Daily Papers

Aligning generative flow models on continuous spaces via online reinforcement learning is constrained by intractable trajectory likelihoods. Existing density-approximated policy gradient methods rely on stochastic SDE samplers to construct tractable transition kernels, which introduce training-inference inconsistencies and necessitates Classifier-Free Guidance (CFG). While implicit frameworks such as DiffusionNFT directly optimize forward-process velocity fields, its heuristic fixed-magnitude corrections prevent optimization strength from relative intra-group quality. We propose Flow Advantage-Weighted Rectification (FlowAWR), a paradigm that recasts continuous generative policy optimization as supervised regression toward a theoretically optimal velocity field. Starting from the optimal policy of a KL-constrained reward maximization, FlowAWR derives the optimal velocity field that admits a magnitude-aware, advantage-weighted rectification form, yielding SDE-free optimization and CFG-free generation. In comparative evaluations on SD3.5-Medium, FlowAWR achieves improved alignment performance alongside a 2times to 5times convergence acceleration over DiffusionNFT (e.g., reaching a 24.12 PickScore in 1.2k steps, versus 23.82 in 2.0k steps for DiffusionNFT and 23.50 in >4k steps for FlowGRPO). Under multi-reward constraints, FlowAWR sustains generation quality, satisfying structural rules while maintaining stable out-of-domain performance.

Exploration is essential in modern learning, from reinforcement learning environments with small neural policies to large language models (LLMs). Existing work, such as DPO, leverages full sequence log-likelihoods to capture an entire trajectory of the model's decisions, while methods like GRPO aggregate per-token ratios into a trajectory-level update. However, both often limit exploration on long-horizon tasks. We introduce History-Aggregated Exploratory Policy Optimization (HAEPO), a history-aware exploratory loss to combat these shortcomings. HAEPO compresses each trajectory into the sum of its logarithmic probabilities (a cumulative logarithmic likelihood), and applies a Plackett-Luce softmax across trajectories to obtain normalized weights proportional to their returns, thus encouraging broader exploration. We add entropy regularization to stabilize the aggressive updates to prevent premature collapse and a soft KL penalty relative to a frozen copy of the previous (reference) policy. Empirically, HAEPO converges fast, explores thoroughly, aligns closely with true rewards, and demonstrates robust learning behavior better or at par with PPO, GRPO, and DPO across diverse tasks. Thus, HAEPO provides a stable and interpretable framework by explicitly leveraging full-trajectory history while balancing exploration and stability.

Specialist epilepsy expertise is scarce in resource-constrained settings, making LLM-based decision support attractive for frontline clinicians managing longitudinal treatment. Such systems must adapt to local prescribing practice and know when to defer. We study this problem in Ugandan pediatric epilepsy care, predicting anti-seizure medication regimens from longitudinal unstructured clinic notes. Standard prompting achieves non-trivial agreement with physician prescriptions, but neurologist review shows that many errors reflect distribution-miscalibrated prescribing defaults rather than failures to parse the local record. We introduce MANANA, a non-parametric prompt-learning framework that learns local prescribing guidance from a small patient-level training set. MANANA converts observed prescription errors into auditable prompt memories, instantiated in single-agent and multi-agent variants, and improves over classical ML models, direct LLM prompting, and prompt-optimization baselines across two independently collected Ugandan cohorts. We further propose Bayesian prompt averaging, which converts the learned prompt trajectory into prescription likelihoods and an uncertainty-based deferral signal. On the independently collected held-out cohort, this improves visit-level top-3 prescription accuracy by 4-8 percentage points over prompt-optimization baselines and enables selective prediction: the system can auto-handle the most confident half of cases at 95% precision, or the most confident quarter at 99% precision, while deferring lower-confidence cases for specialist review.

Closed-loop cooperative driving requires planners that generate realistic multimodal multi-agent trajectories while improving safety and traffic efficiency. Existing diffusion planners can model multimodal behaviors from demonstrations, but they often exhibit weak scene consistency and remain poorly aligned with closed-loop objectives; meanwhile, stable online post-training in reactive multi-agent environments remains difficult. We present Multi-ORFT, which couples scene-conditioned diffusion pre-training with stable online reinforcement post-training. In pre-training, the planner uses inter-agent self-attention, cross-attention, and AdaLN-Zero-based scene conditioning to improve scene consistency and road adherence of joint trajectories. In post-training, we formulate a two-level MDP that exposes step-wise reverse-kernel likelihoods for online optimization, and combine dense trajectory-level rewards with variance-gated group-relative policy optimization (VG-GRPO) to stabilize training. On the WOMD closed-loop benchmark, Multi-ORFT reduces collision rate from 2.04% to 1.89% and off-road rate from 1.68% to 1.36%, while increasing average speed from 8.36 to 8.61 m/s relative to the pre-trained planner, and it outperforms strong open-source baselines including SMART-large, SMART-tiny-CLSFT, and VBD on the primary safety and efficiency metrics. These results show that coupling scene-consistent denoising with stable online diffusion-policy optimization improves the reliability of closed-loop cooperative driving.

Reinforcement learning (RL) post-training has shown to improve reasoning in large language models (LLMs). However, there has been little exploration on the problem of data contamination in RL post-training, potentially undermining generalization and evaluation reliability of the training process itself. Existing detection methods primarily rely on output-level signals such as likelihood or entropy, which become unreliable for RL-trained models since RL shapes behavior through trajectory-level rewards rather than token likelihoods. We propose LaRA, a layer-wise representation analysis framework for detecting contamination in RL post-trained LLMs. LaRA introduces three complementary metrics, measuring perturbation sensitivity, directional collapse, and local representation rigidity under controlled perturbations. We find that contamination produces progressive geometric deviations across layers, including amplified perturbation sensitivity, stronger directional collapse, and enhanced local rigidity. Based on our findings, we also develop a contamination detection protocol that aggregates representation-level deviations across layers and metrics. Experiments on RL-trained reasoning models show that our protocol outperforms existing output-level baselines for contamination detection.

Diffusion-based models decompose sampling into many small Gaussian denoising steps -- an assumption that breaks down when generation is compressed to a few coarse transitions. Existing few-step methods address this through distillation, consistency training, or adversarial objectives, but sacrifice the likelihood framework in the process. We introduce Normalizing Trajectory Models (NTM), which models each reverse step as an expressive conditional normalizing flow with exact likelihood training. Architecturally, NTM combines shallow invertible blocks within each step with a deep parallel predictor across the trajectory, forming an end-to-end network trainable from scratch or initializable from pretrained flow-matching models. Its exact trajectory likelihood further enables self-distillation: a lightweight denoiser trained on the model's own score produces high-quality samples in four steps. On text-to-image benchmarks, NTM matches or outperforms strong image generation baselines in just four sampling steps while uniquely retaining exact likelihood over the generative trajectory.

Test-time scaling improves language-model reasoning, but existing approaches often face a difficult trade-off: long chain-of-thought sampling remains single-threaded, while sentence- or solution-level search can be computationally expensive and hard to train end-to-end. We introduce Local Branch Routing (LBR), a token-level test-time scaling framework that expands a small local lookahead tree, forwards all sampled branches through the language model, and uses a lightweight router to select the depth-1 subtree to commit. By routing over the hidden states of candidate local futures, LBR allows each token decision to use evidence beyond the root next-token distribution while avoiding full solution-level search. The resulting prune-shift-grow decoding process preserves discrete branch identities and defines a tractable tree-trajectory likelihood: newly grown nodes are counted when first sampled, and router decisions are assigned explicit probabilities. This enables end-to-end reinforcement learning with verifiable rewards, jointly optimizing the base model and router under the same likelihood-ratio principle as discrete-token RLVR. On synthetic hierarchical-planning tasks, LBR shows that post-candidate hidden states provide useful routing evidence. On mathematical reasoning benchmarks, LBR improves both Pass@1 and Pass@32 over discrete chain-of-thought, vanilla discrete-token RLVR, and RL-compatible soft-token branching baselines. These results suggest that lightweight local branching offers an efficient, trainable, and discrete form of language-model test-time scaling.

The field of trajectory forecasting has grown significantly in recent years, partially owing to the release of numerous large-scale, real-world human trajectory datasets for autonomous vehicles (AVs) and pedestrian motion tracking. While such datasets have been a boon for the community, they each use custom and unique data formats and APIs, making it cumbersome for researchers to train and evaluate methods across multiple datasets. To remedy this, we present trajdata: a unified interface to multiple human trajectory datasets. At its core, trajdata provides a simple, uniform, and efficient representation and API for trajectory and map data. As a demonstration of its capabilities, in this work we conduct a comprehensive empirical evaluation of existing trajectory datasets, providing users with a rich understanding of the data underpinning much of current pedestrian and AV motion forecasting research, and proposing suggestions for future datasets from these insights. trajdata is permissively licensed (Apache 2.0) and can be accessed online at https://github.com/NVlabs/trajdata

Long chain-of-thought (CoT) trajectories provide rich supervision signals for distilling reasoning from teacher to student LLMs. However, both prior work and our experiments show that trajectories from stronger teachers do not necessarily yield better students, highlighting the importance of data-student suitability in distillation. Existing methods assess suitability primarily through student likelihood, favoring trajectories that closely align with the model's current behavior but overlooking more informative ones. Addressing this, we propose Rank-Surprisal Ratio (RSR), a simple metric that captures both alignment and informativeness to assess the suitability of a reasoning trajectory. RSR is motivated by the observation that effective trajectories typically combine low absolute probability with relatively high-ranked tokens under the student model, balancing learning signal strength and behavioral alignment. Concretely, RSR is defined as the ratio of a trajectory's average token-wise rank to its average negative log-likelihood, and is straightforward to compute and interpret. Across five student models and reasoning trajectories from 11 diverse teachers, RSR strongly correlates with post-training performance (average Spearman 0.86), outperforming existing metrics. We further demonstrate its practical utility in both trajectory selection and teacher selection.

Smartphones and smartwatches are ever-present in daily life, and provide a rich source of information on their users' behaviour. In particular, digital traces derived from the phone's embedded movement sensors present an opportunity for a forensic investigator to gain insight into a person's physical activities. In this work, we present a machine learning-based approach to translate digital traces into likelihood ratios (LRs) for different types of physical activities. Evaluating on a new dataset, NFI\_FARED, which contains digital traces from four different types of iPhones labelled with 19 activities, it was found that our approach could produce useful LR systems to distinguish 167 out of a possible 171 activity pairings. The same approach was extended to analyse likelihoods for multiple activities (or groups of activities) simultaneously and create activity timelines to aid in both the early and latter stages of forensic investigations. The dataset and all code required to replicate the results have also been made public to encourage further research on this topic.

Recent work finds that retrieval-augmented generation with large language models is prone to be influenced by the order of retrieved documents in the context. However, the lack of in-depth analysis limits the use of this phenomenon for prompt engineering in practice. In this study, we posit that likelihoods serve as an effective gauge for language model performance. Through experiments on two question-answering datasets with a variety of state-of-the-art language models, we reveal correlations between answer accuracy and the likelihood of the question at both the corpus level and the instance level. In addition, we find that question likelihood can also indicate the position of the task-relevant information in the context. Based on these findings, we propose two methods that use question likelihood as a gauge for selecting and constructing prompts that lead to better performance. We demonstrate their effectiveness with experiments. In addition, our likelihood-based methods are efficient, as they only need to compute the likelihood of the input, requiring much fewer language model passes than heuristic prompt engineering methods that require generating responses. Our analysis deepens our understanding of how input prompts affect model performance and provides a promising direction for efficient prompt optimization.

In trajectory forecasting tasks for traffic, future output trajectories can be computed by advancing the ego vehicle's state with predicted actions according to a kinematics model. By unrolling predicted trajectories via time integration and models of kinematic dynamics, predicted trajectories should not only be kinematically feasible but also relate uncertainty from one timestep to the next. While current works in probabilistic prediction do incorporate kinematic priors for mean trajectory prediction, variance is often left as a learnable parameter, despite uncertainty in one time step being inextricably tied to uncertainty in the previous time step. In this paper, we show simple and differentiable analytical approximations describing the relationship between variance at one timestep and that at the next with the kinematic bicycle model. These approximations can be easily incorporated with negligible additional overhead into any existing trajectory forecasting framework utilizing probabilistic predictions, whether it is autoregressive or one-shot prediction. In our results, we find that encoding the relationship between variance across timesteps works especially well in unoptimal settings, such as with small or noisy datasets. We observe up to a 50% performance boost in partial dataset settings and up to an 8% performance boost in large-scale learning compared to previous kinematic prediction methods on SOTA trajectory forecasting architectures out-of-the-box, with no fine-tuning. In this paper, we show four analytical formulations of probabilistic kinematic priors which can be used for any Gaussian Mixture Model (GMM)-based deep learning models, quantify the error bound on linear approximations applied during trajectory unrolling, and show results to evaluate each formulation in trajectory forecasting.

Tool-integrated (TI) reinforcement learning (RL) enables large language models (LLMs) to perform multi-step reasoning by interacting with external tools such as search engines and retrievers. Group Relative Policy Optimization (GRPO), exemplified by the recent Search-R1, offers fast convergence and a value-free formulation that makes it appealing for this setting, yet consistently suffers from training collapse. We identify Lazy Likelihood Displacement (LLD), a systematic reduction or stagnation in the likelihood of both correct and incorrect responses, as the core mechanism driving this failure. LLD emerges early and triggers a self-reinforcing LLD Death Spiral, where declining likelihood leads to low-confidence responses, inflating gradients, and ultimately causing collapse. We empirically characterize this process across models on a Search-R1-style, search-integrated question answering task, revealing a consistent three-phase trajectory: early stagnation, steady decay, and accelerated collapse. To address this, we propose a lightweight likelihood-preserving regularization LLDS for GRPO that activates only when a trajectory's likelihood decreases, and regularizes only the tokens responsible. This fine-grained structure mitigates LLD with minimal interference to optimization. Across seven open-domain and multi-hop QA benchmarks, our method stabilizes training, prevents gradient explosion, and yields substantial performance improvements, including +37.8% gains on Qwen2.5-3B and +32.0% gains on Qwen2.5-7B. Our results establish LLD as a fundamental bottleneck in GRPO-based TIRL and provide a practical path toward stable, scalable training of tool-integrated LLM.

