We present AMO-Bench, an Advanced Mathematical reasoning benchmark with Olympiad level or even higher difficulty, comprising 50 human-crafted problems. Existing benchmarks have widely leveraged high school math competitions for evaluating mathematical reasoning capabilities of large language models (LLMs). However, many existing math competitions are becoming less effective for assessing top-tier LLMs due to performance saturation (e.g., AIME24/25). To address this, AMO-Bench introduces more rigorous challenges by ensuring all 50 problems are (1) cross-validated by experts to meet at least the International Mathematical Olympiad (IMO) difficulty standards, and (2) entirely original problems to prevent potential performance leakages from data memorization. Experimental results across 36 LLMs on AMO-Bench highlights three key findings: (1) high-level mathematical reasoning remains challenging for current LLMs, with even the best-performing model achieving only 63.1% accuracy and most LLMs scoring below 50%; (2) scaling test-time compute remains a highly effective strategy for substantially improving reasoning performances, and (3) open-source models are progressively narrowing the performance gap with proprietary models. Additionally, we conduct further analysis about reasoning efficiency, volatility, and cross-lingual robustness, providing deeper insights behind the reasoning performances.

We present the Team Falcons system for the ImageEval 2026 Task 1b English track. The task provides culturally grounded images from the OASIS/EverydayMMQA resource family and three English statements per image, exactly one of which is visually supported(CITATION). Rather than treating the statements as independent binary decisions, we exploit this structural constraint and formulate each item as image-conditioned three-way classification. In Stage 1, we fine-tune Qwen3-VL-8B(CITATION) with 4-bit QLoRA(CITATION) and estimate uncertainty from the first-token probabilities assigned to A, B, and C. Stage 2 we send only examples whose top-two probability margin is below 0.90 to Gemini 3.6 Flash and GPT-5.4-mini. Their answer replaces the Stage 1 prediction only when both verifiers return the same valid option. On the official test set, Stage 1 obtains a Contrastive Instability (CI) of 0.0360 and Combined Accuracy of 0.9640. Consensus verification improves these scores to 0.0290 and 0.9710, respectively, placing our submission first on the Task 1b English leaderboard. After test labels were released, we found that the verifiers agreed on 91 of 138 routed items and changed 17 predictions: 12 corrections and 5 harmful revisions. These results show that structure-aware fine-tuning and conservative uncertainty routing can effectively combine a local open-weight VLM with proprietary multimodal verifiers.