Code World Models

Code world models represent world dynamics through explicit state and executable rules. We investigate how to coordinate object representations, behavioral revisions, and visual memory within this formulation. We present Mallea, a system for building, steering, and memorizing worlds from text. A coding agent infers object interaction requirements from the prompt and jointly plans object structure, properties, and rules, favoring compact representations that support those requirements. The world evolves under the planned rules; optional user actions steer it, while text requests can edit properties or extend capabilities with unaffected state preserved. Object texture memory retains reusable appearance only for whitebox-defined objects and adapts it as those objects change. The program advances world state, while a generative renderer combines current structure with remembered appearance. By organizing construction, intervention, and memory around the same objects, Mallea conditions subsequent observations on the latest state and compatible appearance. Project page: https://lxycopper.github.io/Mallea.

Rapid advances in large language models have made software engineering agents capable of tackling complex coding tasks. Within a containerized environment, a coding agent receives tool responses or execution results, and determines its later actions by those earlier results. However, most existing coding agents never look ahead: their policies do not anticipate the consequences of actions, and the terminal reward barely attributes a failure to certain earlier steps, so an ill-judged edit can corrupt the repository state irreversibly before any signal arrives. Recent code world models aim to address these challenges, but they are either trained and then frozen before reinforcement learning (RL), or reduced to an auxiliary next-token loss on the environment's outputs. We present ANTE (Anticipate, Then Execute), an agentic RL framework that verifies the policy's pre-action predictions by real execution and turns them into per-step credit for its actions and trust-or-abstain decisions. With an internal belief stated before each action, Belief-Anchored Policy Optimization (BAPO) turns the settled predictions into per-step advantages by anchoring credit on the policy's own forecasts. To turn the trained forecasts into better actions at inference, thereby facilitating effective test-time scaling, ANTE-TTO (test-time optimization) selects among candidate actions without an external scorer. ANTE raises Qwen3-32B from 25.0% to 57.2% pass@1 on SWE-bench Verified, 6.2% above a matched GRPO baseline trained without the belief state; its world model's accuracy climbs from 44% to 69% during RL, and the learned foresight capability transfers across harnesses and out-of-distribution domains. In summary, we aim to build a code world model that knows what has happened, what holds now, and what the next action will achieve.

We introduce CoDeR, a new paradigm for world modeling. Unlike existing video world models that implicitly represent world dynamics through visual observations, our system explicitly constructs an executable world with code and employs video generation models for visual realization. Specifically, we coordinate five complementary roles to translate high-level concepts into structured world rules, executable dynamics, and perceptual observations. This design enables long-term memory, open-ended interactions, autonomous world evolution, and multi-agent scenarios, where multiple entities can act, interact, and evolve persistently beyond the current observation. Extensive experiments demonstrate that our framework substantially extends the capabilities of existing world models, enabling long-term memory, open-ended interactions, autonomous evolution, and persistent multi-agent dynamics, while achieving state-of-the-art performance across multiple evaluation settings. Code and model weights will be made publicly available. Project Page: CoDeR.

Code world models represent worlds as executable programs, but this representation alone does not determine how to construct a complex world. We introduce Recursive Code World Models (RCWM), a framework for reconstructing complex 3D worlds in code from a single reference image. RCWM couples a Recursive Scene Program (RSP) representation with a construction solver that recursively calls itself. An RSP represents the executable world as compositional scene code, while each solver call follows the same complete process: establish the whole, recursively reconstruct unresolved parts, and revisit the whole to refine their composition. This global-local-global recursion gives fine-scale structures their own perception-and-editing loops while preserving scene-wide geometry and relationships. Reference-aligned views propagate a shared camera projection across levels, while parent revisitation addresses boundaries, spatial relations, and shared errors that emerge after local refinement. A vision-language coding agent directly compares reference images with scene renders to guide refinement, recursive descent, and return. Across complex scenes, RCWM outperforms prior code-based image-to-scene reconstruction methods. Ablation studies further support the benefits of recursive construction and suggest that deeper calls can improve finer-scale reconstruction. RCWM provides a recursive construction principle for building complex executable worlds from visual evidence.

