arXiv:2502.12187v3 Announce Type: replace Abstract: Hallucinations, a phenomenon where a language model (LM) generates nonfactual content, pose a significant challenge to the practical deployment of LMs. While many empirical methods have been proposed to mitigate hallucinations, recent studies established a computability-theoretic result showing that any LM will inevitably generate hallucinations on an infinite set of inputs, regardless of the quality and quantity of training datasets and the choice of the language model architecture and training and inference algorithms. Although the computability-theoretic result may seem pessimistic, its significance in practical viewpoints has remained unclear. This paper claims that those "innate" inevitability results from computability theory and diagonal argument, in principle, cannot explain practical issues of LLMs. We demonstrate this claim by presenting a positive theoretical result from a probabilistic perspective. Specifically, we prove that hallucinations can be made statistically negligible, provided that the quality and quantity of the training data are sufficient. Interestingly, our positive result coexists with the computability-theoretic result, implying that while hallucinations on an infinite set of inputs cannot be entirely eliminated, their probability can always be reduced by improving algorithms and training data. By evaluating the two seemingly contradictory results through the lens of information theory, we argue that our probability-theoretic positive result better reflects practical considerations than the computability-theoretic negative result.
Science Journals
arXiv:2502.04871v2 Announce Type: replace Abstract: The Landau-Lifshitz equation describes the dynamics of magnetization in ferromagnetic materials. Due to the essential nonlinearity and nonconvex constraint, it is typically solved numerically. In this paper, we developed a finite volume element method (FVEM) with the Gauss-Seidel projection method (GSPM) for the micromagnetics simulations. We provide the approximation error in space and depict the energy law when the FVEM is adopted. Owing to the GSPM for time-marching, the discrete system is decoupled component by component, making the computational complexity comparable to that of solving the scalar heat equation implicitly. This significantly accelerates real simulations. We present several numerical experiments to validate the theoretical analysis and the efficiency gain. Additionally, we study the blow-up solution and efficiently simulate the 2D magnetic textures using the proposed method.
arXiv:2605.15827v1 Announce Type: new Abstract: Caesar is a deductive verifier for probabilistic programs. At its core lies HeyVL, a quantitative intermediate verification language based on the real-valued logic HeyLo. HeyVL allows users to express a probabilistic program, its specifications, and proof rules in a programming-language style, so that new proof rules can be easily integrated into the verifier. Caesar translates HeyVL programs into verification conditions, which are then checked using the Z3 SMT solver. It also includes a backend based on probabilistic model checking for a subset of HeyVL. We report on the results of five years of development of Caesar, highlighting its main features and architecture. In particular, we describe recent improvements such as additional proof rules, a model-checking backend, and better diagnostics.
arXiv:2605.15822v1 Announce Type: new Abstract: Score-based generative models are trained in high-dimensional ambient spaces, yet many data distributions are supported on low-dimensional nonlinear structures. We prove that, for compact $d$-dimensional smooth manifolds $\mathcal{M} \subset [0,1]^D$ with $d > 2$ and $\beta$-H\"older densities strictly positive on $\mathcal{M}$, a variance-preserving SGM estimator attains the intrinsic Wasserstein--1 sample exponent $\tilde{\mathcal{O}}(D^{\mathcal{O}_\beta(d)}n^{-(\beta+1)/(d+2\beta)})$, up to logarithmic factors and explicit geometry and density factors. The full nonasymptotic bound explicitly isolates the finite-order geometry envelope, H\"older radius, density lower bound, ambient dependence, and finite-order correction terms. The analysis separates score approximation into a large-noise tangent-cell regime and a small-noise projection-centered, de-Gaussianized Laplace regime. The key technical ingredient is a ReLU implementation of nearest-projection coordinates via finite intrinsic anchors and Gauss--Newton iterations, rather than approximating the manifold projection as a black-box high-dimensional smooth map. Consequently, for families with polynomially controlled geometry and density lower bounds, the constructed score-network parameters have polynomial ambient dependence.
