Error Begets Error: Causal Self-Excitation in Multi-Turn Language Models

Errors in multi-turn large language model (LLM) interactions are often temporally persistent, but such dependence does not establish that one error causes another: repeated failures may instead arise from shared *latent heterogeneity* across nearby turns. We first identify the downstream causal effect of a committed error using a *randomized shared-prefix intervention*. Across three benchmarks, 50 LLMs, and 56 inference configurations, we find that causal *self-excitation* is strongest at short lags, generally weakens with *model scale*, and shifts toward *self-correction* for several larger models. However, direct estimation of these effects requires extensive paired downstream rollouts. We therefore introduce the Causal Self-Excitation Model (CSEM) to learn a signed, lag-dependent causal error-propagation kernel. CSEM closely matches the direct paired causal-effect estimates on held-out interactions across datasets and downstream lags. To further model the full dynamics of multi-turn failures, we introduce the Causally Anchored Recurrent Survival Model (CAR-Surv), which extends survival analysis from time to first failure to the full recurrent error process while separating lagged *error dependence* from dynamic *unobserved heterogeneity*. CAR-Surv achieves the strongest overall performance across *predictive accuracy*, *discrimination*, and *multi-turn forecasting* for both first-failure and recurrent-event prediction.