VLM-driven self-improvement of web code has a structural flaw: the model that proposes the repair is the model that judges it, and visual plausibility under that judge is a poor proxy for whether the page actually works. What the loop is missing is a counterparty the VLM cannot fool, and the browser already is that counterparty: a deterministic, executable simulator of how an HTML artifact behaves under user actions, and in everything but name a world model for web code. We present WebWorld, the interface that lets a VLM prior interact with this browser-as-world-model autonomously and decides which interactions become supervision. Each round, the VLM emits a critique that the planner compiles into a typed interaction contract; the browser re-executes the candidate and issues an acceptance certificate only when both target progress and preservation of every previously verified capability hold; certified transitions accumulate as a quality ratchet that is the only thing the SFT export ever sees. Under matched training, WebWorld-27B improves Raw-27B by 5.3 points on HTMLBench-400 and 14.9 points on MiniAppBench-Val, and reaches the level of strong frontier systems such as Kimi-K2.6 and GPT-5.4 on interactive HTML generation. Equal-size ablations show that browser-backed admission carries the gain: without the certificate, the matched 9B lift nearly disappears.

A code world model accepted by a sampling gate can be exactly right on everything the gate can see and arbitrarily wrong beyond it. We characterize what a certified model can know, and what its errors can cost, when the omission is an annular freeze mode enclosing an unreachable interior. The gate quotient makes the question precise: acceptance-with-certainty determines the model exactly on the reachable query set; beyond reach is gauge. On a minimal ring instrument we prove the extreme case (a wrong-topology filled-disc artifact unfalsifiable by any sampling gate and bitwise harmless at play) and measure, with LLM synthesis across three model families, how one knob (a channel of width gamma) walks the same artifact through three regimes: unfalsifiable-and-harmless, falsifiable-and-costly, and instantly falsified. Three principles organize the empirics. First, danger is topology relative to reach: a channel the planner can use collapses the blind model's exploitation (play cost 1.09 to ~0 over a knee at gamma ~ 0.1), while a hidden channel with the same first Betti number keeps it at full strength (1.12). Second, repair is parameter-bound and sensor-bound: no family recovers the region from outside evidence; from inside, models pose the right topology but cannot pin its parameters, and the posed topology tracks the guiding persistent-homology summary's wrong beta_1 (a sensor with a measured geometric resolution limit), not the truth. Third, mitigation must match the error's dimension and direction: point fences fail against the one-dimensional boundary, a dimension-matched persisted fence collapses exploitation to a two-lesson transient (0.999 to 0.058), and the dual freedom certificate collapses the invented-mode failure symmetrically (1.769 to 0.029). In n dimensions the shell makes misidentification near-certain while the danger stays fully exploitable: the two axes are independent.

Physical understanding and reasoning depend on forming compact and generalizable representations of the world. While modern vision-language models can recognize and explain diverse physical events, they often lack explicit representations of the underlying mechanisms-such as object states, physical parameters, and governing dynamics-needed for reliably reasoning how the world evolves and responds to interventions. In this work, we introduce Code-as-World, a paradigm that represents physical worlds through executable world representations. By expressing physical composition, dynamic evolution, and visual appearance as executable code, Code-as-World provides a compact, quantitatively grounded, and controllable abstraction of the physical world. To construct such representations from multimodal observations, such as natural-language descriptions or real-world videos, we develop an agentic discovery loop inspired by abductive reasoning, where an agent proposes, executes, renders, verifies, and iteratively refines executable world hypotheses. As a concrete application, we use verified executable worlds to provide scalable physical supervision for training vision-language models on quantitative physical reasoning. Experiments show that Code-as-World-VL achieves state-of-the-art performance on QuantiPhy and surpasses leading proprietary models, highlighting the potential of executable world representations as a scalable foundation for physical intelligence.

World models aim to simulate how complex environments evolve under actions and events, yet existing video-based world models primarily learn dynamics from visual observations, which reveal outcomes rather than the underlying knowledge, rules, and mechanisms governing world evolution. This makes it difficult to maintain persistent consequences and support coherent, open-ended evolution. We introduce Code World Model, a framework that separates world evolution from visual realization by combining the reasoning and coding capabilities of language models with the generative priors of video models. A coding agent serves as the world brain, reasoning about events and their consequences and generating executable code to maintain persistent world state and perform rule-consistent evolution. To connect executable state with visual generation, we introduce a proxy representation that encodes frame-wise spatiotemporal constraints and is compiled into a proxy video, which conditions a video model to render high-fidelity visual observations. We further develop data pipelines for constructing aligned proxy-observation pairs from gameplay and real-world videos. After fine-tuning on paired gameplay data, MiniMax-H3 follows proxy-based spatiotemporal specifications from simple interactive worlds built by the coding agent while preserving rich visual details and dynamics. These results demonstrate the potential of combining code for persistent world evolution with video models for flexible visual realization, providing a new path toward open-ended world models.