arXiv:2605.15815v1 Announce Type: new Abstract: Code agents increasingly help developers work with unfamiliar repositories, but every such task depends on a costly prerequisite: bootstrapping the repository into a usable development state. This process requires substantial trial-and-error exploration, yet the resulting knowledge--resolved dependencies, repair strategies--stays trapped in a single conversation, unavailable to future agents. We therefore formulate repository bootstrapping as a reusable startup knowledge problem and introduce BootstrapAgent, a multi-agent framework that distills the heuristics discovered during bootstrap exploration into a persistent, verifiable, agent-consumable .bootstrap contract. Through evidence extraction, structured planning, deterministic Docker-based verification, and trace-driven repair, BootstrapAgent generates a contract covering environment setup, diagnostic checks, minimal verification, and accumulated repair knowledge. We further propose warm repair with clean replay to accelerate iterative debugging without sacrificing cold-start reproducibility, and a delta repair with sanity check to prevent reward hacking. Experiments on three benchmarks show that BootstrapAgent achieves a 92.9% success rate, outperforming the baseline by over 10% while reducing downstream agent token usage by 25.9% and build time by 22.3%. Our code is available at https://github.com/Vossera/BootstrapAgent.
arXiv:2501.19128v5 Announce Type: replace Abstract: In many real-world scenarios, reward signal for agents are exceedingly sparse, making it challenging to learn an effective reward function for reward shaping. To address this issue, the proposed approach in this paper performs reward shaping not only by utilizing non-zero-reward transitions but also by employing the \emph{Semi-Supervised Learning} (SSL) technique combined with a novel data augmentation to learn trajectory space representations from the majority of transitions, {i.e}., zero-reward transitions, thereby improving the efficacy of reward shaping. Experimental results in Atari and robotic manipulation demonstrate that our method outperforms supervised-based approaches in reward inference, leading to higher agent scores. Notably, in more sparse-reward environments, our method achieves up to twice the peak scores compared to supervised baselines. The proposed double entropy data augmentation enhances performance, showcasing a 15.8\% increase in best score over other augmentation methods
arXiv:2412.12636v3 Announce Type: replace Abstract: Large-scale ML training jobs are frequently interrupted by hardware and software anomalies, failures, and management events. Existing solutions like checkpoint-restart or runtime reconfiguration suffer from long downtimes and degraded performance. We present TrainMover, a resilient LLM training runtime that leverages elastic and standby machines to handle interruptions with minimal downtime and zero memory overhead. To achieve these goals, TrainMover introduces three key techniques: two-phase, delta-based communication group setup; communication-free sandboxed warmup; and general standby design that enables failure recovery from any role. Our evaluation shows that TrainMover consistently achieves around 20 seconds of downtime when handling various interruptions at the 1024-GPU scale. TrainMover is projected to reduce wasted GPU hours by 55% compared to the best alternative, saving 1.4 million GPU-hours per week at the 64K-GPU scale.
arXiv:2412.05887v3 Announce Type: replace Abstract: Many open source software (OSS) projects need more human resources for maintenance, improvements, and sometimes even their survival. These needs allegedly apply even to vital OSS projects that can be seen as being a part of the world's critical infrastructures. To address this resourcing problem, new funding instruments for OSS projects have been established in recent years. The paper examines two such funding bodies for OSS and the projects they have funded. The focus of both funding bodies is on software security and cyber security in general. Based on qualitative thematic analysis, the results indicate that particularly OSS supply chains, network and cryptography libraries, programming languages, and operating systems and their low-level components have been funded and thus seen as critical in terms of cyber security. In addition to the qualitative results presented, the paper makes a contribution by connecting the research branches of critical infrastructure and sustainability of OSS projects. A further contribution is made by connecting the topic examined to recent cyber security regulations. Finally, an important argument is raised that neither cyber security nor project sustainability alone can entirely explain the rationales behind the funding decisions made by the two funding bodies.
arXiv:2412.03932v2 Announce Type: replace Abstract: This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing BCs often relies on an accurate dynamics model; however, such models are often imprecise due to the model complexity involved, particularly when dealing with highly nonlinear systems. In such cases, while scenario approaches effectively address the safety problem using collected data to construct a guaranteed BC for the unknown dynamical system, they often require solving an optimization problem with substantial amounts of data. To address this, we propose a physics-informed scenario approach that selects data samples such that the outputs of the physics-based model and the observed data are sufficiently close. This approach guides the scenario optimization process to eliminate redundant samples and potentially reduce the required dataset size. We validate our approach through three case studies, showcasing its practical application in reducing the required data.
