The Average Treatment Effect (ATE) is a foundational metric in causal inference, widely used to assess intervention efficacy in randomized controlled trials (RCTs). However, in many applications -- particularly in healthcare -- this static summary fails to capture the nuanced dynamics of treatment effects that vary with both dose and time. We propose a framework for modelling treatment effect trajectories as smooth surfaces over dose and time, enabling the extraction of clinically actionable insights such as onset time, peak effect, and duration of benefit. To ensure interpretability, robustness, and verifiability -- key requirements in high-stakes domains -- we adapt SemanticODE, a recent framework for interpretable trajectory modelling, to the causal setting where treatment effects are never directly observed. Our approach decouples the estimation of trajectory shape from the specification of clinically relevant properties (e.g., maxima, inflection points), supporting domain-informed priors, post-hoc editing, and transparent analysis. We show that our method yields accurate, interpretable, and editable models of treatment dynamics, facilitating both rigorous causal analysis and practical decision-making.

Generating human-like and adaptive trajectories is essential for autonomous driving in dynamic environments. While generative models have shown promise in synthesizing feasible trajectories, they often fail to capture the nuanced variability of human driving styles due to dataset biases and distributional shifts. To address this, we introduce TrajHF, a human feedback-driven finetuning framework for generative trajectory models, designed to align motion planning with diverse driving preferences. TrajHF incorporates multi-conditional denoiser and reinforcement learning with human feedback to refine multi-modal trajectory generation beyond conventional imitation learning. This enables better alignment with human driving preferences while maintaining safety and feasibility constraints. TrajHF achieves PDMS of 93.95 on NavSim benchmark, significantly exceeding other methods. TrajHF sets a new paradigm for personalized and adaptable trajectory generation in autonomous driving.

Learning from multiple domains is a primary factor that influences the generalization of a single unified robot system. In this paper, we aim to learn the trajectory prediction model by using broad out-of-domain data to improve its performance and generalization ability. Trajectory model is designed to predict any-point trajectories in the current frame given an instruction and can provide detailed control guidance for robotic policy learning. To handle the diverse out-of-domain data distribution, we propose a sparsely-gated MoE (\textbf{Top-1} gating strategy) architecture for trajectory model, coined as \textbf{Tra-MoE}. The sparse activation design enables good balance between parameter cooperation and specialization, effectively benefiting from large-scale out-of-domain data while maintaining constant FLOPs per token. In addition, we further introduce an adaptive policy conditioning technique by learning 2D mask representations for predicted trajectories, which is explicitly aligned with image observations to guide action prediction more flexibly. We perform extensive experiments on both simulation and real-world scenarios to verify the effectiveness of Tra-MoE and adaptive policy conditioning technique. We also conduct a comprehensive empirical study to train Tra-MoE, demonstrating that our Tra-MoE consistently exhibits superior performance compared to the dense baseline model, even when the latter is scaled to match Tra-MoE's parameter count.

In the classical reach-avoid problem, autonomous mobile robots are tasked to reach a goal while avoiding obstacles. However, it is difficult to provide guarantees on the robot's performance when the obstacles form a narrow gap and the robot is a black-box (i.e. the dynamics are not known analytically, but interacting with the system is cheap). To address this challenge, this paper presents NeuralPARC. The method extends the authors' prior Piecewise Affine Reach-avoid Computation (PARC) method to systems modeled by rectified linear unit (ReLU) neural networks, which are trained to represent parameterized trajectory data demonstrated by the robot. NeuralPARC computes the reachable set of the network while accounting for modeling error, and returns a set of states and parameters with which the black-box system is guaranteed to reach the goal and avoid obstacles. Through numerical experiments, NeuralPARC is shown to outperform PARC in generating provably-safe extreme vehicle drift parking maneuvers, as well as enabling safety on an autonomous surface vehicle (ASV) subjected to large disturbances and controlled by a deep reinforcement learning (RL) policy.

