Evaluating the Generalization Capabilities of Large Language Models on Elementary Mathematical Reasoning

Temel Kavramlar

Many large language models exhibit significant overfitting on established mathematical reasoning benchmarks, suggesting their performance may not reflect true reasoning abilities.

Özet

The authors investigate the reasoning capabilities of large language models (LLMs) by creating a new dataset, Grade School Math 1000 (GSM1k), which is designed to mirror the style and complexity of the established GSM8k benchmark.
Key highlights:

The authors find that several families of models, notably Mistral and Phi, show consistent overfitting across model sizes, with performance drops of up to 13% on GSM1k compared to GSM8k.
However, the authors also find that frontier models, such as Gemini, GPT, and Claude, show minimal signs of overfitting, suggesting they have learned genuine mathematical reasoning abilities.
Further analysis reveals a positive correlation between a model's likelihood of generating examples from GSM8k and its performance gap between GSM8k and GSM1k, suggesting that data contamination is one factor contributing to overfitting.
Despite the overfitting observed, the authors find that even the most overfit models are still capable of solving a significant portion of the novel GSM1k problems, indicating they have learned some generalizable mathematical reasoning.
The authors conclude that while data contamination is a concern, it does not fully explain the overfitting observed, and that the frontier models have made progress in developing genuine mathematical reasoning capabilities.

İstatistikler

The authors find that the worst-performing model on GSM1k compared to GSM8k shows a 13% drop in accuracy.
The authors observe a Spearman's rank correlation of 0.32 between a model's probability of generating GSM8k examples and its performance gap between GSM8k and GSM1k.

Alıntılar

"Several families of models, most notably Mistral and Phi, show consistent evidence of overfitting for nearly all model versions and sizes."
"All frontier models, as well as all sizes of the Llama2 family, show minimal signs of overfitting."
"Even the most overfit models are still capable of successfully generalizing to new mathematical grade school problems, albeit occasionally at lower rates than their benchmark numbers would suggest."

Önemli Bilgiler Şuradan Elde Edildi

A Careful Examination of Large Language Model Performance on Grade School Arithmetic

by Hugh Zhang,J... : arxiv.org 05-02-2024

https://arxiv.org/pdf/2405.00332.pdf

Daha Derin Sorular

How can we further improve the design of benchmarks to better capture genuine mathematical reasoning abilities in large language models?

To enhance the design of benchmarks for assessing mathematical reasoning in large language models (LLMs), several strategies can be implemented:

Diverse Problem Sets: Ensure that benchmark datasets contain a wide range of mathematical problems covering various concepts and difficulty levels. This diversity can help evaluate the model's ability to reason across different mathematical domains.

Contextual Understanding: Incorporate problems that require contextual understanding and application of mathematical concepts in real-world scenarios. This can test the model's ability to apply mathematical reasoning in practical situations.

Multi-Step Problems: Include multi-step problems that necessitate sequential reasoning and problem-solving skills. This can assess the model's capacity to break down complex problems into manageable steps.

Explainability: Design benchmarks that require the model to not only provide the answer but also explain the reasoning behind it. This can evaluate the model's ability to articulate its thought process and reasoning steps.

Adversarial Examples: Introduce adversarial examples that challenge the model's reasoning by including misleading or deceptive information. This can test the model's robustness and ability to discern relevant information.

Human-Annotated Data: Utilize human annotators to curate benchmark datasets, ensuring that the problems are authentic, diverse, and free from biases. Human oversight can help maintain the quality and integrity of the benchmark data.

By incorporating these elements into benchmark design, we can create more comprehensive and challenging assessments that accurately reflect the genuine mathematical reasoning abilities of large language models.

What other factors, beyond data contamination, might contribute to the observed overfitting on established benchmarks?

In addition to data contamination, several other factors may contribute to overfitting on established benchmarks for large language models:

Model Architecture: The design and complexity of the model architecture can influence its propensity to overfit. Models with excessive capacity or complexity may memorize training data instead of learning generalizable patterns.

Training Data Quality: The quality and representativeness of the training data play a crucial role in model performance. Biased or incomplete training data can lead to suboptimal generalization and increased overfitting.

Hyperparameter Tuning: Improper hyperparameter settings, such as learning rate, batch size, or regularization techniques, can impact the model's ability to generalize. Suboptimal hyperparameters may result in overfitting on specific benchmarks.

Fine-Tuning Strategies: The approach used for fine-tuning the model on benchmark datasets can also contribute to overfitting. Inadequate regularization during fine-tuning or excessive tuning on benchmark-specific data can lead to overfitting.

Evaluation Metrics: The choice of evaluation metrics and criteria can influence model performance. Metrics that do not fully capture the model's reasoning abilities or that incentivize memorization over genuine understanding can contribute to overfitting.

Model Selection Bias: The selection of models for evaluation and comparison can introduce bias. Models that are optimized specifically for benchmark performance may exhibit overfitting tendencies on those benchmarks.

Considering these factors alongside data contamination can provide a more comprehensive understanding of the challenges associated with overfitting in large language models on established benchmarks.

How can we leverage the insights from this study to develop large language models with more robust and generalizable mathematical reasoning capabilities?

To leverage the insights from the study for enhancing the mathematical reasoning capabilities of large language models, the following strategies can be implemented:

Regularization Techniques: Implement effective regularization methods during training to prevent overfitting. Techniques like dropout, weight decay, and early stopping can help improve model generalization.

Diverse Training Data: Expand the training data to include a diverse set of mathematical problems beyond benchmark datasets. Incorporating a wide range of problems can enhance the model's ability to reason across various scenarios.

Transfer Learning: Utilize transfer learning approaches to pre-train models on a broad range of mathematical tasks before fine-tuning on specific benchmarks. This can help the model develop more robust reasoning capabilities.

Adversarial Training: Introduce adversarial training during model training to expose the model to challenging and deceptive examples. This can improve the model's resilience to misleading information and enhance its reasoning skills.

Interpretability: Focus on developing models with explainable reasoning processes. Encouraging models to provide transparent explanations for their answers can enhance their overall reasoning capabilities and foster trust in their outputs.

Continuous Evaluation: Regularly evaluate models on diverse and challenging datasets to assess their generalization abilities. Ongoing evaluation can help identify and address overfitting issues promptly.

By incorporating these strategies and leveraging the study's insights, we can work towards developing large language models with more robust, generalizable, and reliable mathematical reasoning capabilities.