Efficiently solving constrained optimization problems is crucial for numerous realworld applications, yet traditional solvers are often computationally prohibitive for real-time use. Machine learning-based approaches have emerged as a promising alternative to provide approximate solutions at faster speeds, but they struggle to strictly enforce constraints, leading to infeasible solutions in practice. To address this, we propose the Feasibility-Seeking Neural Network (FSNet), which integrates a feasibility-seeking step directly into its solution procedure to ensure constraint satisfaction. This feasibility-seeking step solves an unconstrained optimization problem that minimizes constraint violations in a differentiable manner, enabling end-to-end training and providing guarantees on feasibility and convergence. Our experiments across a range of different optimization problems, including both smooth/nonsmooth and convex/nonconvex problems, demonstrate that FSNet can provide feasible solutions with solution quality comparable to (or in some cases better than) traditional solvers, at significantly faster speeds.1

We show how to use low-quality, synthetic, and out-of-distribution images to improve the quality of a diffusion model. Typically, diffusion models are trained on curated datasets that emerge from highly filtered data pools from the Web and other sources. We show that there is immense value in the lower-quality images that are often discarded. We present Ambient Diffusion Omni, a simple, principled framework to train diffusion models that can extract signal from all available images during training. Our framework exploits two properties of natural images - spectral power law decay and locality. We first validate our framework by successfully training diffusion models with images synthetically corrupted by Gaussian blur, JPEG compression, and motion blur. We then use our framework to achieve stateof-the-art ImageNet FID and we show significant improvements in both image quality and diversity for text-to-image generative modeling. The core insight is that noise dampens the initial skew between the desired high-quality distribution and the mixed distribution we actually observe. We provide rigorous theoretical justification for our approach by analyzing the trade-off between learning from biased data versus limited unbiased data across diffusion times.

Computer-Aided Design (CAD) is a time-consuming and complex process, requiring precise, long-horizon user interactions with intricate 3D interfaces. While recent advances in AI-driven user interface (UI) agents show promise, most existing datasets and methods focus on short, low-complexity tasks in mobile or web applications, failing to capture the demands of professional engineering tools. In this work, we introduce VideoCAD, the first attempt to model UI interactions for precision engineering tasks. Specifically, VIDEOCAD is a large-scale synthetic dataset consisting of over 41K annotated video recordings of CAD operations, generated using an automated framework for collecting high-fidelity UI action data from human-made CAD designs. Compared to existing datasets, VIDEOCAD offers an order-of-magnitude increase in complexity for real-world engineering UI tasks, with time horizons up to 20 longer than those in other datasets. We show two important downstream applications of VIDEOCAD: (1) learning UI interactions from professional 3DCAD tools for precision tasks and (2) a visual question-answering (VQA) benchmark designed to evaluate multimodal large language models (LLMs) on spatial reasoning and video understanding. To learn the UI interactions, we propose VIDEOCADFORMER, a state-of-the-art model for learning CAD interactions directly from video, which outperforms existing behavior cloning baselines. Both VIDEOCADFORMER and the VQA benchmark derived from VIDEOCAD reveal key challenges in the current state of video-based UI understanding, including the need for precise action grounding, multi-modal and spatial reasoning, and long-horizon dependencies.

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.

Doctor-patient consultations require multi-turn, context-aware communication tailored to diverse patient personas. Training or evaluating doctor LLMs in such settings requires realistic patient interaction systems. However, existing simulators often fail to reflect the full range of personas seen in clinical practice. To address this, we introduce PATIENTSIM, a patient simulator that generates realistic and diverse patient personas for clinical scenarios, grounded in medical expertise. PATIENTSIM operates using: 1) clinical profiles, including symptoms and medical history, derived from real-world data in the MIMIC-ED and MIMIC-IV datasets, and 2) personas defined by four axes: personality, language proficiency, medical history recall level, and cognitive confusion level, resulting in 37 unique combinations. We evaluate eight LLMs for factual accuracy and persona consistency. The top-performing open-source model, Llama 3.3 70B, is validated by four clinicians to confirm the robustness of our framework. As an open-source, customizable platform, PATIENTSIM provides a reproducible and scalable solution that can be customized for specific training needs. Offering a privacy-compliant environment, it serves as a robust testbed for evaluating medical dialogue systems across diverse patient presentations and shows promise as an educational tool for healthcare.

