Building Blocks

Roofing requires workers to coordinate locomotion, balance, and work-related body motions on pitched surfaces, creating a challenging application for humanoid robots. Directly retargeted human demonstrations, however, may preserve motion appearance while placing the robot's feet or hands incorrectly relative to the roof. This study presents a task-semantic scene-grounded framework for learning roofer-style whole-body motions on a Unitree G1. Human demonstrations are captured using a tracking system and retargeted to the robot, while a metric roof model supplies the spatial reference unavailable from the tracking system. A trajectory-level optimization grounds inferred support contacts and annotated work relations to the roof, and execution-aware reinforcement learning encourages the resulting policy to preserve these relations under dynamic tracking errors. The framework is evaluated through a multi-motion tracking study, a roof-pitch coverage matrix, a five-way nailgun ablation, cross-task experiments on hammering and lateral pushing, and comparisons with pure reinforcement learning and zero-shot teleoperation. Our method enables the robot to satisfy support, work-clearance, and nonpenetration criteria across all evaluated seeds. Across nailgun, hammering, and pushing, it achieves work-clearance errors between 0.256 and 0.531 cm and 3/3 successful evaluations per task. Physical experiments reproduce uphill walking, nailgun, hammering, and bending motions with mean base-frame motion errors below 80 mm. These findings establish scene-grounded human motion learning as a promising basis for construction-oriented humanoid motion primitives.

We introduce LEGO for advanced open-vocabulary scene understanding. Beyond basic concept recognition, its core innovation lies in capturing the intrinsic semantic hierarchies within the scene, such as the "flowerpot -> bouquet -> bud -> petal" lineage. While foundation models like SAM can identify multi-granular structures in 2D, their partitions are strictly perspective-bound and lack cross-view consensus. LEGO self-adaptively re-grades volatile multi-view SAM granularities into a unified, 3D-consistent hierarchy. This provides precise supervision for the structurally coherent, multi-level segmentation of 3D scenes. By grounding these segments with CLIP embeddings, LEGO recovers open-vocabulary semantic logic across hierarchical levels. Furthermore, by incorporating spatial relationships, we elevate these segments into level-wise language scene graphs, effectively empowering Large Language Models to perform complex, context-aware spatial reasoning and precise visual grounding. Experimental results demonstrate that LEGO establishes new state-of-the-art performance across both promptable and open-vocabulary 3D segmentation benchmarks, exhibiting advanced hierarchical scene decomposition and context-aware spatial reasoning.

Producing a hand-buildable, colored brick model of a 3D object from a few casual photographs is a clean testbed for a broader challenge: generating 3D content that meets hard physical-assembly constraints under a discrete, budget-limited voxel grid. On a coarse lattice, visual resemblance and structural stability pull against each other, yet prior brick pipelines address only one side and treat voxelization as fixed preprocessing rather than a variable to optimize. We present ResemBrick, which couples the two. Budgeted occupancy completion reframes discretization as allocation: given a target occupied-voxel count, a single resolution-conditioned network decides in one feed-forward pass which surface voxels to fill for best appearance, one weight set spanning 13 resolutions. Buildability by construction then combines support- and look-ahead-aware greedy placement with a deterministic, provably terminating repair that grounds every floating component. Under a matched budget, ResemBrick surpasses existing voxel selectors in perceptual fidelity while uniquely reaching zero floating and zero unstable bricks on unfiltered held-out objects; as a complete pipeline, it attains the best perceptual fidelity among prior brick-construction systems. Our results point to treating discretization and assembly as tightly coupled stages rather than independent ones.

An interlocking assembly is an assembly in which component parts are connected purely through their geometric arrangement, without relying on external connectors such as glue and nails. Such assemblies have been widely used in a variety of real-world applications due to their structural stability. The problem of generating interlocking assemblies is generally formulated as a shape decomposition problem, where a target 3D object represented as a voxel grid is partitioned into a prescribed number of interlocking pieces. We observe that generating interlocking assemblies is inherently a sequential decision-making problem, where an agent repeatedly decides which piece each voxel should be assigned to. Inspired by the observation, we propose the first reinforcement learning framework RL-Lock for generating interlocking assemblies, without relying on handcrafted search heuristics as existing works did. RL-Lock combines structured action chunking with MCTS-guided policy-value learning to efficiently navigate the large combinatorial search space for interlocking assembly generation. We demonstrate through experiments that RL-Lock allows effective generation of interlocking assemblies, especially for challenging cases in which existing approaches take too long or even fail to find a valid solution.