In the Code World Model paradigm an LLM synthesizes an executable world model that a classical planner searches, and the model is accepted when it reproduces sampled transitions. We ask what that acceptance certifies in continuous control. We define the pipeline's danger as an expected risk and isolate its exact factor: the probability that N i.i.d. gate rollouts all miss a critical event of probability r is exactly (1-r)^N; an independent acceptance sample adds its budget to the exponent. On three hybrid instruments the accepted mode-blind model is exploited: the planner is pinned at the mode boundary at a regret of nearly the whole attainable return. We prove a localization budget, valid at boundary points: models with Lipschitz constant at most L differing by eta at a point disagree above tolerance eps on a region of volume at least kappa((eta-eps)/L)^(d+m); the discontinuous reset modes studied pay no such budget. With real LLM synthesis, GPT-5.x repairs an omitted 1D clamp in 105 of 111 mode-containing draws -- every attempt exact on 50 of 56 instrument-stream blocks (95% CI [0.781, 0.960]). On 2D regions no artifact recovers the rule (0/156); eight targeted interventions leave the failure in place, and positive controls locate it: a located rule is not induced, while given form and location the constants follow exactly. A version-space certificate proves identification is class-relative: at the widest dose the declared fit succeeds in 20/20 blocks and every sample-consistent circle is within tolerance in 18/20. We prove a class of entry rules exactly consistent with every sample yet harmless at play, so identifiability is a measurable property of the instrument. Re-scoring all 1034 artifacts on independent samples confirms acceptance certifies sample consistency and no more: where the gate is provably informative it covers about two percent of the exploited planner's queries.

We present a Test-time World-model Inference (Twin) system, in which a frontier coding agent writes an executable world model for completing continual learning tasks, such as ARC-AGI-3 games. Traditional approaches hand-engineer such models, one custom design per task. Each game hides its rules and goal, and our system constructs them from simulation and interaction alone. Its inductive prior over grid games is strong enough to recover the true transitions of the game and the goal on nearly all levels. Replay validation happens in a twin world model. The harness enforces that an action is not made until the program reproduces every previous observed game transition. Each mismatch between a world model prediction and the actual action result becomes a counterexample that is used to repair the world model. Twin clears 179 out of 183 levels (97.8%), and does so more efficiently than humans in 158 out of 179 levels (88.3%). The system infers the goal before any reward on 156 of the levels it clears (87.2%), and in the remaining levels automatically discovers the goal by search. The benchmark scores completion and action efficiency, between 0 and 100, against humans playing each game for the first time. Played directly, the base model scores only 7.8%; an off-the-shelf harness increases it to 61.1%, whereas our twin world model increases the same base model to 93.3%, clearing 23 out of 25 games. Building a usable world model is simpler than anticipated, whereas the harder problem is inferring the right goal.

Different research lines use the term world model in different ways, yet they share a common aim: to capture how the world evolves under action in a form that supports perception, simulation, and planning. Two prominent realizations are neural predictors that learn dynamics in continuous vector spaces, and hand-built physics engines that expose explicit state and physical laws. Neural predictors scale from data but leave the form of the dynamics implicit; physics engines are inspectable and editable but difficult to construct at scale. We introduce VisualPatchWorld (VPW), which represents world dynamics as code. VPW first selects a qualitative dynamical form with short active probes, then fits that form's free parameters from recorded state-action traces by minimizing multi-step prediction error. The resulting programs can be rolled forward like a simulator, inspected in source form, and used inside model-predictive control; image-derived scene graphs can supply the live state at replan time. Across comparisons with prior code-based world models, VPW attains 69.0% mean planning success and exceeds the strongest code baseline by 23.5 points. The largest gains arise when choosing the correct qualitative dynamics is essential. Under the same planner, the induced models approach ground-truth engine success on navigation and grasp-rich control; a residual gap remains for contact-rich pushing, and checking a shortlist of promising plans in the engine closes most of that gap. These results establish a practical route toward automatically constructed code world models that are useful for planning. Code is available at https://github.com/HKBU-KnowComp/VisualPatchWorld/.

