Synthetic math data is widely used to scale LLM training, but its correctness is not guaranteed. We introduce MathDebugger, the first text-only, type-aware benchmark for jointly detecting *and* classifying errors in synthetic mathematical questions and answers. MathDebugger contains 2,000 correct questions, 2,000 erroneous questions (balanced across four fine-grained error types), and 2,000 annotated answers (610 erroneous, across three error types), each annotated with both a correctness label and an error-type label, with per-error-type Fleiss’ 𝜅 ranging from 0.69 to 0.88. On 14 SOTA LLMs (6 closed-source, 8 open-source, 1.5B–72B) and 3 process reward models, even advanced systems such as GPT-o3 and DeepSeek-R1 remain far from saturating the benchmark, particularly on fine-grained error-type detection; we further surface a *solving-vs-verifying* gap that causes math-tuned and long-chain-reasoning models to trail their general-purpose siblings. Error-type annotations also provide actionable supervision for correction, with gains that are significant under paired bootstrap (p<0.01). Code and data: [https://anonymous.4open.science/r/MathDebugger-7C4A/README.md](https://anonymous.4open.science/r/MathDebugger-7C4A/README.md)

Large language model (LLM)-powered multi-agent systems (MAS) demonstrate remarkable collective intelligence, with multi-agent memory serving as a pivotal mechanism for continual adaptation. However, existing multi-agent memory designs remain constrained by two fundamental bottlenecks: (i) memory homogenization caused by limited role-aware customization, and (ii) information overload induced by exposing agents to excessively fine-grained textual memories. To address these limitations, we propose LatentMem, a learnable multi-agent memory framework that customizes agent-specific experiential memories while reducing textual context. Specifically, LatentMem comprises an experience bank for lightweight storage of raw interaction trajectories and a memory composer that synthesizes compact latent memories conditioned on retrieved experience and agent-specific contexts. Further, we introduce Latent Memory Policy Optimization (LMPO), which propagates task-level optimization signals through latent memories to learn compact, high-utility latent representations. Extensive experiments across six benchmarks and four mainstream MAS frameworks show that LatentMem improves vanilla settings by up to 19.36% and consistently outperforms existing memory architectures, without requiring modifications to the agent-layer workflows.