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Video world models promise general-purpose interactive simulators, but their training is limited by action supervision: action labels are scarce, fragmented across incompatible specifications, and do not scale with the unlabeled video pretraining corpus. A common workaround jointly trains an action encoder to compress consecutive frames into a latent action and a decoder to reconstruct the next frame from the previous frame and that latent, forcing the latent to capture only new information. This has two limitations: learning the action space from scratch can limit generalization to unseen domains, and the bottleneck trades expressiveness for separation, with tighter settings losing nuance and looser ones risking scene leakage under domain shifts. We argue for a different starting point: rather than learning actions from scratch, we start from a pretrained foundation model (V-JEPA 2), whose embeddings of a frame pair already carry substantial action information after large-scale, diverse video pretraining. The remaining challenge is to extract the action while discarding the scene. We propose a label-free contrastive adaptation framework that pulls together frame pairs sharing the same motion under a different scene and pushes apart pairs from the same scene with different motion, reshaping the geometry of the pretrained space without imposing a reconstruction bottleneck. We introduce a unified evaluation protocol along three axes (action expressiveness, scene invariance, and action-conditioned video generation quality) across robot manipulation, camera navigation, game, and driving benchmarks, most of which are unseen during adaptation. Compared with annotation-free latent-action methods, our representations are substantially more expressive while matching their scene invariance, and they yield world models that transfer demonstrated actions to new scenes more faithfully.

Mathematical modeling turns an open-ended real-world problem into assumptions, a model, a solution, and a defended recommendation, and its answers matter only if they are both close to a credible reference and physically feasible; existing benchmarks either score solver fragments or grade reports with an LLM judge, leaving those numbers unchecked. We introduce TB-MathModel (the Terminal-style Mathematical Modeling Bench), the first benchmark to make complete contest-style modeling problems agentic, verifiable, and terminal at once, over 18 real CUMCM and MCM problems (2023--2025). Each task ships the verbatim statement, official attachments, and figures in a containerized terminal; the agent returns one JSON artifact, scored on the numeric core of the final question against a reproduction of the Outstanding-award paper. Two design choices distinguish it: direction-aware, one-sided scoring, which never penalises beating the anchor, and two-layer feasibility verification---a programmatic gate over six decidable invariant forms plus 624 Lean~4 obligations---with a hard gate that zeroes infeasible answers. Each task is scored against a panel of human outstanding papers rather than one, so a model must be close to many accepted answers; across seven multimodal entries (three seeds each) the strongest reach a multi-reference O-Eval of 64.58\%, while the \$2.54 open model holds 59.81\% at $1/100$ the cost. TB-MathModel turns the numeric core of modeling into a reproducible, machine-checkable signal for measuring long-horizon modeling competence and for collecting agent trajectories. The source code is available at https://github.com/wxj630/terminal-bench-math-modeling.

World models learn to predict the temporal evolution of visual observations given a control signal, potentially enabling agents to reason about environments through forward simulation. Because of the focus on forward simulation, current world models generate predictions based on factual observations. For many emerging applications, such as comprehensive evaluations of physical AI behavior under varying conditions, the ability of world models to answer counterfactual queries -- such as "what would happen if this object was removed?" -- is of increasing importance. We formalize counterfactual world models that additionally take interventions as explicit inputs, predicting temporal sequences under hypothetical modifications to observed scene properties. Traditional world models operate directly on entangled pixel-space representations where object properties and relationships cannot be selectively modified. This modeling choice prevents targeted interventions on specific scene properties. We introduce CWMDT, a framework to overcome those limitations, turning standard video diffusion models into effective counterfactual world models. First, CWMDT constructs digital twins of observed scenes to explicitly encode objects and their relationships, represented as structured text. Second, CWMDT applies large language models to reason over these representations and predict how a counterfactual intervention propagates through time to alter the observed scene. Third, CWMDT conditions a video diffusion model with the modified representation to generate counterfactual visual sequences. Evaluations on two benchmarks show that the CWMDT approach achieves state-of-the-art performance, suggesting that alternative representations of videos, such as the digital twins considered here, offer powerful control signals for video forward simulation-based world models.

Reliable evaluation of visual 3D reconstruction and depth estimation in vegetation-rich outdoor environments is limited by the scarcity of geometric ground-truth data and the cost of complete scanner surveys. We present a LiDARbased reference-generation pipeline for evaluating the zero-shot performance of feed-forward visual-geometry models alongside conventional structure-from-motion (SfM) methods. The pipeline reuses camera images, LiDAR scans, and reference poses from existing multi-sensor localization datasets to generate per-view depth maps and visible reference point clouds. To address visibility errors in accumulated LiDAR scans, we introduce the LargeDepth-Gap Visibility Score (LDGVS) for point-wise visibility filtering and automatic scale selection in Hidden Point Removal(HPR). Experiments on TartanAirV2 and TartanGround show that, compared with Poisson surface reconstruction, which is an approach suited to completed scan surveys, the combined HPR and LDGVS filtering retains approximately three times the point density at comparable absolute relative error. We also apply the pipeline to the BotanicGarden dataset to systematically compare depth estimation and 3D reconstruction methods. Feedforward methods produce dense depth predictions efficiently, but their 3D reconstructions can contain duplicated structures. Conventional SfM generally produces more coherent geometry, but its reconstructions remain sparse and more prone to failure in challenging vegetated scenes. The benchmark toolkit and datasets will be released.