In the \emph{latent posterior model} of transformer behavior, the next-token distribution arises from a posterior over latent predictive models conditioned on the context, mixed to generate continuations. We exploit this model in settings where it is exact, namely Bayes-filtered transformers (BFTs) meta-learned on sequences from a hierarchical prior, to introduce \textbf{Posterior Prefix Tuning (PPT)}, a new method for \emph{eliciting} behavior from a transformer: given a utility function on continuations, find a prompt under which the transformer generates continuations of high expected utility. For a BFT, the elicitation objective factors through the latent posterior, and the gradient of this objective can be estimated from samples of the prior alone. PPT optimizes the parameters of a distribution over hard prompts: it draws prior samples once from the BFT via predictive Monte Carlo (PMC), then estimates the gradient by importance sampling against them. The optimization performs no transformer forward passes and no backpropagation through the transformer, and the prior samples are utility-independent, so a single set of samples drives elicitation against any number of utilities at negligible marginal cost. We validate PPT on Beta--Bernoulli and reinforced urn BFTs across three utility families (reverse cross-entropy, frequency matching, Dyck validity).
Garrett Baker, Vinay Pathak, Daniel Murfet et al.· 0 citations
A Bayes-filtered transformer (BFT) is a transformer trained on sequences that are generated in two steps: first a latent task is drawn from a prior, then observations are drawn conditional on that task. Trained under autoregressive log loss, the BFT's next-token prediction, in the idealized limit, is the Bayesian posterior predictive distribution (PPD) induced by that prior and that conditional law. In practice the trained BFT is only an approximation of this ideal PPD, raising an interpretive question: what prior and posterior over the latent task has the trained BFT actually internalized? Existing work answers this question by comparing the trained BFT's predictions against the predictions of various"reference"posteriors, each standing in for a different candidate algorithm or computation the BFT might be implementing. This prediction-space comparison is fragile: different posteriors can share the same posterior-mean predictions. We use predictive Monte Carlo (PMC) as a general interpretability tool for any BFT: using only next-token generation, PMC returns an approximation to the implicit prior and posterior over the latent task, answering the interpretive question directly in latent space. We apply PMC to three stylized task families spanning 0-Markov and 1-Markov exchangeability. The phenomena previously reported in these settings remain visible in latent space. Code is available at https://github.com/afiq-aswadi/bft-pmc
Afiq Abdillah Effiezal Aswadi, Haotong Ma, Susan Wei· 2 citations