Enhancing Numerical Prediction in LLMs via Smooth MMD Alignment

arXiv:2606.27731v1 Announce Type: new 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 numer...