# Priced Guidance: Can Language Models Generate Future Research Ideas?

arXiv: https://arxiv.org/abs/2610.04976 · HTML: https://mlsanity.com/paper/2610.04976/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 47 references that are in the map.
- First posted on arXiv 4 Oct 2026.

## Builds on (most cited first, 30 of 38)

- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [The AI Scientist: Towards Fully Automated Open-Ended Scientific Discovery](https://mlsanity.com/paper/2408.06292/) (2024)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [The AI Scientist-v2: Workshop-Level Automated Scientific Discovery via Agentic Tree Search](https://mlsanity.com/paper/2504.08066/) (2025)
- [Accelerating scientific discovery with Co-Scientist](https://mlsanity.com/paper/2502.18864/) (2025)
- [MLAgentBench: Evaluating Language Agents on Machine Learning Experimentation](https://mlsanity.com/paper/2310.03302/) (2023)
- [Can LLMs Generate Novel Research Ideas? A Large-Scale Human Study with 100+ NLP Researchers](https://mlsanity.com/paper/2409.04109/) (2024)
- [PaperBench: Evaluating AI's Ability to Replicate AI Research](https://mlsanity.com/paper/2504.01848/) (2025)
- [Self-Preference Bias in LLM-as-a-Judge](https://mlsanity.com/paper/2410.21819/) (2024)
- [ScienceAgentBench: Toward Rigorous Assessment of Language Agents for Data-Driven Scientific Discovery](https://mlsanity.com/paper/2410.05080/) (2024)
- [ResearchAgent: Iterative Research Idea Generation over Scientific Literature with Large Language Models](https://mlsanity.com/paper/2404.07738/) (2024)
- [SciMON: Scientific Inspiration Machines Optimized for Novelty](https://mlsanity.com/paper/2305.14259/) (2023)
- [RE-Bench: Evaluating frontier AI R&D capabilities of language model agents against human experts](https://mlsanity.com/paper/2411.15114/) (2024)
- [Kimi K3: Open Frontier Intelligence](https://mlsanity.com/paper/2607.24653/) (2026)
- [DiscoveryBench: Towards Data-Driven Discovery with Large Language Models](https://mlsanity.com/paper/2407.01725/) (2024)
- [MOOSE-Chem: Large Language Models for Rediscovering Unseen Chemistry Scientific Hypotheses](https://mlsanity.com/paper/2410.07076/) (2024)
- [Many Heads Are Better Than One: Improved Scientific Idea Generation by A LLM-Based Multi-Agent System](https://mlsanity.com/paper/2410.09403/) (2024)
- [ResearchBench: Benchmarking LLMs in Scientific Discovery via Inspiration-Based Task Decomposition](https://mlsanity.com/paper/2503.21248/) (2025)
- [The Ideation-Execution Gap: Execution Outcomes of LLM-Generated versus Human Research Ideas](https://mlsanity.com/paper/2506.20803/) (2025)
- [AI Idea Bench 2025: AI Research Idea Generation Benchmark](https://mlsanity.com/paper/2504.14191/) (2025)
- [Predicting the Future of AI with AI: High-quality link prediction in an exponentially growing knowledge network](https://mlsanity.com/paper/2210.00881/) (2022)
- [Evaluating LLMs' Divergent Thinking Capabilities for Scientific Idea Generation with Minimal Context](https://mlsanity.com/paper/2412.17596/) (2024)
- [Towards Execution-Grounded Automated AI Research](https://mlsanity.com/paper/2601.14525/) (2026)
- [SciPIP: An LLM-based Scientific Paper Idea Proposer](https://mlsanity.com/paper/2410.23166/) (2024)
- [IdeaBench: Benchmarking Large Language Models for Research Idea Generation](https://mlsanity.com/paper/2411.02429/) (2024)
- [Estimating the Probabilities of Rare Outputs in Language Models](https://mlsanity.com/paper/2410.13211/) (2024)
- [HindSight: Evaluating LLM-Generated Research Ideas via Future Impact](https://mlsanity.com/paper/2603.15164/) (2026)
- [MOOSE-Chem2: Exploring LLM Limits in Fine-Grained Scientific Hypothesis Discovery via Hierarchical Search](https://mlsanity.com/paper/2505.19209/) (2025)
- [HRM-Text: Efficient Pretraining Beyond Scaling](https://mlsanity.com/paper/2605.20613/) (2026)
- [Learning to Predict Future-Aligned Research Proposals with Language Models](https://mlsanity.com/paper/2603.27146/) (2026)

## Abstract (arXiv)

We evaluate language models' capability to generate novel research ideas through the lens of compression. We aim to lower-bound the potentially tiny probability that a language model generates the essence of a future research idea without any hints. Rather than estimate this probability through expensive repeated sampling, our Priced Guidance framework measures the compression cost: how many additional bits of information are needed to guide the model to recover the target idea. We prove that if the model can recover the target idea with at most K bits of guidance in expectation, then it can generate the idea without any guidance with probability at least 2-K. In our framework, the language model, called the generator, can pose a sequence of multiple-choice questions and specify a probability distribution over possible answers. A guide, which is a language model with access to the target idea, selects answers. If a selected answer has prior probability p, the generator pays -log2 p bits. The generator aims to produce an idea that matches the essence of the target idea with minimal cumulative cost. This cumulative cost equals, up to an additive constant, the number of bits of information sent by the guide. Using this methodology, we evaluate five generator LLMs (Opus 5, Fable 5.1, GPT-6 Astra, GPT-5.6 Sol, and GLM 5.3) on the core ideas in 87 recent high-quality deep learning papers and we use LLM as judge to determine whether the generated idea matches the target in terms of the central research object and defining mechanism. Fable 5.1 achieves the lowest median compression cost at 69.9 bits, substantially lower than gzip's median of 5,712 bits for losslessly compressing the summary of the target idea. A uniform ensemble of Fable 5.1, Opus 5, and Astra further reduces the median compression cost to 55.8 bits and improves the generation probability lower bound by 18,000 times.