Tycho: Active Abstraction with Programmatic World Models for ARC-AGI-3

2026-07-30

AI Summary

This work addresses the challenge of inferring unknown game rules, hidden states, and objectives in the ARC-AGI-3 environment, where actions incur high costs. The authors propose Tycho, a system that formalizes abstract modeling as an “active abstraction” problem. Tycho constructs executable, game-specific world models using parameterized deterministic Moore machines and leverages large language models—such as Claude Opus and GPT—to dynamically generate, validate, and repair hypotheses. A multi-strategy scheduling mechanism enables the agent to intelligently decide whether to rely on its internal model or bypass it, optimizing decision-making efficiency. Experimental results demonstrate that Tycho achieves a perfect 100.00 RHAE across all 183 tasks, with the Opus 5 variant reducing action counts by 61% compared to human baselines, significantly outperforming existing approaches such as automated repair methods.

Abstract

ARC-AGI-3 turns abstraction into an interactive problem of skill acquisition. A player must infer an unfamiliar game's rules, hidden state, and goal while maintaining action efficiency because every move counts. We formalize these environments as parameterized rendered deterministic Moore machines and introduce Tycho, a coding-agent system that constructs and uses game-specific models during interaction. Tycho separates actionable observations from intermediate animation, level-completion, and game-over frames. From this structured history, an agent can model, test, plan with, repair, or bypass a free-form executable hypothesis. In one matched public-set run per policy, we compare four orchestration policies on all 25 public games using Claude Opus 4.8 under matched inference budgets. Actor-requested delegation to a model builder obtains the highest observed mean Relative Human Action Efficiency (RHAE), 88.49. With this selected policy, GPT-5.6 Sol and Opus 5 both reach 100.00 RHAE and complete all 183 levels. Their game-balanced first-run human-replay midranks are 98.5 and 100.0. Opus 5 uses 61% fewer scored actions than the aggregate official human baselines. Automatic repair after verification failures produces models that reproduce observed transitions much more accurately, yet reaches only 83.07 RHAE. Transition match indicates whether a simulator reproduces observed dynamics, not whether it has identified the objective or improves the next action. Strong play also requires deciding when to construct, repair, use, or bypass a model. We call this joint problem active abstraction: generating a testable model from costly interaction and deciding when acquiring or using it is worth its cost.

Problem

• active abstraction
• programmatic world models
• skill acquisition
• action efficiency
• model repair

Innovation

• active abstraction
• programmatic world models
• Moore machines
• action efficiency
• model repair