Urban mobility is naturally expressed both as trajectories in space and as natural-language descriptions of travel intent, constraints, and preferences. However, prior work rarely evaluates these two modalities together on the same real-world trajectories: trajectory modeling often stays geometry-centric, while language-centric mobility benchmarks frequently target route planning and tool use rather than fine-grained, verifiable alignment between text and the underlying route. We introduce TrajPrism, a multi-task benchmark for language-trajectory alignment that unifies (i) instruction-conditioned trajectory generation, (ii) language-driven semantic trajectory retrieval, and (iii) trajectory captioning, together with an evaluation protocol that measures trajectory fidelity, retrieval quality, and language groundedness. We construct TrajPrism by pairing real urban trajectories with judge-filtered language annotations generated under a four-dimensional travel-intent taxonomy. The benchmark contains 300K selected trajectories across Porto, San Francisco, and Beijing, yielding 2.1M task instances from three instruction variants, three retrieval queries, and one caption per trajectory. We further develop proof-of-concept models for each task: TrajAnchor for instruction-conditioned trajectory generation, TrajFuse for semantic trajectory retrieval, and TrajRap for trajectory captioning. These models instantiate the proposed tasks and show that geometry-only trajectory baselines leave a large gap on our protocol, especially where language is part of the input-output interface. We release TrajPrism with code and a reproducible annotation pipeline that is designed to be portable across cities, given compatible trajectory inputs and map resources.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

User profiling and region analysis are two tasks of significant commercial value. However, in practical applications, modeling different features typically involves four main steps: data preparation, data processing, model establishment, evaluation, and optimization. This process is time-consuming and labor-intensive. Repeating this workflow for each feature results in abundant development time for tasks and a reduced overall volume of task development. Indeed, human mobility data contains a wealth of information. Several successful cases suggest that conducting in-depth analysis of population movement data could potentially yield meaningful profiles about users and areas. Nonetheless, most related works have not thoroughly utilized the semantic information within human mobility data and trained on a fixed number of the regions. To tap into the rich information within population movement, based on the perspective that Regions Are Who walk them, we propose a large spatiotemporal model based on trajectories (RAW). It possesses the following characteristics: 1) Tailored for trajectory data, introducing a GPT-like structure with a parameter count of up to 1B; 2) Introducing a spatiotemporal fine-tuning module, interpreting trajectories as collection of users to derive arbitrary region embedding. This framework allows rapid task development based on the large spatiotemporal model. We conducted extensive experiments to validate the effectiveness of our proposed large spatiotemporal model. It's evident that our proposed method, relying solely on human mobility data without additional features, exhibits a certain level of relevance in user profiling and region analysis. Moreover, our model showcases promising predictive capabilities in trajectory generation tasks based on the current state, offering the potential for further innovative work utilizing this large spatiotemporal model.

Capturing high-dimensional social interactions and feasible futures is essential for predicting trajectories. To address this complex nature, several attempts have been devoted to reducing the dimensionality of the output variables via parametric curve fitting such as the B\'ezier curve and B-spline function. However, these functions, which originate in computer graphics fields, are not suitable to account for socially acceptable human dynamics. In this paper, we present EigenTrajectory (ET), a trajectory prediction approach that uses a novel trajectory descriptor to form a compact space, known here as ET space, in place of Euclidean space, for representing pedestrian movements. We first reduce the complexity of the trajectory descriptor via a low-rank approximation. We transform the pedestrians' history paths into our ET space represented by spatio-temporal principle components, and feed them into off-the-shelf trajectory forecasting models. The inputs and outputs of the models as well as social interactions are all gathered and aggregated in the corresponding ET space. Lastly, we propose a trajectory anchor-based refinement method to cover all possible futures in the proposed ET space. Extensive experiments demonstrate that our EigenTrajectory predictor can significantly improve both the prediction accuracy and reliability of existing trajectory forecasting models on public benchmarks, indicating that the proposed descriptor is suited to represent pedestrian behaviors. Code is publicly available at https://github.com/inhwanbae/EigenTrajectory .

Recent advances in large language models (LLMs) have sparked growing interest in integrating language-driven techniques into trajectory prediction. By leveraging their semantic and reasoning capabilities, LLMs are reshaping how autonomous systems perceive, model, and predict trajectories. This survey provides a comprehensive overview of this emerging field, categorizing recent work into five directions: (1) Trajectory prediction via language modeling paradigms, (2) Direct trajectory prediction with pretrained language models, (3) Language-guided scene understanding for trajectory prediction, (4) Language-driven data generation for trajectory prediction, (5) Language-based reasoning and interpretability for trajectory prediction. For each, we analyze representative methods, highlight core design choices, and identify open challenges. This survey bridges natural language processing and trajectory prediction, offering a unified perspective on how language can enrich trajectory prediction.

We consider the inverse problem of reconstructing the spatial layout of a place, a home floorplan for example, from a user`s movements inside that layout. Direct inversion is ill-posed since many floorplans can explain the same movement trajectories. We adopt a diffusion-based posterior sampler to generate layouts consistent with the measurements. While active research is in progress on generative inverse solvers, we find that the forward operator in our problem poses new challenges. The path-planning process inside a floorplan is a non-invertible, non-differentiable function, and causes instability while optimizing using the likelihood score. We break-away from existing approaches and reformulate the likelihood score in a smoother embedding space. The embedding space is trained with a contrastive loss which brings compatible floorplans and trajectories close to each other, while pushing mismatched pairs far apart. We show that a surrogate form of the likelihood score in this embedding space is a valid approximation of the true likelihood score, making it possible to steer the denoising process towards the posterior. Across extensive experiments, our model CoGuide produces more consistent floorplans from trajectories, and is more robust than differentiable-planner baselines and guided-diffusion methods.

Understanding uncertainty in chain-of-thought reasoning is critical for reliable deployment of large language models. In this work, we propose a simple yet effective diagnostic approach based on trajectory shape rather than scalar magnitude. We show that this signal is practical, interpretable, and inexpensive to obtain in black-box settings, while remaining robust across models and datasets. Through extensive ablations and cross-domain replications, we demonstrate its utility for selective prediction and triage. Our findings offer a generalizable insight into uncertainty dynamics in reasoning tasks, with particular focus on numeric and discrete-answer settings.

We propose to extract meaning representations from autoregressive language models by considering the distribution of all possible trajectories extending an input text. This strategy is prompt-free, does not require fine-tuning, and is applicable to any pre-trained autoregressive model. Moreover, unlike vector-based representations, distribution-based representations can also model asymmetric relations (e.g., direction of logical entailment, hypernym/hyponym relations) by using algebraic operations between likelihood functions. These ideas are grounded in distributional perspectives on semantics and are connected to standard constructions in automata theory, but to our knowledge they have not been applied to modern language models. We empirically show that the representations obtained from large models align well with human annotations, outperform other zero-shot and prompt-free methods on semantic similarity tasks, and can be used to solve more complex entailment and containment tasks that standard embeddings cannot handle. Finally, we extend our method to represent data from different modalities (e.g., image and text) using multimodal autoregressive models. Our code is available at: https://github.com/tianyu139/meaning-as-trajectories

In reasoning about sequential events it is natural to pose probabilistic queries such as "when will event A occur next" or "what is the probability of A occurring before B", with applications in areas such as user modeling, medicine, and finance. However, with machine learning shifting towards neural autoregressive models such as RNNs and transformers, probabilistic querying has been largely restricted to simple cases such as next-event prediction. This is in part due to the fact that future querying involves marginalization over large path spaces, which is not straightforward to do efficiently in such models. In this paper we introduce a general typology for predictive queries in neural autoregressive sequence models and show that such queries can be systematically represented by sets of elementary building blocks. We leverage this typology to develop new query estimation methods based on beam search, importance sampling, and hybrids. Across four large-scale sequence datasets from different application domains, as well as for the GPT-2 language model, we demonstrate the ability to make query answering tractable for arbitrary queries in exponentially-large predictive path-spaces, and find clear differences in cost-accuracy tradeoffs between search and sampling methods.

Next point-of-interest (POI) recommendation predicts a user's next destination from historical movements. Traditional models require intensive training, while LLMs offer flexible and generalizable zero-shot solutions but often generate generic or geographically irrelevant results due to missing trajectory and spatial context. To address these issues, we propose RALLM-POI, a framework that couples LLMs with retrieval-augmented generation and self-rectification. We first propose a Historical Trajectory Retriever (HTR) that retrieves relevant past trajectories to serve as contextual references, which are then reranked by a Geographical Distance Reranker (GDR) for prioritizing spatially relevant trajectories. Lastly, an Agentic LLM Rectifier (ALR) is designed to refine outputs through self-reflection. Without additional training, RALLM-POI achieves substantial accuracy gains across three real-world Foursquare datasets, outperforming both conventional and LLM-based baselines. Code is released at https://github.com/LKRcrocodile/RALLM-POI.

Large Reasoning Models (LRMs) introduce new opportunities for safety monitoring through their Chain of Thought (CoT) reasoning. However, CoT is not always faithful to the model's final output, undermining its reliability as a monitoring tool. To address this, we investigate the hidden representations of LRMs to determine whether future behavior can be predicted from prompt and CoT representations. By evaluating a probe at each generated token, we construct a probe trajectory, the continuous evolution of a concept's probability across the reasoning process. We find that future model behavior is more distinguishable when examined over the full trajectory than from a single static prediction. To characterize these temporal dynamics, we extract signal-processing features that capture volatility, trend, and steady-state behavior, significantly improving the separation of future model states. We also present two methodological insights. First, template-based training data achieves near-parity with dynamically generated model responses, eliminating the need for a costly initial inference and labeling. Second, the choice of pooling operation is critical: average-pooling and last-token methods collapse to near-random performance, while max-pooling achieves up to 95% AUROC and yields stable probe trajectories. Using four datasets and four reasoning models across the domains of safety and mathematics, we demonstrate that trajectory features encode task-specific dynamics that improve outcome separability. These findings establish probe trajectories as a complementary framework for monitoring LRM behavior. Warning: This article contains potentially harmful content.

This work investigates the reproducibility of the paper 'Explaining RL decisions with trajectories'. The original paper introduces a novel approach in explainable reinforcement learning based on the attribution decisions of an agent to specific clusters of trajectories encountered during training. We verify the main claims from the paper, which state that (i) training on less trajectories induces a lower initial state value, (ii) trajectories in a cluster present similar high-level patterns, (iii) distant trajectories influence the decision of an agent, and (iv) humans correctly identify the attributed trajectories to the decision of the agent. We recover the environments used by the authors based on the partial original code they provided for one of the environments (Grid-World), and implemented the remaining from scratch (Seaquest, HalfCheetah, Breakout and Q*Bert). While we confirm that (i), (ii), and (iii) partially hold, we extend on the largely qualitative experiments from the authors by introducing a quantitative metric to further support (iii), and new experiments and visual results for (i). Moreover, we investigate the use of different clustering algorithms and encoder architectures to further support (ii). We could not support (iv), given the limited extent of the original experiments. We conclude that, while some of the claims can be supported, further investigations and experiments could be of interest. We recognise the novelty of the work from the authors and hope that our work paves the way for clearer and more transparent approaches.

Real-world data deviating from the independent and identically distributed (i.i.d.) assumption of in-distribution training data poses security threats to deep networks, thus advancing out-of-distribution (OOD) detection algorithms. Detection methods in generative language models (GLMs) mainly focus on uncertainty estimation and embedding distance measurement, with the latter proven to be most effective in traditional linguistic tasks like summarization and translation. However, another complex generative scenario mathematical reasoning poses significant challenges to embedding-based methods due to its high-density feature of output spaces, but this feature causes larger discrepancies in the embedding shift trajectory between different samples in latent spaces. Hence, we propose a trajectory-based method TV score, which uses trajectory volatility for OOD detection in mathematical reasoning. Experiments show that our method outperforms all traditional algorithms on GLMs under mathematical reasoning scenarios and can be extended to more applications with high-density features in output spaces, such as multiple-choice questions.

Trajectory data, capturing human actions and environmental states across various modalities, holds significant potential for enhancing AI agent capabilities, particularly in GUI environments. However, how to model the representation of trajectory-level data presents a significant challenge that has not been systematically addressed amid explosive trajectory data growth. In this work, we introduce Multimodal Trajectory Retrieval, bridging the gap between universal retrieval and agent-centric trajectory modeling. We construct the Unified Agent Trajectory Dataset (UATD) from annotated demonstrations and states across diverse real-world scenarios. Based on this, we present GAE-Bench, a benchmark containing a large number of trajectory-based retrieval pairs. In addition, we propose GAE-Retriever, a multimodal retrieval framework that adopts vision-language models and incorporates optimized contrastive learning through a token selection and the GradCache mechanism. Comprehensive evaluations across multiple datasets show that GAE-Retriever consistently outperforms strong baselines in retrieval recall, highlighting its effectiveness in advancing multimodal trajectory retrieval.

There are five types of trajectory prediction tasks: deterministic, stochastic, domain adaptation, momentary observation, and few-shot. These associated tasks are defined by various factors, such as the length of input paths, data split and pre-processing methods. Interestingly, even though they commonly take sequential coordinates of observations as input and infer future paths in the same coordinates as output, designing specialized architectures for each task is still necessary. For the other task, generality issues can lead to sub-optimal performances. In this paper, we propose SingularTrajectory, a diffusion-based universal trajectory prediction framework to reduce the performance gap across the five tasks. The core of SingularTrajectory is to unify a variety of human dynamics representations on the associated tasks. To do this, we first build a Singular space to project all types of motion patterns from each task into one embedding space. We next propose an adaptive anchor working in the Singular space. Unlike traditional fixed anchor methods that sometimes yield unacceptable paths, our adaptive anchor enables correct anchors, which are put into a wrong location, based on a traversability map. Finally, we adopt a diffusion-based predictor to further enhance the prototype paths using a cascaded denoising process. Our unified framework ensures the generality across various benchmark settings such as input modality, and trajectory lengths. Extensive experiments on five public benchmarks demonstrate that SingularTrajectory substantially outperforms existing models, highlighting its effectiveness in estimating general dynamics of human movements. Code is publicly available at https://github.com/inhwanbae/SingularTrajectory .

