DéjàQ: Open-Ended Evolution of Diverse, Learnable and Verifiable Problems

• URL: http://arxiv.org/abs/2601.01931v1
• Date: Mon, 05 Jan 2026 09:27:49 GMT
• Title: DéjàQ: Open-Ended Evolution of Diverse, Learnable and Verifiable Problems
• Authors: Willem Röpke, Samuel Coward, Andrei Lupu, Thomas Foster, Tim Rocktäschel, Jakob Foerster,
• Abstract summary: We introduce DéjQ, a framework that evolves a diverse set of synthetic mathematical problems alongside model training.<n>This evolutionary process adapts to the model's ability throughout training, optimising problems for learnability.<n>We find that the model can generate novel and meaningful problems, and that these LLM-driven mutations improve RL training.
• Score: 19.381443841718596
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Recent advances in reasoning models have yielded impressive results in mathematics and coding. However, most approaches rely on static datasets, which have been suggested to encourage memorisation and limit generalisation. We introduce DéjàQ, a framework that departs from this paradigm by jointly evolving a diverse set of synthetic mathematical problems alongside model training. This evolutionary process adapts to the model's ability throughout training, optimising problems for learnability. We propose two LLM-driven mutation strategies in which the model itself mutates the training data, either by altering contextual details or by directly modifying problem structure. We find that the model can generate novel and meaningful problems, and that these LLM-driven mutations improve RL training. We analyse key aspects of DéjàQ, including the validity of generated problems and computational overhead. Our results underscore the potential of dynamically evolving training data to enhance mathematical reasoning and indicate broader applicability, which we will support by open-sourcing our code.

Related papers

• Adaptive Problem Generation via Symbolic Representations [16.05958546676182]
  We present a method for generating training data for reinforcement learning with verifiable rewards to improve small open-weights language models on mathematical tasks.<n>We perform modifications in a symbolic problem space, representing each problem as a set of symbolic variables and constraints.<n>This representation enables precise control over problem structure, automatic generation of ground-truth solutions, and decouples mathematical reasoning from linguistic realization.
  arXiv  Detail & Related papers  (2026-02-22T13:33:48Z)
• C2-Evo: Co-Evolving Multimodal Data and Model for Self-Improving Reasoning [78.36259648527401]
  C2-Evo is an automatic, closed-loop self-improving framework that jointly evolves both training data and model capabilities.<n>We show that C2-Evo consistently obtains considerable performance gains across multiple mathematical reasoning benchmarks.
  arXiv  Detail & Related papers  (2025-07-22T12:27:08Z)
• Echo Chamber: RL Post-training Amplifies Behaviors Learned in Pretraining [74.83412846804977]
  Reinforcement learning (RL)-based fine-tuning has become a crucial step in post-training language models.<n>We present a systematic end-to-end study of RL fine-tuning for mathematical reasoning by training models entirely from scratch.
  arXiv  Detail & Related papers  (2025-04-10T17:15:53Z)
• Self-Evolved Preference Optimization for Enhancing Mathematical Reasoning in Small Language Models [17.673293240849787]
  We introduce SPHERE, a self-evolving data generation pipeline that enhances reasoning in small language models (SLMs)<n> SPHERE operates in three stages: (i) Self-Generation, where the model autonomously constructs problem-solving steps; (ii) Self-Correction, enabling it to identify and rectify errors; and (iii) Diversity Induction, improving robustness through multiple valid reasoning trajectories.<n>We show that SPHERE-trained models achieve significant gains over their base versions and match/surpass GPT-4o on certain benchmarks.
  arXiv  Detail & Related papers  (2025-03-04T14:43:25Z)
• Unleashing LLM Reasoning Capability via Scalable Question Synthesis from Scratch [54.12139707822201]
  We propose ScaleQuest, a novel, scalable, and cost-effective data synthesis method.<n>By generating diverse questions from scratch, we produce a dataset of 1 million problem-solution pairs.<n>Our experiments demonstrate that models trained on our data outperform existing open-source datasets.
  arXiv  Detail & Related papers  (2024-10-24T12:42:04Z)
• SIaM: Self-Improving Code-Assisted Mathematical Reasoning of Large Language Models [54.78329741186446]
  We propose a novel paradigm that uses a code-based critic model to guide steps including question-code data construction, quality control, and complementary evaluation. Experiments across both in-domain and out-of-domain benchmarks in English and Chinese demonstrate the effectiveness of the proposed paradigm.
  arXiv  Detail & Related papers  (2024-08-28T06:33:03Z)
• Large Language Models as Surrogate Models in Evolutionary Algorithms: A Preliminary Study [5.6787965501364335]
  Surrogate-assisted selection is a core step in evolutionary algorithms to solve expensive optimization problems. Traditionally, this has relied on conventional machine learning methods, leveraging historical evaluated evaluations to predict the performance of new solutions. In this work, we propose a novel surrogate model based purely on LLM inference capabilities, eliminating the need for training.
  arXiv  Detail & Related papers  (2024-06-15T15:54:00Z)
• MinT: Boosting Generalization in Mathematical Reasoning via Multi-View Fine-Tuning [53.90744622542961]
  Reasoning in mathematical domains remains a significant challenge for small language models (LMs) We introduce a new method that exploits existing mathematical problem datasets with diverse annotation styles. Experimental results show that our strategy enables a LLaMA-7B model to outperform prior approaches.
  arXiv  Detail & Related papers  (2023-07-16T05:41:53Z)
• Theoretical Characterization of the Generalization Performance of Overfitted Meta-Learning [70.52689048213398]
  This paper studies the performance of overfitted meta-learning under a linear regression model with Gaussian features. We find new and interesting properties that do not exist in single-task linear regression. Our analysis suggests that benign overfitting is more significant and easier to observe when the noise and the diversity/fluctuation of the ground truth of each training task are large.
  arXiv  Detail & Related papers  (2023-04-09T20:36:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.