Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data. Most SSL approaches rely on strong, well-established, handcrafted data augmentations to generate diverse views for representation learning. However, designing such augmentations requires domainspecific knowledge and implicitly imposes representational invariances on the model, which can limit generalization. In this work, we propose an unsupervised representation learning method that replaces augmentations by generating views using orthonormal bases and overcomplete frames. We show that embeddings learned from orthonormal and overcomplete spaces reside on distinct manifolds, shaped by the geometric biases introduced by representing samples in different spaces. By jointly leveraging the complementary geometry of these distinct manifolds, our approach achieves superior performance without artificially increasing data diversity through strong augmentations. We demonstrate the effectiveness of our method on nine datasets across five temporal sequence tasks, where signalspecific characteristics make data augmentations particularly challenging. Without relying on augmentation-induced diversity, our method achieves performance gains of up to 15-20% over existing self-supervised approaches.

Motion simulation, prediction and planning are foundational tasks in autonomous driving, each essential for modeling and reasoning about dynamic traffic scenarios. While often addressed in isolation due to their differing objectives, such as generating diverse motion states or estimating optimal trajectories, these tasks inherently depend on shared capabilities: understanding multi-agent interactions, modeling motion behaviors, and reasoning over temporal and spatial dynamics. Despite this underlying commonality, existing approaches typically adopt specialized model designs, which hinders cross-task generalization and system scalability. More critically, this separation overlooks the potential mutual benefits among tasks. Motivated by these observations, we propose UniMotion, a unified motion framework that captures shared structures across motion tasks while accommodating their individual requirements. Built on a decoder-only Transformer architecture, UniMotion employs dedicated interaction modes and tailored training strategies to simultaneously support these motion tasks. This unified design not only enables joint optimization and representation sharing but also allows for targeted fine-tuning to specialize in individual tasks when needed. Extensive experiments on the Waymo Open Motion Dataset demonstrate that joint training leads to robust generalization and effective task integration. With further fine-tuning, UniMotion achieves state-of-the-art performance across a range of motion tasks, establishing it as a versatile and scalable solution for autonomous driving.

We study safe linear bandits (SLBs), where an agent selects actions from a convex set to maximize an unknown linear objective subject to unknown linear constraints in each round. Existing methods for SLBs provide strong regret guarantees, but require solving expensive optimization problems. To address this, we propose Constrained Linear Thompson Sampling (COLTS), a sampling-based framework that selects actions by solving perturbed linear programs, which significantly reduces computational costs while matching the regret and risk of prior methods. We develop two main variants: S-COLTS, which ensures zero risk and eO( d3T) regret given a safe action, and R-COLTS, which achieves eO( d3T)regret and risk with no instance information. In simulations, these methods match or outperform state of the art SLB approaches while substantially improving scalability. On the technical front, we introduce a novel coupled noise design that ensures frequent'local optimism' about the true optimum, and a scaling-based analysis to handle the per-round variability of constraints.

In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by discretizing the predictor's output space and iteratively adjusting its output values. However, this discretization approach departs from the standard empirical risk minimization (ERM) pipeline, introduces rounding error and an additional sensitive hyperparameter, and may distort the predictor's outputs in ways that hinder downstream decision-making. In this work, we propose a discretization-free multicalibration method that directly optimizes an empirical risk objective over an ensemble of depth-two decision trees. Our ERM approach can be implemented using off-the-shelf tree ensemble learning methods such as LightGBM. Our algorithm provably achieves multicalibration, provided that the data distribution satisfies a technical condition we term as loss saturation. Across multiple datasets, our empirical evaluation shows that this condition is always met in practice. Our discretization-free algorithm consistently matches or outperforms existing multicalibration approaches-- even when evaluated using a discretization-based multicalibration metric that shares its discretization granularity with the baselines. Code to replicate the results in this work is available at https://github.com/hjenryin/

World models aim to capture the dynamics of the environment, enabling agents to predict and plan for future states. In most scenarios of interest, the dynamics are highly centered on interactions among objects within the environment. This motivates the development of world models that operate on object-centric rather than monolithic representations, with the goal of more effectively capturing environment dynamics and enhancing compositional generalization. However, the development of object-centric world models has largely been explored in environments with limited visual complexity (such as basic geometries). It remains underexplored whether such models can be effective in more challenging settings. In this paper, we fill this gap by introducing Dyn-O, an enhanced structured world model built upon object-centric representations. Compared to prior work in object-centric representations, Dyn-O improves in both learning representations and modeling dynamics. On the challenging Procgen games, we demonstrate that our method can learn objectcentric world models directly from pixel observations, outperforming DreamerV3 in rollout prediction accuracy. Furthermore, by decoupling object-centric features into dynamic-agnostic and dynamic-aware components, we enable finer-grained manipulation of these features and generate more diverse imagined trajectories.

