RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library
Year: 2026
Type: conference-paper
Abstract: The advancement of reasoning capabilities in Large Language Models (LLMs) requires substantial amounts of high-quality reasoning data, particularly in mathematics.Existing data synthesis methods, such as data augmentation from annotated training sets or direct question generation based on relevant knowledge points and documents, have expanded datasets but face challenges in mastering the internal logic of the problem during generation and ensuring the verifiability of the solutions.To address these issues, we propose RV-Syn, a novel Rational and Verifiable mathematical Synthesis approach.RV-Syn first constructs a structured library of mathematical operations and then composes them into executable computational graphs, which serve as verifiable solution blueprints.These graphs are subsequently back-translated into complex problems, enabling solution-guided, logic-aware problem generation while inherently ensuring the verifiability of the solving process.Experimental results show RV-Syn surpasses existing synthesis methods, including those involving humancrafted problems.Our method achieves a 6.3% performance gain over the previous state-of-theart synthetic data on LLaMA-3-8B and demonstrates superior data efficiency, outperforming others with only half the training data (50k vs. 100k), enabling a more scalable and robust reasoning dataset generation framework.(1) Lack of Reasoning Depth (2) Logical Inconsistency (3) Lack of Ground-Truth RV-Syn Synthesized problem: Michael starts counting at 32, and he counts by fives.What is the 12th number that he counts?Synthesized problem: Consider the piecewise function f(x) defined as: Where a, b, and c are constants.The derivative f'(x) is continuous at x = 2 and x = -2.What is the value of a + b + c? (Contradiction) ๐ ๐ฅ = เต ๐๐ฅ 2 + ๐, ๐๐ ๐ฅ > 2, ๐ฅ -5, ๐๐ -2 โค ๐ฅ โค 2, 2๐ฅ -๐, ๐๐ ๐ฅ < -2,Synthesized problem: Suppose that the sum of the squares of two complex numbers x and y is 7 and the sum of their cubes is 10.List all possible values for x+y, separated by commas.Completion: We are given that ๐ฅ 2 + ๐ฆ 2 = 7 and ๐ฅ 3 + ๐ฆ 3 = 7.We can factor ๐ฅ 3 + ๐ฆ 3 to get ๐ฅ + ๐ฆ ๐ฅ 2 -๐ฅ๐ฆ + ๐ฆ 2 .Thus, we can write 10 = ๐ฅ + ๐ฆ 7 .It follows that ๐ฅ + ๐ฆ must divide 10.The only possibilities are that ๐ฅ + ๐ฆ is 1, 2, 5 or 10. (Incorrect Answer)Synthesized problem: Given a line defined by the point (1, 2, 3) and the direction vector (1, 1, -1), find the intersection point of this line with the xy-plane.Then, count the prime numbers between the x and y coordinates of this intersection point that have the same remainder when divided by 3 and 5. What is the count of such prime numbers? Multi-hopGround-Truth: 0 Synthesized problem: Find the smallest integer ๐ > 2 such that 2 ๐ -1 can be expressed as the product of two integers ๐ and ๐ (i.e., 2 ๐ -1 = ๐๐), and the highest power of two that divides 2 ๐-2 + ๐ -๐ is an even number. Enumeration and Iterative LoopGround-Truth: 3
Institutions: Renmin University of China, Ant Group (China)
Language: English
Topic: Topic Modeling
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7140132769