Adaptive Problem Generation via Symbolic Representations

• URL: http://arxiv.org/abs/2602.19187v1
• Date: Sun, 22 Feb 2026 13:33:48 GMT
• Title: Adaptive Problem Generation via Symbolic Representations
• Authors: Teresa Yeo, Myeongho Jeon, Dulaj Weerakoon, Rui Qiao, Alok Prakash, Armando Solar-Lezama, Archan Misra,
• Abstract summary: 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.
• Score: 16.05958546676182
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a method for generating training data for reinforcement learning with verifiable rewards to improve small open-weights language models on mathematical tasks. Existing data generation approaches rely on open-loop pipelines and fixed modifications that do not adapt to the model's capabilities. Furthermore, they typically operate directly on word problems, limiting control over problem structure. To address this, we perform modifications in a symbolic problem space, representing each problem as a set of symbolic variables and constraints (e.g., via algebraic frameworks such as SymPy or SMT formulations). This representation enables precise control over problem structure, automatic generation of ground-truth solutions, and decouples mathematical reasoning from linguistic realization. We also show that this results in more diverse generations. To adapt the problem difficulty to the model, we introduce a closed-loop framework that learns modification strategies through prompt optimization in symbolic space. Experimental results demonstrate that both adaptive problem generation and symbolic representation modifications contribute to improving the model's math solving ability.

Related papers

• DéjàQ: Open-Ended Evolution of Diverse, Learnable and Verifiable Problems [19.381443841718596]
  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.
  arXiv  Detail & Related papers  (2026-01-05T09:27:49Z)
• Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis for Large Reasoning Models [54.29243291958429]
  We develop a problem generator that reasons explicitly to plan problem directions before synthesis.<n>We treat the solver's feedback on synthetic problems as a reward signal, enabling the generator to calibrate difficulty.<n>Our method achieves an average improvement of 2.5% and generalizes to both language and vision-language models.
  arXiv  Detail & Related papers  (2025-11-13T03:08:51Z)
• Self-Improving Transformers Overcome Easy-to-Hard and Length Generalization Challenges [15.975023196507841]
  Large language models often struggle with length generalization and solving complex problem instances beyond their training distribution.<n>We present a self-improvement approach where models iteratively generate and learn from their own solutions.<n>Our results demonstrate how controlled weak-to-strong curricula can systematically teach a model logical extrapolation.
  arXiv  Detail & Related papers  (2025-02-03T18:45:22Z)
• Bridging Visualization and Optimization: Multimodal Large Language Models on Graph-Structured Combinatorial Optimization [56.17811386955609]
  Graph-structured challenges are inherently difficult due to their nonlinear and intricate nature.<n>In this study, we propose transforming graphs into images to preserve their higher-order structural features accurately.<n>By combining the innovative paradigm powered by multimodal large language models with simple search techniques, we aim to develop a novel and effective framework.
  arXiv  Detail & Related papers  (2025-01-21T08:28:10Z)
• Shape Arithmetic Expressions: Advancing Scientific Discovery Beyond Closed-Form Equations [56.78271181959529]
  Generalized Additive Models (GAMs) can capture non-linear relationships between variables and targets, but they cannot capture intricate feature interactions. We propose Shape Expressions Arithmetic ( SHAREs) that fuses GAM's flexible shape functions with the complex feature interactions found in mathematical expressions. We also design a set of rules for constructing SHAREs that guarantee transparency of the found expressions beyond the standard constraints.
  arXiv  Detail & Related papers  (2024-04-15T13:44:01Z)
• A Causal Framework to Quantify the Robustness of Mathematical Reasoning with Language Models [81.15974174627785]
  We study the behavior of language models in terms of robustness and sensitivity to direct interventions in the input space. Our analysis shows that robustness does not appear to continuously improve as a function of size, but the GPT-3 Davinci models (175B) achieve a dramatic improvement in both robustness and sensitivity compared to all other GPT variants.
  arXiv  Detail & Related papers  (2022-10-21T15:12:37Z)
• SymbolicGPT: A Generative Transformer Model for Symbolic Regression [3.685455441300801]
  We present SymbolicGPT, a novel transformer-based language model for symbolic regression. We show that our model performs strongly compared to competing models with respect to the accuracy, running time, and data efficiency.
  arXiv  Detail & Related papers  (2021-06-27T03:26:35Z)
• Sufficiently Accurate Model Learning for Planning [119.80502738709937]
  This paper introduces the constrained Sufficiently Accurate model learning approach. It provides examples of such problems, and presents a theorem on how close some approximate solutions can be. The approximate solution quality will depend on the function parameterization, loss and constraint function smoothness, and the number of samples in model learning.
  arXiv  Detail & Related papers  (2021-02-11T16:27:31Z)
• SMART: A Situation Model for Algebra Story Problems via Attributed Grammar [74.1315776256292]
  We introduce the concept of a emphsituation model, which originates from psychology studies to represent the mental states of humans in problem-solving. We show that the proposed model outperforms all previous neural solvers by a large margin while preserving much better interpretability.
  arXiv  Detail & Related papers  (2020-12-27T21:03:40Z)
• Joint learning of variational representations and solvers for inverse problems with partially-observed data [13.984814587222811]
  In this paper, we design an end-to-end framework allowing to learn actual variational frameworks for inverse problems in a supervised setting. The variational cost and the gradient-based solver are both stated as neural networks using automatic differentiation for the latter. This leads to a data-driven discovery of variational models.
  arXiv  Detail & Related papers  (2020-06-05T19:53:34Z)

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.