The Impact of Data Ordering on the Efficiency of Large Language Model Training for Proof Generation

Core Concepts

The order in which data is presented significantly impacts the training efficiency of large language models (LLMs) for proof generation tasks, with an "intuitively sequential order" proving optimal.

Abstract

Research Paper Summary

Bibliographic Information: An, C., Imani, S., Yao, F., Dong, C., Abbasi, A., Shrivastava, H., ... & Diesendruck, M. (2024). Next-Token Prediction Task Assumes Optimal Data Ordering for LLM Training in Proof Generation. arXiv preprint arXiv:2411.00863.

Research Objective: This paper investigates the impact of data ordering on the efficiency of large language model (LLM) training for proof generation tasks. The authors hypothesize that the conventional "logically sequential" order commonly found in published proofs is suboptimal for LLM training and propose an alternative "intuitively sequential" order.

Methodology: The researchers test their hypothesis by training LLMs on two distinct proof generation tasks: 4-by-4 digit multiplication and intuitionistic propositional logic theorem-proving. For each task, they create datasets with varying data orderings, including the proposed "intuitively sequential" order, and compare the training efficiency and performance of LLMs trained on these datasets.

Key Findings: The study demonstrates that data ordering significantly impacts LLM training efficiency. LLMs trained on data in the "intuitively sequential" order, where intermediate steps directly precede the steps they inform, consistently outperform models trained on data in other orders, including the conventional "logically sequential" order.

Main Conclusions: The authors conclude that the "intuitively sequential" order is optimal for training LLMs on proof generation tasks. They attribute this to the fact that this order facilitates the model's ability to leverage "intermediate supervision," where previous steps provide context and guidance for predicting subsequent steps.

Significance: This research provides valuable insights into the importance of data ordering for LLM training, particularly for tasks involving logical reasoning and proof generation. The findings have implications for improving the efficiency and effectiveness of LLM training in these domains.

Limitations and Future Research: The study is limited by its focus on two specific proof generation tasks and the computational constraints that prevented testing on larger LLMs. Future research could explore the generalizability of these findings to other reasoning tasks and larger language models. Additionally, developing automated methods for identifying and generating data in the optimal "intuitively sequential" order is a promising avenue for further investigation.

Stats

Models trained on the "intuitively sequential" order showed an 11% improvement in proof success rate compared to those trained on the worst order in the propositional logic theorem-proving task.
For the multiplication task, models trained on the "sequentially reversed" order consistently achieved a 0% success rate across all metrics.
In the early training stages, models trained on the "sequentially reversed" order for the multiplication task exhibited significantly slower convergence in predicting the first step of the proof, indicating the negative impact of learning spurious dependencies.

Quotes

Key Insights Distilled From

Next-Token Prediction Task Assumes Optimal Data Ordering for LLM Training in Proof Generation

by Chenyang An,... at arxiv.org 11-05-2024

https://arxiv.org/pdf/2411.00863.pdf

Deeper Inquiries

How might the concept of "intuitively sequential" data ordering be applied to other domains beyond proof generation, such as natural language understanding or code generation?

The concept of "intuitively sequential" data ordering, where intermediate supervision precedes the target output, can be extended to various domains beyond proof generation. Here's how:
Natural Language Understanding:

Machine Translation: Instead of presenting the source and target sentences directly, the training data could include intermediate steps like word alignments or phrase structure parsing. This would provide the model with a clearer understanding of the mapping between the two languages.
Question Answering: Training data could be structured to first present supporting facts or evidence from the text, followed by the question and answer. This would guide the model to learn how to extract relevant information and reason over it.
Sentiment Analysis: Instead of just providing the text and its sentiment label, the data could include intermediate annotations like identification of subjective phrases or sentiment shifters. This would help the model learn the nuances of language that contribute to sentiment.
Code Generation:

