Entangled by Design: Spurious Intra-Variable Signal Routing in Tabular In-Context Learners
Authors: Athanasios Vlontzos, Giorgos Papanastasiou, Bernhard Kainz, Sotirios Tsaftaris
Abstract
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;αS;η] 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, CSR∝ρS/ρC, 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×; 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× simultaneously: the model does not become agnostic, it reroutes through the causal signal.
As predictive models are increasingly deployed in high-stakes settings such as credit approval, there is a growing need for post-hoc methods that provide recourse to affected individuals. Many such models operate on tabular data, where features correspond to real-world attributes. Recently, in-context learning (ICL) has enabled large language models to perform tabular prediction by conditioning on labeled examples at inference time, without explicit training. However, algorithmic recourse for tabular decision-making under ICL remains largely unexplored. In this work, we present the first study of algorithmic recourse for tabular data under ICL. We carry out a theoretical analysis, showing that recourse remains well-defined and bounded, and we characterize how recourse converges toward classical solutions as the context size increases. In practice, we propose a novel zeroth-order recourse framework, Adaptive Subspace Recourse for In-Context Learning (ASR-ICL), that efficiently generates actionable and sparse recourse for black-box ICL models. The proposed framework naturally extends to multi-class tabular tasks. Experiments across multiple real-world datasets and models demonstrate that ASR-ICL achieves recourse quality comparable to existing methods with fewer queries and empirically confirm the predicted convergence behavior, supporting our theoretical analysis.
This paper investigates context stickiness in in-context learning (ICL), a phenomenon where earlier examples in a prompt interfere with a transformer's ability to adapt to later tasks. Using synthetic regression tasks over linear and quadratic functions, we examine how models trained under sequential, mixed, and random curricula handle abrupt task switches during inference. By sweeping over structured combinations of misleading linear examples followed by recovery quadratic examples, we quantify how prior context biases prediction error and how quickly models realign. Our results show strong evidence of persistent interference: more preceding linear examples reliably degrade quadratic predictions, while additional quadratic examples reduce error but with diminishing returns. We further find that training curricula significantly modulate resilience, with sequential training on the target function class yielding the fastest recovery, and surprisingly, random training producing the least robust behavior.
In-context learning for tabular data sets strong predictive standards in observational settings; it however primarily relies on correlational structure, which becomes unreliable under distribution shift or intervention. While established methods to discover causal structure exist, they are often focused on structure identifiability and decoupled from the predictive architectures that could benefit from them. To bridge these perspectives, we study how to simultaneously infer and enforce causal structure in the form of topological variable orderings into tabular prediction. Unlike standard architectures, our model TabOrder uses causal order-constrained attention, basing predictions only on features that precede a target under a learned causal order. Similar to causal discovery methods, TabOrder learns the optimal variable ordering in an unsupervised manner through a likelihood-based objective. We justify this choice under standard functional model classes and also study how sample missingness, a common challenge in tabular data, interacts with causal direction identification. Empirically, we confirm that TabOrder recovers accurate variable orderings while addressing prediction and imputation tasks, as well as gives insight into real-world biological data under intervention.