Scaling Laws for Fact Memorization of Large Language Models (2406.15720v1)

Abstract: Fact knowledge memorization is crucial for LLMs (LLM) to generate factual and reliable responses. However, the behaviors of LLM fact memorization remain under-explored. In this paper, we analyze the scaling laws for LLM's fact knowledge and LLMs' behaviors of memorizing different types of facts. We find that LLMs' fact knowledge capacity has a linear and negative exponential law relationship with model size and training epochs, respectively. Estimated by the built scaling law, memorizing the whole Wikidata's facts requires training an LLM with 1000B non-embed parameters for 100 epochs, suggesting that using LLMs to memorize all public facts is almost implausible for a general pre-training setting. Meanwhile, we find that LLMs can generalize on unseen fact knowledge and its scaling law is similar to general pre-training. Additionally, we analyze the compatibility and preference of LLMs' fact memorization. For compatibility, we find LLMs struggle with memorizing redundant facts in a unified way. Only when correlated facts have the same direction and structure, the LLM can compatibly memorize them. This shows the inefficiency of LLM memorization for redundant facts. For preference, the LLM pays more attention to memorizing more frequent and difficult facts, and the subsequent facts can overwrite prior facts' memorization, which significantly hinders low-frequency facts memorization. Our findings reveal the capacity and characteristics of LLMs' fact knowledge learning, which provide directions for LLMs' fact knowledge augmentation.

Overview of "Scaling Laws for Fact Memorization of LLMs"

The paper investigates the fundamental characteristics and scaling laws associated with fact memorization within LLMs. This research highlights an under-explored aspect of LLMs, particularly addressing their proficiency in memorizing and generating fact-based content. The paper's focus is on understanding how LLMs capture and recall factual knowledge, which is crucial for producing accurate and consistent outputs. The authors examine the relationships between fact memorization capacity, model size, and training epochs, shedding light on the scalability of LLMs concerning factual knowledge retention.

Key Findings

1. Scaling Laws for Fact Memorization:
   • The paper identifies that LLMs' ability to memorize factual information scales linearly with the model size. This suggests that larger models inherently possess a higher capacity to store factual knowledge.
   • Moreover, there exists a negative exponential relationship between the fact memorization capacity and the number of training epochs. This indicates that increasing training epochs initially boosts the LLM's fact capacity until reaching a saturation point, beyond which further training yields diminishing returns.
2. Capacity Estimation and Implications:
   • Using the derived scaling laws, the authors estimate that an LLM with 1000 billion (1000B) non-embed parameters, trained over 100 epochs, would be required to memorize the entirety of Wikidata's facts—an undertaking that appears cost-prohibitive in typical pre-training scenarios. This underscores the conceptual impracticality of relying solely on LLM parameters for exhaustive fact storage.
3. Generalization of Unseen Facts:
   • The research reveals that LLMs possess a notable degree of capability in generalizing unseen fact knowledge, which aligns with general pre-training scaling laws. This property suggests an underlying potential in LLMs to infer and construct factual knowledge dynamically, rather than merely memorizing static data sets.
4. Memorization Compatibility and Inefficiency:
   • The paper observes inefficiencies in memorizing redundant facts, particularly when facts are presented in different structural forms or directions. LLMs struggle to memorize such redundant information efficiently unless the facts share identical directions and structures, indicating room for enhancing memory strategies.
   • It is also noted that LLMs tend to prioritize frequently encountered and more complex facts over less frequent ones. Memorization preference and sequence also play a critical role, with subsequent facts capable of overwriting previously stored ones.

Practical and Theoretical Implications

The implications of these findings are twofold. Practically, the research suggests that enhancing LLMs with external sources of factual information, such as Retrieval-Augmented Generation methods, could lead to more efficient and scalable fact memorization strategies. Theoretically, the insights into LLM memory dynamics offer guidance for designing future LLM architectures and training protocols that better address the balance between memorization and generalization.

The results invite further investigation into non-parametric means of storing and retrieving knowledge, the development of advanced algorithms to optimize the integration of redundant facts, and adaptive training approaches that consider memorization order and fact frequency. Moreover, exploring the interaction between the memorization of factual and abstract capabilities of LLMs could yield significant improvements in their utility across various application domains.

Conclusion

The paper provides a detailed examination of the scalability of fact memorization in LLMs, emphasizing the challenges and potential strategies for improving factual accuracy. While current models may not feasibly memorize exhaustive facts due to cost and inefficiency, leveraging their generalization abilities and complementing them with external knowledge resources seems to be a promising pathway. This research sets the stage for further advancements in creating more factual and reliable LLMs.