Dense linear probes are used to assess task readability from language model (LM) representations, yet they do not directly reveal how many features are sufficient for prediction. We define $k^*$ as the smallest feature count found by a fixed search protocol that recovers 95% of the dense‑probe AUROC above chance. Evaluating 19 LMs from five labs on 14 core tasks shows that ten base models give the nine reliably readable tasks similar feature counts and almost identical ordering. This agreement extends to the selected features themselves; on three tasks the cross‑model response correspondence exceeds class‑mean differences and a label‑correlation‑matched null. Instruction‑tuned deployment selectively reduces $k^*$, with contributions from both weight updates and input format changes.
In controlled synthetic experiments across 20 models, successfully learned targets admit single‑feature readouts, whereas readable controls require tens of features. The reference‑model $k^*$ correlates with label requirements across eight students following an empirical scaling $N^* \propto (k^*)^{0.65}$. After continual learning, saved heads may fail while linear readability remains high, and recovery needs fewer labels than the initial task learning under the tested procedures. Pruning reduces linear readability, and wider pre‑pruning readouts are generally associated with larger losses. These findings distinguish task readability from readout sparsity and demonstrate their complementary value for predicting learning requirements and diagnosing LM changes.
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