Models of hybrid dynamical systems are widely used to answer questions about the causes and effects of dynamic events in time. Unfortunately, existing causal reasoning formalisms lack support for queries involving the dynamically triggered, discontinuous interventions that characterize hybrid dynamical systems. This mismatch can lead to ad-hoc and error-prone causal analysis workflows in practice. To bridge the gap between the needs of hybrid systems users and current causal inference capabilities, we develop a rigorous counterfactual semantics by formalizing interventions as transformations to the constraints of hybrid systems. Unlike interventions in a typical structural causal model, however, interventions in hybrid systems can easily render the model ill-posed. Thus, we identify mild conditions under which our interventions maintain solution existence, uniqueness, and measurability by making explicit connections to established hybrid systems theory. To illustrate the utility of our framework, we formalize a number of canonical causal estimands and explore a case study on the probabilities of causation with applications to fishery management. Our work simultaneously expands the modeling possibilities available to causal inference practitioners and begins to unlock decades of causality research for users of hybrid systems.

Representation learning is increasingly applied to generate representations that generalize well across multiple downstream tasks. Ensuring fairness guarantees in representation learning is crucial to prevent unfairness toward specific demographic groups in downstream tasks. In this work, we formally introduce the task of learning representations that achieve high-confidence fairness. We aim to guarantee that demographic disparity in every downstream prediction remains bounded by a user-defined error threshold ε, with controllable high probability. To this end, we propose the Fair Representation learning with high-confidence Guarantees (FRG) framework, which provides these high-confidence fairness guarantees by leveraging an optimized adversarial model. We empirically evaluate FRG on three real-world datasets, comparing its performance to six state-of-the-art fair representation learning methods. Our results demonstrate that FRG consistently bounds unfairness across a range of downstream models and tasks. The source code for FRG is available at: https://github.com/JamesLuoyh/FRG.

Machine learning-based decision support systems are increasingly deployed in clinical settings, where probabilistic scoring functions are used to inform and prioritize patient management decisions. However, widely used scoring rules, such as accuracy and AUC-ROC, fail to adequately reflect key clinical priorities, including calibration, robustness to distributional shifts, and sensitivity to asymmetric error costs. In this work, we propose a principled yet practical evaluation framework for selecting calibrated thresholded classifiers that explicitly accounts for uncertainty in class prevalences and domain-specific cost asymmetries. Building on the theory of proper scoring rules, particularly the Schervish representation, we derive an adjusted variant of cross-entropy (log score) that averages cost-weighted performance over clinically relevant ranges of class balance. The resulting evaluation is simple to apply, sensitive to clinical deployment conditions, and designed to prioritize models that are both calibrated and robust to real-world variations.

Machine learning models are often designed to maximize a primary goal, such as accuracy. However, as these models are increasingly used to inform decisions that affect people's lives or well-being, it is often unclear what the real-world repercussions of their deployment might be--making it crucial to understand and manage such repercussions effectively. Models maximizing user engagement on social media platforms, e.g., may inadvertently contribute to the spread of misinformation and content that deepens political polarization. This issue is not limited to social media--it extends to other applications where machine learning-informed decisions can have real-world repercussions, such as education, employment, and lending. Existing methods addressing this issue require prior knowledge or estimates of analytical models describing the relationship between a classifier's predictions and their corresponding repercussions. We introduce THEIA, a novel classification algorithm capable of optimizing a primary objective, such as accuracy, while providing high-confidence guarantees about its potential repercussions. Importantly, THEIA solves the open problem of providing such guarantees based solely on existing data with observations of previous repercussions. We prove that it satisfies constraints on a model's repercussions with high confidence and that it is guaranteed to identify a solution, if one exists, given sufficient data. We empirically demonstrate, using real-life data, that THEIA can identify models that achieve high accuracy while ensuring, with high confidence, that constraints on their repercussions are satisfied.

Recent works have studied fair resource allocation in social settings, where fairness is judged by the impact of allocation decisions rather than more traditional minimum or maximum thresholds on the allocations themselves. Our work significantly adds to this literature by developing continuous resource allocation strategies that adhere to equality of impact, a generalization of equality of opportunity. We derive methods to maximize total welfare across groups subject to minimal violation of equality of impact, in settings where the outcomes of allocations are unknown but have a diminishing marginal effect. While focused on a two-group setting, our study addresses a broader class of welfare dynamics than explored in prior work.