Hyperspectral image classification is complicated by mixed pixels, spectral ambiguity, class imbalance, and limited annotations. Most current classifiers encode a pixel or patch as a deterministic vector and apply a linear or multilayer softmax head. Although effective for discrimination, this representation does not directly expose how mixed or uncertain a sample is. This paper presents \method, a classical density-matrix representation learning framework for hyperspectral images. The spectral bands are divided into groups and each group is mapped to a positive semi-definite, Hermitian, trace-normalized matrix state. A composable stack of spectral, spatial, and inter-group transitions then updates the states while repeatedly projecting them back to the valid state set. Instead of flattening the final features, \method\ aggregates the group states and compares them with learnable class-prototype density matrices through Uhlmann fidelity. The normalized eigenspectrum, von Neumann entropy, purity, and prototype fidelity provide sample-level diagnostics that are unavailable from a conventional vector head. On Indian Pines, ten runs yield an overall accuracy of $96.20\pm0.70\%$, an average accuracy of $95.57\pm1.29\%$, and a kappa coefficient of $95.66\pm0.80\%$. On WHU-Hi-LongKou, the best of ten runs reaches $97.52\%$ overall accuracy. Classification maps and feature projections show that the transition stack produces compact and better separated class structures. The results support constrained matrix-state learning as a practical alternative to vector-only hyperspectral classification without requiring quantum hardware.

Building sensors are embedded in physical topology, spatial hierarchy, and operational context, yet existing forecasters often treat them as isolated time series or rely on fixed covariate sets. We present TopoBrick, a training-free framework for zero-shot building IoT (Internet-of-Things) forecasting. TopoBrick uses building knowledge graphs to construct a compact structural skeleton and employs an agentic topology sampler to select target-specific exogenous variables. The selected variables are organized by deployment-time availability, separating past-known sensor states from future-known calendar, schedule, and meteorological exogenous variables. Across three real-world buildings, TopoBrick outperforms strong zero-shot foundation-model baselines and remains competitive with fully trained building-specific models. Ablations show that topology-aware sampling is more reliable than random, ontology-only, or fixed-hop selection, especially for physically coupled HVAC and weather-driven sensing variables.

We introduce a categorical framework called ODYSSEY for constructing verifiable, local truth-preserving foundation models as compositions of foundries: building-block architectural components that specify a cover of local contexts, local representation families, restriction maps, gluing rules, obstruction policies, update obligations, and human-facing views. A foundry is an organized sheaf of knowledge that carries within it an argumentation component. Concrete foundries are built from generic foundries such as evidence/argument, operational decision, institutional/financial, market meaning, scientific challenge, research-program, assistant-build, and evaluation-harness foundries. Universal Foundry Learning (UFL) formalizes foundry construction as a composition of left and right Kan extensions, with left Kan extension rolling local artifacts into candidate foundries and right Kan extension enforcing the restriction, gluing, obstruction, and argumentation conditions required for promotion. Foundry SQL (FSQL) is a small typed query surface for slicing maintained foundry artifacts that uses TICKET (Topos Integration using Causal Kan Extension Transformers) certification for admitting external or pre-built models into durable ODYSSEY state. ODYSSEY is fully implemented and tested across a wide spectrum of concrete foundries, showing that the same categorical machinery supports domain construction, artifact replay, sheaf diagnostics, grounded Toulmin/local-LLM scrutiny, residual-obstruction ledgers, and optimized TICKET-compatible causal-claim extraction across heterogeneous sources. This paper is to be presented as a 2.5 hour tutorial at ICML 2026. The tutorial home page is at https://bit.ly/4ajS0nA.

Agentic AI systems orchestrate multiple LLM-based agents through workflow architectures that coordinate decisions, tools, and external actions. While current platforms emphasize runtime safeguards, little support exists for verifying workflows during system design. From a Modeling & Simulation perspective, this gap is analogous to composing conceptual models without verifying whether their building blocks interact coherently. We propose a design-time verification approach that models agentic workflows as compositions of reusable building blocks and checks their compatibility through twelve structural rules. We implemented these rules in a software prototype and evaluated them using two openly released datasets: 48 workflows with known design flaws and 168 variants that preserve workflow logic but alter graph structure. Results show that our verifier reliably detects violations even when flawed designs are obscured through structural transformations such as splitting tasks between agents. Future works could combine our verification with community repositories of building blocks to compose safe agentic workflows.

