Same Answer, Different Future: Matched Predictions Do Not Imply Matched Belief Updating in Language Models

Language models can produce similar probabilistic predictions after observing outcomes, reading summaries, receiving instructions, or undergoing activation interventions. Whether these routes induce equivalent belief states remains unclear: agreement in current predictions does not establish how a model will respond to subsequent evidence. We investigate this distinction in a Bernoulli inference task with an analytic Bayesian reference. Across three open-weight language models, we prepare states through four textual routes and two activation-level interventions, measure both next-outcome continuations and explicit probabilistic estimates, and append identical new evidence from each prepared state. We quantify the persistence of the initial belief through its effective evidence weight, the number of new observations it is worth. We find that the format of evidence decides which readouts express its content: outcome sequences primarily affect continuations, whereas summaries and stated rates primarily affect explicit estimates. Moreover, effective weights differ substantially across routes, with summaries receiving weights that scale weakly with their stated observation counts and elicitation questions changing inferred weights by orders of magnitude. In a one-shot steering setting, an intervention that reproduces a natural record's immediate prediction loses most of its effect under subsequent evidence. These results show that agreement in current readouts is insufficient to establish equivalence in belief updating: how a belief is acquired and how it is read jointly determine its subsequent dynamics.