Motion prediction, recently popularized under the term world models, refers to anticipating the future states of agents or the future evolution of a scene, which is rooted in human cognition to bridge perception and decision-making, enabling us to anticipate, adapt, and act within an ever-changing world. It lies at the core of intelligent autonomous systems, such as robotics and self-driving cars, to safely operate in dynamic and human-robot-mixed environments, and also informs broader time-series challenges. With advances in methods, representations, and datasets, the field has seen rapid progress, reflected in rapidly updated benchmark performance. However, when state-of-the-art methods are deployed in the real world, they are often found to struggle to generalize to open-world settings and fall short of deployment standards. This reveals a gap between reality and benchmarks, which are often idealized or ill-posed, and fail to capture real-world complexity. To address the pressing need for problem settings that better reflect real-world challenges and guide future research, this paper focuses on revisiting the generalization and applicability of motion prediction models, with an emphasis on robotics, autonomous driving, and human motion applications. We first provide a comprehensive taxonomy of motion prediction methods, covering representations, modelling methods, application domains, and evaluation protocols. We then revisit two fundamental problems: 1) how to push motion prediction models to be deployable to realistic deployment standards, where motion prediction does not act in a vacuum, but functions as one module of closed-loop autonomy stacks - it takes input from the localization and perception, and informs downstream planning and control.

Vision-Language-Action (VLA) models have shown strong potential for general-purpose robotic manipulation, but their reliance on expert demonstrations limits their ability to learn from failures and perform self-corrections. Reinforcement learning (RL) addresses these through self-improving interactions with the physical environment, but suffers from high sample complexity on real robots. We introduce World-Model-based Policy Optimization (WMPO), a principled framework for on-policy VLA RL without interacting with the real environment. In contrast to widely used latent world models, WMPO focuses on pixel-based predictions that align the "imagined" trajectories with the VLA features pretrained with web-scale images. Crucially, WMPO enables the policy to perform on-policy GRPO that provides stronger performance than the often-used off-policy methods. Extensive experiments in both simulation and real-robot settings demonstrate that WMPO (i) substantially improves sample efficiency, (ii) achieves stronger overall performance, (iii) exhibits emergent behaviors such as self-correction, and (iv) demonstrates robust generalization and lifelong learning capabilities.

Although Large Language Models (LLMs) show exceptional fluency, efforts persist to extract stronger reasoning capabilities from them. Drawing on search-based interpretations of LLM computation, this paper advances a systematic framework for understanding LLM reasoning and optimization. Namely, that enhancing reasoning is best achieved by structuring a multi-agent pipeline to ensure a traversal of the search space in a gradual, incremental, and sequential (GIS) manner. Stated succinctly, high-quality reasoning is a controlled, incremental search. To test this framework, we investigate the efficacy of recursive refinement (RR)--an iterative process of self-criticism, adversarial stress-testing, and integrating critical feedback--as a practical method for implementing GIS search. We designed an experiment comparing a simple, linear pipeline against a complex, explicitly structured pipeline leveraging a recursive refinement layer. The multi-agent models were constructed to reflect the historical personas of three US Founding Fathers (Hamilton, Jefferson, and Madison) using RAG-powered corpora and were prompted to generate responses to three contemporary political issues. Model performance was evaluated using a two-tiered approach: a quantitative score from an LLM arbiter agent and qualitative human judgment. Our results revealed that the complex model consistently outperformed the simple model across all nine test cases with an average arbiter-outputted score of 88.3 versus 71.7. The complex model's arguments were superior in analytical depth, structural nuance, and strategic framing. We conclude that recursive refinement is a robust architectural feature for enhancing LLM reasoning via GIS search.