In this paper, we address the problem of human trajectory forecasting, which aims to predict the inherently multi-modal future movements of humans based on their past trajectories and other contextual cues. We propose a novel motion prediction conditional flow matching model, termed MoFlow, to predict K-shot future trajectories for all agents in a given scene. We design a novel flow matching loss function that not only ensures at least one of the K sets of future trajectories is accurate but also encourages all K sets of future trajectories to be diverse and plausible. Furthermore, by leveraging the implicit maximum likelihood estimation (IMLE), we propose a novel distillation method for flow models that only requires samples from the teacher model. Extensive experiments on the real-world datasets, including SportVU NBA games, ETH-UCY, and SDD, demonstrate that both our teacher flow model and the IMLE-distilled student model achieve state-of-the-art performance. These models can generate diverse trajectories that are physically and socially plausible. Moreover, our one-step student model is 100 times faster than the teacher flow model during sampling. The code, model, and data are available at our project page: https://moflow-imle.github.io

In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the co-Kleisli category under the comonad (Omega x -) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identity-on-objects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood

Accumulating substantial volumes of real-world driving data proves pivotal in the realm of trajectory forecasting for autonomous driving. Given the heavy reliance of current trajectory forecasting models on data-driven methodologies, we aim to tackle the challenge of learning general trajectory forecasting representations under limited data availability. We propose a pipeline-level solution to mitigate the issue of data scarcity in trajectory forecasting. The solution is composed of two parts: firstly, we adopt HD map augmentation and trajectory synthesis for generating driving data, and then we learn representations by pre-training on them. Specifically, we apply vector transformations to reshape the maps, and then employ a rule-based model to generate trajectories on both original and augmented scenes; thus enlarging the driving data without collecting additional real ones. To foster the learning of general representations within this augmented dataset, we comprehensively explore the different pre-training strategies, including extending the concept of a Masked AutoEncoder (MAE) for trajectory forecasting. Without bells and whistles, our proposed pipeline-level solution is general, simple, yet effective: we conduct extensive experiments to demonstrate the effectiveness of our data expansion and pre-training strategies, which outperform the baseline prediction model by large margins, e.g. 5.04%, 3.84% and 8.30% in terms of MR_6, minADE_6 and minFDE_6. The pre-training dataset and the codes for pre-training and fine-tuning are released at https://github.com/yhli123/Pretraining_on_Synthetic_Driving_Data_for_Trajectory_Prediction.

We introduce a learning-guided motion planning framework that generates seed trajectories using a diffusion model for trajectory optimization. Given a workspace, our method approximates the configuration space (C-space) obstacles through an environment representation consisting of a sparse set of task-related key configurations, which is then used as a conditioning input to the diffusion model. The diffusion model integrates regularization terms that encourage smooth, collision-free trajectories during training, and trajectory optimization refines the generated seed trajectories to correct any colliding segments. Our experimental results demonstrate that high-quality trajectory priors, learned through our C-space-grounded diffusion model, enable the efficient generation of collision-free trajectories in narrow-passage environments, outperforming previous learning- and planning-based baselines. Videos and additional materials can be found on the project page: https://kiwi-sherbet.github.io/PRESTO.

How should future neural reasoning systems implement extended computation? Recursive Reasoning Models (RRMs) offer a promising alternative to autoregressive sequence extension by performing iterative latent-state refinement with shared transition functions. Yet existing RRMs are largely deterministic, following a single latent trajectory and converging to a single prediction. We introduce Generative Recursive reAsoning Models (GRAM), a framework that turns recursive latent reasoning into probabilistic multi-trajectory computation. GRAM models reasoning as a stochastic latent trajectory, enabling multiple hypotheses, alternative solution strategies, and inference-time scaling through both recursive depth and parallel trajectory sampling. This yields a latent-variable generative model supporting conditional reasoning via p_θ(y mid x) and, with fixed or absent inputs, unconditional generation via p_θ(x). Trained with amortized variational inference, GRAM improves over deterministic recurrent and recursive baselines on structured reasoning and multi-solution constraint satisfaction tasks, while demonstrating an unconditional generation capability. https://ahn-ml.github.io/gram-website

In this paper, we propose a third-order, i.e., white-noise-on-jerk, Gaussian Process (GP) Trajectory Representation (TR) framework for continuous-time (CT) motion estimation (ME) tasks. Our framework features a unified trajectory representation that encapsulates the kinematic models of both SO(3)timesR^3 and SE(3) pose representations. This encapsulation strategy allows users to use the same implementation of measurement-based factors for either choice of pose representation, which facilitates experimentation and comparison to achieve the best model for the ME task. In addition, unique to our framework, we derive the kinematic models with the closed-form temporal derivatives of the local variable of SO(3) and SE(3), which so far has only been approximated based on the Taylor expansion in the literature. Our experiments show that these kinematic models can improve the estimation accuracy in high-speed scenarios. All analytical Jacobians of the interpolated states with respect to the support states of the trajectory representation, as well as the motion prior factors, are also provided for accelerated Gauss-Newton (GN) optimization. Our experiments demonstrate the efficacy and efficiency of the framework in various motion estimation tasks such as localization, calibration, and odometry, facilitating fast prototyping for ME researchers. We release the source code for the benefit of the community. Our project is available at https://github.com/brytsknguyen/gptr.

Next Location Prediction is a fundamental task in the study of human mobility, with wide-ranging applications in transportation planning, urban governance, and epidemic forecasting. In practice, when humans attempt to predict the next location in a trajectory, they often visualize the trajectory on a map and reason based on road connectivity and movement trends. However, the vast majority of existing next-location prediction models do not reason over maps in the way that humans do. Fortunately, the recent development of Vision-Language Models (VLMs) has demonstrated strong capabilities in visual perception and even visual reasoning. This opens up a new possibility: by rendering both the road network and trajectory onto an image and leveraging the reasoning abilities of VLMs, we can enable models to perform trajectory inference in a human-like manner. To explore this idea, we first propose a method called Vision-Guided Location Search (VGLS), which evaluates whether a general-purpose VLM is capable of trajectory-based reasoning without modifying any of its internal parameters. Based on insights from the VGLS results, we further propose our main approach: VLMLocPredictor, which is composed of two stages: In the first stage, we design two Supervised Fine-Tuning (SFT) tasks that help the VLM understand road network and trajectory structures and acquire basic reasoning ability on such visual inputs. In the second stage, we introduce Reinforcement Learning from Visual Map Feedback, enabling the model to self-improve its next-location prediction ability through interaction with the environment. Experiments conducted on datasets from four different cities show that our method achieves state-of-the-art (SOTA) performance and exhibits superior cross-city generalization compared to other LLM-based approaches.

We present a novel data-driven simulation environment for modeling traffic in metropolitan street intersections. Using real-world tracking data collected over an extended period of time, we train trajectory forecasting models to learn agent interactions and environmental constraints that are difficult to capture conventionally. Trajectories of new agents are first coarsely generated by sampling from the spatial and temporal generative distributions, then refined using state-of-the-art trajectory forecasting models. The simulation can run either autonomously, or under explicit human control conditioned on the generative distributions. We present the experiments for a variety of model configurations. Under an iterative prediction scheme, the way-point-supervised TrajNet++ model obtained 0.36 Final Displacement Error (FDE) in 20 FPS on an NVIDIA A100 GPU.

Large Language Models achieve next-token prediction by transporting a vectorized piece of text (prompt) across an accompanying embedding space under the action of successive transformer layers. The resulting high-dimensional trajectories realize different contextualization, or 'thinking', steps, and fully determine the output probability distribution. We aim to characterize the statistical properties of ensembles of these 'lines of thought.' We observe that independent trajectories cluster along a low-dimensional, non-Euclidean manifold, and that their path can be well approximated by a stochastic equation with few parameters extracted from data. We find it remarkable that the vast complexity of such large models can be reduced to a much simpler form, and we reflect on implications.

Robust pedestrian trajectory forecasting is crucial to developing safe autonomous vehicles. Although previous works have studied adversarial robustness in the context of trajectory forecasting, some significant issues remain unaddressed. In this work, we try to tackle these crucial problems. Firstly, the previous definitions of robustness in trajectory prediction are ambiguous. We thus provide formal definitions for two kinds of robustness, namely label robustness and pure robustness. Secondly, as previous works fail to consider robustness about all points in a disturbance interval, we utilise a probably approximately correct (PAC) framework for robustness verification. Additionally, this framework can not only identify potential counterexamples, but also provides interpretable analyses of the original methods. Our approach is applied using a prototype tool named TrajPAC. With TrajPAC, we evaluate the robustness of four state-of-the-art trajectory prediction models -- Trajectron++, MemoNet, AgentFormer, and MID -- on trajectories from five scenes of the ETH/UCY dataset and scenes of the Stanford Drone Dataset. Using our framework, we also experimentally study various factors that could influence robustness performance.

Language models have demonstrated impressive ability in context understanding and generative performance. Inspired by the recent success of language foundation models, in this paper, we propose LMTraj (Language-based Multimodal Trajectory predictor), which recasts the trajectory prediction task into a sort of question-answering problem. Departing from traditional numerical regression models, which treat the trajectory coordinate sequence as continuous signals, we consider them as discrete signals like text prompts. Specially, we first transform an input space for the trajectory coordinate into the natural language space. Here, the entire time-series trajectories of pedestrians are converted into a text prompt, and scene images are described as text information through image captioning. The transformed numerical and image data are then wrapped into the question-answering template for use in a language model. Next, to guide the language model in understanding and reasoning high-level knowledge, such as scene context and social relationships between pedestrians, we introduce an auxiliary multi-task question and answering. We then train a numerical tokenizer with the prompt data. We encourage the tokenizer to separate the integer and decimal parts well, and leverage it to capture correlations between the consecutive numbers in the language model. Lastly, we train the language model using the numerical tokenizer and all of the question-answer prompts. Here, we propose a beam-search-based most-likely prediction and a temperature-based multimodal prediction to implement both deterministic and stochastic inferences. Applying our LMTraj, we show that the language-based model can be a powerful pedestrian trajectory predictor, and outperforms existing numerical-based predictor methods. Code is publicly available at https://github.com/inhwanbae/LMTrajectory .

Efficient and accurate motion prediction is crucial for ensuring safety and informed decision-making in autonomous driving, particularly under dynamic real-world conditions that necessitate multi-modal forecasts. We introduce TrajFlow, a novel flow matching-based motion prediction framework that addresses the scalability and efficiency challenges of existing generative trajectory prediction methods. Unlike conventional generative approaches that employ i.i.d. sampling and require multiple inference passes to capture diverse outcomes, TrajFlow predicts multiple plausible future trajectories in a single pass, significantly reducing computational overhead while maintaining coherence across predictions. Moreover, we propose a ranking loss based on the Plackett-Luce distribution to improve uncertainty estimation of predicted trajectories. Additionally, we design a self-conditioning training technique that reuses the model's own predictions to construct noisy inputs during a second forward pass, thereby improving generalization and accelerating inference. Extensive experiments on the large-scale Waymo Open Motion Dataset (WOMD) demonstrate that TrajFlow achieves state-of-the-art performance across various key metrics, underscoring its effectiveness for safety-critical autonomous driving applications. The code and other details are available on the project website https://traj-flow.github.io/.

Agentic applications based on large language models increasingly rely on multi-step interaction loops involving planning, action execution, and environment feedback. While such systems are now deployed at scale, improving them post-deployment remains challenging. Agent trajectories are voluminous and non-deterministic, and reviewing each one, whether through human review or auxiliary LLMs, is slow and cost-prohibitive. We propose a lightweight, signal-based framework for triaging agentic interaction trajectories. Our approach computes cheap, broadly applicable signals from live interactions and attaches them as structured attributes for trajectory triage, identifying interactions likely to be informative without affecting online agent behavior. We organize signals into a coarse-grained taxonomy spanning interaction (misalignment, stagnation, disengagement, satisfaction), execution (failure, loop), and environment (exhaustion), designed for computation without model calls. In a controlled annotation study on τ-bench, a widely used benchmark for tool-augmented agent evaluation, we show that signal-based sampling achieves an 82\% informativeness rate compared to 74\% for heuristic filtering and 54\% for random sampling, with a 1.52x efficiency gain per informative trajectory. The advantage is robust across reward strata and task domains, confirming that signals provide genuine per-trajectory informativeness gains rather than merely oversampling obvious failures. These results show that lightweight signals can serve as practical sampling infrastructure for agentic systems, and suggest a path toward preference data construction and post-deployment optimization.

Identifying travelers' transportation modes is important in transportation science and location-based services. It's appealing for researchers to leverage GPS trajectory data to infer transportation modes with the popularity of GPS-enabled devices, e.g., smart phones. Existing studies frame this problem as classification task. The dominant two-stage studies divide the trip into single-one mode segments first and then categorize these segments. The over segmentation strategy and inevitable error propagation bring difficulties to classification stage and make optimizing the whole system hard. The recent one-stage works throw out trajectory segmentation entirely to avoid these by directly conducting point-wise classification for the trip, whereas leaving predictions dis-continuous. To solve above-mentioned problems, inspired by YOLO and SSD in object detection, we propose to reframe change point detection and segment classification as a unified regression task instead of the existing classification task. We directly regress coordinates of change points and classify associated segments. In this way, our method divides the trip into segments under a supervised manner and leverage more contextual information, obtaining predictions with high accuracy and continuity. Two frameworks, TrajYOLO and TrajSSD, are proposed to solve the regression task and various feature extraction backbones are exploited. Exhaustive experiments on GeoLife dataset show that the proposed method has competitive overall identification accuracy of 0.853 when distinguishing five modes: walk, bike, bus, car, train. As for change point detection, our method increases precision at the cost of drop in recall. All codes are available at https://github.com/RadetzkyLi/TrajYOLO-SSD.