In this work, we explore the trade-offs of explicit structural priors, particularly group-equivariance. We address this through theoretical analysis and a comprehensive empirical study focusing on point clouds. To enable controlled and fair comparisons, we introduce Rapidash, a unified group convolutional architecture that allows for different variants of equivariant and non-equivariant models. Our results suggest that more constrained equivariant models outperform less constrained alternatives when aligned with the geometry of the task, and increasing representation capacity does not fully eliminate performance gaps. We see improved performance of models with equivariance and symmetry-breaking through tasks like segmentation, regression, and generation across diverse datasets. Explicit symmetry breaking via geometric reference frames consistently improves performance, while breaking equivariance through geometric input features can be helpful when aligned with task geometry. Our results provide task-specific performance trends that offer a more nuanced way for model selection.

Weak-to-strong generalization--where a student model trained on imperfect labels generated by a weaker teacher nonetheless surpasses that teacher--has been widely observed, but the mechanisms that enable it have remained poorly understood. In this paper, through a theoretical analysis of simple models, we uncover three core mechanisms that can drive this phenomenon. First, by analyzing ridge linear regression, we study the interplay between the teacher and student regularization parameters and prove that a student can compensate for a teacher's under-regularization and achieve lower test error. We also analyze the role of the parameterization regime of the models and show that qualitatively different phenomena can happen in different regimes. Second, by analyzing weighted ridge linear regression, we show that a student model with a regularization structure better aligned to the target function, can outperform its teacher. Third, in a nonlinear multi-index learning setting, we demonstrate that a student can learn easy, task-specific features from the teacher while leveraging its own broader pre-training to learn hard-to-learn features that the teacher cannot capture.

We introduce learning to condition (L2C), a scalable, data-driven framework for accelerating Most Probable Explanation (MPE) inference in Probabilistic Graphical Models (PGMs), a fundamentally intractable problem. L2C trains a neural network to score variable-value assignments based on their utility for conditioning, given observed evidence. To facilitate supervised learning, we develop a scalable data generation pipeline that extracts training signals from the search traces of existing MPE solvers. The trained network serves as a heuristic that integrates with search algorithms, acting as a conditioning strategy prior to exact inference or as a branching and node selection policy within branch-and-bound solvers.

Detecting structural change in dynamic network data has wide-ranging applications. Existing approaches typically divide the data into time bins, extract network features within each bin, and then compare these features over time. This introduces an inherent tradeoff between temporal resolution and statistical stability of the extracted features. Despite this tradeoff, reminiscent of time-frequency tradeoffs in signal processing, most methods rely on a fixed temporal resolution. Choosing an appropriate resolution parameter is typically difficult, and can be especially problematic in domains like cybersecurity, where anomalous behavior may emerge at multiple time scales.

Human intelligence effortlessly interprets visual scenes along a rich spectrum of semantic dimensions. However, existing approaches to language-grounded visual concept learning are limited to a few predefined primitive axes, such as color and shape, and are typically explored in synthetic datasets. In this work, we propose a scalable framework that adaptively identifies image-related concept axes and grounds visual concepts along these axes in real-world scenes. Leveraging a pretrained vision-language model and our universal prompting strategy, our framework identifies a diverse image-related axes without any prior knowledge. Our universal concept encoder adaptively binds visual features to the discovered axes without introducing additional model parameters for each concept. To ground visual concepts along the discovered axes, we optimize a compositional anchoring objective, which ensures that each axis can be independently manipulated without affecting others. We demonstrate the effectiveness of our framework on subsets of ImageNet, CelebA-HQ, and AFHQ, showcasing superior editing capabilities across diverse real-world concepts that are too varied to be manually predefined. Our method also exhibits strong compositional generalization, outperforming existing visual concept learning and text-based editing methods.