Dense linear layers are the dominant computational bottleneck in large neural networks, presenting a critical need for more efficient alternatives. Previous efforts to develop alternatives have focused on a small number of hand-crafted structured matrices, and have neglected to investigate whether these structures can surpass dense layers in terms of compute-optimal scaling laws when both the model size and training examples are optimally allocated. In this work, we present a unifying framework that enables searching among all linear operators expressible via an Einstein summation. This framework encompasses many previously proposed structures, such as low-rank, Kronecker, Tensor-Train, and Monarch, along with many novel structures. We develop a taxonomy of all such operators based on their computational and algebraic properties, which provides insights into their scaling laws.

Semi-supervised learning (SSL) provides an effective means of leveraging unlabeled data to improve a model's performance. This domain has seen fast progress recently, at the cost of requiring more complex methods. In this paper we propose FixMatch, an algorithm that is a significant simplification of existing SSL methods. FixMatch first generates pseudo-labels using the model's predictions on weakly-augmented unlabeled images. For a given image, the pseudo-label is only retained if the model produces a high-confidence prediction.

In recent advancements in unsupervised visual representation learning, the Joint-Embedding Predictive Architecture (JEPA) has emerged as a significant method for extracting visual features from unlabeled imagery through an innovative masking strategy. Despite its success, two primary limitations have been identified: the inefficacy of Exponential Moving Average (EMA) from I-JEPA in preventing entire collapse and the inadequacy of I-JEPA prediction in accurately learning the mean of patch representations. This integration is designed to effectively learn the variance/covariance for preventing entire collapse and ensuring invariance in the mean of augmented views, thereby overcoming the identified limitations. Through empirical and theoretical evaluations, our work demonstrates that C-JEPA significantly enhances the stability and quality of visual representation learning. When pre-trained on the ImageNet-1K dataset, C-JEPA exhibits rapid and improved convergence in both linear probing and fine-tuning performance metrics.

Self-supervised representation learning solves auxiliary prediction tasks (known as pretext tasks), that do not require labeled data, to learn semantic representations. These pretext tasks are created solely using the input features, such as predicting a missing image patch, recovering the color channels of an image from context, or predicting missing words, yet predicting this \textit{known} information helps in learning representations effective for downstream prediction tasks. This paper posits a mechanism based on approximate conditional independence to formalize how solving certain pretext tasks can learn representations that provably decrease the sample complexity of downstream supervised tasks. Formally, we quantify how the approximate independence between the components of the pretext task (conditional on the label and latent variables) allows us to learn representations that can solve the downstream task with drastically reduced sample complexity by just training a linear layer on top of the learned representation.

In this paper, we focus on the out-of-distribution (OOD) generalization of self-supervised learning (SSL). By analyzing the mini-batch construction during the SSL training phase, we first give one plausible explanation for SSL having OOD generalization. Then, from the perspective of data generation and causal inference, we analyze and conclude that SSL learns spurious correlations during the training process, which leads to a reduction in OOD generalization. To address this issue, we propose a post-intervention distribution (PID) grounded in the Structural Causal Model. PID offers a scenario where the spurious variable and label variable is mutually independent. Besides, we demonstrate that if each mini-batch during SSL training satisfies PID, the resulting SSL model can achieve optimal worst-case OOD performance. This motivates us to develop a batch sampling strategy that enforces PID constraints through the learning of a latent variable model. Through theoretical analysis, we demonstrate the identifiability of the latent variable model and validate the effectiveness of the proposed sampling strategy. Experiments conducted on various downstream OOD tasks demonstrate the effectiveness of the proposed sampling strategy.

Manually designing (meta-)heuristics for the Vehicle Routing Problem (VRP) is a challenging task that requires significant domain expertise. Recently, data-driven approaches have emerged as a promising solution, automatically learning heuristics that perform well on training instances and generalize to unseen test cases. Such an approach learns (meta-)heuristics that can perform well on the training instances, expecting it to generalize well on the unseen test instances. A recent method, named GPGLS, uses Genetic Programming (GP) to learn the utility function in Guided Local Search (GLS) and solved large scale VRP effectively. However, the selection of appropriate training instances during the learning process remains an open question, with most existing studies including GPGLS relying on random instance selection. To address this, we propose a novel method, CL-GPGLS, which integrates Curriculum Learning (CL) into GPGLS. Our approach leverages a predefined curriculum to introduce training instances progressively, starting with simpler tasks and gradually increasing complexity, enabling the model to better adapt and optimize for large-scale VRP (LSVRP). Extensive experiments verify the effectiveness of CL-GPGLS, demonstrating significant performance improvements over three baseline methods.

