CAA-X V4: World Models and Action Generation

This repository contains V4 of the CAA-X (Cognitive Atom Architecture eXtension) research program, subtitled "World Models and Action Generation: From Prediction to Purposeful Behavior." V4 extends the CAA-X framework into the domain of embodied intelligence and world model learning, directly engaging with the predictive turn in AI spearheaded by Yann LeCun's JEPA (Joint Embedding Predictive Architecture) and the recent emergence of World Action Models (WAMs). It answers the question: If the brain is primarily a prediction machine, how does prediction become action? Core ThesisV4 formalizes the transition from passive world-modeling to active world-interaction through the Action Atom — a first-class cognitive primitive that couples predictive state representations with motor intention fields. It proves that action generation is not a downstream module appended to perception, but an intrinsic property of the predictive tension field when modulated by the λ-order-parameter's goal-directed dynamics. Key Contributions- JEPA Mapping Theorem: Formal proof that JEPA's joint embedding architecture is a special case of the CAA-X predictive tension field under specific boundary conditions (isometric latent space, deterministic transition kernel).- WAMs Integration & Critique: Comprehensive analysis of World Action Models (WAMs) — their prediction-action joint distribution p(future state, action) — mapped onto CAA-X constructs: predictive state modeling ↔ holographic world model; action generation ↔ action atom; joint distribution ↔ cognitive manifold trajectory planning. Identifies WAMs' critical gaps (no explicit intention layer, fixed resource allocation, undefined inter-atomic communication) and shows how CAA-X resolves each.- Cognitive Manifold Trajectory Planning: Formalization of goal-directed behavior as geodesic optimization on a Riemannian cognitive manifold, with the intention field serving as a bias term that deforms the metric tensor toward task-relevant submanifolds.- Zero-Shot Action Decomposition: Extension of V0's zero-shot decomposition lemma to the action domain — proof that novel motor skills can be composed from existing action atoms without task-specific training.- Closed-Loop Control Architecture: Specification of the Action Atom–Physical Constraint Atom coupling, enabling real-time sensorimotor loops with guaranteed stability bounds. Relationship to Prior VersionsV0 provided the atom formalism. V3 established intention as the driving field. V4 asks: How does intention move matter? It bridges the gap between the "mind" (V3) and the "body" (V5), positioning CAA-X as a complete architecture for embodied AI. Citation & ContextPart of the CAA-X versioned research program. See V0–V2 foundational collection (DOI: 10.5281/zenodo.21835958) and V3 intention manifesto for theoretical prerequisites. Author: Lu Qi (鹿琦) / Dake Alughwan ORCID: 0009-0005-7907-6829 Contact: luqi@alu.fudan.edu.cn