Multimodal Action Diffusion for Robust End-to-End Autonomous Driving

End-to-End Autonomous Driving (E2E-AD) systems have largely converged on predicting intermediate trajectory waypoints, delegating final control to hand-crafted controllers with GPS access. Direct control-signal prediction (outputting throttle, steer and brake in an end-to-end fashion) remains underexplored, and critically, the role of action multimodality in such systems is not well understood. We argue that moving beyond deterministic, single-action outputs is not merely a modelling choice, but a key driver of driving performance, representational quality, and training stability. To validate this, we introduce the Action Diffusion Transformer (ADT), an anchor-free diffusion transformer trained with a MSE objective that natively models the multimodal distribution of plausible driving actions. Rather than committing to a single deterministic command, ADT generates K action candidates and selects the most suitable one at inference via Nearest Neighbour Matching (NNM). Beyond strong benchmark numbers, we show that action multimodality yields measurable benefits in learned representations and behavioral consistency, effects that deterministic architectures cannot replicate. ADT surpasses previous state-of-the-art on the challenging closed-loop Bench2Drive benchmark while achieving ten times lower latency, demonstrating that expressive, multimodal action modelling is both practically efficient and conceptually essential for robust end-to-end driving.

Learning Multi-Modal Trajectory Policies for Data-Efficient Robotic Manipulation

Robotic manipulation requires the effective integration of heterogeneous inputs, including visual observations, language instructions, and trajectory representations, to generate accurate actions. Existing transformer-based policies typically process these heterogeneous modalities within a shared parameter space, which often leads to modality interference and inefficient representation learning, especially in data-scarce scenarios. While Mixture-of-Experts (MoE) offers a scalable solution through expert specialization, conventional routing mechanisms are often sensitive to such cross-modal representation discrepancies, resulting in unstable expert assignment and expert collapse. In this work, we propose MATE (Multi-ModAl TrajEctory Policies), a novel trajectory prediction framework built upon MoE. Specifically, we introduce a Multi-Modal MoE architecture to achieve fine-grained sub-token feature decoupling, and design a cross-modal cosine router for stable and scale-invariant expert assignment across heterogeneous modalities. We further employ temperature-controlled routing and stochastic noise injection to improve expert balance and prevent premature routing collapse under scarce demonstrations. Experiments on the LIBERO benchmark show that our MATE consistently outperforms prior work under data scarcity. It achieves a 4.75% improvement in average success rate over the trajectory-guided counterpart. Real-world experiments on robotic ping-pong also suggest that the predicted trajectories can provide useful guidance for downstream robotic execution, further indicating the practical feasibility of our algorithm.

From Cues to Horizons: Dynamic Risk Horizon Profiling for Trajectory Prediction

Accurate and reliable vehicle trajectory prediction is essential for safe autonomous driving. Recent studies have incorporated safety risk into trajectory prediction to quantify dangers posed by surrounding agents. However, most risk-aware approaches use past risk information as a secondary signal to help guide decisions, overlooking its future evolution and uncertainty. In this paper, we propose a risk horizon profiling (RHP) module that incorporates a continuous, learnable potential field model for risk-aware trajectory prediction. The RHP module calculates the spatial-temporal proximity of surrounding objects to profile risk distributions across future horizons, which supports better trajectory prediction by adaptively identifying what human drivers perceive as critical moments. We evaluate our method on two datasets from different driving settings, highD for highway corridors and SHRP2 for urban streets, which cover diverse risk scenarios including safe, near-crash, and crash events. Compared to the baseline methods, our framework achieves a 25.0\% reduction in 5s RMSE on the highD dataset and a 29.1\% reduction in 5s minFDE on SHRP2. These results indicate strong performance for both short and long horizon prediction and robust generalization across highway and urban scenarios. The proposed method enables more realistic AV path planning and strategic selection, thereby supporting safer autonomous driving and more advanced driver-assistance systems. The source code for this work is available at: https://github.com/bilab-nyu/RHP

Physically-Constrained Mamba-SDE for Remaining Useful Life Prediction under Irregular Observations

