VERIFY-RL: Verifiable Recursive Decomposition for Reinforcement Learning in Mathematical Reasoning
#VERIFY-RL #Large Language Models #Symbolic Differentiation #Recursive Decomposition #Mathematical Reasoning #arXiv #Curriculum Learning
📌 Key Takeaways
- Researchers introduced VERIFY-RL to fix unreliable problem-solving in AI models.
- The framework uses symbolic differentiation to create provably simpler mathematical subproblems.
- Unlike previous heuristic methods, VERIFY-RL provides mathematical guarantees for decomposition.
- The approach enhances reinforcement learning by ensuring a logical progression in curriculum training.
📖 Full Retelling
Researchers specializing in artificial intelligence published a new paper titled "VERIFY-RL: Verifiable Recursive Decomposition for Reinforcement Learning in Mathematical Reasoning" on the arXiv preprint server on February 12, 2025, to address the lack of structural reliability in how language models break down complex math problems. The team introduced VERIFY-RL as a novel framework that utilizes symbolic differentiation to create mathematically grounded subproblems, ensuring that the decomposition process is both verifiable and conducive to effective reinforcement learning. By moving away from heuristic methods that offer no guarantees of accuracy, the researchers aim to improve the reasoning capabilities of large language models through more rigorous curriculum learning strategies.
Historically, training language models to solve intricate mathematical equations has relied on curriculum learning, which involves teaching models to handle simpler components before tackling the full problem. However, the researchers noted a significant flaw in current methodologies: existing decomposition techniques are often arbitrary and lack a formal proof that the generated subproblems are actually simpler or logically connected to the parent task. This lack of theoretical grounding often leads to "hallucinations" or inefficient learning paths where the model fails to grasp the underlying logic of the mathematical operation.
To solve this, VERIFY-RL leverages the inherent structural properties of symbolic differentiation to provide a natural, recursive hierarchy for decomposition. By using calculus-based rules, the framework can guarantee that solving a sub-derivative directly assists in solving the original complex derivative. This creates a verifiable chain of reasoning that models can follow during the reinforcement learning phase. This breakthrough represents a significant shift toward neuro-symbolic AI, combining the flexible learning of neural networks with the rigid, provable logic of mathematical symbols to enhance the reliability of AI-driven scientific discovery.
🏷️ Themes
Artificial Intelligence, Mathematics, Reinforcement Learning
📚 Related People & Topics
Large language model
Type of machine learning model
A large language model (LLM) is a language model trained with self-supervised machine learning on a vast amount of text, designed for natural language processing tasks, especially language generation. The largest and most capable LLMs are generative pre-trained transformers (GPTs) that provide the c...
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📄 Original Source Content
arXiv:2602.07559v1 Announce Type: new Abstract: Training language models to solve complex mathematical problems benefits from curriculum learning progressively training on simpler subproblems. However, existing decomposition methods are often heuristic, offering no guarantees that subproblems are simpler, that solving them aids the parent task, or that their relationships are mathematically grounded. We observe that symbolic differentiation provides a natural structure for verified decompositio