Model-based Reinforcement Learning (MBRL) has achieved remarkable success in continuous control by leveraging latent world models. However, prevailing approaches typically rely on monolithic latent dynamics, entangling environment dynamics into a coupled process. This coupling severely limits reusability: altering the agent necessitates retraining the entire world from scratch, even if the environment remains constant. To address this, we introduce BRICKS-WM (Building Reusability via Interface Composition Kinetics for Structured World Models), a framework for the modular assembly of structured world models. Driven by the insight that the physical world is composed of independent entities, we posit that global dynamics can be modeled as a composition of distinct dynamical modules interacting via latent interfaces. As a minimal instantiation, we factorize the latent state space into an actuated Agent module and an external Background module, bridged by a learned latent interface. Unlike prior object-centric methods that prioritize visual segmentation, BRICKS-WM enforces a functional separation in transition dynamics, ensuring that background dynamics remains agnostic to the agent's dynamics. Empirically, BRICKS-WM achieves control performance comparable to strong monolithic baselines when trained from scratch, and enables the reuse of frozen background dynamics across agents.

Reinforcement Learning (RL) with verifiable environments has emerged as a powerful approach for enhancing the reasoning capabilities of Large Language Models (LLMs). While prior research demonstrates that scaling environment quantity improves RL performance, existing manual or individual construction methods suffer from linear scaling limits, thereby hindering scalable reasoning generalization. This paper introduces RACES (\textbf{R}ecursive \textbf{A}utomated \textbf{C}omposition for \textbf{E}nvironment \textbf{S}caling), a framework that conceptualizes verifiable environments as composable building blocks that can be recursively assembled. The key insight is that when the codomain (output type) of one environment matches the domain (input type) of another, they can be automatically fused into a new verifiable environment, enabling recursive composition. RACES is implemented with 300 individual environments and defines a set of composition operators (\textsc{SEQUENTIAL}, \textsc{PARALLEL}, \textsc{SORT}, and \textsc{SELECT}) that induce diverse reasoning patterns. Extensive experiments show that RL training on these composite environments consistently enhances reasoning generalization. Specifically, RACES improves DeepSeek-R1-Distill-Qwen-14B by an average of 3.1 points (from 48.2 to 51.3) and boosts Qwen3-14B performance from 58.8 to 61.1 on six benchmarks, which are unseen during the construction of training environments. Moreover, RACES achieves performance comparable to training on 300 individual environments using only 50 base environments, demonstrating significant efficiency in environment utilization.

We dream of AI agents that can read arbitrary designs and construct real-world objects from reusable building blocks. As a first step toward this vision, we study whether multimodal large language models (MLLMs) possess the visual grounding and spatial reasoning capabilities required for brick assembly. We formulate brick assembly as a sequential decision-making problem, where each step involves two subtasks: brick selection, identifying the target brick from candidate components, and brick pose estimation, predicting where and how the selected brick should be placed. To support this study, we introduce BC-Bench (Brick Construction Benchmark), the first benchmark for evaluating MLLMs on assembly with diverse bricks. Experiments show that current state-of-the-art MLLMs remain far from reliable builders, struggling with fine-grained brick selection and failing at precise pose estimation. To bridge this gap, we propose Brick-Composer, a learning framework that equips MLLMs with assembly skills through three complementary signals: Human Design Sparks, which provide affordance-rich construction demonstrations; World Feedback, which grounds predicted actions in visual and physical consequences; and Synthetic Experience, which scales learning beyond existing object designs. Brick-Composer improves brick selection accuracy by over three times, substantially reduces pose estimation errors, and raises strict step-level assembly success from less than 1% to around 15%. After training, a Qwen-3-8B can correctly compose up to 42% of the steps for a complete object, suggesting that MLLMs can acquire assembly capabilities through targeted, physically grounded learning.

LLM-based LEGO assembly generation requires both semantic grounding and physical feasibility. We identify a data-induced failure mode, PhysHack, in which the assemblies satisfy physical-validity constraints while producing structures that are geometrically misaligned, semantically inconsistent, or poorly calibrated. To address this challenge, we propose a model-based data selection approach that uses only a small fraction of the training data while improving physically grounded LEGO assembly generation. Building on the selected trajectories, we introduce PVPO, a sample-efficient reinforcement learning method that couples physical feasibility with voxel-space geometric rewards. Our results show that physical validity alone is an insufficient proxy for reliable physical reasoning: models can learn to generate valid structures without preserving semantic or geometric fidelity. Experiments across model backbones and test-time scaling settings demonstrate that PVPO improves structural and semantic alignment, physical validity, structural stability, and calibration, while reducing reliance on extensive post-hoc rejection sampling. In particular, results on calibration show that PVPO mitigates PhysHack by making test-time selection more predictive of semantic and structural quality.

