Large language models (LLMs) can memorize and reproduce training sequences verbatim, raising privacy and copyright concerns. Existing mitigation methods apply interventions uniformly, often degrading performance on the majority of tokens that generalize normally. We study a token-level log-likelihood ratio between a target model and a domain-competent reference with lower exposure to the evaluated sequences. Exposure-controlled experiments support its use for localizing positions associated with sequence-level verbatim recall. Across evaluated settings, a minority of positions carries a disproportionate share of the positive signal, motivating selective activation correction. From the ideal memorization reduction objective, we derive a probe--steer framework which decomposes intervention into a probe that detects memorization-relevant activations and a steer that applies targeted correction only when the probe exceeds a threshold. We propose Gated Subspace Steering (GSS) as its practical instantiation: the optimal probe--steer pair admits a closed-form solution as the leading singular vectors of a gradient-weighted activation matrix. Across four benchmarks, GSS matches or exceeds state-of-the-art memorization reduction while requiring 10--100$\times$ less compute than optimization-based alternatives.

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