arXiv:2410.02832v2 Announce Type: replace Abstract: This paper proposes a simple yet effective jailbreak attack named FlipAttack against black-box LLMs. First, from the autoregressive nature, we reveal that LLMs tend to understand the text from left to right and find that they struggle to comprehend the text when noise is added to the left side. Motivated by these insights, we propose to disguise the harmful prompt by constructing left-side noise merely based on the prompt itself, then generalize this idea to 4 flipping modes. Second, we verify the strong ability of LLMs to perform the text-flipping task, and then develop 4 variants to guide LLMs to denoise, understand, and execute harmful behaviors accurately. These designs keep FlipAttack universal, stealthy, and simple, allowing it to jailbreak black-box LLMs within only 1 query. Experiments on 8 LLMs demonstrate the superiority of FlipAttack. Remarkably, it achieves $\sim$98\% attack success rate on GPT-4o, and $\sim$98\% bypass rate against 5 guardrail models on average. The codes are available at GitHub\footnote{https://github.com/yueliu1999/FlipAttack}.
arXiv:2509.23352v3 Announce Type: replace Abstract: The integration of Reinforcement Learning (RL) into flow matching models for text-to-image (T2I) generation has driven substantial advances in generation quality. However, these gains often come at the cost of exhaustive exploration and inefficient sampling strategies due to slight variation in the sampling group. Building on this insight, we propose Dynamic-TreeRPO, which implements the sliding-window sampling strategy as a tree-structured search with dynamic noise intensities along depth. We perform GRPO-guided optimization and constrained Stochastic Differential Equation (SDE) sampling within this tree structure. By sharing prefix paths of the tree, our design effectively amortizes the computational overhead of trajectory search. With well-designed noise intensities for each tree layer, Dynamic-TreeRPO can enhance the variation of exploration without any extra computational cost. Furthermore, we seamlessly integrate Supervised Fine-Tuning (SFT) and RL paradigm within Dynamic-TreeRPO to construct our proposed LayerTuning-RL, reformulating the loss function of SFT as a dynamically weighted Progress Reward Model (PRM) rather than a separate pretraining method. By associating this weighted PRM with dynamic-adaptive clipping bounds, the disruption of exploration process in Dynamic-TreeRPO is avoided. Benefiting from the tree-structured sampling and the LayerTuning-RL paradigm, our model dynamically explores a diverse search space along effective directions. Compared to existing baselines, our approach demonstrates significant superiority in terms of semantic consistency, visual fidelity, and human preference alignment on established benchmarks, including HPS-v2.1, PickScore, and ImageReward. In particular, our model outperforms SoTA by $4.9\%$, $5.91\%$, and $8.66\%$ on those benchmarks, respectively, while improving the training efficiency by nearly $50\%$.
arXiv:2312.05975v3 Announce Type: replace Abstract: Explainability is a vital aspect of modern AI for real-world impact and usability. The main objective of this paper is to emphasise the need to understand the predictions of Computer Vision models, specifically Convolutional Neural Network (CNN) models. Existing methods for explaining CNN predictions are largely based on Gradient-weighted Class Activation Maps (Grad-CAM) and focus solely on a single target class; this assumption about the target class selection neglects a large portion of the predictor CNN's prediction process. In this paper, we present an exhaustive methodology, called Fused Multi-class Gradient-weighted Class Activation Map (FM-G-CAM), that considers multiple top-predicted classes and provides a holistic explanation of the predictor CNN's rationale. We also provide a detailed mathematical and algorithmic description of our method. Furthermore, alongside a concise comparison of existing methods, we compare FM-G-CAM with Grad-CAM, quantitatively and qualitatively highlighting its benefits through real-world practical use cases. Finally, we present an open-source Python library with an FM-G-CAM implementation to conveniently generate saliency maps for CNN-based model predictions.
