Paper Detail
Rishab Balasubramanian, Pin-Jie Lin, Rituraj Sharma, Anjie Fang, Fardin Abdi, Viktor Rozgic, Zheng Du, Mohit Bansal, Tu Vu
We investigate whether post-trained capabilities can be transferred across models without retraining, with a focus on transfer across different model scales. We propose the Master Key Hypothesis, which states that model capabilities correspond to directions in a low-dimensional latent subspace that induce specific behaviors and are transferable across models through linear alignment. Based on this hypothesis, we introduce UNLOCK, a training-free and label-free framework that extracts a capability direction by contrasting activations between capability-present and capability-absent Source variants, aligns it with a Target model through a low-rank linear transformation, and applies it at inference time to elicit the behavior. Experiments on reasoning behaviors, including Chain-of-Thought (CoT) and mathematical reasoning, demonstrate substantial improvements across model scales without training. For example, transferring CoT reasoning from Qwen1.5-14B to Qwen1.5-7B yields an accuracy gain of 12.1% on MATH, and transferring a mathematical reasoning direction from Qwen3-4B-Base to Qwen3-14B-Base improves AGIEval Math accuracy from 61.1% to 71.3%, surpassing the 67.8% achieved by the 14B post-trained model. Our analysis shows that the success of transfer depends on the capabilities learned during pre-training, and that our intervention amplifies latent capabilities by sharpening the output distribution toward successful reasoning trajectories.
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@misc{balasubramanian2026master,
title = {The Master Key Hypothesis: Unlocking Cross-Model Capability Transfer via Linear Subspace Alignment},
author = {Rishab Balasubramanian and Pin-Jie Lin and Rituraj Sharma and Anjie Fang and Fardin Abdi and Viktor Rozgic and Zheng Du and Mohit Bansal and Tu Vu},
year = {2026},
abstract = {We investigate whether post-trained capabilities can be transferred across models without retraining, with a focus on transfer across different model scales. We propose the Master Key Hypothesis, which states that model capabilities correspond to directions in a low-dimensional latent subspace that induce specific behaviors and are transferable across models through linear alignment. Based on this hypothesis, we introduce UNLOCK, a training-free and label-free framework that extracts a capabilit},
url = {https://huggingface.co/papers/2604.06377},
keywords = {Master Key Hypothesis, capability direction, latent subspace, linear alignment, UNLOCK, source variants, target model, Chain-of-Thought, mathematical reasoning, pre-training, post-training, inference time, output distribution, huggingface daily},
eprint = {2604.06377},
archiveprefix = {arXiv},
}
{}