Spatiotemporal Reasoning

Embodied-AI agents must reason about how objects move and interact in 3-D space over time, yet existing smaller frontier Large Language Models (LLMs) still mis-handle fine-grained spatial relations, metric distances, and temporal orderings. We introduce the general framework Formally Explainable Spatio-Temporal Scenes (FESTS) that injects verifiable spatio-temporal supervision into an LLM by compiling natural-language queries into Spatial Regular Expression (SpRE) -- a language combining regular expression syntax with S4u spatial logic and extended here with universal and existential quantification. The pipeline matches each SpRE against any structured video log and exports aligned (query, frames, match, explanation) tuples, enabling unlimited training data without manual labels. Training a 3-billion-parameter model on 27k such tuples boosts frame-level F1 from 48.5% to 87.5%, matching GPT-4.1 on complex spatio-temporal reasoning while remaining two orders of magnitude smaller, and, hence, enabling spatio-temporal intelligence for Video LLM.

Executing complex manipulation in cluttered environments requires satisfying coupled geometric and temporal constraints. Although Spatio-Temporal Logic (SpaTiaL) offers a principled specification framework, its use in gradient-based optimization is limited by non-differentiable geometric operations. Existing differentiable temporal logics focus on the robot's internal state and neglect interactive object-environment relations, while spatial logic approaches that capture such interactions rely on discrete geometry engines that break the computational graph and preclude exact gradient propagation. To overcome this limitation, we propose Differentiable SpaTiaL, a fully tensorized toolbox that constructs smooth, autograd-compatible geometric primitives directly over polygonal sets. To the best of our knowledge, this is the first end-to-end differentiable symbolic spatio-temporal logic toolbox. By analytically deriving differentiable relaxations of key spatial predicates--including signed distance, intersection, containment, and directional relations--we enable an end-to-end differentiable mapping from high-level semantic specifications to low-level geometric configurations, without invoking external discrete solvers. This fully differentiable formulation unlocks two core capabilities: (i) massively parallel trajectory optimization under rigorous spatio-temporal constraints, and (ii) direct learning of spatial logic parameters from demonstrations via backpropagation. Experimental results validate the effectiveness and scalability of the proposed framework.

Spatiotemporal reasoning is a fundamental capability for artificial intelligence (AI) in soft tissue surgery, paving the way for intelligent assistive systems and autonomous robotics. While 2D vision-language models show increasing promise at understanding surgical video, the spatial complexity of surgical scenes suggests that reasoning systems may benefit from explicit 4D representations. Here, we propose a framework for equipping surgical agents with spatiotemporal tools based on an explicit 4D representation, enabling AI systems to ground their natural language reasoning in both time and 3D space. Leveraging models for point tracking, depth, and segmentation, we develop a coherent 4D model with spatiotemporally consistent tool and tissue semantics. A Multimodal Large Language Model (MLLM) then acts as an agent on tools derived from the explicit 4D representation (e.g., trajectories) without any fine-tuning. We evaluate our method on a new dataset of 134 clinically relevant questions and find that the combination of a general purpose reasoning backbone and our 4D representation significantly improves spatiotemporal understanding and allows for 4D grounding. We demonstrate that spatiotemporal intelligence can be "assembled" from 2D MLLMs and 3D computer vision models without additional training. Code, data, and examples are available at https://tum-ai.github.io/surg4d/

The growing interest in embodied agents increases the demand for spatiotemporal video understanding, yet existing benchmarks largely emphasize extractive reasoning, where answers can be explicitly presented within spatiotemporal events. It remains unclear whether multimodal large language models can instead perform abstractive spatiotemporal reasoning, which requires integrating observations over time, combining dispersed cues, and inferring implicit spatial and contextual structure. To address this gap, we formalize abstractive spatiotemporal reasoning from videos by introducing a structured evaluation taxonomy that systematically targets its core dimensions and constructs a controllable, scenario-driven synthetic egocentric video dataset tailored to evaluate abstractive spatiotemporal reasoning capabilities, spanning object-, room-, and floor-plan-level scenarios. Based on this framework, we present VAEX-BENCH, a benchmark comprising five abstractive reasoning tasks together with their extractive counterparts. Our extensive experiments compare the performance of state-of-the-art MLLMs under extractive and abstractive settings, exposing their limitations on abstractive tasks and providing a fine-grained analysis of the underlying bottlenecks. The dataset will be released soon.

