To Explore The Strange New World Beyond Data Distribution: System Behavior, Causality Tax, and Non-causal Base Model

We show that the causality of language models (LMs) may not be necessary nor optimal. This is the case when system behavior (denoted as $S$) is incorporated as a first-principle Bayesian feature. Here, $S$ refers to extra dominant factors beyond the data space, and they involve coupled effects. Despite being the de facto foundation of modern architecture, recent studies indicate persistent mismatches and contradictions with causality. These issues largely stem from system behavior rather than the data distribution. We therefore propose the SBD framework, which incorporates $S$ as an irreducible component of the evidence lower bound (ELBO). SBD theoretically reveals a counter-intuitive Causality Tax phenomenon, where causality emerges as a suboptimal approximation with an additional structural error, due to the obliviousness to $S$. To address the challenge of latent variable analysis, we validate the SBD-predicted impact of $S$ via implicit measurements, theoretical-bound-guided controls, and Neural Tangent Kernel (NTK) evaluations. In particular, we construct Green Shell (GSH) to show the possibility of reducing Causality Tax. GSH is a non-causal variational family, and it replaces the sequential dependency chain of $S$ components with a divide-and-conquer partition. NTK spectra in the lazy-training regime confirm that GSH always achieves significantly tighter error bounds than causality, with $7dB+$ improvement in signal-to-noise ratio. In the relatively later stage of lazy-training, GSH further leads to superior generalization (up to $20\%$ richer multi-scale fitting capabilities). Taken together, SBD establishes system behavior as a complementary theoretical abstraction besides causality and distribution fitting, opening new research avenues such as designing and optimizing LM base models.