Intensity,as defined in the classical temporal point process(TPP) sense, can be interpreted as the expected number of eventsz z0 withinthetimeinterval[t,t+dt].

State preparation is a cornerstone of quantum technologies, underpinning applications in computation, communication, and sensing. Its importance becomes even more pronounced in non-Markovian open quantum systems, where environmental memory and model uncertainties pose significant challenges to achieving high-fidelity control. Invariant-based inverse engineering provides a principled framework for synthesizing analytic control fields, yet existing parameterizations often lead to experimentally infeasible, singular pulses and are limited to simplified noise models such as those of Lindblad form. Here, we introduce a generalized invariant-based protocol for single-qubit state preparation under arbitrary noise conditions. The control proceeds in two-stages: first, we construct a family of bounded pulses that achieve perfect state preparation in a closed system; second, we identify the optimal member of this family that minimizes the effect of noise. The framework accommodates both (i) characterized noise, enabling noise-aware control synthesis, and (ii) uncharacterized noise, where a noise-agnostic variant preserves robustness without requiring a master-equation description. Numerical simulations demonstrate high-fidelity state preparation across diverse targets while producing smooth, hardware-feasible control fields. This singularity-free framework extends invariant-based control to realistic open-system regimes, providing a versatile route toward robust quantum state engineering on NISQ hardware and other platforms exhibiting non-Markovian dynamics.

Long-term trajectory anomaly detection is a challenging problem due to the diversity and complex spatiotemporal dependencies in trajectory data. Existing trajectory anomaly detection methods fail to simultaneously consider both the high-level intentions of agents as well as the low-level details of the agent's navigation when analysing an agent's trajectories. This limits their ability to capture the full diversity of normal trajectories. In this paper, we propose an unsupervised trajectory anomaly detection method named Intention-aware Hierarchical Diffusion model (IHiD), which detects anomalies through both high-level intent evaluation and low-level sub-trajectory analysis. Our approach leverages Inverse Q Learning as the high-level model to assess whether a selected subgoal aligns with an agent's intention based on predicted Q-values. Meanwhile, a diffusion model serves as the low-level model to generate sub-trajectories conditioned on subgoal information, with anomaly detection based on reconstruction error. By integrating both models, IHiD effectively utilises subgoal transition knowledge and is designed to capture the diverse distribution of normal trajectories. Our experiments show that the proposed method IHiD achieves up to 30.2% improvement in anomaly detection performance in terms of F1 score over state-of-the-art baselines.

In recent months, substantial progress has been made in complex reasoning of Large Language Models, particularly through the application of test-time scaling. Notable examples include o1/o3/o4 series and DeepSeek-R1. When responding to a query, these models generate an extended reasoning trajectory, during which the model explores, reflects, backtracks, and self-verifies before arriving at a conclusion. However, fine-tuning models with such reasoning trajectories may not always be optimal. Our findings indicate that not all components within these reasoning trajectories contribute positively to the reasoning process; in fact, some components may affect the overall performance negatively. In this study, we divide a reasoning trajectory into individual subtrajectories and develop a "5+2" framework to: (1) systematically identify suboptimal subtrajectories within the reasoning trajectory based on five human-established criteria; (2) assess the independence of the suboptimal subtrajectories identified in (1) from the subsequent content, ensuring that their elimination does not compromise overall flow and coherence of the reasoning process. Additionally, a sampling algorithm, built upon the "5+2" framework, is employed to select data whose reasoning process is free from suboptimal subtrajectories to the highest degree. Experimental results demonstrate that our method can reduce the number of suboptimal subtrajectories by 25.9\% during the inference. Furthermore, our method achieves an average accuracy of 58.92\% on highly challenging math benchmarks with only two thirds of training data, surpassing the average accuracy of 58.06\% achieved with the entire data, and outperforming open-source datasets, when fine-tuning Qwen2.5-Math-7B. Finally, We validated our method under resource constraints and observed improved performance across various inference token limits.

An effective approach for sampling from unnormalized densities is based on the idea of gradually transporting samples from an easy prior to the complicated target distribution. Two popular methods are (1) Sequential Monte Carlo (SMC), where the transport is performed through successive annealed densities via prescribed Markov chains and resampling steps, and (2) recently developed diffusion-based sampling methods, where a learned dynamical transport is used. Despite the common goal, both approaches have different, often complementary, advantages and drawbacks. The resampling steps in SMC allow focusing on promising regions of the space, often leading to robust performance. While the algorithm enjoys asymptotic guarantees, the lack of flexible, learnable transitions can lead to slow convergence. On the other hand, diffusion-based samplers are learned and can potentially better adapt themselves to the target at hand, yet often suffer from training instabilities. In this work, we present a principled framework for combining SMC with diffusion-based samplers by viewing both methods in continuous time and considering measures on path space. This culminates in the new Sequential Controlled Langevin Diffusion (SCLD) sampling method, which is able to utilize the benefits of both methods and reaches improved performance on multiple benchmark problems, in many cases using only 10% of the training budget of previous diffusion-based samplers.

While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at achieving explainable AI, namely the Gradient-weighted Class Activation Map (Grad-CAM), to investigate how deep learning (implemented by ResNets) recognizes the distinctive features of a particular anomalous diffusion model from the raw trajectory data. Our results show that Grad-CAM reveals the portions of the trajectory that hold crucial information about the underlying mechanism of anomalous diffusion, which can be utilized to enhance the robustness of the trained classifier against the measurement noise. Moreover, we observe that deep learning distills unique statistical characteristics of different diffusion mechanisms at various spatiotemporal scales, with larger-scale (smaller-scale) features identified at higher (lower) layers.

Offline Reinforcement Learning (Offline RL) presents challenges of learning effective decision-making policies from static datasets without any online interactions. Data augmentation techniques, such as noise injection and data synthesizing, aim to improve Q-function approximation by smoothing the learned state-action region. However, these methods often fall short of directly improving the quality of offline datasets, leading to suboptimal results. In response, we introduce \textbf{GTA}, Generative Trajectory Augmentation, a novel generative data augmentation approach designed to enrich offline data by augmenting trajectories to be both high-rewarding and dynamically plausible. GTA applies a diffusion model within the data augmentation framework. GTA partially noises original trajectories and then denoises them with classifier-free guidance via conditioning on amplified return value. Our results show that GTA, as a general data augmentation strategy, enhances the performance of widely used offline RL algorithms in both dense and sparse reward settings. Furthermore, we conduct a quality analysis of data augmented by GTA and demonstrate that GTA improves the quality of the data. Our code is available at https://github.com/Jaewoopudding/GTA

In the context of imitation learning applied to dexterous robotic hands, the high complexity of the systems makes learning complex manipulation tasks challenging. However, the numerous datasets depicting human hands in various different tasks could provide us with better knowledge regarding human hand motion. We propose a method to leverage multiple large-scale task-agnostic datasets to obtain latent representations that effectively encode motion subtrajectories that we included in a transformer-based behavior cloning method. Our results demonstrate that employing latent representations yields enhanced performance compared to conventional behavior cloning methods, particularly regarding resilience to errors and noise in perception and proprioception. Furthermore, the proposed approach solely relies on human demonstrations, eliminating the need for teleoperation and, therefore, accelerating the data acquisition process. Accurate inverse kinematics for fingertip retargeting ensures precise transfer from human hand data to the robot, facilitating effective learning and deployment of manipulation policies. Finally, the trained policies have been successfully transferred to a real-world 23Dof robotic system.