arXiv:2605.20369v1 Announce Type: cross Abstract: Number prediction stands as a fundamental capability of large language models (LLMs) in mathematical problem-solving and code generation. The widely adopted maximum likelihood estimation (MLE) for LLM training is not tailored to number prediction. Recently, penalty-driven approaches, e.g., Number Token Loss and Discretized Distance Loss, introduce an inductive bias of numerical distance but induce over-sharpened and over-flattened digit distributions, respectively. In this paper, we make an in-depth analysis on LLM numerical learning, and show
The continuous development and scaling of LLMs necessitate improved numerical reasoning, a known limitation, making research into specialized loss functions for this domain timely and critical.
Improved numerical learning in LLMs will directly enhance their capabilities in critical applications like mathematical problem-solving, scientific computation, and code generation, areas vital for AI advancement.
This research introduces a novel loss function, 'Digit Entropy Loss' (DEL), promising more accurate and robust numerical prediction for LLMs compared to existing methods, potentially resolving previous issues of over-sharpened or over-flattened digit distributions.
- · AI researchers and developers
- · Companies building advanced LLMs
- · Industries relying on AI for complex calculations and code
- · Users of AI for mathematical problem-solving
- · LLM architectures or training methodologies that do not integrate advanced numer
LLMs will demonstrate significantly improved accuracy and reliability in tasks requiring numerical understanding and generation.
The enhanced numerical capabilities could unlock new applications for LLMs in scientific discovery, financial modeling, and engineering design that were previously inaccessible.
More reliable numerical AI could accelerate automation in highly technical fields, potentially impacting specialized white-collar labor markets that involve quantitative problem-solving.
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Read at arXiv cs.LG