Liu Yang

Chenghan Wu, Zongmin Yu, Liu Yang

Intelligence is commonly understood as the ability to acquire and apply knowledge, adapt to unfamiliar situations and solve new problems. Large language models exhibit this capacity by inferring task-relevant knowledge from textual context and applying it to new tasks. Yet intelligence need not be confined to language. For scientific and social systems, we need models that acquire and apply knowledge from numerical context-an ability we call numerical intelligence. Here we introduce UNified In-Context Operator Networks (UNICON), a foundation model that exhibits numerical intelligence across disciplines. Using graph-based examples from a system as context, UNICON infers the predictive relation shared across them and applies it to queries from the same system. Across scientific and social systems, including those from disciplines absent from training, the same model approaches specialist performance without retraining. Combining UNICON with language-model agents yields further gains, enabling it to surpass state-of-the-art specialists in a discipline unseen in training. We further show that training-corpus diversity improves generalization to unseen disciplines. Together, these results establish UNICON as a foundation model of numerical intelligence and position it as a building block for a broader ecosystem of artificial intelligence.

Yuran Wang, Zekun Wang, Bohan Zeng et al.

Large language model training in open-ended domains lacks verifiable rewards, making task preferences difficult to formalize as effective supervision. Contexts can convey such preferences, yet provide little additional supervision once distilled into the student, motivating contexts that evolve with student performance. However, directly using evolving contexts as in-training supervision results in an unstable distillation target and conflicting distributions, requiring mechanisms to stabilize target and downweight conflicts. In this paper, we analyze the effect of contexts through a decomposition of the reverse KL objective, revealing two findings: the student is distilled toward the geometric mean of context-conditioned teachers, and the objective contains a conflict term that measures conflicts among these teachers. Based on this decomposition, we propose Flux-OPD, an OPD paradigm that uses evolving contexts as in-training supervision to capture task preferences in open-ended domains. Flux-OPD treats the differences between context-conditioned and context-free teachers as contextual difference signals, injects them as contextual corrections into the context-free teacher anchor, and weights their correction strength using the conflict term as an indicator. Experiments on open-ended tasks show that Flux-OPD outperforms existing OPD paradigms, highlighting the potential to combine teacher supervision with evolving contexts.