This work plants a controllable latent variable inside natural-looking text and arranges the 8 states themselves on a ring, in the exact order of the Markov chain, which is supporting evidence that a concept's geometry can be formed by the statistical dynamics of the latent variable behind it.
Abstract
LLMs are thought to track"belief states,"i.e., running probability distributions over the latent variables that govern language (Shai et al., 2024; Sarfati et al., 2026), but so far this has only been comprehensively demonstrated on toy synthetic data and in a few isolated case studies. It has also never been empirically connected to the geometry of LLM features (the concepts interpretability finds in model activations). In this work, we plant a controllable latent variable inside natural-looking text. An LLM teacher writes ordinary text while we"subliminally"steer it along one of K = 8 unrelated sparse autoencoder directions at each token, with the active directions following a ring-shaped Markov chain. A small transformer model trained on this corpus does indeed track the Bayesian posterior belief about our planted latent variable. Moreover, it also arranges the 8 states themselves on a ring, in the exact order of the Markov chain, which is supporting evidence that a concept's geometry can be formed by the statistical dynamics of the latent variable behind it.
It is proposed that a model's uncertainty about a token is reflected not only in the breadth of its output distribution but also in whether a confident prediction is \emph{fragile} under perturbation of its attention pathways, a training-free estimator that masks attention heads and measures the BALD mutual information among the resulting subnetworks.
Minsoo Kim, Sungyoung Ji, Kisung Moon et al.· 0 citations
It is suggested that models possess relevant subpopulation knowledge but do not reliably propagate it into aggregate estimates, and this gap establishes statistical self-consistency as an unsaturated, reference-free criterion for evaluating LLMs.
Patrik Wolf, Thomas Kleine Buening, Andreas Krause et al.· 0 citations
Stochastic-process models are, as a rule, far easier to simulate than to condition. Non-linear observations, non-Gaussian likelihoods, black-box information, and global constraints all induce intractable conditional laws, requiring bespoke, model-specific constructions. We introduce LatentFlow, a single framework for conditioning stochastic processes, with no learned neural approximations and no training. Our starting point is to write the stochastic process as the deterministic image of a tractable latent innovation, $f_0 = T_{\vartheta}(\xi_0)$, with $\xi_0$ sampled from a simple reference distribution. This reduces process-level conditioning to latent-space inference: pull the likelihood back through $T_{\vartheta}$, sample the resulting latent law with a tractable guided probability flow, and push the samples forward. This construction is provably exact at the level of the target law; in practice, approximation enters only through finite terminal noising, Monte Carlo guidance, and time discretisation of the continuous-time dynamics, each of which is explicit and systematically reducible. As LatentFlow is training-free, conditioning reduces to solving a single reverse-time SDE. This enables conditional sampling in seconds on a single desktop CPU across model classes that have never shared a scalable method: classical spatial priors, nonlinear stochastic dynamics, mechanistic models from the physical and life sciences, stochastic PDEs, heavy-tails and extremes, point and discrete-state processes, and neural or simulator-defined processes.
Louis Sharrock, L. Astfalck, Henry Moss· 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
Large language models (LLMs) are increasingly deployed as decision-making agents in settings that require sophisticated environmental exploration. However, existing work has raised questions about how LLMs actually balance exploration and exploitation. Unlike classical agents, LLM agents engage with tasks through natural language, exposing them to semantic information with no formal counterpart in the task structure. We introduce the semantic bandit, an extension of the multi-armed bandit setting that explicitly considers the textual labels assigned to actions, and use it to study how semantic priors --- inductive biases arising from associations between language and expected reward learned during pre-training, shape LLM exploration behaviour. We find that semantically informative action labels reduce exploration in favour of exploitation, improving performance when aligned with the reward structure and severely degrading it when misaligned. We further find that negative rewards trigger substantially more exploration than equivalent positive rewards, consistent with an expected-scale bias induced by reward conventions common in pre-training data. Overall, we argue that the use of language to define the environment and rewards introduces unavoidable biases derived from the fact that the model is trained on word co-occurence, with implications for the reliability and robustness of LLM agents in real-world decision-making settings.