The life trajectories of notable people have been studied to pinpoint the times and places of significant events such as birth, death, education, marriage, competition, work, speeches, scientific discoveries, artistic achievements, and battles. Understanding how these individuals interact with others provides valuable insights for broader research into human dynamics. However, the scarcity of trajectory data in terms of volume, density, and inter-person interactions, limits relevant studies from being comprehensive and interactive. We mine millions of biography pages from Wikipedia and tackle the generalization problem stemming from the variety and heterogeneity of the trajectory descriptions. Our ensemble model COSMOS, which combines the idea of semi-supervised learning and contrastive learning, achieves an F1 score of 85.95%. For this task, we also create a hand-curated dataset, WikiLifeTrajectory, consisting of 8,852 (person, time, location) triplets as ground truth. Besides, we perform an empirical analysis on the trajectories of 8,272 historians to demonstrate the validity of the extracted results. To facilitate the research on trajectory extractions and help the analytical studies to construct grand narratives, we make our code, the million-level extracted trajectories, and the WikiLifeTrajectory dataset publicly available.

Predicting future trajectories for other road agents is an essential task for autonomous vehicles. Established trajectory prediction methods primarily use agent tracks generated by a detection and tracking system and HD map as inputs. In this work, we propose a novel method that also incorporates visual input from surround-view cameras, allowing the model to utilize visual cues such as human gazes and gestures, road conditions, vehicle turn signals, etc, which are typically hidden from the model in prior methods. Furthermore, we use textual descriptions generated by a Vision-Language Model (VLM) and refined by a Large Language Model (LLM) as supervision during training to guide the model on what to learn from the input data. Despite using these extra inputs, our method achieves a latency of 53 ms, making it feasible for real-time processing, which is significantly faster than that of previous single-agent prediction methods with similar performance. Our experiments show that both the visual inputs and the textual descriptions contribute to improvements in trajectory prediction performance, and our qualitative analysis highlights how the model is able to exploit these additional inputs. Lastly, in this work we create and release the nuScenes-Text dataset, which augments the established nuScenes dataset with rich textual annotations for every scene, demonstrating the positive impact of utilizing VLM on trajectory prediction. Our project page is at https://moonseokha.github.io/VisionTrap/

Autonomous Vehicles (AVs) collect and pseudo-label terabytes of multi-modal data localized to HD maps during normal fleet testing. However, identifying interesting and safety-critical scenarios from uncurated driving logs remains a significant challenge. Traditional scenario mining techniques are error-prone and prohibitively time-consuming, often relying on hand-crafted structured queries. In this work, we revisit spatio-temporal scenario mining through the lens of recent vision-language models (VLMs) to detect whether a described scenario occurs in a driving log and, if so, precisely localize it in both time and space. To address this problem, we introduce RefAV, a large-scale dataset of 10,000 diverse natural language queries that describe complex multi-agent interactions relevant to motion planning derived from 1000 driving logs in the Argoverse 2 Sensor dataset. We evaluate several referential multi-object trackers and present an empirical analysis of our baselines. Notably, we find that naively repurposing off-the-shelf VLMs yields poor performance, suggesting that scenario mining presents unique challenges. Our code and dataset are available at https://github.com/CainanD/RefAV/ and https://argoverse.github.io/user-guide/tasks/scenario_mining.html

The Retrieval-Augmented Language Model (RALM) has shown remarkable performance on knowledge-intensive tasks by incorporating external knowledge during inference, which mitigates the factual hallucinations inherited in large language models (LLMs). Despite these advancements, challenges persist in the implementation of RALMs, particularly concerning their reliability and traceability. To be specific, the irrelevant document retrieval may result in unhelpful response generation or even deteriorate the performance of LLMs, while the lack of proper citations in generated outputs complicates efforts to verify the trustworthiness of the models. To this end, we propose a novel self-reasoning framework aimed at improving the reliability and traceability of RALMs, whose core idea is to leverage reasoning trajectories generated by the LLM itself. The framework involves constructing self-reason trajectories with three processes: a relevance-aware process, an evidence-aware selective process, and a trajectory analysis process. We have evaluated our framework across four public datasets (two short-form QA datasets, one long-form QA dataset, and one fact verification dataset) to demonstrate the superiority of our method, which can outperform existing state-of-art models and can achieve comparable performance with GPT-4, while only using 2,000 training samples.

Cascaded models are multi-scale generative models with a marked capacity for producing perceptually impressive samples at high resolutions. In this work, we show that they can also be excellent likelihood models, so long as we overcome a fundamental difficulty with probabilistic multi-scale models: the intractability of the likelihood function. Chiefly, in cascaded models each intermediary scale introduces extraneous variables that cannot be tractably marginalized out for likelihood evaluation. This issue vanishes by modeling the diffusion process on latent spaces induced by a class of transformations we call hierarchical volume-preserving maps, which decompose spatially structured data in a hierarchical fashion without introducing local distortions in the latent space. We demonstrate that two such maps are well-known in the literature for multiscale modeling: Laplacian pyramids and wavelet transforms. Not only do such reparameterizations allow the likelihood function to be directly expressed as a joint likelihood over the scales, we show that the Laplacian pyramid and wavelet transform also produces significant improvements to the state-of-the-art on a selection of benchmarks in likelihood modeling, including density estimation, lossless compression, and out-of-distribution detection. Investigating the theoretical basis of our empirical gains we uncover deep connections to score matching under the Earth Mover's Distance (EMD), which is a well-known surrogate for perceptual similarity. Code can be found at https://github.com/lihenryhfl/pcdm{this https url}.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Multi-modal trajectory forecasting methods commonly evaluate using single-agent metrics (marginal metrics), such as minimum Average Displacement Error (ADE) and Final Displacement Error (FDE), which fail to capture joint performance of multiple interacting agents. Only focusing on marginal metrics can lead to unnatural predictions, such as colliding trajectories or diverging trajectories for people who are clearly walking together as a group. Consequently, methods optimized for marginal metrics lead to overly-optimistic estimations of performance, which is detrimental to progress in trajectory forecasting research. In response to the limitations of marginal metrics, we present the first comprehensive evaluation of state-of-the-art (SOTA) trajectory forecasting methods with respect to multi-agent metrics (joint metrics): JADE, JFDE, and collision rate. We demonstrate the importance of joint metrics as opposed to marginal metrics with quantitative evidence and qualitative examples drawn from the ETH / UCY and Stanford Drone datasets. We introduce a new loss function incorporating joint metrics that, when applied to a SOTA trajectory forecasting method, achieves a 7% improvement in JADE / JFDE on the ETH / UCY datasets with respect to the previous SOTA. Our results also indicate that optimizing for joint metrics naturally leads to an improvement in interaction modeling, as evidenced by a 16% decrease in mean collision rate on the ETH / UCY datasets with respect to the previous SOTA.

Recent research has made substantial progress on video reasoning, with many models leveraging spatio-temporal evidence chains to strengthen their inference capabilities. At the same time, a growing set of datasets and benchmarks now provides structured annotations designed to support and evaluate such reasoning. However, little attention has been paid to reasoning about how objects move between observations: no prior work has articulated the motion patterns by connecting successive observations, leaving trajectory understanding implicit and difficult to verify. We formalize this missing capability as Spatial-Temporal-Trajectory (STT) reasoning and introduce Motion-o, a motion-centric video understanding extension to visual language models that makes trajectories explicit and verifiable. To enable motion reasoning, we also introduce a trajectory-grounding dataset artifact that expands sparse keyframe supervision via augmentation to yield denser bounding box tracks and a stronger trajectory-level training signal. Finally, we introduce Motion Chain of Thought (MCoT), a structured reasoning pathway that makes object trajectories through discrete <motion/> tag summarizing per-object direction, speed, and scale (of velocity) change to explicitly connect grounded observations into trajectories. To train Motion-o, we design a reward function that compels the model to reason directly over visual evidence, all while requiring no architectural modifications. Empirical results demonstrate that Motion-o improves spatial-temporal grounding and trajectory prediction while remaining fully compatible with existing frameworks, establishing motion reasoning as a critical extension for evidence-based video understanding. Code is available at https://github.com/ostadabbas/Motion-o.

The emergence of multi-modal foundation models has markedly transformed the technology for autonomous driving, shifting away from conventional and mostly hand-crafted design choices towards unified, foundation-model-based approaches, capable of directly inferring motion trajectories from raw sensory inputs. This new class of methods can also incorporate natural language as an additional modality, with Vision-Language-Action (VLA) models serving as a representative example. In this review, we provide a comprehensive examination of such methods through a unifying taxonomy to critically evaluate their architectural design choices, methodological strengths, and their inherent capabilities and limitations. Our survey covers 37 recently proposed approaches that span the landscape of trajectory planning with foundation models. Furthermore, we assess these approaches with respect to the openness of their source code and datasets, offering valuable information to practitioners and researchers. We provide an accompanying webpage that catalogues the methods based on our taxonomy, available at: https://github.com/fiveai/FMs-for-driving-trajectories

We present MotionDiffuser, a diffusion based representation for the joint distribution of future trajectories over multiple agents. Such representation has several key advantages: first, our model learns a highly multimodal distribution that captures diverse future outcomes. Second, the simple predictor design requires only a single L2 loss training objective, and does not depend on trajectory anchors. Third, our model is capable of learning the joint distribution for the motion of multiple agents in a permutation-invariant manner. Furthermore, we utilize a compressed trajectory representation via PCA, which improves model performance and allows for efficient computation of the exact sample log probability. Subsequently, we propose a general constrained sampling framework that enables controlled trajectory sampling based on differentiable cost functions. This strategy enables a host of applications such as enforcing rules and physical priors, or creating tailored simulation scenarios. MotionDiffuser can be combined with existing backbone architectures to achieve top motion forecasting results. We obtain state-of-the-art results for multi-agent motion prediction on the Waymo Open Motion Dataset.

Trajectory prediction plays an important role in various applications, including autonomous driving, robotics, and scene understanding. Existing approaches mainly focus on developing compact neural networks to increase prediction precision on public datasets, typically employing a standardized input duration. However, a notable issue arises when these models are evaluated with varying observation lengths, leading to a significant performance drop, a phenomenon we term the Observation Length Shift. To address this issue, we introduce a general and effective framework, the FlexiLength Network (FLN), to enhance the robustness of existing trajectory prediction techniques against varying observation periods. Specifically, FLN integrates trajectory data with diverse observation lengths, incorporates FlexiLength Calibration (FLC) to acquire temporal invariant representations, and employs FlexiLength Adaptation (FLA) to further refine these representations for more accurate future trajectory predictions. Comprehensive experiments on multiple datasets, ie, ETH/UCY, nuScenes, and Argoverse 1, demonstrate the effectiveness and flexibility of our proposed FLN framework.

Accurate prediction of pedestrians' future motions is critical for intelligent driving systems. Developing models for this task requires rich datasets containing diverse sets of samples. However, the existing naturalistic trajectory prediction datasets are generally imbalanced in favor of simpler samples and lack challenging scenarios. Such a long-tail effect causes prediction models to underperform on the tail portion of the data distribution containing safety-critical scenarios. Previous methods tackle the long-tail problem using methods such as contrastive learning and class-conditioned hypernetworks. These approaches, however, are not modular and cannot be applied to many machine learning architectures. In this work, we propose a modular model-agnostic framework for trajectory prediction that leverages a specialized mixture of experts. In our approach, each expert is trained with a specialized skill with respect to a particular part of the data. To produce predictions, we utilise a router network that selects the best expert by generating relative confidence scores. We conduct experimentation on common pedestrian trajectory prediction datasets and show that besides achieving state-of-the-art performance, our method significantly performs better on long-tail scenarios. We further conduct ablation studies to highlight the contribution of different proposed components.

Recent work has demonstrated the effectiveness of formulating decision making as a supervised learning problem on offline-collected trajectories. However, the benefits of performing sequence modeling on trajectory data is not yet clear. In this work we investigate if sequence modeling has the capability to condense trajectories into useful representations that can contribute to policy learning. To achieve this, we adopt a two-stage framework that first summarizes trajectories with sequence modeling techniques, and then employs these representations to learn a policy along with a desired goal. This design allows many existing supervised offline RL methods to be considered as specific instances of our framework. Within this framework, we introduce Goal-Conditioned Predicitve Coding (GCPC), an approach that brings powerful trajectory representations and leads to performant policies. We conduct extensive empirical evaluations on AntMaze, FrankaKitchen and Locomotion environments, and observe that sequence modeling has a significant impact on some decision making tasks. In addition, we demonstrate that GCPC learns a goal-conditioned latent representation about the future, which serves as an "implicit planner", and enables competitive performance on all three benchmarks.

Recent successful generative models are trained by fitting a neural network to an a-priori defined tractable probability density path taking noise to training examples. In this paper we investigate the space of Gaussian probability paths, which includes diffusion paths as an instance, and look for an optimal member in some useful sense. In particular, minimizing the Kinetic Energy (KE) of a path is known to make particles' trajectories simple, hence easier to sample, and empirically improve performance in terms of likelihood of unseen data and sample generation quality. We investigate Kinetic Optimal (KO) Gaussian paths and offer the following observations: (i) We show the KE takes a simplified form on the space of Gaussian paths, where the data is incorporated only through a single, one dimensional scalar function, called the data separation function. (ii) We characterize the KO solutions with a one dimensional ODE. (iii) We approximate data-dependent KO paths by approximating the data separation function and minimizing the KE. (iv) We prove that the data separation function converges to 1 in the general case of arbitrary normalized dataset consisting of n samples in d dimension as n/drightarrow 0. A consequence of this result is that the Conditional Optimal Transport (Cond-OT) path becomes kinetic optimal as n/drightarrow 0. We further support this theory with empirical experiments on ImageNet.

We study the problem of estimating the distribution of the return of a policy using an offline dataset that is not generated from the policy, i.e., distributional offline policy evaluation (OPE). We propose an algorithm called Fitted Likelihood Estimation (FLE), which conducts a sequence of Maximum Likelihood Estimation (MLE) and has the flexibility of integrating any state-of-the-art probabilistic generative models as long as it can be trained via MLE. FLE can be used for both finite-horizon and infinite-horizon discounted settings where rewards can be multi-dimensional vectors. Our theoretical results show that for both finite-horizon and infinite-horizon discounted settings, FLE can learn distributions that are close to the ground truth under total variation distance and Wasserstein distance, respectively. Our theoretical results hold under the conditions that the offline data covers the test policy's traces and that the supervised learning MLE procedures succeed. Experimentally, we demonstrate the performance of FLE with two generative models, Gaussian mixture models and diffusion models. For the multi-dimensional reward setting, FLE with diffusion models is capable of estimating the complicated distribution of the return of a test policy.

