# Spectrum Tuning: Post-Training for Distributional Coverage and In-Context Steerability

arXiv: https://arxiv.org/abs/2510.06084 · HTML: https://mlsanity.com/paper/2510.06084/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2025.

## Built on by (most cited first, 20 of 20)

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- [Maximizing Mutual Information Between Prompt and Response Improves LLM Performance With No Additional Data](https://mlsanity.com/paper/2603.19294/) (2026)
- [Magic, Madness, Heaven, Sin: LLM Output Diversity is Everything, Everywhere, All at Once](https://mlsanity.com/paper/2604.01504/) (2026)
- [The Role of Ambiguity in Error Prediction via Uncertainty Quantification](https://mlsanity.com/paper/2606.02093/) (2026)
- [A Model of Multi-turn Human Persuadability Using Probabilistic Belief Tracing](https://mlsanity.com/paper/2606.05330/) (2026)
- [Will Scaling Improve Social Simulation with LLMs?](https://mlsanity.com/paper/2607.02464/) (2026)
- [A Roadmap to Impactful Pluralistic Alignment Research](https://mlsanity.com/paper/2607.22305/) (2026)
- [Breaking Homogeneity: Diversifying Persona Sets for Creative LLM Outputs](https://mlsanity.com/paper/2609.30492/) (2026)
- [How Far Do Persona Effects Generalize in Language Models?](https://mlsanity.com/paper/2609.32758/) (2026)
- [Sample What You Say: Aligning Language Models to Sample the Distributions They State](https://mlsanity.com/paper/2609.34929/) (2026)
- [Gacha Decoding: Eliciting Diverse Generations Through Instruction Following](https://mlsanity.com/paper/2610.01382/) (2026)
- [NepPlural: A Human-Anchored Benchmark for Persona Annotation in Nepali Migration Discourse](https://mlsanity.com/paper/2610.15732/) (2026)

## Abstract (arXiv)

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.