arXiv:2605.15782v1 Announce Type: new Abstract: In this work, we address the problem of ensuring real-time safety in autonomous robot navigation, in spatially constrained dynamic environments, by utilizing only onboard sensors. We present a real-time control architecture that integrates a 3D LIDAR perception-based composite control barrier function(CBF)-based safety filter directly into the autonomy pipeline. The proposed perception-driven framework enforces collision avoidance constraints dynamically from onboard point cloud data, thus allowing a large number of constraints to be handled at the control frequency, while remaining minimally invasive to nominal task execution. The safety region is defined as an ellipsoid in the body-frame, consistent with the geometry of the platform, which induces time-varying constraints in the world frame as the robot rotates; this effect is handled through a dedicated formulation of time-varying (CBF) for each LIDAR point. We validate the system through multiple field experiments in underground environments by utilizing a quadruped platform performing a visual inspection task, demonstrating reliable operation in the presence of dynamic obstacles, unsafe high-level references, abrupt localization anomalies, and while traversing through narrow corridors.
arXiv:2605.16145v1 Announce Type: cross Abstract: We develop a skew-adaptive extension of split conformal prediction for regression. The method starts from an asymmetric interval family centered at a point prediction and uses the gauge approach to deduce the conformity score induced by this family. The inverse hyperbolic sine transform of signed scaled residuals provides the training target for an additional predictive model, whose role is to learn how predictive uncertainty should tilt across the feature space. The resulting procedure preserves the finite-sample marginal validity of split conformal prediction under exchangeability, while producing intervals that adapt to both local scale and local skewness. We also develop a calibration-sample-based estimator for comparing the expected relative future width of the skew-adaptive and classical scaled-score intervals. Experiments on a variety of datasets indicate gains in prediction interval efficiency over the scaled-score construction and conformalized quantile regression, and show that the proposed estimator closely matches the corresponding average width ratio observed on the test sample.
arXiv:2605.16065v1 Announce Type: new Abstract: 3D Gaussian Splatting (3D-GS) enables real-time 3D scene reconstruction but lacks robust segmentation for editing tasks such as object removal, extraction, and recoloring. Existing approaches that lift 2D segmentations to the 3D domain suffer from view inconsistencies and coarse masks. In this paper, we propose a novel framework that leverages the Segment Anything Model High Quality (SAM-HQ) to generate accurate 2D masks, addressing the limitations of the standard SAM in boundary fidelity and fine-structure preservation. To achieve robust 3D segmentation of any target object in a given scene, we introduce a prior-guided label reassignment method that assigns labels to 3D Gaussians by enforcing multiview consistency with learned priors. Our approach achieves state-of-the-art segmentation accuracy and enables interactive, real-time object editing while maintaining high visual fidelity. Qualitative results demonstrate superior boundary preservation and practical utility in Virtual Reality (VR) and robotics, advancing 3D scene editing.
arXiv:2605.16067v1 Announce Type: new Abstract: We propose a variational quantum classifier operating on high dimensional deep representations via amplitude encoding, stabilized by a learnable classical pre encoding layer.By combining normalized amplitude embeddings with bounded quantum observables, the resulting model induces a structured and smooth hypothesis class with controlled sensitivity to input variations. Model reliability is assessed using SAFE-AI metrics derived from the Cramer von Mises divergence, enabling consistent evaluation across accuracy, robustness, and explainability dimensions. Empirical results show that the proposed quantum model provides competitive predictive performance compared with strong classical baselines while exhibiting a more balanced SAFE reliability profile, with improved robustness to noise and stability under structured feature removal. These findings suggest that variational quantum circuits offer a principled mechanism for stability oriented SAFE learning in safety critical settings.
arXiv:2605.15382v1 Announce Type: new Abstract: Low-rank methods for kinetic equations have attracted increasing attention due to their effectiveness in reducing the high dimensionality of phase space. In our previous work [G. Wang & J. Hu, J. Comput. Phys. 558 (2026) 114884], we developed a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT) format, in which explicit time integration is employed in all substeps. As a result, the method is subject to severe stability constraints in the strongly collisional regimes. In this paper, we consider kinetic equations with the (nonlinear) Fokker--Planck collision operator and develop a dynamical low-rank method that employs implicit or implicit-explicit (IMEX) discretizations in appropriate substeps to overcome stiffness. In these implicit substeps, the resulting equations can be formulated as matrix or tensor Sylvester equations, for which we propose efficient direct solvers by exploiting their underlying structure. The overall computational cost of the proposed method scales linearly with respect to the number of grid points in a single velocity dimension, comparable to that of a fully explicit low-rank scheme. We demonstrate the accuracy and efficiency of the proposed method on several representative kinetic test problems.