Enabling reliable long-horizon robotic manipulation is a crucial step toward open-world embodied intelligence. However, VLM-based planners treat each step as an isolated observation-to-action mapping, forcing them to reinfer scene geometry from raw pixels at every decision point while remaining unaware of how prior actions have reshaped the environment. Despite strong short-horizon performance, these systems lack the spatio-temporal reasoning required for persistent geometric anchoring and memory of action-triggered state transitions. Without persistent state tracking, perceptual errors accumulate across the execution horizon, temporarily occluded objects are catastrophically forgotten, and these compounding failures lead to precondition violations that cascade through subsequent steps. In contrast, humans maintain a persistent mental model that continuously tracks spatial relations and action consequences across interactions rather than reconstructing them at each instant. Inspired by this human capacity for causal spatio-temporal reasoning with persistent memory, we propose RoboStream, a training-free framework that achieves geometric anchoring through Spatio-Temporal Fusion Tokens (STF-Tokens), which bind visual evidence to 3D geometric attributes for persistent object grounding, and maintains causal continuity via a Causal Spatio-Temporal Graph (CSTG) that records action-triggered state transitions across steps. This design enables the planner to trace causal chains and preserve object permanence under occlusion without additional training or fine-tuning. RoboStream achieves 90.5% on long-horizon RLBench and 44.4% on challenging real-world block-building tasks, where both SoFar and VoxPoser score 11.1%, demonstrating that spatio-temporal reasoning and causal memory are critical missing components for reliable long-horizon manipulation.

Humans inhabit a physical 4D world where geometric structure and semantic content evolve over time, constituting a dynamic 4D reality (spatial with temporal dimension). While current Multimodal Large Language Models (MLLMs) excel in static visual understanding, can they also be adept at "thinking in dynamics", i.e., perceive, track and reason about spatio-temporal dynamics in evolving scenes? To systematically assess their spatio-temporal reasoning and localized dynamics perception capabilities, we introduce Dyn-Bench, a large-scale benchmark built from diverse real-world and synthetic video datasets, enabling robust and scalable evaluation of spatio-temporal understanding. Through multi-stage filtering from massive 2D and 4D data sources, Dyn-Bench provides a high-quality collection of dynamic scenes, comprising 1k videos, 7k visual question answering (VQA) pairs, and 3k dynamic object grounding pairs. We probe general, spatial and region-level MLLMs to express how they think in dynamics both linguistically and visually, and find that existing models cannot simultaneously maintain strong performance in both spatio-temporal reasoning and dynamic object grounding, often producing inconsistent interpretations of motion and interaction. Notably, conventional prompting strategies (e.g., chain-of-thought or caption-based hints) provide limited improvement, whereas structured integration approaches, including Mask-Guided Fusion and Spatio-Temporal Textual Cognitive Map (ST-TCM), significantly enhance MLLMs' dynamics perception and spatio-temporal reasoning in the physical 4D world. Code and benchmark are available at https://dyn-bench.github.io/.

Spatial reasoning, the ability to understand spatial relations, causality, and dynamic evolution, is central to human intelligence and essential for real-world applications such as autonomous driving and robotics. Existing studies, however, primarily assess models on visible spatio-temporal understanding, overlooking their ability to infer unseen past or future spatial states. In this work, we introduce Spatial Causal Prediction (SCP), a new task paradigm that challenges models to reason beyond observation and predict spatial causal outcomes. We further construct SCP-Bench, a benchmark comprising 2,500 QA pairs across 1,181 videos spanning diverse viewpoints, scenes, and causal directions, to support systematic evaluation. Through comprehensive experiments on {23} state-of-the-art models, we reveal substantial gaps between human and model performance, limited temporal extrapolation, and weak causal grounding. We further analyze key factors influencing performance and propose perception-enhancement and reasoning-guided strategies toward advancing spatial causal intelligence. The project page is https://guangstrip.github.io/SCP-Bench.

