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This paper investigates the phenomenon of spurious routing in tabular in-context learners (ICLs), where models trained on data from a single source may rely on systematic artefacts instead of true causal signals when making predictions. The authors formalize this issue, demonstrating that larger context sizes can inadvertently amplify reliance on spurious signals, leading to significant performance degradation when models are deployed in different environments. They propose two effective mitigations that significantly reduce spurious routing while enhancing causal sensitivity, achieving up to 98.8% reduction in spurious routing for state-of-the-art models like TabPFN.
Larger context sizes can amplify spurious signal reliance in tabular ICLs, leading to a 1.74x increase in routing errors when models are deployed in new environments.
Consider a model trained at a single hospital to predict patient recovery, where the measured feature $X$ bundles the patient's true health signal ($C$) with a systematic artefact from that hospital's equipment ($S$). Within that hospital, the artefact correlates with outcomes through unmeasured confounders such as patient demographics; an in-context learner rationally routes predictions through $S$, not $C$, and fails silently when deployed at a new hospital with different equipment. We formalise this as \emph{spurious routing in composite representations}: when a feature $X = [C;\,\alpha S;\,\eta]$ encodes a causal signal $C$ and a spurious signal $S$ in distinct subspaces, the ICL cannot determine which drives predictions. We prove that under ridge ICL, a linear in-context learner, this routing is unavoidable regardless of context size; TabPFN, a state-of-the-art pretrained tabular ICL model, shows qualitatively consistent behaviour empirically. We derive a closed-form characterisation, $\mathrm{CSR} \propto \rho_S/\rho_C$, confirmed at $r = 0.997$ for linear ICL and $r = 0.979$ for TabPFN. Contrary to intuition, larger context sharpens commitment to the dominant in-context signal, amplifying spurious routing by up to $1.74\times$; in the high-spurious corner, more expressive models show greater vulnerability empirically ($+2.22$ CSR gap at high entanglement). We introduce two lightweight mitigations: environment-stratified context construction and S-swap augmentation, that require only weak environment labels and no knowledge of the causal partition. S-swap reduces spurious routing by $74\%$ for linear ICL and $98.8\%$ for TabPFN, with TabPFN's causal sensitivity increasing $8.4\times$ simultaneously: the model does not become agnostic, it reroutes through the causal signal.