Accurate Remaining Useful Life prediction is critical for industrial predictive maintenance. However, real-world deployment is challenging due to the irregular nature of sensor observations, characterized by asynchronous sampling, burst missingness, and temporal jitter. Compounding this issue, purely data-driven models often generate physically implausible degradation trajectories that violate the irreversible nature of damage accumulation. To address this, we propose PC-MambaSDE, a unified continuous-time framework for robust RUL prediction under irregular observations. Specifically, we design a Mask-Aware Continuous Mamba Encoder that explicitly leverages observation masks to extract context-rich control signals. Furthermore, we introduce a Physics-Guided Latent SDE with parametrically rectified hybrid drift, superimposing a global physical bias to enforce monotonic degradation even amid severe observation gaps. Additionally, we formulate RUL prediction as a boundary value problem via a Terminal Degradation Penalty, which decouples a Health Index dimension and applies a penalty loss to guide trajectories toward the failure state. Theoretically, we prove that our variational objective is mathematically equivalent to minimizing the KL divergence via Girsanov's theorem, and we guarantee the global asymptotic stability of the learned dynamics through Lyapunov analysis. To enable rigorous evaluation, we develop a Hybrid Irregularity Generation Scheme that simulates realistic industrial imperfections. Extensive experiments on public benchmarks demonstrate that PC-MambaSDE significantly outperforms state-of-the-art methods, particularly under extreme observation scarcity, validating the efficacy of embedding physical priors into continuous-time latent dynamics.

Bayesian meta-learning for modeling Alzheimer's disease progression

Predicting whether an individual with Alzheimer's disease will experience mild or severe disease progression is essential for personalized treatment. Typically, practitioners seek to predict the distribution of a discrete disease score, conditional on an individual's current MRI volume and their historical disease trajectory. Classical statistical regression models and single-task neural networks are not well-suited for this purpose because fitting separate models is infeasible (since each individual typically has few observations), while ignoring individual-level correlation leads to poor generalization. Meta-learning, in contrast, provides a natural avenue to dynamically predict distributions without retraining and model nonlinear relationships between the outcome and covariates. Motivated by this, we propose a Bayesian meta-learner that is trained on multiple individuals but tailors the predictive disease score distribution to each individual's historical data. Our model predicts on unseen individuals without retraining, scales linearly with the number of historical observations, and is guaranteed to be less overconfident when predicting long-term disease scores compared to its deterministic counterpart. On real-world data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database, our model achieves performance competitive with both single-task models and deterministic meta-learners, while substantially improving performance when predicting long-term disease progression.

Learning Chaotic Dynamics through Second-Order Geometric Supervision

Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector field, but neither constrains how the field bends away from its tangent plane. A model can thus match values and tangents at the supervised states yet curve differently from the truth, remaining locally accurate while drifting toward spurious attractors and distorting long-time statistics. We show that enforcing second-order consistency mitigates these failures, but forming the full Hessian is prohibitive in high dimensions. We propose model-constrained randomized Jacobian matching, which compares the Jacobians of the true and learned vector fields at randomly perturbed inputs. A Taylor expansion shows that the expected randomized Jacobian loss decomposes into the nominal Jacobian mismatch plus a Hessian mismatch scaled by the noise variance, implicitly enforcing second-order consistency at $\mathcal{O}(d^2)$ cost without forming the $\mathcal{O}(d^3)$ Hessian tensor. Using only Jacobian evaluations, the method scales to high dimensions where explicit Hessian matching does not. Numerical experiments confirm that second-order methods are robust. For Lorenz~63, first-order methods produce catastrophic Lyapunov-exponent outliers under minimal temporal supervision, which second-order methods eliminate while recovering the correct attractor. For coupled Lorenz~96, an out-of-distribution forcing sweep separates the methods: all agree up to $F=16$, but beyond $F=18$ only second-order methods preserve the invariant measure and Lyapunov spectrum. On both systems, randomized Jacobian matching performs comparably to explicit Hessian matching at much lower cost.

