Financial agents are expected to answer factual investment queries through open search, but financial multi-hop retrieval differs from general multi-hop QA in a crucial way: each intermediate answer is an exact typed constraint, such as an entity, date, event, or numerical indicator, that determines the next query. This strict answer-conditioned dependency makes small intermediate errors cascade into plausible but wrong search trajectories. We introduce FinHopper, a benchmark for complex financial agents with controlled reasoning depth from 1 to 6 hops, covering stocks, funds, and macroeconomic facts, with gold intermediate answers for process-level evaluation. To construct FinHopper at scale, we design a state-transition-based synthesis framework that composes verified atomic financial QA patterns into dependency-preserving chains, followed by targeted in-synthesis verification, model-ensemble checking, and public-search validation by financial experts. Experiments with 20 LLM-agent configurations show that public search tools are necessary but insufficient: performance drops sharply as hop depth increases, the best model remains far below human experts, and process-aware scoring reveals partial reasoning progress hidden by final-answer-only evaluation. The benchmark is available at https://anonymous.4open.science/r/FinHopper-aabb/

Accurately identifying student misconceptions is crucial for personalized education but faces three challenges: (1) data scarcity with long-tail distribution, where authentic student reasoning is difficult to synthesize; (2) fuzzy boundaries between error categories with high annotation noise; (3) deployment paradox—large models overlook unconventional approaches due to pretraining bias and cannot be deployed on edge, while small models overfit to noise. Unlike traditional methods that increase diversity through large-scale data synthesis, we propose a two-stage knowledge distillation framework that mines high-value samples from existing data. The first stage performs standard distillation to transfer task capabilities. The second stage introduces a dual-layer marginal selection mechanism based on cognitive uncertainty, identifying four types of critical samples based on teacher model uncertainty and confidence differences. For different data subsets, we design difficulty-adaptive mechanism to balance hard/soft label contributions, enabling student models to inherit inter-class relationships from teacher soft labels while distinguishing ambiguous error types. Experiments show that with augmented training on only 10.30% of filtered samples, we achieve MAP@3 of 0.9585 (+17.8%) on the MAP-Charting dataset, and using only a 4B parameter model, we attain 84.38% accuracy on cross-topic tests of middle school algebra misconception benchmarks, significantly outperforming sota LLM (67.73%) and standard fine-tuned 72B models (81.25%). Our code is available at https://anonymous.4open.science/r/acl2026_map-5847/.