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Third, returning to pre-trained LLMs, we introduce the Principal Activations Probe (PAP), a layer-wise probing and intervention method that isolates algo","title":"Extracting Algorithms in Pre-trained LLMs: A Case on Hidden Markov Models","url":"https://arxiv.org/abs/2607.22646","vendor":"arxiv_cs_ai"},"summary":"arXiv:2607.22646v1 Announce Type: new \nAbstract: Large language models (LLMs) display a striking ability to predict next observations from Hidden Markov Models (HMMs) via in-context learning (ICL), but the algorithm underlying this capability remains undetermined: prior work has proposed several candidates without consensus, and none has been grounded in the model's internal activations. We close this gap with a three-stage pipeline. First, we empirically compare LLM behavior against a suite of candidate algorithms and narrow the space to three classes -- though no single class explains LLM behavior across all HMM settings and sequence lengths. 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