Safety-critical applications such as autonomous vehicles and social robots require fast computation and accurate probability density estimation on trajectory prediction. To address both requirements, this paper presents a new normalizing flow-based trajectory prediction model named FlowChain. FlowChain is a stack of conditional continuously-indexed flows (CIFs) that are expressive and allow analytical probability density computation. This analytical computation is faster than the generative models that need additional approximations such as kernel density estimation. Moreover, FlowChain is more accurate than the Gaussian mixture-based models due to fewer assumptions on the estimated density. FlowChain also allows a rapid update of estimated probability densities. This update is achieved by adopting the newest observed position and reusing the flow transformations and its log-det-jacobians that represent the motion trend. This update is completed in less than one millisecond because this reuse greatly omits the computational cost. Experimental results showed our FlowChain achieved state-of-the-art trajectory prediction accuracy compared to previous methods. Furthermore, our FlowChain demonstrated superiority in the accuracy and speed of density estimation. Our code is available at https://github.com/meaten/FlowChain-ICCV2023

Ensuring vertical separation is a key means of maintaining safe separation between aircraft in congested airspace. Aircraft trajectories are modelled in the presence of significant epistemic uncertainty, leading to discrepancies between observed trajectories and the predictions of deterministic models, hampering the task of planning to ensure safe separation. In this paper a probabilistic model is presented, for the purpose of emulating the trajectories of aircraft in climb and bounding the uncertainty of the predicted trajectory. A monotonic, functional representation exploits the spatio-temporal correlations in the radar observations. Through the use of Gaussian Process Emulators, features that parameterise the climb are mapped directly to functional outputs, providing a fast approximation, while ensuring that the resulting trajectory is monotonic. The model was applied as a probabilistic digital twin for aircraft in climb and baselined against BADA, a deterministic model widely used in industry. When applied to an unseen test dataset, the probabilistic model was found to provide a mean prediction that was 21% more accurate, with a 34% sharper forecast.

We consider the problem of predicting the future trajectory of scene agents from egocentric views obtained from a moving platform. This problem is important in a variety of domains, particularly for autonomous systems making reactive or strategic decisions in navigation. In an attempt to address this problem, we introduce TITAN (Trajectory Inference using Targeted Action priors Network), a new model that incorporates prior positions, actions, and context to forecast future trajectory of agents and future ego-motion. In the absence of an appropriate dataset for this task, we created the TITAN dataset that consists of 700 labeled video-clips (with odometry) captured from a moving vehicle on highly interactive urban traffic scenes in Tokyo. Our dataset includes 50 labels including vehicle states and actions, pedestrian age groups, and targeted pedestrian action attributes that are organized hierarchically corresponding to atomic, simple/complex-contextual, transportive, and communicative actions. To evaluate our model, we conducted extensive experiments on the TITAN dataset, revealing significant performance improvement against baselines and state-of-the-art algorithms. We also report promising results from our Agent Importance Mechanism (AIM), a module which provides insight into assessment of perceived risk by calculating the relative influence of each agent on the future ego-trajectory. The dataset is available at https://usa.honda-ri.com/titan

Learning behavioral patterns from observational data has been a de-facto approach to motion forecasting. Yet, the current paradigm suffers from two shortcomings: brittle under distribution shifts and inefficient for knowledge transfer. In this work, we propose to address these challenges from a causal representation perspective. We first introduce a causal formalism of motion forecasting, which casts the problem as a dynamic process with three groups of latent variables, namely invariant variables, style confounders, and spurious features. We then introduce a learning framework that treats each group separately: (i) unlike the common practice mixing datasets collected from different locations, we exploit their subtle distinctions by means of an invariance loss encouraging the model to suppress spurious correlations; (ii) we devise a modular architecture that factorizes the representations of invariant mechanisms and style confounders to approximate a sparse causal graph; (iii) we introduce a style contrastive loss that not only enforces the structure of style representations but also serves as a self-supervisory signal for test-time refinement on the fly. Experiments on synthetic and real datasets show that our proposed method improves the robustness and reusability of learned motion representations, significantly outperforming prior state-of-the-art motion forecasting models for out-of-distribution generalization and low-shot transfer.

Reasoning about human motion is an important prerequisite to safe and socially-aware robotic navigation. As a result, multi-agent behavior prediction has become a core component of modern human-robot interactive systems, such as self-driving cars. While there exist many methods for trajectory forecasting, most do not enforce dynamic constraints and do not account for environmental information (e.g., maps). Towards this end, we present Trajectron++, a modular, graph-structured recurrent model that forecasts the trajectories of a general number of diverse agents while incorporating agent dynamics and heterogeneous data (e.g., semantic maps). Trajectron++ is designed to be tightly integrated with robotic planning and control frameworks; for example, it can produce predictions that are optionally conditioned on ego-agent motion plans. We demonstrate its performance on several challenging real-world trajectory forecasting datasets, outperforming a wide array of state-of-the-art deterministic and generative methods.

We present Orbit-Space Geometric Probability Paths (OGPP), a particle-native flow-matching framework for generative modeling of particle systems. OGPP is motivated by two insights: (i) particles are defined up to permutation symmetries, so anonymous indexing inflates per-index target variance and yields curved, hard-to-learn flows; and (ii) particles live in physical space, so the flow terminal velocity has physical meaning and can encode geometric attributes, e.g., surface normals. OGPP instantiates three key components: (1) orbit-space canonicalization of the probability-path terminal endpoint, (2) particle index embeddings for role specialization, and (3) geometric probability paths with arc-length-aware terminal velocities that generate normals as a byproduct of the flow. We evaluate OGPP on minimal-surface benchmarks, where it reduces metric error by up to two orders of magnitude in a single inference step; on ShapeNet, where it matches the state of the art with 5x fewer steps and reaches airplane EMD comparable to DiT-3D with 26x fewer parameters and 5x fewer steps; and on single-shape encoding, where it produces normals and reconstructions competitive with 6D generators while operating entirely in 3D.

MLLM agents demonstrate potential for complex embodied tasks by retrieving multimodal task-relevant trajectory data. However, current retrieval methods primarily focus on surface-level similarities of textual or visual cues in trajectories, neglecting their effectiveness for the specific task at hand. To address this issue, we propose a novel method, MLLM as ReTriever (MART), which enhances the performance of embodied agents by utilizing interaction data to fine-tune an MLLM retriever based on preference learning, such that the retriever fully considers the effectiveness of trajectories and prioritize them for unseen tasks. We also introduce Trajectory Abstraction, a mechanism that leverages MLLMs' summarization capabilities to represent trajectories with fewer tokens while preserving key information, enabling agents to better comprehend milestones in the trajectory. Experimental results across various environments demonstrate our method significantly improves task success rates in unseen scenes compared to baseline methods. This work presents a new paradigm for multimodal retrieval in embodied agents, by fine-tuning a general-purpose MLLM as the retriever to assess trajectory effectiveness. All benchmark task sets and simulator code modifications for action and observation spaces will be released.

Modeling human mobility is vital for extensive applications such as transportation planning and epidemic modeling. With the rise of the Artificial Intelligence Generated Content (AIGC) paradigm, recent works explore synthetic trajectory generation using autoregressive and diffusion models. While these methods show promise for generating single-day trajectories, they remain limited by inefficiencies in long-term generation (e.g., weekly trajectories) and a lack of explicit spatiotemporal multi-scale modeling. This study proposes Multi-Scale Spatio-Temporal AutoRegression (M-STAR), a new framework that generates long-term trajectories through a coarse-to-fine spatiotemporal prediction process. M-STAR combines a Multi-scale Spatiotemporal Tokenizer that encodes hierarchical mobility patterns with a Transformer-based decoder for next-scale autoregressive prediction. Experiments on two real-world datasets show that M-STAR outperforms existing methods in fidelity and significantly improves generation speed. The data and codes are available at https://github.com/YuxiaoLuo0013/M-STAR.

Reasoning models improve their problem-solving ability through inference-time scaling, allocating more compute via longer token budgets. Identifying which reasoning traces are likely to succeed remains a key opportunity: reliably predicting productive paths can substantially reduce wasted computation and improve overall efficiency. We introduce Latent-Trajectory signals that characterize the temporal evolution of a model's internal representations during the generation of intermediate reasoning tokens. By measuring the overall change in latent representations between the start and end of reasoning, the change accumulated across intermediate steps, and the extent to which these changes advance toward the final state, we show that these signals predict solution accuracy more reliably than both cross-layer metrics and output-based confidence measures. When used to guide answer selection across multiple sampled generations, Latent-Trajectory signals make test-time scaling more effective and efficient than majority voting, reducing token usage by up to 70% while preserving and even improving accuracy by 2.6% on average. Moreover, these predictive signals often emerge early in the reasoning trace, enabling early selection and allocation of compute to the most promising candidates. Our findings contribute not only practical strategies for inference-time efficiency, but also a deeper interpretability perspective on how reasoning processes are represented and differentiated in latent space.

Vehicle trajectory prediction has increasingly relied on data-driven solutions, but their ability to scale to different data domains and the impact of larger dataset sizes on their generalization remain under-explored. While these questions can be studied by employing multiple datasets, it is challenging due to several discrepancies, e.g., in data formats, map resolution, and semantic annotation types. To address these challenges, we introduce UniTraj, a comprehensive framework that unifies various datasets, models, and evaluation criteria, presenting new opportunities for the vehicle trajectory prediction field. In particular, using UniTraj, we conduct extensive experiments and find that model performance significantly drops when transferred to other datasets. However, enlarging data size and diversity can substantially improve performance, leading to a new state-of-the-art result for the nuScenes dataset. We provide insights into dataset characteristics to explain these findings. The code can be found here: https://github.com/vita-epfl/UniTraj

Automated Vehicles (AVs) promise significant advances in transportation. Critical to these improvements is understanding AVs' longitudinal behavior, relying heavily on real-world trajectory data. Existing open-source trajectory datasets of AV, however, often fall short in refinement, reliability, and completeness, hindering effective performance metrics analysis and model development. This study addresses these challenges by creating a Unified Longitudinal TRAjectory dataset for AVs (Ultra-AV) to analyze their microscopic longitudinal driving behaviors. This dataset compiles data from 13 distinct sources, encompassing various AV types, test sites, and experiment scenarios. We established a three-step data processing: 1. extraction of longitudinal trajectory data, 2. general data cleaning, and 3. data-specific cleaning to obtain the longitudinal trajectory data and car-following trajectory data. The validity of the processed data is affirmed through performance evaluations across safety, mobility, stability, and sustainability, along with an analysis of the relationships between variables in car-following models. Our work not only furnishes researchers with standardized data and metrics for longitudinal AV behavior studies but also sets guidelines for data collection and model development.

Reasoning-trained language models often spend more tokens on harder problems, but longer chains of thought do not show whether a model is merely computing for more steps or following a different internal trajectory. We study this distinction through hidden-state trajectories during chain-of-thought generation across competitive programming, mathematics, and Boolean satisfiability. Raw trajectory geometry is strongly shaped by generation length: longer generations mechanically alter path statistics, so difficulty-dependent comparisons are misleading without adjustment. After residualizing trajectory statistics on length, difficulty remains systematically coupled to corrected trajectory geometry across all domains studied. The clearest reasoning-specific separation appears in the code domain, where harder problems show more direct corrected trajectories and less heterogeneous local curvature in reasoning-trained models than in matched instruction-tuned baselines. Corrected difficulty-geometry coupling is weaker, but still present, in mathematics and Boolean satisfiability. Prompt-stage linear probes do not mirror the code-domain separation, and behavioral annotations show that stronger corrected coupling co-occurs with strategy shifts and uncertainty monitoring. Together, these findings establish length correction as a prerequisite for generation-time trajectory analysis and show that reasoning training can be associated with distinct corrected trajectory geometry, with the strength of the effect depending on the domain.

Suppose Alice trains an open-weight language model and Bob uses a blackbox derivative of Alice's model to produce text. Can Alice prove that Bob is using her model, either by querying Bob's derivative model (query setting) or from the text alone (observational setting)? We formulate this question as an independence testing problem--in which the null hypothesis is that Bob's model or text is independent of Alice's randomized training run--and investigate it through the lens of palimpsestic memorization in language models: models are more likely to memorize data seen later in training, so we can test whether Bob is using Alice's model using test statistics that capture correlation between Bob's model or text and the ordering of training examples in Alice's training run. If Alice has randomly shuffled her training data, then any significant correlation amounts to exactly quantifiable statistical evidence against the null hypothesis, regardless of the composition of Alice's training data. In the query setting, we directly estimate (via prompting) the likelihood Bob's model gives to Alice's training examples and order; we correlate the likelihoods of over 40 fine-tunes of various Pythia and OLMo base models ranging from 1B to 12B parameters with the base model's training data order, achieving a p-value on the order of at most 1e-8 in all but six cases. In the observational setting, we try two approaches based on estimating 1) the likelihood of Bob's text overlapping with spans of Alice's training examples and 2) the likelihood of Bob's text with respect to different versions of Alice's model we obtain by repeating the last phase (e.g., 1%) of her training run on reshuffled data. The second approach can reliably distinguish Bob's text from as little as a few hundred tokens; the first does not involve any retraining but requires many more tokens (several hundred thousand) to achieve high power.

We propose a new class of parameterizations for spatio-temporal point processes which leverage Neural ODEs as a computational method and enable flexible, high-fidelity models of discrete events that are localized in continuous time and space. Central to our approach is a combination of continuous-time neural networks with two novel neural architectures, i.e., Jump and Attentive Continuous-time Normalizing Flows. This approach allows us to learn complex distributions for both the spatial and temporal domain and to condition non-trivially on the observed event history. We validate our models on data sets from a wide variety of contexts such as seismology, epidemiology, urban mobility, and neuroscience.

