Steering vectors worked as a post-training signal, reaching a 12 percent gain when distilling from thinking-mode teachers
AspireAI community · arXiv
Steering vectors are residual-stream directions that shift model behaviour when added to hidden states at inference, and prior work has mostly used them as post-hoc controls. This paper asks whether the same directions can guide parameter updates during post-training, across supervised learning (SFT and distillation) and reinforcement learning with verifiable rewards. Two regimes are studied: a hidden-state hook during teacher-forced supervised training, and an advantage-repair mechanism on wrong rollouts in GRPO. In supervised settings the injection beats plain SFT and distillation, with gains that scale with the off-policy gap and reach up to 12 percent when distilling from thinking-mode teachers across three random seeds. In RL, applying a correctness-contrast direction as advantage repair on wrong rollouts, including all-wrong groups with otherwise zero gradient, recovers a learning signal that transfers to held-out math benchmarks and composes with entropy-aware advantage shaping. The paper names three failure boundaries, including code generation breaking the direction.
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Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.