Compositional Transfer in Neural World Models via Symbolic Law Discovery

Abstract

Title: Compositional Transfer in Neural World Models via Symbolic Law Discovery Core Thesis This research establishes a mathematically grounded paradigm for Modular World Modeling, where physical invariants are recovered as additive vector fields rather than monolithically memorized. We prove that by framing learning as Tangent-Space Residual Superposition, neural networks can internalize isolated physical laws that compose zero-shot to predict complex, unseen multi-physics environments. Key Breakthroughs & Upgrades The Compositional Scaling Law (2D to 12D) Our experiments reveal a fundamental divergence in high-dimensional scaling. While monolithic models suffer from "Baseline Washout" and entanglement, our modular ensembles maintain physical integrity across 12-dimensional manifolds. In chaotic triple-force environments, the modular framework achieves a 6.5× reduction in trajectory MSE ($71.5 \times 10^{-4}$ vs. $470.2 \times 10^{-4}$ for the monolith). Causal Discovery: Active Gradient Conflict ($\rho \approx -0.99$) We provide the first empirical proof identifying the causal driver of monolithic failure. Gradient alignment analysis reveals that monolithic models are trapped in a state of Active Gradient Sabotage, where the update required for one force (e.g., Gravity) almost perfectly cancels out the update for another (e.g., Spring). Our framework bypasses this bottleneck by isolating gradients in tangent space, ensuring 100% of task-specific knowledge is preserved. Benchmark vs. Physics-Informed Neural Operators (PINO) A head-to-head comparison with the PINO paradigm reveals a fundamental Compositional Utility Gap. While PINOs are powerful solvers for specific partial differential equations, they fail the Zero-Shot test because solution operators are inherently non-additive. Our framework is not only capable of additive operator composition but is also 2.5× faster at inference and provides a direct path to SINDy Symbolic Discovery (99.25% recovery accuracy). Hierarchical Physical Discovery The framework scales hierarchically, enabling the unsupervised decomposition of environments into continuous dynamics (gravity) and discrete contact events. This allowed the discovery of hidden physical constants, such as the coefficient of restitution ($\epsilon=0.80$), without target-domain supervision. Scientific Impact These results transform world modeling from a holistic storage problem into a sparse algebraic retrieval problem. By bridging the gap between black-box simulation and verifiable symbolic laws, this work provides a scalable roadmap toward interpretable Artificial General Intelligence (AGI) that respects the structural symmetries of the physical universe.