# Beyond Solvability: Task Learnability as a Static Prior for LLM RL Post-Training

arXiv: https://arxiv.org/abs/2608.09217 · HTML: https://mlsanity.com/paper/2608.09217/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 21 of its 31 references that are in the map.
- First posted on arXiv 10 Aug 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 21 of 21)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [s1: Simple test-time scaling](https://mlsanity.com/paper/2501.19393/) (2025)
- [OlympiadBench: A Challenging Benchmark for Promoting AGI with Olympiad-Level Bilingual Multimodal Scientific Problems](https://mlsanity.com/paper/2402.14008/) (2024)
- [PyTorch FSDP: Experiences on Scaling Fully Sharded Data Parallel](https://mlsanity.com/paper/2304.11277/) (2023)
- [Deep Learning on a Data Diet: Finding Important Examples Early in Training](https://mlsanity.com/paper/2107.07075/) (2021)
- [LIMO: Less is More for Reasoning](https://mlsanity.com/paper/2502.03387/) (2025)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [ARC-AGI-2: A New Challenge for Frontier AI Reasoning Systems](https://mlsanity.com/paper/2505.11831/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [Act Only When It Pays: Efficient Reinforcement Learning for LLM Reasoning via Selective Rollouts](https://mlsanity.com/paper/2506.02177/) (2025)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [Combining Induction and Transduction for Abstract Reasoning](https://mlsanity.com/paper/2411.02272/) (2024)
- [Can Prompt Difficulty be Online Predicted for Accelerating RL Finetuning of Reasoning Models?](https://mlsanity.com/paper/2507.04632/) (2025)
- [Prompt Curriculum Learning for Efficient LLM Post-Training](https://mlsanity.com/paper/2510.01135/) (2025)
- [BOTS: A Unified Framework for Bayesian Online Task Selection in LLM Reinforcement Finetuning](https://mlsanity.com/paper/2510.26374/) (2025)
- [Train at Moving Edge: Online-Verified Prompt Selection for Efficient RL Training of Large Reasoning Model](https://mlsanity.com/paper/2603.25184/) (2026)
- [Actor-Curator: Co-adaptive Curriculum Learning via Policy-Improvement Bandits for RL Post-Training](https://mlsanity.com/paper/2602.20532/) (2026)

## Built on by (most cited first, 2 of 2)

- [Rollout Efficiency in Reinforcement Learning for Reasoning Large Language Models: A Taxonomy and Future Directions](https://mlsanity.com/paper/2609.25463/) (2026)
- [What Will Post-Training Fix? Per-Problem Gains Are Shared Across Independent RL Runs, and Existing Checkpoints Predict Them Better Than A Priori Signals](https://mlsanity.com/paper/2610.04978/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) has become a central post-training paradigm for eliciting reasoning capabilities in large language models, yet uniform task sampling allocates compute without regard to differences in how tasks respond to optimization. Existing task-valuation methods mostly rely on snapshot-based signals such as current pass rate or reward, which estimate how solvable a task is under the current policy. However, tasks with similar current solvability can still differ substantially in how positively they respond to further training. We study this residual axis as task learnability: a regime-conditional measure of expected positive response to continued training under a fixed RL post-training regime. By analyzing per-task reward trajectories, we find that learnability is reproducible across independently sampled training contexts and predictive of downstream utility. To make this signal practical before training begins, we propose TrajVal, a lightweight probe-based estimator that approximates per-task learnability from a short probe run and two endpoint evaluations. TrajVal can be used either as a standalone static prior for task sampling or as a multiplicative prior for existing online schedulers. Experiments on mathematical and logical reasoning benchmarks across multiple model scales show that TrajVal improves data efficiency over uniform sampling and provides complementary gains when combined with online scheduling methods.