Large language models are increasingly trained on GPUs distributed across multiple regions, but geo-distributed training is challenging in practice. Real clusters often contain GPUs with different speeds and memory capacities, and they communicate over slow wide-area networks. Our analysis shows that this creates serious problems: existing synchronous methods preserve stable updates, but fast GPUs wait up to 20.9% of their runtime for slower ones, and all workers spend, on average, 65.8% of their runtime on synchronization. Recent asynchronous methods reduce waiting time but worsen the model accuracy due to stale updates. To address the problems, we present GeoMesh, a synchronous geo-distributed training framework for heterogeneous GPUs. GeoMesh balances per-worker workloads by assigning each GPU a suitable batch size and number of inner steps, so faster GPUs do more useful work instead of waiting. It also reduces communication volume by nearly 32× by exchanging compressed sign-based pseudo-gradients with lightweight magnitude and token count. Across heterogeneous GPUs and Azure-derived WAN, GeoMesh reduces time-to-target perplexity by up to 70.2% over representative baselines and lowers straggler- and WAN-induced GPU idle by up to 8.0× and 5.6×, respectively, while preserving comparable zero-shot accuracy.

Agents often repeatedly solve similar task instances from scratch, leading to unnecessary reasoning cost and long execution traces. Prior work has explored workflow reuse and executable skill induction, but it remains unclear which task scenarios admit procedural skills and how the shared procedural structure should be represented across successful traces. We study this problem in FSM-defined scenarios, where successful traces can be viewed as paths through partially observed instance-level transition graphs, and formulate procedural skills as reusable parameterized control-flow subgraphs. Based on this view, we introduce SkillDisCo, a distillation-and-compilation framework that distills reusable PFSM subgraphs from successful traces and compiles them into callable, executable, and verifiable procedural skills. Experiments on ALFWorld and WebArena show that SkillDisCo improves success rates and reduces agent turns across benchmarks and model scales, demonstrating the benefits of representing shared experience as reusable execution structures