arXiv:2605.16076v1 Announce Type: new Abstract: Plant disease detection is still largely manual in Bangladesh, where extension workers eyeball leaf samples across millions of smallholdings. We built AgriMind to automate this: an ensemble of ResNet50, EfficientNet-B0, and DenseNet121 trained on 20,638 PlantVillage images across 15 pepper, potato, and tomato disease classes. Transfer learning with frozen ImageNet backbones and 10 epochs of head-only training keeps the pipeline lightweight. Individual models hit 96--97% on the held-out test set, but averaging their softmax outputs pushes the ensemble to 99.23% -- a two-thirds cut in error rate. We tried biasing the average toward the best validation model; it backfired. Dropping any single model also hurt. Pepper and potato classify perfectly; tomato, with ten visually similar classes, still reaches 99.01%. On an NVIDIA T4 GPU the full ensemble runs at 53 FPS. Whether that translates to real-time mobile use depends on TensorFlow Lite optimization -- work we have not yet completed.
arXiv:2605.16077v1 Announce Type: new Abstract: Accurate assessment of cognitive decline from spontaneous speech remains challenging due to limited dataset size and class imbalance. In this work, we propose a large language model (LLM)-driven data augmentation framework to improve the prediction of cognitive scores from speech. Experiments are conducted on a Japanese corpus in which each participant provides both a spontaneous oral narrative and a written response to the same clinical prompt. The written responses serve as semantic anchors to generate multiple oral-like monologues in different styles using GPT-5. We then predict Hasegawa Dementia Scale scores, a widely used cognitive screening tool in Japan, using a Partial Least Squares regression model trained on Sentence-BERT speech embeddings. We investigate two augmentation strategies: random class-balanced selection, which yields moderate but unstable improvements, and similarity-guided class-balanced selection. The latter prioritizes semantically close synthetic samples, leading to more consistent improvements and substantially reducing prediction error for minority low-score participants while maintaining performance for the majority group. Overall, our findings demonstrate the potential of semantically guided LLM-driven augmentation as a principled approach for addressing class imbalance and improving data efficiency in clinical speech analysis.
arXiv:2605.16079v1 Announce Type: new Abstract: Large Vision-Language Models (LVLMs) have shown significant progress in video understanding, yet they face substantial challenges in tasks requiring precise spatiotemporal localization at the instance level. Existing methods primarily rely on text prompts for human-model interaction, but these prompts struggle to provide precise spatial and temporal references, resulting in poor user experience. Furthermore, current approaches typically decouple visual perception from language reasoning, centering reasoning around language rather than visual content, which limits the model's ability to proactively perceive fine-grained visual evidence. To address these challenges, we propose VideoSeeker, a novel paradigm for instance-level video understanding through visual prompts. VideoSeeker seamlessly integrates agentic reasoning with instance-level video understanding tasks, enabling the model to proactively perceive and retrieve relevant video segments on demand. We construct a four-stage fully automated data synthesis pipeline to efficiently generate large-scale, high-quality instance-level video data. We internalize tool-calling and proactive perception capabilities into the model via cold-start supervision and RL training, building a powerful video understanding model. Experiments demonstrate that our model achieves an average improvement of +13.7% over baselines on instance-level video understanding tasks, surpassing powerful closed-source models such as GPT-4o and Gemini-2.5-Pro, while also showing effective transferability on general video understanding benchmarks. The relevant datasets and code will be released publicly.
arXiv:2510.25404v3 Announce Type: replace Abstract: Optimizing an experimental system can be extremely challenging when each experiment is expensive, time-consuming, or difficult to perform. Existing optimizers for expensive black-box problems, such as Bayesian optimization, are typically limited to numerical or categorical observations. They do not make use of broader domain knowledge, such as expert heuristics, relevant scientific papers, or similar previous experiments. Large language models (LLMs) can interpret this semantic information; however, even state-of-the-art LLMs struggle to reliably solve black-box optimization problems. We introduce SemanticOpt, a framework for semantic black-box optimization that equips LLMs with optimization capabilities by fine-tuning them on structured Bayesian optimization trajectories augmented with natural-language context. SemanticOpt jointly uses numerical and semantic evidence when proposing new experiments, while producing interpretable predictions aligned with Bayesian surrogate models. We construct a range of real-world optimization problems paired with semantic information to create a diverse benchmark for evaluating semantic black-box optimization. Across these domains, SemanticOpt outperforms both classical optimizers and existing LLM-based approaches on average when given relevant semantic information.
