperGNN). Specifically, (i) BIPNN reformulates BIPs-constrained, discrete, and nonlinear (sin, log, exp) optimization problems-into unconstrained, differentiable, and polynomial loss functions.

Deep neural networks, particularly neural operators, provide an efficient alternative to costly simulations in surrogate modeling. However, their performance is often constrained by the need for large-scale labeled datasets, which are costly and challenging to acquire in many scientific domains. Semi-supervised learning reduces label reliance by leveraging unlabeled data yet remains vulnerable to noisy pseudo-labels that mislead training and undermine robustness. To address these challenges, we propose a novel framework, Uncertainty-Informed Meta Pseudo Labeling (UMPL). The core mechenism is to refine pseudo-label quality through uncertainty-informed feedback signals. Specifically, the teacher model generates pseudo labels via epistemic uncertainty, while the student model learns from these labels and provides feedback based on aleatoric uncertainty.

Semi-supervised learning (SSL) enhances model performance by leveraging abundant unlabeled data alongside limited labeled data. As vision foundation models (VFMs) become central to modern vision applications, this paper revisits SSL in the context of these powerful pre-trained models. We conduct a systematic study on tasks where frozen VFMs underperform and reveal several key insights when fine-tuning them. First, parameter-efficient fine-tuning (PEFT) using only labeled data often surpasses traditional SSL methods---even without access to unlabeled data. Second, pseudo-labels generated by PEFT models offer valuable supervisory signals for unlabeled data, and different PEFT techniques yield complementary pseudo-labels. These findings motivate a simple yet effective SSL baseline for the VFM era: \emph{ensemble pseudo-labeling across diverse PEFT methods and VFM backbones}.

Recent research shows that in-context learning (ICL) can be effective even when demonstrations have missing or incorrect labels. To shed light on this capability, we examine a canonical setting where the demonstrations are drawn according to a binary Gaussian mixture model (GMM) and a certain fraction of the demonstrations have missing labels. We provide a comprehensive theoretical study to show that: (1) The loss landscape of one-layer linear attention models recover the optimal fully-supervised estimator but completely fail to exploit unlabeled data; (2) In contrast, multilayer or looped transformers can effectively leverage unlabeled data by implicitly constructing estimators of the form $\sum_{i\ge 0} a_i (X^\top X)^iX^\top y$ with $X$ and $y$ denoting features and partially-observed labels (with missing entries set to zero). We characterize the class of polynomials that can be expressed as a function of depth and draw connections to Expectation Maximization, an iterative pseudo-labeling algorithm commonly used in semi-supervised learning. Importantly, the leading polynomial power is exponential in depth, so mild amount of depth/looping suffices. As an application of theory, we propose looping off-the-shelf tabular foundation models to enhance their semi-supervision capabilities. Extensive evaluations on real-world datasets show that our method significantly improves the semisupervised tabular learning performance over the standard single pass inference.

Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to the number of classes and underutilize the rich prototype information available at intermediate hierarchical levels. We introduce deep taxonomic networks, a novel deep latent variable approach designed to bridge these gaps. Our method optimizes a large latent taxonomic hierarchy, specifically a complete binary tree structured mixture-of-Gaussian prior within a variational inference framework, to automatically discover taxonomic structures and associated prototype clusters directly from unlabeled data without assuming true label sizes. We analytically show that optimizing the ELBO of our method encourages the discovery of hierarchical relationships among prototypes. Empirically, our learned models demonstrate strong hierarchical clustering performance, outperforming baselines across diverse image classification datasets using our novel evaluation mechanism that leverages prototype clusters discovered at all hierarchical levels. Qualitative results further reveal that deep taxonomic networks discover rich and interpretable hierarchical taxonomies, capturing both coarse-grained semantic categories and fine-grained visual distinctions.

Diffusion models are increasingly used as powerful conditional generators, yet real deployments often involve multiple target distributions arising from different tasks, e.g., diverse prompt domains in text-to-image generation, or multiple environments in robotics with diffusion policies. This naturally leads to a multi-objective learning (MOL) problem. A key challenge is that achieving good Pareto trade-offs can require a generalist model class with substantially larger capacity than what suffices for solving any individual task, thereby increasing statistical cost since sample complexity typically scales with the model complexity. To reconcile this, we develop a principled MOL framework for diffusion models with limited data: a semi-supervised regime where paired (labeled) samples are scarce, but (unlabeled) condition data are abundant. We propose a two-stage training procedure that first fits lightweight specialist models from limited paired data, and then distills them into a generalist model by generating pseudo-samples. We establish generalization bounds showing that the required number of paired samples only depends on the complexity of the specialist model classes. We further extend the theory to diffusion policies for sequential decision making to account for distribution shift in on-policy rollouts. Extensive experiments on robotic control and image restoration tasks are conducted to verify our theoretical results.

In many prediction problems, we have extra information during training (for example, measurements that are expensive or slow to collect) that will not be available when the model is deployed. A common strategy is to first train a model that uses all training information, then use its predictions on unlabeled examples to train a second model that only uses the inputs available at test time. However, when the extra training-only information is weak or noisy, this Two-Stage approach can mislead the deployment model and even hurt accuracy. We propose a joint training method that learns the two models together, so the deployment model can benefit from the extra information only when it actually helps, instead of inheriting its mistakes. We provide guarantees that describe when joint training improves prediction accuracy and analyze a simple alternating training algorithm for large, high-dimensional models. Experiments on synthetic data and real-world prediction tasks show that our approach avoids these failures and robustly outperforms standard Two-Stage baselines.

When modeling class-imbalanced data, it is crucial to address the imbalance, as models trained on such data tend to be biased towards the majority classes. This problem is amplified under partial supervision, where pseudo-labels for unlabeled data are predicted based on imbalanced labeled data, propagating the bias. While recent semi-supervised models address class imbalance, they typically assume single-modal input data. However, with the growing availability of multimodal data, it is essential to leverage complementary modalities. In this article, we propose a multimodal deep generative model for semi-supervised learning under class imbalance. Our approach uses separate encoders for each modality, sharing latent variables across modalities, and simplifies joint posterior computation with a product-of-experts method. To further address class imbalance, we replace typical Gaussian distributions with Student's t-distributions for the prior, encoder, and decoder, better capturing the heavy-tailed latent distributions in imbalanced data. We derive a new objective function for training the proposed model on both labeled and unlabeled data using $γ$-power divergence. Empirical results on benchmark and real-world datasets demonstrate that our model outperforms baseline methods in generalization, achieving superior classification performance for partially labeled multimodal data with imbalanced class distributions.

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.