# Ask-E: An Environment for Calibrated Question Generation

arXiv: https://arxiv.org/abs/2608.06933 · HTML: https://mlsanity.com/paper/2608.06933/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 41 of its 64 references that are in the map.
- First posted on arXiv 7 Aug 2026.

## Builds on (most cited first, 30 of 41)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [Self-Rewarding Language Models](https://mlsanity.com/paper/2401.10020/) (2024)
- [Self-Play Fine-Tuning Converts Weak Language Models to Strong Language Models](https://mlsanity.com/paper/2401.01335/) (2024)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Phi-4-Mini Technical Report: Compact yet Powerful Multimodal Language Models via Mixture-of-LoRAs](https://mlsanity.com/paper/2503.01743/) (2025)
- [RewardBench: Evaluating Reward Models for Language Modeling](https://mlsanity.com/paper/2403.13787/) (2024)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [MiniMax-M1: Scaling Test-Time Compute Efficiently with Lightning Attention](https://mlsanity.com/paper/2506.13585/) (2025)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [Beyond Benchmarks: MathArena as an Evaluation Platform for Mathematics with LLMs](https://mlsanity.com/paper/2605.00674/) (2026)
- [SPIRAL: Self-Play on Zero-Sum Games Incentivizes Reasoning via Multi-Agent Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2506.24119/) (2025)
- [DyVal: Dynamic Evaluation of Large Language Models for Reasoning Tasks](https://mlsanity.com/paper/2309.17167/) (2023)
- [Curiosity-driven Red-teaming for Large Language Models](https://mlsanity.com/paper/2402.19464/) (2024)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [Towards Robust Mathematical Reasoning](https://mlsanity.com/paper/2511.01846/) (2025)
- [QuestBench: Can LLMs ask the right question to acquire information in reasoning tasks?](https://mlsanity.com/paper/2503.22674/) (2025)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [Self-Questioning Language Models](https://mlsanity.com/paper/2508.03682/) (2025)
- [AutoBencher: Towards Declarative Benchmark Construction](https://mlsanity.com/paper/2407.08351/) (2024)
- [Language Self-Play For Data-Free Training](https://mlsanity.com/paper/2509.07414/) (2025)
- [Learning to Ask: When LLM Agents Meet Unclear Instruction](https://mlsanity.com/paper/2409.00557/) (2024)
- [AI-Assisted Generation of Difficult Math Questions](https://mlsanity.com/paper/2407.21009/) (2024)
- [SPELL: Self-Play Reinforcement Learning for Evolving Long-Context Language Models](https://mlsanity.com/paper/2509.23863/) (2025)
- [The Delta Learning Hypothesis: Preference Tuning on Weak Data can Yield Strong Gains](https://mlsanity.com/paper/2507.06187/) (2025)

## Abstract (arXiv)

Today, we improve models by training and evaluating them on problems at the frontier of their abilities. Creating such problems is itself a demanding task, requiring the ability to probe model limits and generalize beyond existing question distributions. It also means placing problems at a precise difficulty level, which requires understanding what it takes to solve them. In short, generating problems calibrated to a model's current frontier demands capability beyond it, an increasingly burdensome constraint as models improve. Our key insight is that we can leverage this constraint to our advantage: a model that can generate problems consistently calibrated to a given frontier must possess capability beyond it. Accordingly, we present Ask-E, an environment that benchmarks and trains models on their ability to write questions at a given skill level, rather than answer them. Concretely, we define target skill levels as ranges bounded by the capabilities of two existing language models. A generated question is successfully calibrated if exactly one of the two models can solve it, placing it precisely within the target range and differentiating the capabilities of these models. Ask-E serves both as a benchmark and a training environment, where models generate problems calibrated to a variety of skill levels. We find that even frontier models achieve below 50% calibration on the benchmark, leaving significant headroom to measure future progress. We also show that training on this environment leads to improvements across a number of downstream math benchmarks even with no new math data, no interaction with stronger models, and no correctness-based reward.