WorldKernel: A World Model is the Coupling Kernel of Admissible Possible Worlds
A common assumption holds that enough observational and interventional data, given to a strong enough predictor, suffices. We report a failure mode that contradicts it. Across hundreds of structural causal models, on identified quantities a strong predictor and a Bayesian baseline both succeed, but on unidentified quantities (the couplings between counterfactual worlds) the predictor collapses to a point, on 28% of models to one no valid model can produce, while the truth is an admissible interval more data never narrows. The gap is structural: prediction cannot represent uncertainty over counterfactual couplings. We cast a world model as a single positive semidefinite coupling kernel K(T,T') over admissible worlds, whose diagonal is the ordinary posterior (what a predictor recovers) and whose off-diagonal is the cross-world coupling it cannot, which every counterfactual reads. The paper is the theory of that off-diagonal. It is real: two states with identical posteriors differ on a cross-world query, and the off-diagonal is the coupling that fixes counterfactuals. It can be bounded: positive semidefiniteness is partial-identifying information the marginals lack, and enforcing it bounds counterfactuals in polynomial time where the exact response-type program is intractable. Logical structure sharpens it: ontology axioms tighten the bound by up to a third, propagating to couplings they never touch. It can be acquired: targeted scars, constraints learned from encountered infeasibilities, close the gap several times faster than untargeted ones. Its full reconstruction is approximate counting of the admissible worlds, tractable below the Sly-Sun threshold and inapproximable above; we do not claim to beat the worst case.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A characterisation of cross-impact kernels
Trading a financial asset pushes its price as well as the prices of other assets, a phenomenon known as cross-impact. We consider a general class of kernel-based cross-impact models and investigate suitable parameterisat…
Reproducing kernel Hilbert space methods for modelling the discount curve
We consider the theory of bond discounts, defined as the difference between the terminal payoff of the contract and its current price. Working in the setting of finite-dimensional realizations in the HJM framework, under…
Safe Approximate Dynamic Programming Via Kernelized Lipschitz Estimation
We develop a method for obtaining safe initial policies for reinforcement learning via approximate dynamic programming (ADP) techniques for uncertain systems evolving with discrete-time dynamics. We employ kernelized Lip…
reinforcement-learningReinforcement LearningReinforcement Learning (RL)Multitask Kernel-based Learning with First-Order Logic Constraints
In this paper we propose a general framework to integrate supervised and unsupervised examples with background knowledge expressed by a collection of first-order logic clauses into kernel machines. In particular, we cons…
Multi-Task LearningToward Large Kernel Models
Recent studies indicate that kernel machines can often perform similarly or better than deep neural networks (DNNs) on small datasets. The interest in kernel machines has been additionally bolstered by the discovery of t…