Code Summarization/Documentation: Training data could present code snippets followed by explanations of individual functions or modules, culminating in the overall code summary. This would allow the model to learn how to break down complex code into understandable units.
Code Completion: Instead of simply predicting the next token, the training data could include intermediate steps like API documentation or type information relevant to the current context. This would provide the model with more context for accurate and efficient code completion.
Key Considerations:

Domain Knowledge: Identifying the appropriate "intermediate supervision" for each domain requires careful consideration of the underlying task and relevant domain knowledge.
Data Availability: Obtaining data with the desired intuitively sequential structure might be challenging, requiring manual annotation or development of specific data generation techniques.
Overall, applying "intuitively sequential" data ordering in these domains could potentially improve LLMs' learning efficiency and generalization ability by providing them with a more structured and interpretable learning process.

Could there be alternative explanations for the observed order effect, such as limitations in the attention mechanisms of current LLMs, and how might these be addressed?

While the paper focuses on the inability of LLMs to effectively utilize "future" information during training due to the nature of next-token prediction, limitations in attention mechanisms could indeed contribute to the observed order effect. Here are some possibilities:

Limited Attention Span: Current LLMs, even with long context windows, might struggle to maintain attention to distant tokens that are crucial for understanding earlier parts of the sequence. This is especially relevant for tasks like proof generation, where dependencies can span multiple steps.

Addressing the Limitation: Exploring architectures with more sophisticated attention mechanisms, such as hierarchical attention or mechanisms that explicitly model long-range dependencies, could help alleviate this issue.

Positional Encoding Limitations: The way positional information is encoded in current LLMs might not be optimal for capturing the importance of intermediate supervision when it appears later in the sequence.

Addressing the Limitation: Experimenting with alternative positional encoding schemes, such as relative positional encodings or learned positional embeddings that are sensitive to the underlying task structure, could be beneficial.

Inductive Biases in Attention: The attention mechanism itself might have inherent inductive biases that favor attending to information appearing earlier in the sequence. This could be due to the training process or the specific architecture used.

Addressing the Limitation: Analyzing and understanding these biases, and potentially developing attention mechanisms that are more flexible and less reliant on positional information, could lead to more robust learning from data in various orders.
Further research is needed to disentangle the contributions of data ordering and attention mechanisms to the observed order effect. Combining insights from both areas could lead to more effective training strategies and architectural improvements for LLMs.

If LLMs could be trained to effectively utilize data in any order, what implications might this have for our understanding of human learning and cognition, which often relies on structured, sequential information processing?

If LLMs could effectively learn from data in any order, it would challenge the current understanding of human learning and cognition, which heavily relies on structured, sequential information processing. This development could have several implications:

Rethinking Sequential Processing: Humans rely on a step-by-step approach to learning, building upon previously acquired knowledge. If LLMs can bypass this constraint, it might suggest alternative learning mechanisms that are less dependent on sequential order. This could lead to new theories about how the brain processes and integrates information.

New Insights into Cognitive Biases: Humans exhibit biases towards information presented earlier in a sequence (primacy effect). If LLMs can overcome this bias, it might provide insights into the neural mechanisms underlying such biases and potentially offer strategies for mitigating them.

Bridging the Gap Between Human and Machine Learning: The ability to learn from unstructured data could narrow the gap between human and machine learning. Humans excel at learning from diverse, unorganized experiences. If LLMs can replicate this ability, it could lead to more human-like AI systems.

Implications for Education and Knowledge Transfer: Current educational methods are designed around sequential learning. If LLMs demonstrate the effectiveness of alternative learning paradigms, it could revolutionize how we design curricula and impart knowledge.
However, it's crucial to remember that LLMs are fundamentally different from human brains. Even if LLMs achieve order-agnostic learning, it doesn't necessarily invalidate our understanding of human cognition. Instead, it might point towards a broader spectrum of learning mechanisms, some of which humans might not utilize or even be capable of.
Ultimately, the ability of LLMs to learn effectively from data in any order would raise profound questions about the nature of learning and intelligence, potentially leading to a paradigm shift in our understanding of both human and artificial cognition.