arXiv:2606.27731v1 Announce Type: cross Abstract: Despite their strong general capabilities, large language models (LLMs) often remain unreliable when outputs must be numerically precise. A key reason is the training objective: standard cross-entropy treats numeric tokens as unstructured categories and ignores the metric structure of their values. We address this mismatch with Smooth Maximum Mean Discrepancy (SMMD), which builds on the classic MMD by incorporating value-distance kernels over numeric tokens and graph-based smoothness. With this kernel defined over a numeric sub-vocabulary, SMMD
The continuous drive to improve LLM accuracy for complex applications highlights existing limitations in numerical reasoning, prompting novel solutions like SMMD.
Improved numerical precision in LLMs is critical for their adoption in fields requiring high accuracy, such as scientific research, engineering, and finance, expanding their utility and trustworthiness.
LLMs can now potentially handle numerically sensitive tasks with greater reliability, reducing the need for human oversight or specialized models for numeric output.
- · AI developers
- · Scientific research
- · Financial modeling
- · Engineering
- · Domain-specific numerical models
- · Manual data verification processes
LLMs become more reliable for tasks requiring numerical accuracy, opening new application areas.
Reduced human intervention in numerical data processing workflows, leading to efficiency gains in various sectors.
Enhanced trust in AI systems for critical decision-making processes dependent on precise quantitative analysis.
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Read at arXiv cs.LG