BiVerify：双向验证框架提升数学推理自纠错能力
BiVerify: Closing the Loop Between Backward and Forward Verification for Mathematical Self-Correction
arXiv 上的新论文，教 LLM 做数学题时同时用前向和后向验证交叉纠错，比单向验证平均高 13.5 个百分点，在 GPT 上差距到 31.2 个点。做推理智能体或数学评测的工程师值得看看它的调度逻辑。
论文提出 BiVerify，一个双向动态调度的数学验证框架，解决 LLM 数学推理中单向验证的局限。在五个数学推理基准上，BiVerify 超过论文中评估的最强公开基线 13.5 个百分点，在 GPT 系模型上差距达到 31.2 个百分点。
其机制分两步：先用后向验证把候选答案对照原始约束做筛查，跳过复杂中间推理；再用前向验证沿着题目条件检查推理过程，定位错误并评估完整性。验证失败时，系统会重置状态、切换方向并重新验证，直到同一候选在两个方向都通过。团队还引入共享数学工具，把逻辑推理与精确计算分离。
实验覆盖 DeepSeek、GPT、Gemini 多个主流模型，结果显示双向结合的效果超过任一单向验证，说明后向验证能补上前向验证容易漏掉的关键约束。对做推理增强或智能体自纠错的开发者，这套验证调度思路可以直接参考。
BiVerify: Closing the Loop Between Backward and Forward Verification for Mathematical Self-Correction
Large language models (LLMs) have made substantial progress in mathematical reasoning but still produce incorrect solutions to complex problems, indicating the need for more reliable self-correction mechanisms. Mathematical self-correction typically identifies errors through verification, which can proceed backward or forward. The two directions provide complementary verification capabilities. Backward verification checks a candidate answer against the original constraints, bypassing complex intermediate reasoning, but cannot ensure correct reasoning or objective completeness. Forward verification follows the problem conditions and current solution, enabling it to locate reasoning errors and assess objective completeness, but may overlook key constraints in complex solution chains. We propose BiVerify, a dynamically scheduled framework for bidirectional mathematical verification. BiVerify begins with backward verification to screen the answer against the original constraints, followed by forward verification of the reasoning process; subsequent direction switching, state resetting, and re-verification are governed by verification outcomes. Upon failure, the system revises the candidate or verification flow until the same candidate passes both directions. We also introduce shared mathematical tools that separate logical reasoning from precise computation. We systematically evaluate BiVerify on five challenging mathematical reasoning benchmarks using multiple mainstream DeepSeek, GPT, and Gemini models. BiVerify exceeds the strongest representative public baseline evaluated in this work by 13.5 percentage points in average accuracy, with the margin reaching 31.2 percentage points on GPT. Further analysis shows that BiVerify's overall performance exceeds that of either verification direction alone.
This report is categorized under AITOP's "Papers" desk. Within our cross-regional analytical framework, it directly maps to AI developer toolchains, coding agents, and engineering workflows. Key entities and technical topics under continuous tracking include BiVerify, DeepSeek, GPT, Gemini.
Primary source verification: published directly by arXiv: DeepSeek with first-party authority.