We present a multi-modal classification framework that fuses satellite and street-level imagery through a Perceiver IO architecture operating on spatial patch tokens from a shared DINOv2 backbone. The design naturally handles a variable number of street-level views per building without padding or fixed-size pooling, and jointly predicts multi-label roof element and roof material classes. We construct a large-scale dataset of 32,135 buildings (61,672 segments) spanning ten countries, pairing satellite images with up to eight street-level views per segment and evaluating four masking strategies for isolating the target building. We propose an RGB-M masking strategy that appends the building footprint mask as a fourth input channel, providing a soft spatial prior that outperforms hard cropping across both modalities. The Perceiver IO fusion model improves over all other fusion strategies and yields substantial per-class gains for attributes visible from street level (e.g., +11.3 AP for slate, +1.3 AP for dormers), though the satellite-only baseline retains a slight advantage in macro-averaged mAP for classes that are predominantly visible from above. These results establish a scalable, flexible architecture for multi-modal building inspection that can accommodate heterogeneous inputs and multiple output tasks.

We present a method for jointly predicting instance-level roof segment masks together with three continuous geometric attributes -- building height, roof slope, and roof azimuth -- from a single aerial orthophoto. Our approach extends Mask R-CNN with a dedicated attribute regression branch and introduces two key innovations: a conditional azimuth loss that suppresses supervision for flat roof segments where azimuth labels are inherently noisy, and a log-normalized height representation that addresses the heavily skewed distribution of building heights. We train and evaluate on a large-scale dataset of Dutch aerial images paired with automatically derived ground truth from 3DBAG, a nationwide LiDAR-based 3D building dataset. Using a DINOv3 ConvNeXt-Base backbone, our method achieves a mean absolute error of approximately 4 degrees for roof slope, 7 degrees for azimuth, and 1 meter for building height, with an instance segmentation AP$_{50}$ of 0.566. The predicted per-segment masks and attributes are sufficient to reconstruct simplified 3D building models (LoD2) from a single overhead image, requiring expensive 3D reference data only for training.

Generating physically buildable brick structures from 3D shapes requires more than geometric reconstruction: the output must also satisfy discrete part constraints and structural stability. Existing brick generation methods either rely on heuristic optimization, which can break down when the target 3D shape does not admit a feasible structure under predefined constraints, or generate brick sequences without explicitly modeling the underlying 3D geometry and assembly relations. In this work, we present BrickAnything, a geometry-conditioned autoregressive framework for generating buildable brick structures from diverse 3D representations. BrickAnything uses point clouds as a unified geometric interface and predicts brick sequences that reconstruct the target shape under assembly constraints. To model structural dependencies among bricks, we introduce a structure-aware tree tokenization, which represents brick structures through local attachment relations. This formulation makes sequence generation more consistent with the physical construction process, and reduces invalid intermediate states. We further introduce preference-based alignment post-training, validity-constrained decoding and adaptive rollback to improve buildability objectives such as stability and geometric fidelity. Extensive experiments demonstrate that BrickAnything produces geometrically faithful and physically realizable brick structures, and that the proposed tokenization effectively reduces rollback and regeneration compared with conventional ordering strategies.

Autonomous robotic assembly of interlocking bricks demands seamless integration of long-horizon task reasoning, spatial grounding, and fine-grained manipulation. This paper presents BrickCraft, a compositional framework designed for long-horizon and generalizable interlocking brick assembly. BrickCraft models the assembly process using a relative formulation, where each step is anchored to a reference brick within the partial structure, thereby decomposing complex tasks into a finite set of reusable primitive skills. BrickCraft bridges the gap between high-level assembly plans and physical execution through situated manuals, which provide explicit spatial guidance for learned visuomotor skills by projecting the assembly intent onto real-time robot observations. Finally, BrickCraft employs a compositional execution pipeline that chains these spatially grounded skills to accomplish long-horizon assembly tasks. Extensive experimental validations demonstrate that BrickCraft acquires proficient assembly skills from a limited set of demonstrations and exhibits strong compositional generalization to unseen structures. The project website is available at https://intelligent-control-lab.github.io/BrickCraft.