While Vision-Language Models (VLMs) post-trained with Reinforcement Learning (RL) show impressive general reasoning, their evaluation is often confined to language-dominant tasks (e.g., math). This raises a critical question: can RL post-training truly extend the inherent capability boundary of a base VLM, particularly for visual-centric spatial tasks where it initially fails? To investigate this, we introduce Ariadne, a framework utilizing synthetic mazes for multi-step spatial reasoning where task difficulty (e.g., path length, turns) is precisely controlled. We leverage this controllable environment to train VLMs using Reinforcement Learning with Verified Rewards (RLVR) in a difficulty-aware curriculum. Surprisingly, post-RLVR training, the VLM achieves over 50% accuracy on a problem set where the base model scored 0%, demonstrating that our approach expands the model's initial capability boundary. To assess real-world viability, we evaluate out-of-distribution (OOD) generalization on practical benchmarks. Despite training only on synthetic maze samples, Ariadne achieves significant zero-shot improvements, averaging 16% on MapBench (e.g., museum navigation) and 24% on ReasonMap (subway transfer tasks). These results confirm that our method not only broadens the model's fundamental limits but also enhances its generalization to real-world spatial reasoning. We acknowledge our study is limited to the post-training phase, given the opaqueness of pre-training data, and hope our research motivates further work on specialized, capability-extending alignment.

Complex Query Answering (CQA) over incomplete Knowledge Graphs (KGs), typically formalized as reasoning with Existential First-Order predicate logic with one free variable (EFO\textsubscript{1}), faces a fundamental tradeoff between logic fidelity and computational efficiency. This work establishes a Grounding-Skolemization dichotomy to systematically analyze this challenge and motivate a paradigm shift in CQA. While Grounding-based methods inherently suffer from combinatorial explosion, most Skolemization-based methods neglect to explicitly model Skolem functions and compromise logical consistency. To address these limitations, we propose the Logic-constrained Vector Symbolic Architecture (LVSA), a neuro-symbolic framework that unifies a differentiable Skolemization module and a neural negator, as well as a logical constraint-driven optimization protocol to harmonize geometric and logical requirements. Theoretically, LVSA guarantees universality for all EFO\textsubscript{1} queries with low computational complexity. Empirically, it outperforms state-of-the-art Skolemization-based methods and reduces inference costs by orders of magnitude compared to Grounding-based baselines.

Machine learning and data processing techniques relying on covariance information are widespread as they identify meaningful patterns in unsupervised and unlabeled settings. As a prominent example, Principal Component Analysis (PCA) projects data points onto the eigenvectors of their covariance matrix, capturing the directions of maximum variance. This mapping, however, falls short in two directions: it fails to capture information in low-variance directions, relevant when, e.g., the data contains high-variance noise; and it provides unstable results in low-sample regimes, especially when covariance eigenvalues are close. CoVariance Neural Networks (VNNs), i.e., graph neural networks using the covariance matrix as a graph, show improved stability to estimation errors and learn more expressive functions in the covariance spectrum than PCA, but require training and operate in a labeled setup. To get the benefits of both worlds, we propose Covariance Scattering Transforms (CSTs), deep untrained networks that sequentially apply filters localized in the covariance spectrum to the input data and produce expressive hierarchical representations via nonlinearities. We define the filters as covariance wavelets that capture specific and detailed covariance spectral patterns. We improve CSTs' computational and memory efficiency via a pruning mechanism, and we prove that their error due to finite-sample covariance estimations is less sensitive to close covariance eigenvalues compared to PCA, improving their stability. Our experiments on age prediction from cortical thickness measurements on 4 datasets collecting patients with neurodegenerative diseases show that CSTs produce stable representations in low-data settings, as VNNs but without any training, and lead to comparable or better predictions w.r.t. more complex learning models.

