Markovian Circuit Tracing for Transformer State Dynamic

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

Reading a transformer's internal states in token space is easy to do and hard to trust: a logit lens on a single hidden state is dominated, at intermediate layers, by the generic tokens the model would predict for almost any input. We read the difference instead. Subtracting two closely matched prompts' hidden states and projecting through the unembedding cancels the shared component and surfaces what separates them, an operation equivalent to reading a RepE/ActAdd steering vector through a logit lens. Built into a training-free tracer that reads at every position, sub-layer, and head and averages over designed baselines, it traces a compound- noun MLP->attention chain in Phi-2, confirmed there by activation patching, with the same distinction recovered across three architectures by readout and probe rather than by patching; it reads what retrieval surfaces for real versus fictional entities, and reads metaphor as a set of domain-to-domain mappings rather than a single figurativity feature. A cross-seed control marks the boundary: across five networks differing only in initialization, the same distinction surfaces as almost entirely different tokens (top-10 overlap 0.08). What a computation looks like in token space is network-specific; the distinction it draws is not

Language modeling has shown us that transformers can discover latent structure from context, but the dynamics of how they acquire different components of that structure remain poorly understood, leading to assertions that models just remix training data. In this work, we use the Alchemy benchmark in a controlled setting (Wang et al.,2021) to investigate latent structure learning. We train a small decoder-only transformer on three task variants: 1) inferring missing transitions from partial contextual information, 2) composing simple rules to solve multi-transition sequences, and 3) decomposing complex multi-step examples to infer intermediate transitions. By factorizing each task into interpretable components, we show that the model learns the different latent structure components in discrete stages. We also observe an asymmetry: the model composes fundamental transitions robustly, but struggles to decompose complex examples to discover the atomic transitions. Finally, using causal interventions, we identify layer-specific plasticity windows during which freezing substantially delays or prevents stage completion. These findings provide insight into how a transformer model acquires latent structure, offering a detailed view of how capabilities evolve during training.