An Introspective Lens for Mining Reasoning Features in Language Models

Language models expose only a small part of their computation through final text. We study \emph{introspectability}: the operational task of extracting model-relative reasoning features from activations, in contrast to whether a model can verbally report on its own state. Our instrument is a \emph{prefix lens}: a fixed natural-language transformation $Q$ is applied uniformly to every input $p$, and we treat the difference $m(Q \mathbin{\|} p)-m(p)$ at a single readout point as a feature of the model's reasoning about $p$ under $Q$. We define eight lens operators that isolate parts of the prefix-induced shift, all computed from cached activations. On Llama-3.1-8B-Instruct and Gemma-2-9B-it we show that the lens is \emph{readable} against the model's own self-label on an 18-dataset prompt-injection corpus and an 80-object concept set, \emph{linear} at the readout, \emph{causally controlling} under a per-model-calibrated steering procedure that flips $11$--$12$ of $12$ neutral objects on the in-distribution yes/no probe, and \emph{composable}: a context-loaded prefix induces a direction that generalises out of sample and is geometrically separated from its named pieces. We then use the same operator family as a similarity score for a six-way training-data selection problem over $50$ candidate-selection shuffles. Centroid cosine on the unprefixed activation is essentially uncorrelated with downstream accuracy ($\rho\!\in\![0.01,0.05]$, $p\!>\!0.1$ on six of eight metrics), but lens-derived geometry, aggregated by Borda rank-mean over per-class similarities, reaches $94.7\%$ Top-1 with $100\%$ Top-2 against a $16.7\%$ random floor. The lens does not require fine-tuning, does not require labelled data at selection time, and is parameter-free at the aggregation step.