While autoregressive models have advanced 3D generation, creating physically stable brick structures remains a challenge due to the strict requirements of gravity and interconnectivity. Existing approaches rely on external physical simulators during inference to perform rejection sampling and brick-by-brick rollbacks, which severely bottlenecks efficiency. To address this, we propose a reinforcement learning paradigm that shifts physical validity enforcement from test-time correction to training-time policy optimization. By utilizing assembly-level rewards, the model optimizes for collision avoidance, global connectivity, structural interlocking, and shape conformity. This paradigm allows the model to internalize physical priors, enabling the first rollback-free generation of stable brick structures. Experimental results demonstrate that our approach achieves state-of-the-art generation quality while accelerating inference speed by orders of magnitude. Our code and dataset are available at https://github.com/miniHuiHui/STABLE. Our models are available at https://huggingface.co/miniHui/STABLE.

Foundation models excel at language, where sentences become tokens, and vision, where images become pixels, because both reduce to discrete symbols on a shared, fixed grid. Knowledge Graphs share the discreteness, but not the geometry. Their entities and relations are discrete symbols, yet their arrangement is relational and lacks a common, fixed grid. Knowledge Graphs (KGs) share the discreteness, but not the geometry. They form irregular, non-Euclidean topologies whose local neighborhoods differ from graph to graph. Therefore, Knowledge Graph Foundation Models (KGFMs) rely on identifying structural invariances to produce transferable representations. Without a universal token set, KGFMs are limited in their ability to transfer representations across unseen KGs. We close this gap by treating graphlets, small connected graphs, as structural tokens that recur in heterogeneous KGs. In this paper, We introduce a model-agnostic framework based on a vocabulary of graphlets that mines a KG between relations via pattern matching. In particular, we considered closed and open 2- and 3-path, and star graphlets, to obtain robust invariances. The framework is evaluated on 51 KGs from a wide range of domains, for zero-shot inductive and transductive link prediction. Experiments show that adding simple graphlets to the vocabulary yields models that outperform prior KGFMs.

Despite transformative advances in generative motion synthesis, real-time interactive motion control remains dominated by traditional techniques. In this work, we identify two key challenges in bridging research and production: 1) Real-time scalability: Industry applications demand real-time generation of a vast repertoire of motion skills, while generative methods exhibit significant degradation in quality and scalability under real-time computation constraints, and 2) Integration: Industry applications demand fine-grained multi-modal control involving velocity commands, style selection, and precise keyframes, a need largely unmet by existing text- or tag-driven models. To overcome these limitations, we introduce MotionBricks: a large-scale, real-time generative framework with a two-fold solution. First, we propose a large-scale modular latent generative backbone tailored for robust real-time motion generation, effectively modeling a dataset of over 350,000 motion clips with a single model. Second, we introduce smart primitives that provide a unified, robust, and intuitive interface for authoring both navigation and object interaction. Applications can be designed in a plug-and-play manner like assembling bricks without expert animation knowledge. Quantitatively, we show that MotionBricks produces state-of-the-art motion quality on open-source and proprietary datasets of various scales, while also achieving a real-time throughput of 15,000 FPS with 2ms latency. We demonstrate the flexibility and robustness of MotionBricks in a complete production-level animation demo, covering navigation and object-scene interaction across various styles with a unified model. To showcase our framework's application beyond animation, we deploy MotionBricks on the Unitree G1 humanoid robot to demonstrate its flexibility and generalization for real-time robotic control.

Existing LLM-based EDA agents are often isolated task-specific systems. This leads to repeated engineering effort and limited reuse of successful design and debugging strategies. We present LEGO, a unified skill-based platform for front-end design generation. It decomposes the digital front-end flow into six independent steps and represents every agent capability as a standardized composable circuit skill within a plug-and-play architecture. To build this skill library, we survey more than 100 papers, select 11 representative open-source projects, and extract 42 executable circuit skills within a six-step finite state machine formulation. Circuit Skill Builder automates skill extraction with linear scalability. Agent Skill RAG achieves submillisecond retrieval without relying on embedding models. Empirical evaluation on a hard subset of 41 VerilogEval v2 problems that gpt-5.2-codex fails to solve under extra-high reasoning effort shows that individual circuit skills constructed within LEGO raise Pass@1 from 0.000 to 0.805. This is an 80.5% gain over the baseline. Cross-project skill compositions also reach 0.805 Pass@1. They outperform hierarchy-verilog by 14.6% and VerilogCoder by 2.5%. They also match MAGE. These results show that modular skill composition supports both effective and flexible RTL design automation. The LEGO platform and all circuit skills are publicly available at GitHub: https://github.com/loujc/LEGO-An-LLM-Skill-Based-Front-End-Design-Generation-Platform