Large language models can synthesize a game's rules as executable code - a Code World Model (CWM) - which a classical planner then searches over. Such models are typically accepted when they reach high transition accuracy on sampled trajectories. We argue this is the wrong notion of adequacy for planning. We show four things. (1) An LLM-synthesized CWM can pass a sampling gate at 100% transition accuracy and be $\geq 98\%$ state-accurate on the planner's own search distribution, yet lose systematically at play, because the $<1\%$ it gets wrong is exactly the pivotal dynamics; the play cost of the omitted rule is $0.091$ (seed-clustered 95% CI $[0.065,0.117]$, $n=4800$). We call this the verified-vs-correct gap, and confirm it end-to-end through the synthesis pipeline. (2) The harm follows a quantitative law, $\mathrm{danger}=\mathrm{play\_cost}\times(1-\mathrm{rarity})^N$, whose $(1-\mathrm{rarity})^N$ gate-miss factor is proven exact and whose play cost is empirically bounded. (3) The failure is not repaired by more data: LLM synthesis behaves as rule translation, not rule inference, and did not infer the omitted rule across models (GPT-5.x) and data regimes (including DAgger and targeted examples). (4) The same mechanism recurs on the belief-inference function of imperfect-information CWMs: we prove a coverage bound (a size-$N$ gate is identifying when $N\gtrsim b^{d_{\max}}$), explaining why shallow games such as Kuhn poker show no gap, and hand-construct Beacon, a verified-but-wrong inference function that passes the gate yet loses every game. These results suggest adequacy for planning-oriented world models should be measured on the search distribution or by play directly, not by prediction accuracy on sampled transitions.

Text-agent environments are typically modeled as partially observable Markov decision processes (POMDPs), assuming that the simulator's latent state and transition dynamics are hidden from the agent. Yet little work has examined whether executable code can be induced to serve as a world model for prediction and planning under partial observability. We introduce PatchWorld, a gradient-free framework that turns offline trajectories into executable Python world models through counterexample-guided code repair. Instead of predicting the next observation with a black-box model, PatchWorld induces symbolic belief-state programs whose action updates can be inspected, replayed, and locally patched. Across seven AgentGym environments, PatchWorld-Simple achieves the highest code-based planning score among evaluated methods, reaching 76.4% macro success in live one-step lookahead while invoking no LLM calls inside the world-model prediction module itself. We further find that a human-specified residual-memory bias improves surface observation fidelity but weakens decision utility. This exposes a tradeoff in executable world models, since improving observation fidelity can come at the expense of action-discriminative dynamics, and vice versa. Code is available at https://github.com/HKBU-KnowComp/PatchWorld.

Autoregressive (AR) language models have driven significant progress in automated software engineering, enabling powerful code generation and assistance systems. However, the next-token prediction paradigm introduces structural limitations for code reasoning, including restricted global planning, challenges in maintaining long-range dependencies, and limited grounding in program execution semantics. Noting the heavy skewness of existing literature towards AR models, we discuss emerging paradigms that could potentially overcome the logic and scaling bottlenecks of next-token prediction by unlocking next-generation architectural capabilities for code intelligence. Specifically, we discuss the potential of Diffusion Models, which generate code via holistic denoising that captures long-range syntactic constraints often missed by AR models. We also discuss Code World Models (CWMs), which simulate execution states to support reasoning, and State Space Models (SSMs), which provide linear-time efficiency for massive contexts. By connecting these developments with findings from cognitive neuroscience, we outline directions for developing "System 2" code generation agents.

Can an LLM learn how an optimizer behaves -- and use that knowledge to control it? We extend Code World Models (CWMs), LLM-synthesized Python programs that predict environment dynamics, from deterministic games to stochastic combinatorial optimization. Given suboptimal trajectories of $(1{+}1)$-$\text{RLS}_k$, the LLM synthesizes a simulator of the optimizer's dynamics; greedy planning over this simulator then selects the mutation strength $k$ at each step. On \lo{} and \onemax{}, CWM-greedy performs within 6% of the theoretically optimal policy -- without ever seeing optimal-policy trajectories. On \jump{$_k$}, where a deceptive valley causes all adaptive baselines to fail (0% success rate), CWM-greedy achieves 100% success rate -- without any collection policy using oracle knowledge of the gap parameter. On the NK-Landscape, where no closed-form model exists, CWM-greedy outperforms all baselines across fifteen independently generated instances ($36.94$ vs.\ $36.32$; $p<0.001$) when the prompt includes empirical transition statistics. The CWM also outperforms DQN in sample efficiency (200 offline trajectories vs.\ 500 online episodes), success rate (100% vs.\ 58%), and generalization ($k{=}3$: 78% vs.\ 0%). Robustness experiments confirm stable synthesis across 5 independent runs.