Retraining a model using its own predictions together with the original, potentially noisy labels is a well-known strategy for improving the model performance. While prior works have demonstrated the benefits of specific heuristic retraining schemes, the question of how to optimally combine the model's predictions and the provided labels remains largely open. This paper addresses this fundamental question for binary classification tasks. We develop a principled framework based on approximate message passing (AMP) to analyze iterative retraining procedures for two ground truth settings: Gaussian mixture model (GMM) and generalized linear model (GLM). Our main contribution is the derivation of the Bayes optimal aggregator function to combine the current model's predictions and the given labels, which when used to retrain the same model, minimizes its prediction error. We also quantify the performance of this optimal retraining strategy over multiple rounds. We complement our theoretical results by proposing a practically usable version of the theoretically-optimal aggregator function for linear probing with the cross-entropy loss, and demonstrate its superiority over baseline methods in the high label noise regime.

Graph-structured data pervades domains such as social networks, biological systems, knowledge graphs, and recommender systems. While foundation models have transformed natural language processing, vision, and multimodal learning through large-scale pretraining and generalization, extending these capabilities to graphs -- characterized by non-Euclidean structures and complex relational semantics -- poses unique challenges and opens new opportunities. To this end, Graph Foundation Models (GFMs) aim to bring scalable, general-purpose intelligence to structured data, enabling broad transfer across graph-centric tasks and domains. This survey provides a comprehensive overview of GFMs, unifying diverse efforts under a modular framework comprising three key components: backbone architectures, pretraining strategies, and adaptation mechanisms. We categorize GFMs by their generalization scope -- universal, task-specific, and domain-specific -- and review representative methods, key innovations, and theoretical insights within each category. Beyond methodology, we examine theoretical foundations including transferability and emergent capabilities, and highlight key challenges such as structural alignment, heterogeneity, scalability, and evaluation. Positioned at the intersection of graph learning and general-purpose AI, GFMs are poised to become foundational infrastructure for open-ended reasoning over structured data. This survey consolidates current progress and outlines future directions to guide research in this rapidly evolving field. Resources are available at https://github.com/Zehong-Wang/Awesome-Foundation-Models-on-Graphs.

Pulmonary segment segmentation is crucial for cancer localization and surgical planning. However, the pixel-wise annotation of pulmonary segments is laborious, as the boundaries between segments are indistinguishable in medical images. To this end, we propose a weakly supervised learning (WSL) method, termed Anatomy-Hierarchy Supervised Learning (AHSL), which consults the precise clinical anatomical definition of pulmonary segments to perform pulmonary segment segmentation. Since pulmonary segments reside within the lobes and are determined by the bronchovascular tree, i.e., artery, airway and vein, the design of the loss function is founded on two principles. First, segment-level labels are utilized to directly supervise the output of the pulmonary segments, ensuring that they accurately encompass the appropriate bronchovascular tree. Second, lobe-level supervision indirectly oversees the pulmonary segment, ensuring their inclusion within the corresponding lobe. Besides, we introduce a two-stage segmentation strategy that incorporates bronchovascular priori information. Furthermore, a consistency loss is proposed to enhance the smoothness of segment boundaries, along with an evaluation metric designed to measure the smoothness of pulmonary segment boundaries. Visual inspection and evaluation metrics from experiments conducted on a private dataset demonstrate the effectiveness of our method.

Parkinson's disease (PD) poses a growing global health challenge, with Bangladesh experiencing a notable rise in PD-related mortality. Early detection of PD remains particularly challenging in resource-constrained settings, where voice-based analysis has emerged as a promising non-invasive and cost-effective alternative. However, existing studies predominantly focus on English or other major languages; notably, no voice dataset for PD exists for Bengali - posing a significant barrier to culturally inclusive and accessible healthcare solutions. Moreover, most prior studies employed only a narrow set of acoustic features, with limited or no hyperparameter tuning and feature selection strategies, and little attention to model explainability. This restricts the development of a robust and generalizable machine learning model. To address this gap, we present BenSparX, the first Bengali conversational speech dataset for PD detection, along with a robust and explainable machine learning framework tailored for early diagnosis. The proposed framework incorporates diverse acoustic feature categories, systematic feature selection methods, and state-of-the-art machine learning algorithms with extensive hyperparameter optimization. Furthermore, to enhance interpretability and trust in model predictions, the framework incorporates SHAP (SHapley Additive exPlanations) analysis to quantify the contribution of individual acoustic features toward PD detection. Our framework achieves state-of-the-art performance, yielding an accuracy of 95.77%, F1 score of 95.57%, and AUC-ROC of 0.982. We further externally validated our approach by applying the framework to existing PD datasets in other languages, where it consistently outperforms state-of-the-art approaches. To facilitate further research and reproducibility, the dataset has been made publicly available at https://github.com/Riad071/BenSParX.