Zae Myung Kim, Young-Jun Lee, Seungyeon Jwa +1cs.AI cs.CL eess.SY
Self-improving LLM agents refine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We present Meta$^n$, which keeps the meta-operation fixed and recurses on its input instead. That operation, $Ω$, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because $Ω$ never changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set by convergence rather than fixed in advance, and an evolutionary archive searches over layer chains. Across two backbones, Meta$^n$ outperforms prior self-improving agents on all eight benchmark families. The sharpest case is ARC-AGI-2, built to resist skill memorization, where it alone scores above zero. Ablations indicate that most of the gain from recursion comes from the conditioning each layer passes to the next, and distinct layer roles emerge with depth although no prompt prescribes them. Code available at https://github.com/minnesotanlp/meta-n
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.
Hard symbolic-reasoning tasks such as Sudoku, maze pathfinding, and ARC remain challenging for LLMs due to their fixed-depth autoregressive reasoning, which limits systematic search, refinement, and backtracking. While recursive models such as Hierarchical Reasoning Model (HRM) and Tiny Recursive Model (TRM) address this limitation through iterative latent-state refinement, they are typically task-specific and do not leverage pretrained language priors. We propose R-Qwen, a recursive reasoning framework built upon a pretrained Qwen backbone. R-Qwen repeatedly refines a candidate solution through programmatic self-recursion and deep supervision, combining the structured iterative computation of recursive models with the linguistic and reasoning priors of pretrained LLMs. We further adapt Hierarchical Supervision Weighting (HSW) to autoregressive models by exponentially weighting losses across recursive steps. HSW reduces gradient variance by at least 50\%, improves the signal-to-noise ratio of stochastic gradients, and accelerates convergence. Across eight challenging benchmarks, R-Qwen consistently outperforms prior recursive reasoning models and substantially larger LLMs while using a comparable number of trainable parameters. Notably, on ARC-AGI dataset, our model achieves a 27.6\% improvement over the baseline, highlighting the effectiveness of recursive refinement for general symbolic reasoning. These results suggest that recursive reasoning mechanisms and pretrained language model priors are complementary approaches for improving symbolic puzzle-solving. Code and models will be released after acceptance.
Our previous ARC-AGI-3 agent bundled executable world modeling, prompted simplification, and exact replay verification, leaving their individual contributions unclear. An executable world model is a persistent, agent-authored environment hypothesis embodied in runnable code. We compare four Codex-based variants: textual; flexible-interface executable; executable with simplification prompts; and a fixed-interface variant with simplification and exact replay verification against recorded observations. The main study evaluates them with gpt-5.4 and gpt-5.5 at high and xhigh reasoning effort on 25 public games; exploratory follow-ups compare textual and verification with gpt-5.6-sol. In the main study, every variant scores higher as model capability and reasoning effort increase. These gains often exceed variant differences, which are smaller than anticipated and vary across settings. Requiring an executable deliverable is not universally beneficial: textual outperforms flexible-interface executable in both gpt-5.5 conditions. The simplification variant scores higher than its executable-only counterpart in three of four settings; the weakest is the exception. The complete verification treatment ranks first throughout, sometimes narrowly, but uses substantially more resources. With gpt-5.6-sol, the verification variant completes every public level at xhigh and max with about 99% human-relative action efficiency while using fewer than half the human baseline's total actions. At max, however, the textual variant completes every level with 41% fewer actions than the human baseline. Thus, at max, the three imposed mechanisms are not required for action-efficient public-set completion; verification nevertheless scores higher and succeeds at lower effort. Because gpt-5.6-sol postdates the games and held-out performance is untested, results indicate public-set saturation only.
Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.
We present ARCANA, a collaborative multi agent framework for solving ARC AGI 2 tasks under strict test time and hardware constraints. ARCANA decomposes each task into iterative perception, hypothesis generation, symbolic execution, and reflective refinement. A perceptual grounding agent builds object centric scene graphs from raw grids, a latent program policy proposes diverse DSL programs, a symbolic executor verifies candidates on demonstrations, and a reflective agent synthesizes failure driven feedback for the next turn. These agents communicate through a shared differentiable blackboard and are scheduled by a learned meta controller. The design combines structured program search with adaptive multi turn correction, improving reasoning efficiency and solution quality on challenging abstract transformation tasks.
