When can isotropy help adapt LLMs' next word prediction to numerical domains?
Keywords: Contextual embedding space, clusters, isotropy, language model representation, numeric downstream task
Abstract: Recent studies have shown that vector representations of embeddings learned by pre-trained large language models (LLMs) are effective in various downstream tasks in numerical domains. Despite their significant benefits, the tendency of LLMs to hallucinate in such domains can have severe consequences in applications like finance, energy, retail, climate science, wireless networks, synthetic tabular generation, among others. To guarantee prediction reliability and accuracy in numerical domains, it is necessary to have performance guarantees through explainability. However, there is little theoretical understanding of when pre-trained language models help solve numeric downstream tasks. This paper seeks to bridge this gap by understanding when the next-word prediction capability of LLMs can be adapted to numerical domains through the lens of isotropy. Specifically, we first provide a general numeric data generation process that captures the core characteristics of numeric data across various numerical domains. Then, we consider a log-linear model for LLMs in which numeric data can be predicted from its context through a network with softmax as its last layer. We demonstrate that, in order to achieve state-of-the-art performance in numerical domains, the hidden representations of the LLM embeddings must possess a structure that accounts for the shift-invariance of the softmax function. We show how the isotropic property of LLM embeddings preserves the underlying structure of representations, thereby resolving the shift-invariance problem problem of softmax function. In other words, isotropy allows numeric downstream tasks to effectively leverage pre-trained representations, thus providing performance guarantees in the numerical domain. Experiments show that different characteristics of numeric data could have different impacts on isotropy.
Primary Area: learning on time series and dynamical systems
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Submission Number: 12874
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