Classroom Final Exam: An Instructor-Tested Reasoning Benchmark
Organizations: Northwestern University · UC Santa Cruz · Duke University · University of Birmingham ·
Abstract
We introduce CFE-Bench (Classroom Final Exam), a multimodal benchmark for evaluating the reasoning capabilities of large language models across more than 20 STEM domains. CFE-Bench is curated from repeatedly used, authentic university homework and exam problems, paired with reference solutions provided by course instructors. CFE-Bench remains challenging for frontier models: the newly released Gemini-3.1-pro-preview achieves 59.69% overall accuracy, while the second-best model, Gemini-3-flash-preview, reaches 55.46%, leaving substantial room for improvement. Beyond aggregate scores, we conduct a diagnostic analysis by decomposing instructor reference solutions into structured reasoning flows. We find that while frontier models often answer intermediate sub-questions correctly, they struggle to reliably derive and maintain correct intermediate states throughout multi-step solutions. We further observe that model-generated solutions typically contain more reasoning steps than instructor solutions, indicating lower step efficiency and a higher risk of error accumulation. Data and code are available at https://github.com/Analogy-AI/CFE_Bench.
Figures & tables
| Setting | Acc (%) | AUC | P | R | F1 | FN | FP |
| S2S | |||||||
| L2S | |||||||
| L2L |
| Text subset ( ) | |||
| Model | Variable Accuracy | Question Accuracy | |
| Gemma-3-27B-it | 13.79% | 9.84% | |
| Ministral-3-14B-Reasoning | 17.92% | 13.11% | |
| Llama-4-Maverick | 24.53% | 19.67% | |
| GPT-oss-120b | 41.15% | 34.43% | |
| Qwen3-235B-Instruct | 37.41% | 32.46% | |
| Text + Multimodal ( ) | |||
| Model | Variable Accuracy | Question Accuracy | |
| Llama-4-Maverick | 21.82% | 16.48% | |
| Qwen3.5-397B | 53.60% | 47.44% | |
| Qwen3.5-plus | 53.60% | 47.00% | |
| claude-opus-4.6 | 54.15% | 47.66% | |
| Grok-4-0709 | 47.78% | 41.65% | |
| Text subset ( ) | Multimodal subset ( ) | |||||
| Statistic | Solved | Unsolved | Overall | Solved | Unsolved | Overall |
| # Questions | 179 | 126 | 305 | 74 | 70 | 144 |
| GT len. (mean std) | ||||||
| Resp. len. (mean std) | ||||||
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
| Question: Short-circuited parallel plate electrodes of area enclose a lossy dielectric of thickness with dielectric permittivity and ohmic conductivity . The lossy dielectric at time has a uniformly distributed free volume charge density . Neglect fringing field effects. What is the current flowing through the short circuit? | ||
|---|---|---|
| Step | Question | Answer |
| / | Write the expression for the total current density in a lossy dielectric in terms of , , and at the electrode ( ). | |
| / | For a uniform free volume charge density inside the slab of thickness , state the relation between and using Gauss’s law. | |
| / | Differentiate the expression from Step 2 with respect to time to obtain at . | |
| / | Substitute the expressions for and from Steps 2 and 3 into the current density expression from Step 1. | |
| / | Simplify the expression from Step 4 algebraically. | |
RealMath-Eval: Why SOTA Judges Struggle with Real Human Reasoning
Evaluation Gap'': judges are considerably more accurate and consistent on synthetic text (MSE $\sim$1.17) but struggle to generalize to authentic student reasoning. Through semantic embedding analysis, we find that synthetic errors suffer from a structural collapse'' into predictable, low-dimensional linear subspaces, whereas human errors form a more diverse error space. Furthermore, generative probability probes suggest that human reasoning involves significantly higher information-theoretic surprisal, indicating that student reasoning transitions are more out-of-distribution for current models. Finally, we find that surface-level style transfer fails to close this gap. Our findings suggest that current LLM evaluation pipelines relying heavily on synthetic data may not adequately capture the diversity of authentic student mathematical reasoning.