Simple Math Benchmark
Key Insight
The data shows that some small language models (under 0.5B parameters) can demonstrate significant mathematical abilities, challenging the assumption that large parameter counts are required for basic math reasoning. Models tested using this link.
Model Overview
This analysis compares the performance of various language models on mathematical problems, with a focus on compact models:
The highest performer among tested models, demonstrating remarkable mathematical abilities despite its tiny parameter count. Shows particular strength in addition operations with 58.3% accuracy and subtraction with 57.1% accuracy.
The second best performer, scoring 39.0% overall accuracy. Shows exceptional performance in subtraction (76.2%) and solid performance in addition (54.5%).
Shows moderate mathematical abilities with 12.0% overall accuracy. Demonstrates particular strength in division operations (38.9%) and subtraction (22.7%).
Performance Analysis
Detailed Accuracy Results
| Model | Addition (+) | Subtraction (-) | Multiplication (*) | Division (/) | Exponentiation (**) | Overall |
|---|---|---|---|---|---|---|
| MathGPT2 (81.9M) | 58.3% | 57.1% | 45.0% | 24.1% | 0.0% | 42.0% |
| aquif-moe-800m (800M) | 54.5% | 76.2% | 21.9% | 18.2% | 0.0% | 39.0% |
| BrainrotLM-Assistant-362M (362M) | 0.0% | 22.7% | 0.0% | 38.9% | 0.0% | 12.0% |
| gonzalez-v1 | 5.3% | 8.3% | 0.0% | 0.0% | 0.0% | 3.0% |
| VLM-1 (124M) | 3.4% | 0.0% | 0.0% | 4.3% | 0.0% | 2.0% |
| gpt2 | 0.0% | 7.4% | 0.0% | 0.0% | 0.0% | 2.0% |
| Snowflake-G0-Release | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% | 0.0% |
Key Observations
- Size doesn't always matter: MathGPT2 with only 81.9M parameters demonstrates impressive mathematical abilities, achieving 42.0% overall accuracy.
- Operation specialization: MathGPT2 excels at addition (58.3%) and subtraction (57.1%), while aquif-moe-800m shows exceptional strength in subtraction operations (76.2%).
- Architectural importance: The results suggest that architecture design and training approach may be more important than raw parameter count for specialized tasks.
- Zero performance: One of the tested models (Snowflake-G0-Release) showed no measurable mathematical ability on this test set.
- Division specialists: BrainrotLM-Assistant-362M shows specific strength in division operations (38.9%) despite lower performance in other areas.
Research Implications
These results challenge conventional wisdom about language model scaling laws for mathematical reasoning capabilities. They suggest that highly specialized, compact models might offer a more efficient approach for specific reasoning tasks compared to general-purpose large models.
Conclusion
This analysis demonstrates that extremely small language models can exhibit significant mathematical reasoning abilities, with models as small as 81.9M parameters showing the ability to solve basic arithmetic problems. The standout performer, MathGPT2 with only 81.9M parameters, achieved an impressive 42.0% accuracy on a diverse set of 100 mathematical questions.
These findings suggest that efficient architectural design and specialized training approaches may be more important than raw parameter count when optimizing for specific reasoning capabilities. This could have significant implications for resource-constrained applications where deploying massive models is impractical.
Future research directions could include investigating what specific architectural choices enable these compact models to perform mathematical operations, and how these insights might be applied to develop more efficient specialized models for other reasoning tasks.