Pedestrian trajectory modelling in an urban complex is challenging because pedestrians can have many possible destinations, such as shops, escalators, and attractions. Moreover, weather and time-of-day may affect pedestrian behavior. In this paper, a new weather-time-trajectory fusion network (WTTFNet) is proposed to improve the performance of baseline deep neural network architecture. By incorporating weather and time-of-day information as an embedding structure, a novel WTTFNet based on gate multimodal unit is used to fuse the multimodal information and deep representation of trajectories. A joint loss function based on focal loss is used to co-optimize both the deep trajectory features and final classifier, which helps to improve the accuracy in predicting the intended destination of pedestrians and hence the trajectories under possible scenarios of class imbalances. Experimental results using the Osaka Asia and Pacific Trade Center (ATC) dataset shows improved performance of the proposed approach over state-of-the-art algorithms by 23.67% increase in classification accuracy, 9.16% and 7.07% reduction of average and final displacement error. The proposed approach may serve as an attractive approach for improving existing baseline trajectory prediction models when they are applied to scenarios with influences of weather-time conditions. It can be employed in numerous applications such as pedestrian facility engineering, public space development and technology-driven retail.

Trajectory planning is a fundamental problem in robotics. It facilitates a wide range of applications in navigation and motion planning, control, and multi-agent coordination. Trajectory planning is a difficult problem due to its computational complexity and real-world environment complexity with uncertainty, non-linearity, and real-time requirements. The multi-agent trajectory planning problem adds another dimension of difficulty due to inter-agent interaction. Existing solutions are either search-based or optimization-based approaches with simplified assumptions of environment, limited planning speed, and limited scalability in the number of agents. In this work, we make the first attempt to reformulate single agent and multi-agent trajectory planning problem as query problems over an implicit neural representation of trajectories. We formulate such implicit representation as Neural Trajectory Models (NTM) which can be queried to generate nearly optimal trajectory in complex environments. We conduct experiments in simulation environments and demonstrate that NTM can solve single-agent and multi-agent trajectory planning problems. In the experiments, NTMs achieve (1) sub-millisecond panning time using GPUs, (2) almost avoiding all environment collision, (3) almost avoiding all inter-agent collision, and (4) generating almost shortest paths. We also demonstrate that the same NTM framework can also be used for trajectories correction and multi-trajectory conflict resolution refining low quality and conflicting multi-agent trajectories into nearly optimal solutions efficiently. (Open source code will be available at https://github.com/laser2099/neural-trajectory-model)

Abstract--We present the results of training a large trajectory model using real-world user check-in data. Our approach follows a pre-train and fine-tune paradigm, where a base model is pre-trained via masked trajectory modeling and then adapted through fine-tuning for various downstream tasks. To address challenges posed by noisy data and large spatial vocabularies, we propose a novel spatial tokenization block. Our empirical analysis utilizes a comprehensive dataset of over 2 billion checkins generated by more than 6 million users. Through fine-tuning on 3 downstream tasks we demonstrate that our base model has effectively learned valuable underlying patterns in raw data, enabling its application in meaningful trajectory intelligence tasks. Despite some limitations, we believe this work represents an important step forward in the realization of a foundation model for trajectory intelligence.

In recent years, there has been a growing interest in visualizing the loss landscape of neural networks. Linear landscape visualization methods, such as principal component analysis, have become widely used as they intuitively help researchers study neural networks and their training process. However, these linear methods suffer from limitations and drawbacks due to their lack of flexibility and low fidelity at representing the high dimensional landscape. In this paper, we present a novel auto-encoder-based non-linear landscape visualization method called Neuro-Visualizer that addresses these shortcoming and provides useful insights about neural network loss landscapes. To demonstrate its potential, we run experiments on a variety of problems in two separate applications of knowledge-guided machine learning (KGML). Our findings show that Neuro-Visualizer outperforms other linear and non-linear baselines and helps corroborate, and sometime challenge, claims proposed by machine learning community. All code and data used in the experiments of this paper are available at an anonymous link https://anonymous.4open.science/r/NeuroVisualizer-FDD6