The ability to accurately predict the trajectory of surrounding vehicles is a critical hurdle to overcome on the journey to fully autonomous vehicles. To address this challenge, we pioneer a novel behavior-aware trajectory prediction model (BAT) that incorporates insights and findings from traffic psychology, human behavior, and decision-making. Our model consists of behavior-aware, interaction-aware, priority-aware, and position-aware modules that perceive and understand the underlying interactions and account for uncertainty and variability in prediction, enabling higher-level learning and flexibility without rigid categorization of driving behavior. Importantly, this approach eliminates the need for manual labeling in the training process and addresses the challenges of non-continuous behavior labeling and the selection of appropriate time windows. We evaluate BAT's performance across the Next Generation Simulation (NGSIM), Highway Drone (HighD), Roundabout Drone (RounD), and Macao Connected Autonomous Driving (MoCAD) datasets, showcasing its superiority over prevailing state-of-the-art (SOTA) benchmarks in terms of prediction accuracy and efficiency. Remarkably, even when trained on reduced portions of the training data (25%), our model outperforms most of the baselines, demonstrating its robustness and efficiency in predicting vehicle trajectories, and the potential to reduce the amount of data required to train autonomous vehicles, especially in corner cases. In conclusion, the behavior-aware model represents a significant advancement in the development of autonomous vehicles capable of predicting trajectories with the same level of proficiency as human drivers. The project page is available at https://github.com/Petrichor625/BATraj-Behavior-aware-Model.

Agentic search leverages LLMs to solve complex user information needs by executing a multi-step process of planning, searching, and synthesizing information to provide answers. This paradigm introduces unique challenges for LLMs' agentic reasoning capabilities when interacting with search systems. In this paper, we propose an LLM-based pipeline to study effective reasoning behavior patterns in agentic search by analyzing agentic search trajectories. Using this pipeline, we identify four beneficial reasoning behaviors: Information Verification, Authority Evaluation, Adaptive Search, and Error Recovery. Based on these findings, we propose a technique called Behavior Priming to train agentic search models. It synthesizes trajectories that exhibit these four behaviors and integrates them into the agentic search model through SFT, followed by standard reinforcement learning. Experiments on Qwen3-1.7B and Llama3.2-3B-Instruct across three web benchmarks and seven multi-hop QA benchmarks demonstrate that behavior priming 1) yields significant performance gains compared to training with direct RL, and 2) outperforms other SFT-then-RL baselines, such as those SFT on randomly selected trajectories or on trajectories with merely correct outcomes. Crucially, we demonstrate that the reasoning behaviors, rather than the correctness of the final answer, is the critical factor for achieving strong performance in RL: SFT on trajectories with reasoning behaviors but incorrect answers leads to comparable performance with SFT on those with reasoning behaviors and correct answers. Our analysis further reveals that the introduced reasoning behaviors endow models with more effective exploration (higher pass@k and entropy) and test-time scaling (longer trajectories) capabilities, providing a strong foundation for RL. Our code are avalible at https://github.com/cxcscmu/Behavior_Priming_For_Agentic_Search.

Latent Gaussian process (GP) models are widely used in neuroscience to uncover hidden state evolutions from sequential observations, mainly in neural activity recordings. While latent GP models provide a principled and powerful solution in theory, the intractable posterior in non-conjugate settings necessitates approximate inference schemes, which may lack scalability. In this work, we propose cvHM, a general inference framework for latent GP models leveraging Hida-Mat\'ern kernels and conjugate computation variational inference (CVI). With cvHM, we are able to perform variational inference of latent neural trajectories with linear time complexity for arbitrary likelihoods. The reparameterization of stationary kernels using Hida-Mat\'ern GPs helps us connect the latent variable models that encode prior assumptions through dynamical systems to those that encode trajectory assumptions through GPs. In contrast to previous work, we use bidirectional information filtering, leading to a more concise implementation. Furthermore, we employ the Whittle approximate likelihood to achieve highly efficient hyperparameter learning.

Player attribution in American football remains an open problem due to the complex nature of twenty-two players interacting on the field, but the granularity of player tracking data provides ample opportunity for novel approaches. In this work, we introduce the first public framework to evaluate spatial and trajectory tracking data of players relative to a baseline distribution of "ghost" defenders. We demonstrate our framework in the context of modeling the nearest defender positioning at the moment of catch. In particular, we provide estimates of how much better or worse their observed positioning and trajectory compared to the expected play value of ghost defenders. Our framework leverages multi-dimensional tracking data features through flexible random forests for conditional density estimation in two ways: (1) to model the distribution of receiver yards gained enabling the estimation of within-play expected value, and (2) to model the 2D spatial distribution of baseline ghost defenders. We present novel metrics for measuring player and team performance based on tracking data, and discuss challenges that remain in extending our framework to other aspects of American football.

Conventional supervised learning methods typically assume i.i.d samples and are found to be sensitive to out-of-distribution (OOD) data. We propose Generative Causal Representation Learning (GCRL) which leverages causality to facilitate knowledge transfer under distribution shifts. While we evaluate the effectiveness of our proposed method in human trajectory prediction models, GCRL can be applied to other domains as well. First, we propose a novel causal model that explains the generative factors in motion forecasting datasets using features that are common across all environments and with features that are specific to each environment. Selection variables are used to determine which parts of the model can be directly transferred to a new environment without fine-tuning. Second, we propose an end-to-end variational learning paradigm to learn the causal mechanisms that generate observations from features. GCRL is supported by strong theoretical results that imply identifiability of the causal model under certain assumptions. Experimental results on synthetic and real-world motion forecasting datasets show the robustness and effectiveness of our proposed method for knowledge transfer under zero-shot and low-shot settings by substantially outperforming the prior motion forecasting models on out-of-distribution prediction. Our code is available at https://github.com/sshirahmad/GCRL.

Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths have been designed principally under the assumption of Euclidean geometry, resulting in straight interpolations. However, this can be particularly restrictive for tasks such as trajectory inference, where straight paths might lie outside the data manifold, thus failing to capture the underlying dynamics giving rise to the observed marginals. In this paper, we propose Metric Flow Matching (MFM), a novel simulation-free framework for conditional flow matching where interpolants are approximate geodesics learned by minimizing the kinetic energy of a data-induced Riemannian metric. This way, the generative model matches vector fields on the data manifold, which corresponds to lower uncertainty and more meaningful interpolations. We prescribe general metrics to instantiate MFM, independent of the task, and test it on a suite of challenging problems including LiDAR navigation, unpaired image translation, and modeling cellular dynamics. We observe that MFM outperforms the Euclidean baselines, particularly achieving SOTA on single-cell trajectory prediction.

Trajectory generation has garnered significant attention from researchers in the field of spatio-temporal analysis, as it can generate substantial synthesized human mobility trajectories that enhance user privacy and alleviate data scarcity. However, existing trajectory generation methods often focus on improving trajectory generation quality from a singular perspective, lacking a comprehensive semantic understanding across various scales. Consequently, we are inspired to develop a HOlistic SEmantic Representation (HOSER) framework for navigational trajectory generation. Given an origin-and-destination (OD) pair and the starting time point of a latent trajectory, we first propose a Road Network Encoder to expand the receptive field of road- and zone-level semantics. Second, we design a Multi-Granularity Trajectory Encoder to integrate the spatio-temporal semantics of the generated trajectory at both the point and trajectory levels. Finally, we employ a Destination-Oriented Navigator to seamlessly integrate destination-oriented guidance. Extensive experiments on three real-world datasets demonstrate that HOSER outperforms state-of-the-art baselines by a significant margin. Moreover, the model's performance in few-shot learning and zero-shot learning scenarios further verifies the effectiveness of our holistic semantic representation.

Generative models can now produce photorealistic synthetic data which is virtually indistinguishable from the real data used to train it. This is a significant evolution over previous models which could produce reasonable facsimiles of the training data, but ones which could be visually distinguished from the training data by human evaluation. Recent work on OOD detection has raised doubts that generative model likelihoods are optimal OOD detectors due to issues involving likelihood misestimation, entropy in the generative process, and typicality. We speculate that generative OOD detectors also failed because their models focused on the pixels rather than the semantic content of the data, leading to failures in near-OOD cases where the pixels may be similar but the information content is significantly different. We hypothesize that estimating typical sets using self-supervised learners leads to better OOD detectors. We introduce a novel approach that leverages representation learning, and informative summary statistics based on manifold estimation, to address all of the aforementioned issues. Our method outperforms other unsupervised approaches and achieves state-of-the art performance on well-established challenging benchmarks, and new synthetic data detection tasks.

Large Language Models (LLMs) are widely used to evaluate natural language generation tasks as automated metrics. However, the likelihood, a measure of LLM's plausibility for a sentence, can vary due to superficial differences in sentences, such as word order and sentence structure. It is therefore possible that there might be a likelihood bias if LLMs are used for evaluation: they might overrate sentences with higher likelihoods while underrating those with lower likelihoods. In this paper, we investigate the presence and impact of likelihood bias in LLM-based evaluators. We also propose a method to mitigate the likelihood bias. Our method utilizes highly biased instances as few-shot examples for in-context learning. Our experiments in evaluating the data-to-text and grammatical error correction tasks reveal that several LLMs we test display a likelihood bias. Furthermore, our proposed method successfully mitigates this bias, also improving evaluation performance (in terms of correlation of models with human scores) significantly.

In this paper, we present a novel trajectory prediction model for autonomous driving, combining a Characterized Diffusion Module and a Spatial-Temporal Interaction Network to address the challenges posed by dynamic and heterogeneous traffic environments. Our model enhances the accuracy and reliability of trajectory predictions by incorporating uncertainty estimation and complex agent interactions. Through extensive experimentation on public datasets such as NGSIM, HighD, and MoCAD, our model significantly outperforms existing state-of-the-art methods. We demonstrate its ability to capture the underlying spatial-temporal dynamics of traffic scenarios and improve prediction precision, especially in complex environments. The proposed model showcases strong potential for application in real-world autonomous driving systems.

Human trajectory prediction is a practical task of predicting the future positions of pedestrians on the road, which typically covers all temporal ranges from short-term to long-term within a trajectory. However, existing works attempt to address the entire trajectory prediction with a singular, uniform training paradigm, neglecting the distinction between short-term and long-term dynamics in human trajectories. To overcome this limitation, we introduce a novel Progressive Pretext Task learning (PPT) framework, which progressively enhances the model's capacity of capturing short-term dynamics and long-term dependencies for the final entire trajectory prediction. Specifically, we elaborately design three stages of training tasks in the PPT framework. In the first stage, the model learns to comprehend the short-term dynamics through a stepwise next-position prediction task. In the second stage, the model is further enhanced to understand long-term dependencies through a destination prediction task. In the final stage, the model aims to address the entire future trajectory task by taking full advantage of the knowledge from previous stages. To alleviate the knowledge forgetting, we further apply a cross-task knowledge distillation. Additionally, we design a Transformer-based trajectory predictor, which is able to achieve highly efficient two-step reasoning by integrating a destination-driven prediction strategy and a group of learnable prompt embeddings. Extensive experiments on popular benchmarks have demonstrated that our proposed approach achieves state-of-the-art performance with high efficiency. Code is available at https://github.com/iSEE-Laboratory/PPT.

Traffic forecasting is a challenging spatio-temporal modeling task and a critical component of urban transportation management. Current studies mainly focus on deterministic predictions, with limited considerations on the uncertainty and stochasticity in traffic dynamics. Therefore, this paper proposes an elegant yet universal approach that transforms existing models into probabilistic predictors by replacing only the final output layer with a novel Gaussian Mixture Model (GMM) layer. The modified model requires no changes to the training pipeline and can be trained using only the Negative Log-Likelihood (NLL) loss, without any auxiliary or regularization terms. Experiments on multiple traffic datasets show that our approach generalizes from classic to modern model architectures while preserving deterministic performance. Furthermore, we propose a systematic evaluation procedure based on cumulative distributions and confidence intervals, and demonstrate that our approach is considerably more accurate and informative than unimodal or deterministic baselines. Finally, a more detailed study on a real-world dense urban traffic network is presented to examine the impact of data quality on uncertainty quantification and to show the robustness of our approach under imperfect data conditions. Code available at https://github.com/Weijiang-Xiong/OpenSkyTraffic

Reliable forecasting of the future behavior of road agents is a critical component to safe planning in autonomous vehicles. Here, we represent continuous trajectories as sequences of discrete motion tokens and cast multi-agent motion prediction as a language modeling task over this domain. Our model, MotionLM, provides several advantages: First, it does not require anchors or explicit latent variable optimization to learn multimodal distributions. Instead, we leverage a single standard language modeling objective, maximizing the average log probability over sequence tokens. Second, our approach bypasses post-hoc interaction heuristics where individual agent trajectory generation is conducted prior to interactive scoring. Instead, MotionLM produces joint distributions over interactive agent futures in a single autoregressive decoding process. In addition, the model's sequential factorization enables temporally causal conditional rollouts. The proposed approach establishes new state-of-the-art performance for multi-agent motion prediction on the Waymo Open Motion Dataset, ranking 1st on the interactive challenge leaderboard.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package.

We present MiniVLA-Nav v1, a simulation dataset for Language-Conditioned Object Approach (LCOA) navigation: given a short natural-language instruction, an NVIDIA Nova Carter differential-drive robot must navigate to the named object and stop within 1 m across four photorealistic Isaac Sim environments (Office, Hospital, Full Warehouse, and Warehouse with Multiple Shelves). Each of the 1,174 episodes pairs an instruction with synchronized 640x640 RGB images, metric depth maps (float32, metres), and instance segmentation masks, together with continuous (v,omega) and 7x7 tokenized expert action labels recorded at 60 Hz from a vision-based proportional controller. Trajectory diversity is ensured through three spawn-distance tiers (near: 1.5-3.5 m, mid: 3.5-7.0 m, far: global curated points; Pearson r=0.94 between spawn distance and trajectory length), 12 object categories, 18 training templates, and 12 paraphrase-OOD templates. Five evaluation splits support in-distribution accuracy, template-paraphrase robustness, and OOD object-category benchmarking. The dataset is publicly available at https://huggingface.co/datasets/alibustami/miniVLA-Nav

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

Mobility traces represent a critical class of personal data, often subjected to privacy-preserving transformations before public release. In this study, we analyze the anonymized Yjmob100k dataset, which captures the trajectories of 100,000 users in Japan, and demonstrate how existing anonymization techniques fail to protect their sensitive attributes. We leverage population density patterns, structural correlations, and temporal activity profiles to re-identify the dataset's real-world location and timing. Our results reveal that the anonymization process carried out for Yjmob100k is inefficient and preserves enough spatial and temporal structure to enable re-identification. This work underscores the limitations of current trajectory anonymization methods and calls for more robust privacy mechanisms in the publication of mobility data.

