Length-Induced Embedding Collapse in PLM-based Models (2410.24200v2)

Abstract: Text embeddings from PLM-based models enable a wide range of applications, yet their performance often degrades on longer texts. In this paper, we introduce a phenomenon we call Length Collapse, where embeddings of longer texts tend to cluster together. This clustering results in a distributional inconsistency between the embeddings of short and long texts. We further investigate how these differences contribute to the performance decline observed with longer texts across various downstream tasks. Through a rigorous theoretical analysis of the self-attention mechanism, which acts as a low-pass filter in PLM-based models, we demonstrate that as text length increases, the strength of low-pass filtering intensifies, causing embeddings to retain more low-frequency components. As a result, input token features become more similar, leading to clustering and ultimately the collapse of embeddings for longer texts. To address this issue, we propose a simple method, TempScale, which mitigates the Length Collapse phenomenon. By narrowing the gap in low-pass filtering rates between long and short texts, TempScale ensures more consistent embeddings across different text lengths. This approach leads to performance improvements of 0.94% on MTEB and 1.10% on LongEmbed, which focuses specifically on long-context retrieval, providing strong evidence for the validity of our analysis. The source code is available at https://github.com/Yuqi-Zhou/Length_Collapse.

• The paper identifies "Length Collapse" in transformer models, showing text embeddings degrade with increasing input length due to the self-attention mechanism acting as a length-dependent low-pass filter.
• To mitigate this, the authors introduce TempScale, a tuning-free method that significantly improves performance on long text embeddings, with gains up to 0.82% on datasets like LongEmbed.
• This work has practical implications for improving NLP model robustness across varying text lengths and provides theoretical insights into transformer architecture and input interactions.

Overview of "Length-Induced Embedding Collapse in Transformer-based Models"

The research paper titled "Length-Induced Embedding Collapse in Transformer-based Models" presents a meticulous study of the degradation in performance of text embeddings as the input text length increases in transformer-based models. Text embeddings, which are dense vector representations of text that retain semantic meaning, are critical for numerous NLP applications. However, their efficacy lessens with longer text inputs, a phenomenon the authors identify as "Length Collapse."

The authors hypothesize that Length Collapse stems from the clustering of long text embeddings in a narrow space, causing distributional inconsistencies that impair downstream tasks. They attribute this to the self-attention mechanism in transformers, which functions akin to a low-pass filter. Theoretically, they demonstrate that longer sequences exacerbate the attenuation rate of the low-pass filter effect intrinsic to self-attention. Consequently, deeper layers excessively filter out token signals, confining them primarily to their Direct-Current (DC) component. This notably impacts longer texts, pushing their embeddings into a restricted space.

To combat this issue, the authors introduce TempScale, a method that involves incorporating a temperature factor in the $softmax(\cdot)$ calculation, which can alleviate the constraints of length collapse by adjusting the filter's attenuation rate. TempScale is presented as a tuning-free method that can be generalized across various transformer-based embedding models.

Numerical Results and Claims

The paper showcases TempScale's empirical efficacy on extensive datasets such as the Massive Text Embedding Benchmark (MTEB) and LongEmbed. Significant performance improvements were observed: a maximum of 0.53% on MTEB's 40 datasets and up to 0.82% on LongEmbed's long-context retrieval datasets. These findings substantiate the method’s potential to enhance embedding models, especially for longer text inputs.

Theoretical Analysis

The study provides a rigorous examination of the self-attention mechanism via Fourier analysis, exposing its role as a low-pass filter whose filtering strength scales with sequence length. This realization underscores the necessity of managing this attenuation to maintain high-frequency components vital for diverse and expressive text embeddings.

Implications and Future Directions

The insights from this paper have practical and theoretical implications. Practically, they provide a pathway to improve NLP models' robustness to input length variations, potentially advancing applications like text analysis, search, and generation. Theoretically, it offers a deeper understanding of how model architecture interacts with input characteristics, prompting further exploration of optimal model configurations or novel architectures that mitigate such collapse phenomena.

Future work might involve expanding this analysis to LLMs, which often employ unidirectional attention mechanisms, to see if similar collapse effects occur. There's also a prospect for developing adaptive temperature tuning methods that dynamically adjust based on input characteristics without manual intervention. Additionally, further analysis on other transformer components like LayerNorm or FFN in relation to embedding collapse would enrich the understanding initiated by this work.

Overall, the study advances the discourse on maintaining embedding model performance across varying input lengths, crucial for real-world NLP tasks.