# Ridge Regression

Interpretability tools are usually built inside one model from labeled data and rebuilt for the next. This work carries a refusal direction, a correctness direction and a sentiment probe between models through a ridge-regression map fit only on unlabeled prompts, across 110 ordered pairs from five families and 1B to 72B parameters. A map fit on ordinary questions recovers 54% of refusal steering; adding unlabeled prompts from the tool's operating region raises refusal to 102% and correctness gains to 88% to 98%, while random and orthogonal controls recover at most 1%.

Interpretability tools are usually built inside one model from labeled data and rebuilt for the next. This work carries a refusal direction, a correctness direction and a sentiment probe between models through a ridge-regression map fit only on unlabeled prompts, across 110 ordered pairs from five families and 1B to 72B parameters. A map fit on ordinary questions recovers 54% of refusal steering; adding unlabeled prompts from the tool's operating region raises refusal to 102% and correctness gains to 88% to 98%, while random and orthogonal controls recover at most 1%.

A laboratory mouse's age can be read from an ordinary photograph, but what transfers is relative age rather than absolute age. Across 2,846 photographs of 1,292 mice from seven facilities, a frozen DINOv2 vision model with ridge regression predicted age; on unseen facilities the median absolute error was 138 days, yet within a session the older of two mice was ranked older in 65% of pairs, rising above 95% for age gaps over 500 days. Mice predicted older than their age were frailer, with each 100 days of photographic age gap linked to 0.12 SD more frailty and a 14% higher hazard of death.

A laboratory mouse's age can be read from an ordinary photograph, but what transfers is relative age rather than absolute age. Across 2,846 photographs of 1,292 mice from seven facilities, a frozen DINOv2 vision model with ridge regression predicted age; on unseen facilities the median absolute error was 138 days, yet within a session the older of two mice was ranked older in 65% of pairs, rising above 95% for age gaps over 500 days. Mice predicted older than their age were frailer, with each 100 days of photographic age gap linked to 0.12 SD more frailty and a 14% higher hazard of death.

The work proposes affine post-processing: splitting a fixed score-estimation compute budget across multiple signal levels, querying the base estimator at each, and pooling the estimates by a linear combination (ridge regression / linear smoother); it proves that at matched compute this split-and-pool estimate has lower score error than a single on-policy estimate, and reports up to two orders of magnitude smaller terminal Wasserstein distance on ill-conditioned Gaussians, multimodal mixtures, and high-dimensional targets.

The work proposes affine post-processing: splitting a fixed score-estimation compute budget across multiple signal levels, querying the base estimator at each, and pooling the estimates by a linear combination (ridge regression / linear smoother); it proves that at matched compute this split-and-pool estimate has lower score error than a single on-policy estimate, and reports up to two orders of magnitude smaller terminal Wasserstein distance on ill-conditioned Gaussians, multimodal mixtures, and high-dimensional targets.