Maritime vessel maneuvers, characterized by their inherent complexity and indeterminacy, requires vessel trajectory prediction system capable of modeling the multi-modality nature of future motion states. Conventional stochastic trajectory prediction methods utilize latent variables to represent the multi-modality of vessel motion, however, tends to overlook the complexity and dynamics inherent in maritime behavior. In contrast, we explicitly simulate the transition of vessel motion from uncertainty towards a state of certainty, effectively handling future indeterminacy in dynamic scenes. In this paper, we present a novel framework (DiffuTraj) to conceptualize the trajectory prediction task as a guided reverse process of motion pattern uncertainty diffusion, in which we progressively remove uncertainty from maritime regions to delineate the intended trajectory. Specifically, we encode the previous states of the target vessel, vessel-vessel interactions, and the environment context as guiding factors for trajectory generation. Subsequently, we devise a transformer-based conditional denoiser to capture spatio-temporal dependencies, enabling the generation of trajectories better aligned for particular maritime environment. Comprehensive experiments on vessel trajectory prediction benchmarks demonstrate the superiority of our method.

This paper reports on the second "Throughput" phase of the Tracking Machine Learning (TrackML) challenge on the Codalab platform. As in the first "Accuracy" phase, the participants had to solve a difficult experimental problem linked to tracking accurately the trajectory of particles as e.g. created at the Large Hadron Collider (LHC): given O(10^5) points, the participants had to connect them into O(10^4) individual groups that represent the particle trajectories which are approximated helical. While in the first phase only the accuracy mattered, the goal of this second phase was a compromise between the accuracy and the speed of inference. Both were measured on the Codalab platform where the participants had to upload their software. The best three participants had solutions with good accuracy and speed an order of magnitude faster than the state of the art when the challenge was designed. Although the core algorithms were less diverse than in the first phase, a diversity of techniques have been used and are described in this paper. The performance of the algorithms are analysed in depth and lessons derived.

Diffusion models have shown strong competitiveness in offline reinforcement learning tasks by formulating decision-making as sequential generation. However, the practicality of these methods is limited due to the lengthy inference processes they require. In this paper, we address this problem by decomposing the sampling process of diffusion models into two decoupled subprocesses: 1) generating a feasible trajectory, which is a time-consuming process, and 2) optimizing the trajectory. With this decomposition approach, we are able to partially separate efficiency and quality factors, enabling us to simultaneously gain efficiency advantages and ensure quality assurance. We propose the Trajectory Diffuser, which utilizes a faster autoregressive model to handle the generation of feasible trajectories while retaining the trajectory optimization process of diffusion models. This allows us to achieve more efficient planning without sacrificing capability. To evaluate the effectiveness and efficiency of the Trajectory Diffuser, we conduct experiments on the D4RL benchmarks. The results demonstrate that our method achieves it 3-it 10 times faster inference speed compared to previous sequence modeling methods, while also outperforming them in terms of overall performance. https://github.com/RenMing-Huang/TrajectoryDiffuser Keywords: Reinforcement Learning and Efficient Planning and Diffusion Model

Trajectory prediction models often fail in real-world automated driving due to distributional shifts between training and test conditions. Such distributional shifts, whether behavioural or environmental, pose a critical risk by causing the model to make incorrect forecasts in unfamiliar situations. We propose a self-supervised method that trains a decoder in a post-hoc fashion on the self-supervised task of forecasting the second half of observed trajectories from the first half. The L2 norm of the gradient of this forecasting loss with respect to the decoder's final layer defines a score to identify distribution shifts. Our approach, first, does not affect the trajectory prediction model, ensuring no interference with original prediction performance and second, demonstrates substantial improvements on distribution shift detection for trajectory prediction on the Shifts and Argoverse datasets. Moreover, we show that this method can also be used to early detect collisions of a deep Q-Network motion planner in the Highway simulator. Source code is available at https://github.com/Michedev/forecasting-the-past.

We address the problem of incrementally modeling and forecasting long-term goals of a first-person camera wearer: what the user will do, where they will go, and what goal they seek. In contrast to prior work in trajectory forecasting, our algorithm, DARKO, goes further to reason about semantic states (will I pick up an object?), and future goal states that are far in terms of both space and time. DARKO learns and forecasts from first-person visual observations of the user's daily behaviors via an Online Inverse Reinforcement Learning (IRL) approach. Classical IRL discovers only the rewards in a batch setting, whereas DARKO discovers the states, transitions, rewards, and goals of a user from streaming data. Among other results, we show DARKO forecasts goals better than competing methods in both noisy and ideal settings, and our approach is theoretically and empirically no-regret.

Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by maximizing the logarithm of the likelihood function under the observed data. In this work, we examine this approach and identify potential hazards associated with the use of log-likelihood in conjunction with gradient-based optimizers. First, we present a synthetic example illustrating how this approach can lead to very poor but stable parameter estimates. Second, we identify the culprit to be the log-likelihood loss, along with certain conditions that exacerbate the issue. Third, we present an alternative formulation, termed β-NLL, in which each data point's contribution to the loss is weighted by the β-exponentiated variance estimate. We show that using an appropriate β largely mitigates the issue in our illustrative example. Fourth, we evaluate this approach on a range of domains and tasks and show that it achieves considerable improvements and performs more robustly concerning hyperparameters, both in predictive RMSE and log-likelihood criteria.

Flight trajectory data plays a vital role in the traffic management community, especially for downstream tasks such as trajectory prediction, flight recognition, and anomaly detection. Existing works often utilize handcrafted features and design models for different tasks individually, which heavily rely on domain expertise and are hard to extend. We argue that different flight analysis tasks share the same useful features of the trajectory. Jointly learning a unified representation for flight trajectories could be beneficial for improving the performance of various tasks. However, flight trajectory representation learning (TRL) faces two primary challenges, \ie unbalanced behavior density and 3D spatial continuity, which disable recent general TRL methods. In this paper, we propose Flight2Vec , a flight-specific representation learning method to address these challenges. Specifically, a behavior-adaptive patching mechanism is used to inspire the learned representation to pay more attention to behavior-dense segments. Moreover, we introduce a motion trend learning technique that guides the model to memorize not only the precise locations, but also the motion trend to generate better representations. Extensive experimental results demonstrate that Flight2Vec significantly improves performance in downstream tasks such as flight trajectory prediction, flight recognition, and anomaly detection.

In autonomous driving tasks, trajectory prediction in complex traffic environments requires adherence to real-world context conditions and behavior multimodalities. Existing methods predominantly rely on prior assumptions or generative models trained on curated data to learn road agents' stochastic behavior bounded by scene constraints. However, they often face mode averaging issues due to data imbalance and simplistic priors, and could even suffer from mode collapse due to unstable training and single ground truth supervision. These issues lead the existing methods to a loss of predictive diversity and adherence to the scene constraints. To address these challenges, we introduce a novel trajectory generator named Controllable Diffusion Trajectory (CDT), which integrates map information and social interactions into a Transformer-based conditional denoising diffusion model to guide the prediction of future trajectories. To ensure multimodality, we incorporate behavioral tokens to direct the trajectory's modes, such as going straight, turning right or left. Moreover, we incorporate the predicted endpoints as an alternative behavioral token into the CDT model to facilitate the prediction of accurate trajectories. Extensive experiments on the Argoverse 2 benchmark demonstrate that CDT excels in generating diverse and scene-compliant trajectories in complex urban settings.

The quality of many modern machine learning models improves as model complexity increases, an effect that has been quantified, for predictive performance, with the non-monotonic double descent learning curve. Here, we address the overarching question: is there an analogous theory of double descent for models which estimate uncertainty? We provide a partially affirmative and partially negative answer in the setting of Gaussian processes (GP). Under standard assumptions, we prove that higher model quality for optimally-tuned GPs (including uncertainty prediction) under marginal likelihood is realized for larger input dimensions, and therefore exhibits a monotone error curve. After showing that marginal likelihood does not naturally exhibit double descent in the input dimension, we highlight related forms of posterior predictive loss that do exhibit non-monotonicity. Finally, we verify empirically that our results hold for real data, beyond our considered assumptions, and we explore consequences involving synthetic covariates.

A significant number of traffic crashes are secondary crashes that occur because of an earlier incident on the road. Thus, early detection of traffic incidents is crucial for road users from safety perspectives with a potential to reduce the risk of secondary crashes. The wide availability of GPS devices now-a-days gives an opportunity of tracking and recording vehicle trajectories. The objective of this study is to use vehicle trajectory data for advance real-time detection of traffic incidents on highways using machine learning-based algorithms. The study uses three days of unevenly sequenced vehicle trajectory data and traffic incident data on I-10, one of the most crash-prone highways in Louisiana. Vehicle trajectories are converted to trajectories based on virtual detector locations to maintain spatial uniformity as well as to generate historical traffic data for machine learning algorithms. Trips matched with traffic incidents on the way are separated and along with other trips with similar spatial attributes are used to build a database for modeling. Multiple machine learning algorithms such as Logistic Regression, Random Forest, Extreme Gradient Boost, and Artificial Neural Network models are used to detect a trajectory that is likely to face an incident in the downstream road section. Results suggest that the Random Forest model achieves the best performance for predicting an incident with reasonable recall value and discrimination capability.

We present a new dataset, dedicated to the development of simultaneous localization and mapping methods for underwater vehicles navigating close to the seabed. The data sequences composing this dataset are recorded in three different environments: a harbor at a depth of a few meters, a first archaeological site at a depth of 270 meters and a second site at a depth of 380 meters. The data acquisition is performed using Remotely Operated Vehicles equipped with a monocular monochromatic camera, a low-cost inertial measurement unit, a pressure sensor and a computing unit, all embedded in a single enclosure. The sensors' measurements are recorded synchronously on the computing unit and seventeen sequences have been created from all the acquired data. These sequences are made available in the form of ROS bags and as raw data. For each sequence, a trajectory has also been computed offline using a Structure-from-Motion library in order to allow the comparison with real-time localization methods. With the release of this dataset, we wish to provide data difficult to acquire and to encourage the development of vision-based localization methods dedicated to the underwater environment. The dataset can be downloaded from: http://www.lirmm.fr/aqualoc/

Generative Models (GMs) have attracted considerable attention due to their tremendous success in various domains, such as computer vision where they are capable to generate impressive realistic-looking images. Likelihood-based GMs are attractive due to the possibility to generate new data by a single model evaluation. However, they typically achieve lower sample quality compared to state-of-the-art score-based diffusion models (DMs). This paper provides a significant step in the direction of addressing this limitation. The idea is to borrow one of the strengths of score-based DMs, which is the ability to perform accurate density estimation in low-density regions and to address manifold overfitting by means of data mollification. We connect data mollification through the addition of Gaussian noise to Gaussian homotopy, which is a well-known technique to improve optimization. Data mollification can be implemented by adding one line of code in the optimization loop, and we demonstrate that this provides a boost in generation quality of likelihood-based GMs, without computational overheads. We report results on image data sets with popular likelihood-based GMs, including variants of variational autoencoders and normalizing flows, showing large improvements in FID score.

Understanding urban mobility patterns and analyzing how people move around cities helps improve the overall quality of life and supports the development of more livable, efficient, and sustainable urban areas. A challenging aspect of this work is the collection of mobility data by means of user tracking or travel surveys, given the associated privacy concerns, noncompliance, and high cost. This work proposes an innovative AI-based approach for synthesizing travel surveys by prompting large language models (LLMs), aiming to leverage their vast amount of relevant background knowledge and text generation capabilities. Our study evaluates the effectiveness of this approach across various U.S. metropolitan areas by comparing the results against existing survey data at different granularity levels. These levels include (i) pattern level, which compares aggregated metrics like the average number of locations traveled and travel time, (ii) trip level, which focuses on comparing trips as whole units using transition probabilities, and (iii) activity chain level, which examines the sequence of locations visited by individuals. Our work covers several proprietary and open-source LLMs, revealing that open-source base models like Llama-2, when fine-tuned on even a limited amount of actual data, can generate synthetic data that closely mimics the actual travel survey data, and as such provides an argument for using such data in mobility studies.

The next Point of Interest (POI) recommendation task is to predict users' immediate next POI visit given their historical data. Location-Based Social Network (LBSN) data, which is often used for the next POI recommendation task, comes with challenges. One frequently disregarded challenge is how to effectively use the abundant contextual information present in LBSN data. Previous methods are limited by their numerical nature and fail to address this challenge. In this paper, we propose a framework that uses pretrained Large Language Models (LLMs) to tackle this challenge. Our framework allows us to preserve heterogeneous LBSN data in its original format, hence avoiding the loss of contextual information. Furthermore, our framework is capable of comprehending the inherent meaning of contextual information due to the inclusion of commonsense knowledge. In experiments, we test our framework on three real-world LBSN datasets. Our results show that the proposed framework outperforms the state-of-the-art models in all three datasets. Our analysis demonstrates the effectiveness of the proposed framework in using contextual information as well as alleviating the commonly encountered cold-start and short trajectory problems.

Trajectory planning is commonly used as part of a local planner in autonomous driving. This paper considers the problem of planning a continuous-curvature-rate trajectory between fixed start and goal states that minimizes a tunable trade-off between passenger comfort and travel time. The problem is an instance of infinite dimensional optimization over two continuous functions: a path, and a velocity profile. We propose a simplification of this problem that facilitates the discretization of both functions. This paper also proposes a method to quickly generate minimal-length paths between start and goal states based on a single tuning parameter: the second derivative of curvature. Furthermore, we discretize the set of velocity profiles along a given path into a selection of acceleration way-points along the path. Gradient-descent is then employed to minimize cost over feasible choices of the second derivative of curvature, and acceleration way-points, resulting in a method that repeatedly solves the path and velocity profiles in an iterative fashion. Numerical examples are provided to illustrate the benefits of the proposed methods.

