# Escaping the Mode Lottery: Multi-Response Training Improves Language Model Generalization

arXiv: https://arxiv.org/abs/2606.00544 · HTML: https://mlsanity.com/paper/2606.00544/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 54 references that are in the map.
- First posted on arXiv 30 May 2026.

## Builds on (most cited first, 27 of 27)

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- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Competition-Level Code Generation with AlphaCode](https://mlsanity.com/paper/2203.07814/) (2022)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Open Problems and Fundamental Limitations of Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2307.15217/) (2023)
- [RAFT: Reward rAnked FineTuning for Generative Foundation Model Alignment](https://mlsanity.com/paper/2304.06767/) (2023)
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- [RRHF: Rank Responses to Align Language Models with Human Feedback without tears](https://mlsanity.com/paper/2304.05302/) (2023)
- [UltraFeedback: Boosting Language Models with Scaled AI Feedback](https://mlsanity.com/paper/2310.01377/) (2023)
- [What Makes Good Data for Alignment? A Comprehensive Study of Automatic Data Selection in Instruction Tuning](https://mlsanity.com/paper/2312.15685/) (2023)
- [Magpie: Alignment Data Synthesis from Scratch by Prompting Aligned LLMs with Nothing](https://mlsanity.com/paper/2406.08464/) (2024)
- [Principle-Driven Self-Alignment of Language Models from Scratch with Minimal Human Supervision](https://mlsanity.com/paper/2305.03047/) (2023)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Reward Model Ensembles Help Mitigate Overoptimization](https://mlsanity.com/paper/2310.02743/) (2023)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking](https://mlsanity.com/paper/2312.09244/) (2023)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [Theoretical guarantees on the best-of-n alignment policy](https://mlsanity.com/paper/2401.01879/) (2024)
- [#InsTag: Instruction Tagging for Analyzing Supervised Fine-tuning of Large Language Models](https://mlsanity.com/paper/2308.07074/) (2023)
- [Scaling Data Diversity for Fine-Tuning Language Models in Human Alignment](https://mlsanity.com/paper/2403.11124/) (2024)
- [DELIFT: Data Efficient Language model Instruction Fine Tuning](https://mlsanity.com/paper/2411.04425/) (2024)

## Abstract (arXiv)

Modern language-model fine-tuning typically pairs each prompt with a single response, even though many prompts admit multiple valid completions. This effectively reduces a multi-modal conditional distribution to a one-sample view, a phenomenon we call the "mode lottery," where training emphasizes a subset of plausible modes while leaving others underrepresented. We study multi-response training (MRT), which retains multiple responses per prompt, and develop a principled account of when and why it helps. Our key insight is that prompts and responses are distinct statistical resources: additional prompts reduce uncertainty about the input distribution, while additional responses reduce uncertainty about the conditional output distribution. This yields a variance-budget tradeoff that predicts when retaining multiple responses is worthwhile, shows diminishing returns as prompt-level uncertainty dominates, and explains why large redundant corpora can exhibit an implicit multi-response effect. We further analyze response selection, and show that Random-K-of-N is the unbiased default for distributional fine-tuning, reward-based selection can induce mode collapse, and a submodular quality-diversity objective provides an efficient alternative with theoretical guarantees. Controlled simulations validate the predicted variance and selection effects, including a striking failure mode where reward-only selection produces gradients misaligned with the true objective. Across structured and real-world datasets, including a new multi-prompt, multi-response benchmark, MRT consistently improves distributional generalization, with the largest gains in high response-diversity, low prompt-redundancy regimes. MRT reframes response multiplicity as a data-allocation problem with clear guidance: when responses are cheap and diverse, keeping more than one is not a heuristic, but a statistically grounded choice.