aiqbench analysis
This study demonstrates that large language models maintain interpretable belief state geometries within their residual streams when processing Hidden Markov Model data, effectively approximating optimal Bayesian inference. By successfully decoding and intervening in these representations, researchers confirm that in-context learning relies on structured internal states rather than mere statistical pattern matching. These findings provide critical evidence for understanding the mechanistic foundations of how LLMs generalize from context without explicit training.
Large Language Models Develop Belief State Geometry In-Context
arXiv:2609.17376v1 Announce Type: cross Abstract: Large language models (LLMs) trained on next-token prediction exhibit remarkable in-context learning (ICL) abilities, yet the representations that support ICL remain poorly understood. We consider such representations in a controlled setting: prompting LLMs with data emitted from hidden Markov models (HMMs) and probing for the corresponding belief state -- the posterior distribution over the HMM's hidden states given the observed token history. Across six open-source LLMs prompted with data from 40 HMMs selected for non-trivial belief structure, we find that belief states are linearly decodable from residual stream activations, with peak probe $R^2$-values from 0.83-0.99 across HMM and LLM combinations, ranging from early to late layers. To establish functional relevance, we intervene directly on the probe-identified subspace via patching and steering, resulting in downstream prediction quality on the order of the untampered model, while controls degrade performance substantially. Together, these results provide representation-level evidence that ICL in open-source LLMs approximates optimal Bayesian prediction over a context-inferred generative model. More broadly, our findings extend prior results linking input-distribution structure to activation geometry: from toy networks trained explicitly on HMM data to production-scale LLMs.
Abstract:Large language models (LLMs) trained on next-token prediction exhibit remarkable in-context learning (ICL) abilities, yet the representations that support ICL remain poorly understood. We consider such representations in a controlled setting: prompting LLMs with data emitted from hidden Markov models (HMMs) and probing for the corresponding belief state -- the posterior distribution over the HMM's hidden states given the observed token history. Across six open-source LLMs prompted with data from 40 HMMs selected for non-trivial belief structure, we find that belief states are linearly decodable from residual stream activations, with peak probe $R^2$-values from 0.83-0.99 across HMM and LLM combinations, ranging from early to late layers. To establish functional relevance, we intervene directly on the probe-identified subspace via patching and steering, resulting in downstream prediction quality on the order of the untampered model, while controls degrade performance substantially. Together, these results provide representation-level evidence that ICL in open-source LLMs approximates optimal Bayesian prediction over a context-inferred generative model. More broadly, our findings extend prior results linking input-distribution structure to activation geometry: from toy networks trained explicitly on HMM data to production-scale LLMs.
Machine Learning (cs.LG); Computation and Language (cs.CL)
arXiv:2609.17376 [cs.LG]
(or arXiv:2609.17376v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.17376 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 280 words