Understanding complex biomolecular mechanisms requires multi-step reasoning across molecular interactions, signaling cascades, and metabolic pathways. While large language models(LLMs) show promise in such tasks, their application to biomolecular problems is hindered by logical inconsistencies and the lack of grounding in domain knowledge. Existing approaches often exacerbate these issues: reasoning steps may deviate from biological facts or fail to capture long mechanistic dependencies. To address these challenges, we propose a Knowledge-Augmented Long-CoT Reasoning framework that integrates LLMs with knowledge graph-based multi-hop reasoning chains. The framework constructs mechanistic chains via guided multi-hop traversal and pruning on the knowledge graph; these chains are then incorporated into supervised fine-tuning to improve factual grounding and further refined with reinforcement learning to enhance reasoning reliability and consistency. Furthermore, to overcome the shortcomings of existing benchmarks, which are often restricted in scale and scope and lack annotations for deep reasoning chains, we introduce PrimeKGQA, a comprehensive benchmark for biomolecular question answering. Experimental results on both PrimeKGQA and existing datasets demonstrate that although larger closed-source models still perform well on relatively simple tasks, our method demonstrates clear advantages as reasoning depth increases, achieving state-of-the-art performance on multi-hop tasks that demand traversal of structured biological knowledge. These findings highlight the effectiveness of combining structured knowledge with advanced reasoning strategies for reliable and interpretable biomolecular reasoning.

Object-centric world models (OCWM) aim to decompose visual scenes into object-level representations, providing structured abstractions that could improve compositional generalization and data efficiency in reinforcement learning. We hypothesize that explicitly disentangled object-level representations, by localizing task-relevant information, can enhance policy performance across novel feature combinations. To test this hypothesis, we introduce DLPWM, a fully unsupervised, disentangled object-centric world model that learns object-level latents directly from pixels. DLPWM achieves strong reconstruction and prediction performance, including robustness to several out-of-distribution (OOD) visual variations. However, when used for downstream model-based control, policies trained on DLPWM latents underperform compared to DreamerV3. Through latent-trajectory analyses, we identify representation shift during multi-object interactions as a key driver of unstable policy learning. Our results suggest that, although object-centric perception supports robust visual modeling, achieving stable control requires mitigating latent drift.

However, most existing multimodal mathematical reasoning benchmarks focus primarily on 2D plane geometry, rely on static datasets prone to data contamination and memorization, and evaluate models solely by final answers, overlooking the reasoning process. T o address these limitations, we introduce DynaSolidGeo, the first dynamic benchmark for evaluating genuine spatial reasoning in Vision-Language Models (VLMs). Constructed through a semi-automatic annotation pipeline, DynaSolidGeo contains 503 expert-curated seed questions that can, in principle, dynamically generate an unbounded number of diverse multimodal text-visual instances. Beyond answer accuracy, we incorporate process evaluation based on expert-annotated reasoning chains to measure logical validity and causal coherence. Experiments across representative open-source and closed-source VLMs reveal large performance gaps, severe degradation in dynamic settings, and poor performance on tasks requiring high-level spatial intelligence, such as mental rotation and visualization. The code and dataset are available at DynaSolidGeo.

In complex embodied long-horizon manipulation tasks, effective task decomposition and execution require synergistic integration of textual logical reasoning and visual-spatial imagination to ensure efficient and accurate operation. Current methods fail to adopt a unified generation framework for multimodal planning, lead to inconsistent in multimodal planning. To address this challenge, we present \textbf{EVLP (Embodied Vision-Language Planner)}, an innovative multimodal unified generation framework that jointly models linguistic reasoning and visual generation. Our approach achieves multimodal planning for long-horizon tasks through a novel training pipeline incorporating dynamic pretraining and reinforced alignment. Our core innovations consist of three key components: \textbf{1) Unified Multimodal Generation Framework}: For understanding, We integrate semantic information with spatial features to provide comprehensive visual perception. For generation, we directly learn the joint distribution of discrete images for one-step visual synthesis, enabling coordinated language-visual modeling through learnable cross-modal attention mechanisms. \textbf{2) Dynamic Perception Pretraining}: We propose a bidirectional dynamic alignment strategy employing inverse dynamics tasks and forward dynamics tasks, effectively strengthening multimodal correlations within a unified feature space. \textbf{3) Reinforced Supervised Fine-Tuning}: While conducting instruction-based fine-tuning in the unified generation space, we construct a reinforce loss to align the spatial logic between textual actions and generated images, enabling the model to acquire spatio-awared multimodal planning capabilities.