Understanding LLM Embeddings for Regression (2411.14708v3)

Abstract: With the rise of LLMs for flexibly processing information as strings, a natural application is regression, specifically by preprocessing string representations into LLM embeddings as downstream features for metric prediction. In this paper, we provide one of the first comprehensive investigations into embedding-based regression and demonstrate that LLM embeddings as features can be better for high-dimensional regression tasks than using traditional feature engineering. This regression performance can be explained in part due to LLM embeddings over numeric data inherently preserving Lipschitz continuity over the feature space. Furthermore, we quantify the contribution of different model effects, most notably model size and language understanding, which we find surprisingly do not always improve regression performance.

• The paper demonstrates that LLM embeddings robustly maintain regression performance in high-dimensional scenarios compared to traditional feature engineering methods.
• The study finds that LLM embeddings preserve Lipschitz continuity in numeric data, enhancing regression efficacy when coupled with downstream MLPs.
• Results reveal that factors like model size and pre-training nuances do not directly improve regression outcomes, underscoring the unique utility of LLM embeddings.

Understanding LLM Embeddings for Regression

The paper "Understanding LLM Embeddings for Regression" by Tang, Yang, and Song, examines a relatively unexplored application of LLMs, specifically leveraging their embedding capabilities for high-dimensional regression tasks. This investigation offers a thorough analysis of utilizing LLM-derived embeddings as alternative feature representations for regression, contrasting them against conventional feature engineering methods.

Key Findings

The paper highlights several notable findings regarding the characteristics and efficacy of LLM embeddings in regression tasks:

1. Dimensional Robustness: LLM embeddings exhibit a robust capacity for maintaining regression performance as input dimensionality increases. In particular, the paper demonstrates that high-dimensional data, which traditionally challenges regression models, can be effectively managed by utilizing LLM embeddings.
2. Preservation of Lipschitz Continuity: The authors find that, over numeric data, LLM embeddings preserve Lipschitz continuity within the feature space. This smoothness property aligns naturally with regression tasks, particularly when coupled with downstream multi-layer perceptrons (MLPs).
3. Nuanced Role of Model Effects: Intriguingly, factors typically associated with improved language understanding—such as model size, detailed pre-training, and input formatting—do not straightforwardly translate to enhanced regression performance. This suggests that the utility of LLMs for regression is not solely reliant on their linguistic prowess.

Methodology and Experiments

To substantiate their claims, the authors embarked on a comprehensive experimental regime. The paper evaluates regression tasks on both synthetic functions from the BBOB suite and real-world scenarios typical in industry, like AutoML and compiler optimization tasks. Notably, LLM-based methods outperform traditional approaches such as XGBoost in tasks characterized by a high degree of freedom.

The investigation into embedding smoothness through Lipschitz factor distributions further elucidates how LLM embeddings facilitate regression, drawing a correlation between embedding smoothness and regression efficacy. Additionally, the paper explores the effect of model specifics like initialization and token embedding strategies, concluding that pre-trained model forward passes are generally beneficial, albeit with nuances.

Implications and Future Directions

Practically, this research suggests that LLM embeddings can be a valuable alternative feature set for regression tasks, particularly in high-dimensional contexts where traditional methods falter. The findings open the door for LLM usage beyond language tasks, potentially influencing domains that rely on complex feature interactions.

Theoretically, this paper encourages further exploration into the characteristics of embeddings derived from LLMs and their applicability to a wider array of domains. Future work might consider extending these techniques to other data representations and modalities, such as graph structures or multimodal inputs, which could yield important insights into both the embeddings’ versatile applications and their limitations.

In summation, this paper provides a detailed and critical examination of LLM embeddings in regression tasks. It delineates the conditions and domains where LLMs offer a tangible advantage, laying a foundation for further empirical and theoretical investigations into embedding-based methodologies in machine learning.