A foundation model of numerical intelligence with cross-disciplinary generalization
Authors: Chenghan Wu, Zongmin Yu, Liu Yang
Organizations: Department of Mathematics, National University of Singapore, Singapore, Singapore.
Abstract
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 to perform contextual ensemble learning (CEL) yields further gains, enabling it to surpass state-of-the-art specialists in a discipline unseen during 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.
AI systems based on artificial neural networks are being developed with aspirations of pushing the boundary of human mathematical knowledge. A key question for these systems is how much they can reach beyond their training data. Mathematical discovery requires a strong form of out of distribution generalization; the ability to hypothesize genuinely new - and potentially logically more powerful - mathematical structures. It has been hypothesized that language abilities support such generalizations in human cognition. In this work, we use simple arithmetic as a case study for examining how modern AI models could expand their mathematical horizons, evaluating whether these models can independently discover the concept of "zero". We show that (1) language models of a GPT-2 size are unable to perform this generalization at test time regardless of language pretraining, but (2) models can improve substantially after training on tens or hundreds of examples of zero. Additionally, we find that language pretraining reduces the number of required examples by approximately 50%, showing that language abilities can scaffold mathematical discovery in neural models.
Two transformative classes of AI systems are reshaping how organizations operate: \textit{digital AI}, which reasons over enterprise knowledge to power chatbots and agent workflows; and \textit{physical AI}, which learns to control robots and autonomous systems from video, gameplay, and sensor telemetry. Both face the same foundational bottleneck: raw knowledge at scale, spanning heterogeneous modalities, locked in private corpora that existing AI infrastructure cannot access reliably or efficiently. We propose \textit{Universal Knowledge Perception (UniK)} as a common platform for both classes, covering the full knowledge lifecycle (ingestion, enrichment, indexing, retrieval, and continuous evaluation) across modalities from rich text and video to molecular data and sensor telemetry. We present UniK, built on Polymath Retrieval (multi-index fusion over automatically enriched indices) with no task-specific fine-tuning. Across five digital AI domains (medical literature, open-domain QA, chemistry, legal video proceedings, and government open data) UniK combined with an open-source 70-billion-parameter model consistently matches or outperforms frontier proprietary LLMs that are orders of magnitude larger: 76% RAG accuracy on government data versus 47% for GPT-5; 77.9% on medical QA without fine-tuning; topping all open-source chemistry pipelines. We show that the same infrastructure directly addresses the data curation, indexing, and retrieval challenges facing physical AI world model training, where the knowledge problem is harder but structurally identical.
In-context learning (ICL) enables fast task adaptation from demonstrations without per-task parameter updates but remains highly sensitive to example selection and formatting. In unified multimodal models spanning understanding and generation, this sensitivity is exacerbated by cross-modal interference and varying cognitive demands. Consequently, in-context learning efficacy is often non-monotonic and highly task-dependent. To diagnose these behaviors, we introduce a six-level Capability-Oriented Taxonomy that categorizes the functional role of demonstrations from basic perception to high-order discernment. Guided by this cognitive framework, we construct UniICL-760K, a large-scale corpus featuring curated 8-shot in-context learning episodes across 15 subtasks, alongside UniICL-Bench for rigorous, controlled evaluation. We show that this data-driven assembly is the primary source of our gains. As a complementary, lightweight stabilizer, we additionally propose the Context-Adaptive Prototype Modulator, a plug-and-play module that further improves few-shot stability. Evaluations on UniICL-Bench show that our approach yields highly competitive unified results, outperforming larger-parameter multimodal large language model baselines on most understanding in-context learning tasks. Data and code are available at https://github.com/xuyicheng-zju/UniICL.