arXiv:2605.15990v1 Announce Type: new Abstract: Tremendous efforts have been put into evaluating the inclusivity and effectiveness of AI systems across cultures. However, the cultural capabilities considered in much of the literature remain vaguely defined, are referred to using interchangeable terminology, and are typically limited to recalling accurate information about various demographics, regions, and nationalities. To address this construct ambiguity, we draw from Intercultural Communication scholarship and propose a three-level taxonomy of AI-relevant cultural capabilities: Cultural Awareness answers "Does the model know?", Cultural Sensitivity answers "How does it frame its knowledge?", and Cultural Competence answers "Can it adapt as the interaction evolves?". Beyond conceptual clarification, we position this taxonomy as a practical tool for improving the validity and interpretability of AI evaluation in real-world, multicultural settings. Without such construct clarity, evaluation results risk overstating model capabilities and may lead to inappropriate deployment decisions in culturally sensitive contexts.
arXiv:2605.15808v1 Announce Type: cross Abstract: Integrated sensing and communication (ISAC) relies on monostatic sensing (MS) and bistatic positioning (BP) to enable comprehensive environmental awareness and user localization. However, existing frameworks predominantly assume static geometries and optimize these modalities independently, neglecting user mobility and sequential information sharing. In this paper, we propose a velocity-aware sequential beamforming framework that dynamically couples MS and BP in time. We derive the Cramer-Rao bounds (CRBs) in the position domain to formulate a non-convex resource allocation problem. Instead of relying on static weighted-sum tradeoffs, we introduce a sequential Bayesian optimization strategy where MS is executed first to construct a reliable structural prior on the UE and passive targets (PTs). This covariance prior is subsequently passed to the UE to regularize the BP estimation stage. We demonstrate that optimizing a single shared beamformer globally across both phases yields superior synergistic gains compared to a two-stage greedy approach. Simulation results validate that the shared sequential design efficiently balances limited symbol resources, achieving centimeter-level positioning accuracy for both the UE and PTs, robust velocity estimation, and a significantly reduced computational runtime.
arXiv:2605.16211v1 Announce Type: new Abstract: Traditional scientific modeling typically begins with fixed, instance-wise effective equations and then carries out equation-specific analysis and computation, a procedure that becomes exceptionally challenging in complex applications such as multiscale systems. We propose an alternative paradigm by learning mesoscopic dynamics within a mathematically constrained hypothesis class. Building upon a generalized Onsager principle, we introduce a unified framework encompassing both dissipative and conservative mesoscopic dynamics. We establish uniform and a priori theoretical guarantees, including global well-posedness, asymptotic stability, unique factorization identifiability, and discrete energy dissipation, applicable to all spatio-temporal evolution equations within this hypothesis class prior to all learning stages. Data from each problem instance is then used to guide the identification of members within our hypothesis class, giving rise to accurate, robust and interpretable dynamical models. We empirically validate this framework on both data from continuum PDE models as a check, and on data arising from microscopic chain models for which exact meso-scale models are unknown. The proposed approach not only acts as an effective dynamics learner, but also offers vital interpretable diagnostics of the underlying physics.
arXiv:2510.10454v2 Announce Type: replace Abstract: Large language models (LLMs) offer a generalizable approach for modeling patient trajectories, but suffer from the long and noisy nature of electronic health records (EHR) data in temporal reasoning. To address these challenges, we introduce Traj-CoA, a multi-agent system involving chain-of-agents for patient trajectory modeling. Traj-CoA employs a chain of worker agents to process EHR data in manageable chunks sequentially, distilling critical events into a shared long-term memory module, EHRMem, to reduce noise and preserve a comprehensive timeline. A final manager agent synthesizes the worker agents' summary and the extracted timeline in EHRMem to make predictions. In a zero-shot one-year lung cancer risk prediction task based on five-year EHR data, Traj-CoA outperforms baselines of four categories. Analysis reveals that Traj-CoA exhibits clinically aligned temporal reasoning, establishing it as a promisingly robust and generalizable approach for modeling complex patient trajectories. Implementation of Traj-CoA is available on https://github.com/zengsihang/Traj-CoA.