Geo-temporal understanding, the ability to infer location, time, and contextual properties from visual input alone, underpins applications such as disaster management, traffic planning, embodied navigation, world modeling, and geography education. Although recent vision-language models (VLMs) have advanced image geo-localization using cues like landmarks and road signs, their ability to reason about temporal signals and physically grounded spatial cues remains limited. To address this gap, we introduce TimeSpot, a benchmark for evaluating real-world geo-temporal reasoning in VLMs. TimeSpot comprises 1,455 ground-level images from 80 countries and requires structured prediction of temporal attributes (season, month, time of day, daylight phase) and geographic attributes (continent, country, climate zone, environment type, latitude-longitude) directly from visual evidence. It also includes spatial-temporal reasoning tasks that test physical plausibility under real-world uncertainty. Evaluations of state-of-the-art open- and closed-source VLMs show low performance, particularly for temporal inference. While supervised fine-tuning yields improvements, results remain insufficient, highlighting the need for new methods to achieve robust, physically grounded geo-temporal understanding TimeSpot is available at: https://TimeSpot-GT.github.io.

Humans are born with vision-based 4D spatial-temporal intelligence, which enables us to perceive and reason about the evolution of 3D space over time from purely visual inputs. Despite its importance, this capability remains a significant bottleneck for current multimodal large language models (MLLMs). To tackle this challenge, we introduce MLLM-4D, a comprehensive framework designed to bridge the gaps in training data curation and model post-training for spatiotemporal understanding and reasoning. On the data front, we develop a cost-efficient data curation pipeline that repurposes existing stereo video datasets into high-quality 4D spatiotemporal instructional data. This results in the MLLM4D-2M and MLLM4D-R1-30k datasets for Supervised Fine-Tuning (SFT) and Reinforcement Fine-Tuning (RFT), alongside MLLM4D-Bench for comprehensive evaluation. Regarding model training, our post-training strategy establishes a foundational 4D understanding via SFT and further catalyzes 4D reasoning capabilities by employing Group Relative Policy Optimization (GRPO) with specialized Spatiotemporal Chain of Thought (ST-CoT) prompting and Spatiotemporal reward functions (ST-reward) without involving the modification of architecture. Extensive experiments demonstrate that MLLM-4D achieves state-of-the-art spatial-temporal understanding and reasoning capabilities from purely 2D RGB inputs. Project page: https://github.com/GVCLab/MLLM-4D.

Understanding the complex, multi-agent dynamics of urban traffic remains a fundamental challenge for video language models. This paper introduces Urban Dynamics VideoQA, a benchmark dataset that captures the unscripted real-world behavior of dynamic urban scenes. UDVideoQA is curated from 16 hours of traffic footage recorded at multiple city intersections under diverse traffic, weather, and lighting conditions. It employs an event-driven dynamic blur technique to ensure privacy preservation without compromising scene fidelity. Using a unified annotation pipeline, the dataset contains 28K question-answer pairs generated across 8 hours of densely annotated video, averaging one question per second. Its taxonomy follows a hierarchical reasoning level, spanning basic understanding and attribution to event reasoning, reverse reasoning, and counterfactual inference, enabling systematic evaluation of both visual grounding and causal reasoning. Comprehensive experiments benchmark 10 SOTA VideoLMs on UDVideoQA and 8 models on a complementary video question generation benchmark. Results reveal a persistent perception-reasoning gap, showing models that excel in abstract inference often fail with fundamental visual grounding. While models like Gemini Pro achieve the highest zero-shot accuracy, fine-tuning the smaller Qwen2.5-VL 7B model on UDVideoQA bridges this gap, achieving performance comparable to proprietary systems. In VideoQGen, Gemini 2.5 Pro, and Qwen3 Max generate the most relevant and complex questions, though all models exhibit limited linguistic diversity, underscoring the need for human-centric evaluation. The UDVideoQA suite, including the dataset, annotation tools, and benchmarks for both VideoQA and VideoQGen, provides a foundation for advancing robust, privacy-aware, and real-world multimodal reasoning. UDVideoQA is available at https://ud-videoqa.github.io/UD-VideoQA/UD-VideoQA/.

The special Galilean group, usually denoted SGal(3), is a 10-dimensional Lie group whose important subgroups include the special orthogonal group, the special Euclidean group, and the group of extended poses. We briefly describe SGal(3) and its Lie algebra and show how the group structure supports a unified representation of uncertainty in space and time. Our aim is to highlight the potential usefulness of this group for several robotics problems.