Causal interventions in language model representations have largely targeted discrete features, like grammatical number. However, language models must also make use of features that are graded. We introduce a method for causal intervention on continuous variables: given activation vectors paired with a graded target variable, we localize a low-dimensional direction for that variable and use this direction to edit a vectors toward counterfactual target values. We apply this method to a continuous feature that is well-studied in psycholinguistics, namely verb bias (which reflects which syntactic structures tend to follow a given verb). We show that verb bias is causally represented in steering vectors extracted from large language models: counterfactual edits to verb bias systematically shift downstream structural preferences. Verb bias has also previously been linked to in-context learning; in further analyses, we find that steering vectors encode error signals that could drive the error-driven update behavior seen in in-context learning but that these aspects of the steering vectors are not causally used in downstream production. Overall, these results show causal interventions can be applied to continuous variables, though connecting continuous variables to in-context learning remains a challenge.
Interventional data is widely regarded as the gold standard for teaching models causal reasoning. We test this assumption in a fully controlled synthetic environment pitting observational correlation against causal effect, and find it fails instructively. In Simpson's-paradox worlds, where the two have systematically opposite signs, increasing the fraction of interventional samples in pretraining does not improve causal direction: the magnitude of the model's do()-response grows monotonically, yet its sign is copied from the observational context. What governs whether interventional evidence is used is not the training mixture but the evidence type present in the context at inference time. Under an identical training recipe, a purely observational context induces systematic sign reversal in 29/50 worlds, a mixed context in 19/50, while aligned interventional probes alone yield 41/50 correct. Erasing observational evidence from the context immediately releases the suppressed causal interpolation ability (ratio_true = +0.56); a four-state content manipulation shows the switch is content-mediated and graded. The suppression is stable across training seeds (11/11 strong reversals persist on a matched-protocol second seed) and robust as a rate at 0.93B parameters (31.8% vs. 6% reversals in the matched probe-only arm), even as absolute gains shrink four-fold. An external audit on CLadder exposes a learned positive-effect prior with a two-layer structure: sign-randomized retraining removes it in-distribution but not out-of-distribution. We summarize: the capability lives in the weights; the switch lives in the context, and activation patching localizes the switch to the middle layers' observational rows. We further quantify the sampling noise floor of probe-based causal evaluation and an evidence-averaging protocol that cuts sign errors from 26% to 9%.
A central premise in mechanistic interpretability is that meaningful concepts in language models are represented by linear features in activation space. For such features to support reliable interventions, manipulating one feature should not substantially alter the effects of others. In practice, however, feature entanglement leads to interference such that localized interventions can have unintended downstream effects. Motivated by the \textit{Independent Causal Mechanisms} principle, we propose to constrain internal features to be almost orthogonal. We argue that this promotes modular representations amenable to causal intervention. We formalize this problem by characterizing the gap between an idealized isolated intervention and its realized effect on model outputs in terms of feature interference. We upper-bound the propagation of feature interference in terms of the self-coherence of the feature dictionary, and relate this discrepancy to an explicit orthogonality regularization on the dictionary itself. Empirically, we show that this regularization enables more isolated interventions on mathematical reasoning concepts while preserving model performance. Our code is available under \texttt{https://github.com/mrtzmllr/sae-icm}.
Causal discovery is a cornerstone of scientific reasoning, yet whether large language models can perform it reliably remains an open question. Recent benchmarks show that even fine-tuned models plateau on simple causal graphs and degrade as complexity grows, but why they fail has not been established. We prove the failure is fundamental: supervised fine-tuning, direct preference optimization, and in-context learning all produce predictors that cannot distinguish between causal graphs generating similar observational data, and any attempt to do so requires the model's internal representations to grow unboundedly, violating the very conditions under which these methods work. We formalize this as a kernel obstruction theorem, establishing that the limitation is intrinsic to the learning paradigm, \emph{not any particular model or dataset}. We propose Agentic Causal Bayesian Optimization (A-CBO), wherein a frozen language model serves as an interventional oracle answering targeted queries about intervention effects, while an external Bayesian loop concentrates beliefs over candidate graphs in logarithmically many rounds. Because the decision operates outside the space where the obstruction applies, A-CBO provably converges while the underlying model remains unchanged. On Corr2Cause, A-CBO matches fine-tuned baselines without any training. On Extended Corr2Cause, a new benchmark scaling to 24 variables with 18K test samples, A-CBO significantly outperforms both fine-tuning and preference optimization, with the advantage growing