Emergent properties with repeated examples (2410.07041v1)

Abstract: We study the performance of transformers as a function of the number of repetitions of training examples with algorithmically generated datasets. On three problems of mathematics: the greatest common divisor, modular multiplication, and matrix eigenvalues, we show that for a fixed number of training steps, models trained on smaller sets of repeated examples outperform models trained on larger sets of single-use examples. We also demonstrate that two-set training - repeated use of a small random subset of examples, along normal sampling on the rest of the training set - provides for faster learning and better performance. This highlights that the benefits of repetition can outweigh those of data diversity. These datasets and problems provide a controlled setting to shed light on the still poorly understood interplay between generalization and memorization in deep learning.

• The paper demonstrates that models trained with a small, repeated dataset significantly outperform those using larger, single-use datasets on mathematical tasks.
• It introduces a two-set training methodology that combines repeated examples with broader data to accelerate learning and achieve up to 92% accuracy on modular multiplication.
• The findings reveal how data repetition leads to emergent properties and enhanced model scaling, challenging traditional deep learning strategies.

Emergent Properties with Repeated Examples: An Analysis

This paper presents a thorough examination of how transformers behave when the repetition of training examples varies, using algorithmically generated datasets across three mathematical problems: the greatest common divisor (GCD), modular multiplication, and matrix eigenvalues. The authors propose that a smaller set of examples, when repeated during training, can enhance model performance compared to larger sets of single-use examples. The research explores the counterintuitive notion that repetition might outweigh data diversity in specific settings.

Key Findings

1. Repetition and Performance: The paper demonstrates that models trained on a smaller set of repeated examples outperform those trained on larger, single-use datasets. This is consistently observed across various mathematical tasks. For instance, on the GCD problem, models with a data budget of 25 million examples or repeated 42 times predict 62 outcomes correctly, whereas models with unlimited training data predict only 27.
2. Two-Set Training Methodology: By introducing a technique termed "two-set training," the authors show that models trained on a small repeated subset alongside a broader dataset exhibit faster learning and improved performance. For instance, models employing two-set training on the modular multiplication problem achieve 92% accuracy, compared to those trained traditionally, which struggle to learn the task at all.
3. Emergent Phenomena and Model Scaling: Specific tasks display emergent phenomena—unique capabilities arising solely from repeated, smaller datasets. Moreover, two-set training enhances the scaling abilities of models, enabling smaller transformers to tackle complex problems, like eigenvalues of 10x10 matrices, typically addressed by larger models.
4. Robustness Across Optimizers: The effects of repetition and two-set training were found to be robust across different optimizers, indicating a universal applicability of the findings despite variations in training techniques.

Implications and Future Directions

The research challenges prevailing notions in deep learning regarding data reuse and suggests that revisiting the amount of repetition in training data could significantly impact model development strategies. The notion that more data isn't universally advantageous, and that intentional repetition of subsets can yield better generalization, opens several speculative avenues in both theoretical and practical domains.

1. Theoretical Implications: The insights gained call into question established beliefs that repetition negatively impacts generalization. The interplay between memorization and generalization, highlighted here, warrants deeper exploration to understand underlying mechanisms.
2. Application to LLMs: Considering these findings within the domain of LLMs, which inherently deal with large and often repeated datasets, could optimize pre-training strategies and improve efficiency. Particularly, the two-set training paradigm could be adapted for fine-tuning, possibly enhancing transferability and tuning outcomes.
3. Curriculum Learning Correlations: While distinct from curriculum learning, the results could inspire curriculum learning adaptations where repetition frequency is systematically adjusted rather than solely relying on difficulty progression.

The authors emphasize that these insights, though gleaned from mathematical problems, might inform broader AI advancements, especially in environments where data availability does not naturally lead to significant diversity. Future research could focus on bridging these findings with more complex tasks, thereby advancing our understanding of efficient learning in neural networks.