Predicting the risk of colorectal anastomotic leak based on preoperative mapping of the blood supply of the bowel

Anastomotic leak remains one of the most serious complications following colorectal cancer surgery, substantially affecting patient outcomes, recovery trajectories, and healthcare costs. Despite advances in imaging technology, current preoperative assessment relies only on clinical assessment, a process that is subjective, error-prone, and highly dependent on individual expertise. To date, no validated CT-based method exists to predict anastomotic leak risk prior to surgery. This protocol paper outlines a comprehensive framework for developing and validating an AI-driven system for preoperative risk assessment using pre- and post-contrast CT imaging. The study describes the stages of data collection, ethical handling, and preprocessing of patient data in accordance with GDPR, image preprocessing, and the exploration of deep learning architectures designed to generate clinically interpretable outputs. Two integrated tools constitute the main deliverables of this workflow: 1) a risk assessment module, which quantifies the likelihood of leakage by analyzing vascular and tissue features in CT scans, and 2) a Content-Based Medical Image Retrieval (CBMIR) module, which identifies and displays similar historical cases to support evidence-based surgical decision making. The protocol paper requires close collaboration between hospitals and universities; this protocol demonstrates that such a system is technically feasible and clinically implementable within existing healthcare infrastructures. By following the proposed methodological stages and regulatory principles, other institutions can reproduce this workflow to develop analogous decision-support tools. Ultimately, this interdisciplinary framework aims to enhance surgical planning, reduce leak incidence, and contribute to a broader paradigm shift toward explainable, data-driven precision surgery.

Geometric Latent Reasoning Induces Shorter Generations in LLMs

Large language models solve complex problems by generating lengthy chains of explicit reasoning tokens. While effective, this makes reasoning expensive, length-sensitive, and constrained to (discrete) natural language. While latent reasoning offers a continuous alternative, determining useful structures for intermediate latent states is an open challenge. In this paper, we formulate latent reasoning as a geometric path-approximation problem within the model's pretrained token-embedding space. We introduce Geometric Latent Reasoning (GLR), which uses a lightweight transition head to predict iterative direction updates in embedding space. Using textual chain-of-thought traces as anchors, GLR learns to approximate discrete reasoning trajectories while permitting continuous deviations from exact token embeddings. Evaluations on mathematical reasoning benchmarks using Qwen3 models reveal an emergent phenomenon: geometric latent reasoning induces substantially shorter generations without an explicit length objective. By replacing early explicit reasoning with continuous latent steps, models often reach correct answers using substantially fewer total generation steps. These findings suggest that continuous trajectories act as compact intermediate reasoning states, exposing a new tradeoff between latent computation budget, output length, and accuracy.

COMAP: Co-Evolving World Models and Agent Policies for LLM Agents

Equipping language agents with world models enables them to anticipate environment dynamics and evaluate candidate actions before execution. However, existing textual world models are typically fixed after training, preventing them from adapting to the on-policy state-action distributions induced by an evolving agent. Meanwhile, agent-improvement methods often rely on external rewards or verifiers, limiting their applicability in realistic interactive environments. In this paper, we propose COMAP, a novel framework that co-evolves textual world models and agent policies through closed-loop interaction. At each decision step, the world model predicts future state feedback for candidate actions, and the agent performs future-aware reflection by estimating the reliability of this feedback and refining its action accordingly. The resulting on-policy trajectories are then used to update the world model via self-distillation, allowing it to better match the agent's evolving interaction distribution. Across embodied task planning, Web navigation, and tool-use benchmarks, COMAP consistently outperforms competitive baselines, e.g., +16.75% relative improvement with Qwen3-4B. Further analyses show that the co-evolutionary loop improves the world model's prediction accuracy over time and leads to more effective long-horizon decision-making. Our code is available at: https://github.com/loyiv/CoMAP.

The Lie We Tell: Correcting the Euclidean Fallacy in Vision Language Action Policies via Score Matching on Tangent Space

Diffusion-based Vision-Language-Action policies achieve remarkable success in robotic manipulation, yet commit a fundamental geometric error we term the $\textbf{Euclidean Fallacy}$: representing SE(3) poses as flat $\mathbb{R}^{12}$ vectors. This approximation induces (1) manifold drift violating SO(3) constraints, (2) broken equivariance under coordinate transformations, and (3) non-geodesic trajectories with excessive kinematic cost. We introduce $\textbf{Lie Diffuser Actor (LDA)}$, a diffusion framework operating intrinsically on SE(3). Our method injects noise through left-invariant SDEs, predicts scores in the tangent space, and retracts samples via the exponential map. This formulation eliminates manifold drift by construction while guaranteeing coordinate-frame equivariance and geodesic optimality. On CALVIN ABC$\rightarrow$D, LDA improves average task length from $3.27$ to $3.51$ ($+7.3\%$). We further validate our method on real robot and the results show that our methodology outperforms the baseline on majority tasks.