We train a language model to generate LEGO-brick build sequences. While prior work has been restricted to discrete, voxel-like towers, we consider a much broader set of pieces, encompassing thousands of part types with diverse connection semantics. To enable this, we first collect a large-scale dataset of over 100,000 human-designed LDraw brick objects and scenes. The complexity of our setting makes it challenging to autoregressively assemble structures that satisfy physical constraints. When predicting block pose directly, build sequences quickly become invalid after a small number of steps. Although pieces are placed in 3D space, it is the spatial relationships of the parts which define the whole. With this in mind, we design a graph-based program representation that parametrizes structure through connectivity, improving the physical grounding of generated sequences. To enable future applications, we make our dataset and models available for research purposes. https://kulits.github.io/BrickNet

Recently, code-oriented large language models (LLMs) have demonstrated strong capabilities in translating natural language into executable code. Text-to-SQL is a significant application of this ability, enabling non-technical users to interact with relational databases using natural language. However, state-of-the-art models continue to struggle with highly complex logic, particularly deeply nested statements involving multiple joins and conditions, as well as with real-world database schemas that are noisy or poorly structured. In this paper, we investigate whether curriculum learning can improve the performance of code-based LLMs on Text-to-SQL tasks. Employing benchmarks including Spider and BIRD, we fine-tune models under different curriculum strategies. Our experiments show that naive curriculum, simply ordering training samples by complexity in a single epoch, fails to surpass standard fine-tuning due to catastrophic forgetting. To overcome this, we propose a Modular Adapter Composition (MAC) strategy. By sequentially training tier-specific adapters on incremental complexity levels (Easy to Extra-Hard), we create a scaffolded learning environment that improves performance on complex queries. Our approach not only produces measurable performance gains on the Spider and BIRD benchmarks but also provides a flexible, "Lego-like" architecture, allowing models to be composed and deployed based on specific schema difficulty requirements. These findings demonstrate that structured, modular learning is a superior alternative to monolithic fine-tuning for mastering the syntax and logic of complex code generation.

Accurately synthesizing 3D scenes from user-provided text descriptions is crucial for developing embodied agents. Despite the importance of scene-description alignment, existing evaluation methods for such text-guided 3D scene synthesis either capture only coarse similarity between the synthesized scene and the user description, or ignore the spatial reasoning for verifying object placement. None of them addressed the fine-grained constraints (e.g., X needs to be in the scene in a Y manner) implied by the description from users. To address this, we introduce LEGO, a benchmark dataset that pairs each user description with human-annotated constraints and a reference scene, and LEGO-Eval, an evaluation framework that decomposes a description into atomic constraints and verifies each one using tools that ground textual references to 3D objects and reason about their spatial relationships. We show that (i) LEGO-Eval evaluates misalignment far more accurately than existing methods and (ii) current scene synthesis approaches achieve at most 10% success rate in LEGO-Eval.

Today's AI models learn primarily through mimicry and refining, so it is not surprising that they struggle to solve problems beyond the limits set by existing data. To solve novel problems, agents should acquire skills by exploring and learning through experience. Finding a scalable learning mechanism for developing agents that learn through interaction remains a major open problem. In this work, we introduce BuilderBench, a benchmark to accelerate research into agent training that centers open-ended exploration. BuilderBench requires agents to learn how to build any structure using blocks. BuilderBench is equipped with (1) a simulator of a robot interacting with various physical blocks, and (2) a task-suite with over 50 diverse target structures that are carefully curated to test an understanding of physics, mathematics, and long-horizon planning. Agents are provided with a target structure at the start, and can interact with the environment for multiple episodes to experiment and learn various skills for building the structure. Solving these tasks requires \emph{embodied reasoning} in a way that is not reflected in words but rather in actions, experimenting with different strategies and piecing them together. Our experiments with multiple state-of-the-art frontier language model based agents and tabula rasa reinforcement learning algorithms show that these agents cannot solve any of the non-trivial tasks in the BuilderBench. Our analysis throws light on the lack of exploration abilities in these models.