Decoding LLM's: The Interplay of Transformation Matrices and Input Complexity
Keywords: Transformation Matrices, Intrinsic Dimensionality, Causal Inferencing, In-Context Learning (ICL)
TL;DR: Through a mathematical lens, this paper explores how Large Language Models (LLMs) function, emphasizing their pattern-matching nature, the role of input complexity, and the benefits of training on reasoning tasks
Abstract: In the realm of Large Language Models (LLMs) like GPT-3, methodologies such as In-Context Learning (ICL) and the "Chain of Thoughts" (CoT) approach have become prominent. Yet, a significant research gap persists: the underlying mechanics explaining their efficacy remain vague. While existing hypotheses provide some insights, they fall short in offering a comprehensive understanding. To bridge this gap, we introduce a rigorous mathematical analysis, interpreting LLM parameters as transformation matrices that convert the complexities of textual data into high-dimensional vector spaces. Our analysis robustly postulates the correctness of this interpretation, providing a fresh perspective on LLM behaviors. At their heart, LLMs primarily operate as pattern matchers. They recognize patterns from the input text, drawing from their vast training, and produce outputs. Here, the complexity of the input prompts becomes crucial. A complex input can nudge the LLM to generate a more refined response, hinting at the concept of intrinsic dimensionality, which gauges the inherent complexity of input. In light of our insights, we advocate for a strategic shift in fine-tuning LLMs. We propose fine-tuning them on logical reasoning tasks, specifically leveraging reasoning questions (Verbal Reasoning, Probability, Assertion and Reason). This approach, rooted in our mathematical framework, enables LLMs with the technique to decipher the logical layers in the data, promising to harness the true potential of LLMs, guiding them beyond mere pattern matching to deeper textual comprehension. This in turn also improves their causal inferencing ability. In essence, our paper offers a structured blueprint, seamlessly transitioning from identifying research gaps to actionable strategies, aiming to elevate the capabilities and understanding of Large Language Models.
Primary Area: visualization or interpretation of learned representations
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Submission Number: 9368
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