📄 TreeCut: A Synthetic Unanswerable Math Word Problem Dataset for LLM Hallucination Evaluation

Summary

LLMs score near human level on math word problem benchmarks such as GSM8K. However, they often give confident answers to problems that cannot be solved. Earlier unanswerable-problem sets were built by editing existing benchmarks, which brings contamination risk, small scale and little structural control. TreeCut instead generates problems synthetically. Each problem is a tree: nodes are item prices, edges from the root assign values, and other edges are linear relations between two items. Deleting one edge on the path to the asked variable makes the problem unsolvable, while the intact tree serves as an answerable control. Generation parameters set the number of variables, the depth of the target, whether item names are composite, and the cut's position. Six models were tested: Llama 3.1, Qwen2.5, GPT-4o and o3-mini. All showed substantial hallucination, and most could solve the answerable versions far better than they could spot the unanswerable ones. The dataset gives a contamination-free and controllable way to probe whether models recognize missing information.

Key points

• Generator design: prices are integers from 5 to 15, and coefficients are non-zero integers from −3 to 3. The controllable parameters are numVars, ansDepth, compositeName and cutDepth. Code and samples are at github.com/j-bagel/treecut-math.
• Zero-shot worst cases: GPT-4o hallucinated on 64% of problems at ansDepth = 8, and o3-mini on 44% at ansDepth = 2. In the shallow case, o3-mini tended to invent assumptions. Llama-8B and both Qwen models failed almost entirely, with hallucination rates around 80–95%.
• Few-shot prompting (3 answerable + 3 unanswerable examples) lowered o3-mini to about 3%. Rates for the other five models stayed roughly the same, which suggests an intrinsic weakness.
• Solving vs. detecting: GPT-4o solved 84% of answerable problems at ansDepth = 8 but recognized only 36% of the matching unanswerable ones.
• What raises hallucination (GPT-4o, 500 problems per configuration): deeper target variables, extra unrelated conditions in the tree, composite item names, and a cut placed near the middle of the path.