The prediction of ship trajectories is a growing field of study in artificial intelligence. Traditional methods rely on the use of LSTM, GRU networks, and even Transformer architectures for the prediction of spatio-temporal series. This study proposes a viable alternative for predicting these trajectories using only GNSS positions. It considers this spatio-temporal problem as a natural language processing problem. The latitude/longitude coordinates of AIS messages are transformed into cell identifiers using the H3 index. Thanks to the pseudo-octal representation, it becomes easier for language models to learn the spatial hierarchy of the H3 index. The method is compared with a classical Kalman filter, widely used in the maritime domain, and introduces the Fr\'echet distance as the main evaluation metric. We show that it is possible to predict ship trajectories quite precisely up to 8 hours with 30 minutes of context. We demonstrate that this alternative works well enough to predict trajectories worldwide.

This paper presents the development of a comprehensive dataset capturing interactions between Autonomous Vehicles (AVs) and traffic control devices, specifically traffic lights and stop signs. Derived from the Waymo Motion dataset, our work addresses a critical gap in the existing literature by providing real-world trajectory data on how AVs navigate these traffic control devices. We propose a methodology for identifying and extracting relevant interaction trajectory data from the Waymo Motion dataset, incorporating over 37,000 instances with traffic lights and 44,000 with stop signs. Our methodology includes defining rules to identify various interaction types, extracting trajectory data, and applying a wavelet-based denoising method to smooth the acceleration and speed profiles and eliminate anomalous values, thereby enhancing the trajectory quality. Quality assessment metrics indicate that trajectories obtained in this study have anomaly proportions in acceleration and jerk profiles reduced to near-zero levels across all interaction categories. By making this dataset publicly available, we aim to address the current gap in datasets containing AV interaction behaviors with traffic lights and signs. Based on the organized and published dataset, we can gain a more in-depth understanding of AVs' behavior when interacting with traffic lights and signs. This will facilitate research on AV integration into existing transportation infrastructures and networks, supporting the development of more accurate behavioral models and simulation tools.

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Rapidly-exploring random trees (RRTs) are popular in motion planning because they find solutions efficiently to single-query problems. Optimal RRTs (RRT*s) extend RRTs to the problem of finding the optimal solution, but in doing so asymptotically find the optimal path from the initial state to every state in the planning domain. This behaviour is not only inefficient but also inconsistent with their single-query nature. For problems seeking to minimize path length, the subset of states that can improve a solution can be described by a prolate hyperspheroid. We show that unless this subset is sampled directly, the probability of improving a solution becomes arbitrarily small in large worlds or high state dimensions. In this paper, we present an exact method to focus the search by directly sampling this subset. The advantages of the presented sampling technique are demonstrated with a new algorithm, Informed RRT*. This method retains the same probabilistic guarantees on completeness and optimality as RRT* while improving the convergence rate and final solution quality. We present the algorithm as a simple modification to RRT* that could be further extended by more advanced path-planning algorithms. We show experimentally that it outperforms RRT* in rate of convergence, final solution cost, and ability to find difficult passages while demonstrating less dependence on the state dimension and range of the planning problem.

Motion behaviour is driven by several factors -- goals, presence and actions of neighbouring agents, social relations, physical and social norms, the environment with its variable characteristics, and further. Most factors are not directly observable and must be modelled from context. Trajectory prediction, is thus a hard problem, and has seen increasing attention from researchers in the recent years. Prediction of motion, in application, must be realistic, diverse and controllable. In spite of increasing focus on multimodal trajectory generation, most methods still lack means for explicitly controlling different modes of the data generation. Further, most endeavours invest heavily in designing special mechanisms to learn the interactions in latent space. We present Conditional Speed GAN (CSG), that allows controlled generation of diverse and socially acceptable trajectories, based on user controlled speed. During prediction, CSG forecasts future speed from latent space and conditions its generation based on it. CSG is comparable to state-of-the-art GAN methods in terms of the benchmark distance metrics, while being simple and useful for simulation and data augmentation for different contexts such as fast or slow paced environments. Additionally, we compare the effect of different aggregation mechanisms and show that a naive approach of concatenation works comparable to its attention and pooling alternatives.

Sequential learning with Gaussian processes (GPs) is challenging when access to past data is limited, for example, in continual and active learning. In such cases, errors can accumulate over time due to inaccuracies in the posterior, hyperparameters, and inducing points, making accurate learning challenging. Here, we present a method to keep all such errors in check using the recently proposed dual sparse variational GP. Our method enables accurate inference for generic likelihoods and improves learning by actively building and updating a memory of past data. We demonstrate its effectiveness in several applications involving Bayesian optimization, active learning, and continual learning.

Generating trajectory data is among promising solutions to addressing privacy concerns, collection costs, and proprietary restrictions usually associated with human mobility analyses. However, existing trajectory generation methods are still in their infancy due to the inherent diversity and unpredictability of human activities, grappling with issues such as fidelity, flexibility, and generalizability. To overcome these obstacles, we propose ControlTraj, a Controllable Trajectory generation framework with the topology-constrained diffusion model. Distinct from prior approaches, ControlTraj utilizes a diffusion model to generate high-fidelity trajectories while integrating the structural constraints of road network topology to guide the geographical outcomes. Specifically, we develop a novel road segment autoencoder to extract fine-grained road segment embedding. The encoded features, along with trip attributes, are subsequently merged into the proposed geographic denoising UNet architecture, named GeoUNet, to synthesize geographic trajectories from white noise. Through experimentation across three real-world data settings, ControlTraj demonstrates its ability to produce human-directed, high-fidelity trajectory generation with adaptability to unexplored geographical contexts.

Trajectory prediction is fundamental in computer vision and autonomous driving, particularly for understanding pedestrian behavior and enabling proactive decision-making. Existing approaches in this field often assume precise and complete observational data, neglecting the challenges associated with out-of-view objects and the noise inherent in sensor data due to limited camera range, physical obstructions, and the absence of ground truth for denoised sensor data. Such oversights are critical safety concerns, as they can result in missing essential, non-visible objects. To bridge this gap, we present a novel method for out-of-sight trajectory prediction that leverages a vision-positioning technique. Our approach denoises noisy sensor observations in an unsupervised manner and precisely maps sensor-based trajectories of out-of-sight objects into visual trajectories. This method has demonstrated state-of-the-art performance in out-of-sight noisy sensor trajectory denoising and prediction on the Vi-Fi and JRDB datasets. By enhancing trajectory prediction accuracy and addressing the challenges of out-of-sight objects, our work significantly contributes to improving the safety and reliability of autonomous driving in complex environments. Our work represents the first initiative towards Out-Of-Sight Trajectory prediction (OOSTraj), setting a new benchmark for future research. The code is available at https://github.com/Hai-chao-Zhang/OOSTraj.

Process Reward Models (PRMs) have recently emerged as a powerful framework for supervising intermediate reasoning steps in large language models (LLMs). Previous PRMs are primarily trained on model final output responses and struggle to evaluate intermediate thinking trajectories robustly, especially in the emerging setting of trajectory-response outputs generated by frontier reasoning models like Deepseek-R1. In this work, we introduce ReasonFlux-PRM, a novel trajectory-aware PRM explicitly designed to evaluate the trajectory-response type of reasoning traces. ReasonFlux-PRM incorporates both step-level and trajectory-level supervision, enabling fine-grained reward assignment aligned with structured chain-of-thought data. We adapt ReasonFlux-PRM to support reward supervision under both offline and online settings, including (i) selecting high-quality model distillation data for downstream supervised fine-tuning of smaller models, (ii) providing dense process-level rewards for policy optimization during reinforcement learning, and (iii) enabling reward-guided Best-of-N test-time scaling. Empirical results on challenging downstream benchmarks such as AIME, MATH500, and GPQA-Diamond demonstrate that ReasonFlux-PRM-7B selects higher quality data than strong PRMs (e.g., Qwen2.5-Math-PRM-72B) and human-curated baselines. Furthermore, our derived ReasonFlux-PRM-7B yields consistent performance improvements, achieving average gains of 12.1% in supervised fine-tuning, 4.5% in reinforcement learning, and 6.3% in test-time scaling. We also release our efficient ReasonFlux-PRM-1.5B for resource-constrained applications and edge deployment. Projects: https://github.com/Gen-Verse/ReasonFlux

In this paper, we present the findings of our Project ALPINE which stands for ``Autoregressive Learning for Planning In NEtworks." Project ALPINE initiates a theoretical investigation into the development of planning capabilities in Transformer-based language models through their autoregressive learning mechanisms, aiming to identify any potential limitations in their planning abilities. We abstract planning as a network path-finding task where the objective is to generate a valid path from a specified source node to a designated target node. In terms of expressiveness, we show that the Transformer is capable of executing path-finding by embedding the adjacency and reachability matrices within its weights. Our theoretical analysis of the gradient-based learning dynamic of the Transformer reveals that the Transformer is capable of learning both the adjacency matrix and a limited form of the reachability matrix. These theoretical insights are then validated through experiments, which demonstrate that the Transformer indeed learns the adjacency matrix and an incomplete reachability matrix, which aligns with the predictions made in our theoretical analysis. Additionally, when applying our methodology to a real-world planning benchmark, called Blocksworld, our observations remain consistent. Our theoretical and empirical analyses further unveil a potential limitation of Transformer in path-finding: it cannot identify reachability relationships through transitivity, and thus would fail when path concatenation is needed to generate a path. In summary, our findings shed new light on how the internal mechanisms of autoregressive learning enable planning in networks. This study may contribute to our understanding of the general planning capabilities in other related domains.

We incorporate discrete and continuous time Markov processes as building blocks into probabilistic graphical models with latent and observed variables. We introduce the automatic Backward Filtering Forward Guiding (BFFG) paradigm (Mider et al., 2021) for programmable inference on latent states and model parameters. Our starting point is a generative model, a forward description of the probabilistic process dynamics. We backpropagate the information provided by observations through the model to transform the generative (forward) model into a pre-conditional model guided by the data. It approximates the actual conditional model with known likelihood-ratio between the two. The backward filter and the forward change of measure are suitable to be incorporated into a probabilistic programming context because they can be formulated as a set of transformation rules. The guided generative model can be incorporated in different approaches to efficiently sample latent states and parameters conditional on observations. We show applicability in a variety of settings, including Markov chains with discrete state space, interacting particle systems, state space models, branching diffusions and Gamma processes.

Words of estimative probability (WEP) are expressions of a statement's plausibility (probably, maybe, likely, doubt, likely, unlikely, impossible...). Multiple surveys demonstrate the agreement of human evaluators when assigning numerical probability levels to WEP. For example, highly likely corresponds to a median chance of 0.90+-0.08 in Fagen-Ulmschneider (2015)'s survey. In this work, we measure the ability of neural language processing models to capture the consensual probability level associated to each WEP. Firstly, we use the UNLI dataset (Chen et al., 2020) which associates premises and hypotheses with their perceived joint probability p, to construct prompts, e.g. "[PREMISE]. [WEP], [HYPOTHESIS]." and assess whether language models can predict whether the WEP consensual probability level is close to p. Secondly, we construct a dataset of WEP-based probabilistic reasoning, to test whether language models can reason with WEP compositions. When prompted "[EVENTA] is likely. [EVENTB] is impossible.", a causal language model should not express that [EVENTA&B] is likely. We show that both tasks are unsolved by off-the-shelf English language models, but that fine-tuning leads to transferable improvement.

Flow-based generative models (Dinh et al., 2014) are conceptually attractive due to tractability of the exact log-likelihood, tractability of exact latent-variable inference, and parallelizability of both training and synthesis. In this paper we propose Glow, a simple type of generative flow using an invertible 1x1 convolution. Using our method we demonstrate a significant improvement in log-likelihood on standard benchmarks. Perhaps most strikingly, we demonstrate that a generative model optimized towards the plain log-likelihood objective is capable of efficient realistic-looking synthesis and manipulation of large images. The code for our model is available at https://github.com/openai/glow

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Classification of movement trajectories has many applications in transportation. Supervised neural models represent the current state-of-the-art. Recent security applications require this task to be rapidly employed in environments that may differ from the data used to train such models for which there is little training data. We provide a neuro-symbolic rule-based framework to conduct error correction and detection of these models to support eventual deployment in security applications. We provide a suite of experiments on several recent and state-of-the-art models and show an accuracy improvement of 1.7% over the SOTA model in the case where all classes are present in training and when 40% of classes are omitted from training, we obtain a 5.2% improvement (zero-shot) and 23.9% (few-shot) improvement over the SOTA model without resorting to retraining of the base model.

Diffusion models have exhibited excellent performance in various domains. The probability flow ordinary differential equation (ODE) of diffusion models (i.e., diffusion ODEs) is a particular case of continuous normalizing flows (CNFs), which enables deterministic inference and exact likelihood evaluation. However, the likelihood estimation results by diffusion ODEs are still far from those of the state-of-the-art likelihood-based generative models. In this work, we propose several improved techniques for maximum likelihood estimation for diffusion ODEs, including both training and evaluation perspectives. For training, we propose velocity parameterization and explore variance reduction techniques for faster convergence. We also derive an error-bounded high-order flow matching objective for finetuning, which improves the ODE likelihood and smooths its trajectory. For evaluation, we propose a novel training-free truncated-normal dequantization to fill the training-evaluation gap commonly existing in diffusion ODEs. Building upon these techniques, we achieve state-of-the-art likelihood estimation results on image datasets (2.56 on CIFAR-10, 3.43/3.69 on ImageNet-32) without variational dequantization or data augmentation.

We present a novel framework for predicting next actions in soccer possessions by leveraging path signatures to encode their complex spatio-temporal structure. Unlike existing approaches, we do not rely on fixed historical windows and handcrafted features, but rather encode the entire recent possession, thereby avoiding the inclusion of potentially irrelevant or misleading historical information. Path signatures naturally capture the order and interaction of events, providing a mathematically grounded feature encoding for variable-length time series of irregular sampling frequencies without the necessity for manual feature engineering. Our proposed approach outperforms a transformer-based benchmark across various loss metrics and considerably reduces computational cost. Building on these results, we introduce a new possession evaluation metric based on well-established frameworks in soccer analytics, incorporating both predicted action type probabilities and action location. Our metric shows greater reliability than existing metrics in domain-specific comparisons. Finally, we validate our approach through a detailed analysis of the 2017/18 Premier League season and discuss further applications and future extensions.