Modern mobile GUI agents can perceive visible screens and execute local actions, but they still lack persistent app-specific navigation knowledge: where functions live, which pages contain them, and which screens are equivalent across repeated visits. We introduce TAG-Nav, a Task-Agnostic Graph Navigation framework that wraps existing GUI-agent backbones with reusable destination memory. Offline exploration is distilled into compact records of app functions, target pages, and waypoint routes before any evaluated instruction is seen. When a future task’s destination is covered by this memory, TAG-Nav can retrieve the destination and provide route guidance without requiring a task-specific demonstration. This separates mobile GUI destination navigation from full task completion: many tasks share the prefix of reaching the right page, while final actions may enter content, send data, make purchases, delete information, or change sensitive settings. To evaluate route finding without downstream execution confounds, we introduce DestBench, a navigation-only protocol that asks whether an agent reaches the correct pre-action destination screen. DestBench enables a controlled graph-memory study comparing no-memory agents with random, automated BFS, and clean graph memory. Graph-derived memory improves strict navigation success rate of UI-TARS-1.5-7B from 52.4% without graph memory to 58.3% with automated BFS memory, and improves Qwen-VL-Max success rate from 59.5% to 71.4% on the same conditions. Together, TAG-Nav and DestBench show that destination coverage and route cleanliness strongly shape graph-memory value, making graph quality a measured variable rather than an assumed benefit of exploration.

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy–efficiency trade-off, improving DeepSeek-R1-Distill-7B by +9.9% accuracy while reducing CoT length by 67% across four benchmarks.