Recent progress on ARC-AGI-1 from disclosed architectures has come broadly from two regimes: heavy test-time compute over frontier models (evolutionary search, exhaustive sampling, extended chain-of-thought), or benchmark-specific training in which small models are fine-tuned on ARC data, often with task-specialized architectures. We study a third regime: an open-weight model in non-thinking mode (DeepSeek V3.2) under a strict budget, with no ARC-specific fine-tuning. We study what is recoverable through architecture alone, building agentic harnesses that decompose pattern-discovery and program-synthesis stages explicitly. First, we introduce an Explorer-Definer Pipeline that separates pattern discovery from executable transformation synthesis, implemented as a two-stage agent pipeline. Next, we present the Reflective Orchestrator, which augments the pipeline with autonomous exploration of new transformations when previous hypotheses fail on training pairs. On the ARC-AGI-1 public 400-task evaluation set, the pipeline reaches 57.50% pass@2 at \$0.25 per task, and the orchestrator reaches 67.25% pass@2 at \$0.62 per task. Together these architectures lift a 15.50% one-shot baseline by ~52 points without benchmark-specific training or heavy test-time compute. Furthermore, the orchestrator-driven lift tests a falsifiable diagnostic the pipeline produces; unbiased pass@k analysis suggests the pipeline is generation-bound, not selection-bound (selection via training-pair accuracy captures ~95% of the candidate ceiling) and predicts that significant improvement requires broader generation, not better ranking. The orchestrator implements this prediction via adaptive re-exploration and confirms it (unbiased pass@1 lift +9.81 pp, matching selection-mediated pass@2 lift). An additional pipeline ablation identifies its think tool as a significant component, with removal reducing pass@2 by 5.75 pp.
We ask whether structural properties of intermediate grid states predict whether a symbolic ARC-AGI solver will succeed, framed as a test of conditional mutual information I(X;Y|task) > 0. Across 44,800 runs spanning two architecturally distinct solvers (beam search and Stochastic DFS), 400 ARC tasks, 28 configurations per solver, and both training and evaluation splits, hand-crafted grid descriptors measured at 50% trajectory completion discriminate successful from failed runs within the same task (mean within-task best-feature AUC = 0.885, p < 0.001 under within-task label permutation). Most predictive content lies along a single grid-complexity axis. The result generalizes across solver architectures: a feature selected on one solver predicts success on the other with AUC 0.747-0.762 in all four transfer directions (p < 0.001, leakage controlled). On a pre-registered held-out set of 41 reliable tasks, the frozen feature n_components_final achieves AUC = 0.765 (95% CI [0.717, 0.810], p < 0.001), robust under task-clustered bootstrap resampling and cross-solver task collapsing. The signal is not explained by solver capacity (configuration-residualized AUC = 0.927 and 0.896 for beam search and SDFS, p < 0.001) and is only weakly coupled to score trajectories (R^2 approximately 0). Early stopping at 50% completion reduces beam-search compute by 33.6% while retaining 98.9% of solves; degenerate-trajectory detection reduces SDFS compute by 65.3% with no solve loss. Finally, on 229 of 400 evaluation tasks the DSL primitive library produces no valid transition from the input grid. This 0-step collapse is invariant to search budget and universally failed by beam search, indicating a DSL coverage limitation rather than a search-budget effect.
We evaluate an initial coding-agent system for ARC-AGI-3 in which the agent maintains an executable Python world model, verifies it against previous observations, refactors it toward simpler abstractions as a practical proxy for an MDL-like simplicity bias, and plans through the model before acting. The system is intentionally direct: it uses a scripted controller, predefined world-model interfaces, verifier programs, and a plan executor, but no hand-coded game-specific logic. We report results on the 25 public ARC-AGI-3 games. Each recorded playthrough uses a fresh agent instance with no access to previous playthrough-specific files or conversation state. Most games have a single recorded playthrough; for a few games, we report multiple independent fresh-agent playthroughs to expose run-to-run variability. The agent fully solved 7 games, achieved a Relative Human Action Efficiency greater than 75%, on 6 games, and obtained a mean per-game RHAE of 32.58%. Because the system uses no game-specific code, it can serve as a game-general baseline for ARC-AGI-3. Performance on the private validation set remains to be tested. Overall, the results provide preliminary evidence that verifier-driven executable world models are a promising approach for ARC-AGI-3 agents.