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 aligns the predicted numeric distribution to the target via kernel matching and smooths the prediction-target residual over the induced kernel graph to encourage local consistency. We evaluate SMMD on four numeric-target tasks: mathematical reasoning, arithmetic calculation, clock-time recognition, and chart question answering, across multiple open-weight LLM and VLM backbones. SMMD consistently improves accuracy over both cross-entropy and recent numeric-target losses; analyses show complementary effects between MMD and smoothness and underscore the importance of distance-based kernel design. Code is available at https://github.com/Zuozhuo/smmd-loss.
Structure-property relationships are foundational to biology, chemistry and materials science, where function, reactivity and physical response emerge from spatial, chemical and periodic organization. Mechanistically explaining these relationships requires interpreting structural…
Synthesis planning aiming to find pathways of reactions for a target molecule is one of the most important and challenging tasks in drug discovery. Recent progress has produced both specialized deep-learning retrosynthesis systems and general-purpose large language models, but ob…
Large language models (LLMs) are increasingly deployed as critical decision-making components in high-stakes real-world AI systems, rendering LLM reliability a foremost practical concern. In this paper, we focus on enhancing LLM reliability through selective prediction (SP), a st…
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Efficient multimodal document question answering with explicit visual grounding, locating the precise document region that supports each answer remains an open challenge. Current approaches bifurcate into Supervised Fine-Tuning (SFT), which requires large annotated datasets and r…