arXiv:2510.06084v2 Announce Type: replace-cross Abstract: Language model post-training has enhanced instruction-following and performance on many downstream tasks, but also comes with an often-overlooked cost on tasks with many possible valid answers. On many tasks such as creative writing, synthetic data generation, or steering to diverse preferences, models must cover an entire distribution of outputs, rather than a single correct answer. We characterize three desiderata for conditional distributional modeling: in-context steerability, valid output space coverage, and distributional alignment, and document across three model families how current post-training can reduce these properties. In particular, we disambiguate between two kinds of in-context learning: ICL for eliciting existing underlying knowledge or capabilities, and in-context steerability, where a model must use in-context information to override its priors and steer to a novel data generating distribution. To better evaluate and improve these desiderata, we introduce Spectrum Suite, a large-scale resource compiled from >40 data sources and spanning >90 tasks requiring models to steer to and match diverse distributions ranging from varied human preferences to numerical distributions and more. We find that while current post-training techniques elicit underlying capabilities and knowledge, they hurt models' ability to flexibly steer in-context. To mitigate these issues, we propose Spectrum Tuning, a post-training method using Spectrum Suite to improve steerability and distributional coverage. We find that Spectrum Tuning often improves over pretrained and typical instruction-tuned models, enhancing steerability, spanning more of the output space, and improving distributional alignment on held-out datasets.

arXiv:2602.17560v2 Announce Type: replace Abstract: Activation steering, or representation engineering, offers a lightweight approach to align large language models (LLMs) by manipulating their internal activations at inference time. However, current methods suffer from two key limitations: (i) the lack of a unified theoretical framework for guiding the design of steering directions, and (ii) an over-reliance on one-step steering that fail to capture complex patterns of activation distributions. In this work, we propose a unified ordinary differential equations (ODEs)-based theoretical framework for activation steering in LLM alignment. We show that conventional activation addition can be interpreted as a first-order approximation to the solution of an ODE. Based on this ODE perspective, identifying a steering direction becomes equivalent to designing a barrier function from control theory. Derived from this framework, we introduce ODESteer, a kind of ODE-based steering guided by barrier functions, which shows empirical advancement in LLM alignment. ODESteer identifies steering directions by defining the barrier function as the log-density ratio between positive and negative activations, and employs it to construct an ODE for multi-step and adaptive steering. Compared to state-of-the-art activation steering methods, ODESteer achieves consistent empirical improvements on diverse LLM alignment benchmarks, a notable $5.7\%$ improvement over TruthfulQA, $2.5\%$ over UltraFeedback, and $2.4\%$ over RealToxicityPrompts. Our work establishes a principled new view of activation steering in LLM alignment by unifying its theoretical foundations via ODEs, and validating it empirically through the proposed ODESteer method.