A foundation model of numerical intelligence with cross-disciplinary generalization

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.

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.

Foundation models have progressed from learning and reasoning over existing knowledge, to increasingly learning through action, tool use, and outcome feedback. We argue that the next frontier is a further transition: from solving and acting within problems specified by humans to participating in the process by which new problems, representations, explanations, and knowledge are created. We refer to this capability as Discovery Intelligence. We formulate Discovery Foundation Models (DFMs) as general-purpose model systems for open-ended discovery. A DFM operates over a revisable research state and supports seven coupled capabilities spanning problem discovery, formulation, representation construction, hypothesis formation, intervention, evidence-grounded revision, and continual discovery improvement. We instantiate this framework with Zetema, which couples explicit research-state dynamics, verification and experimental gating, external grounding, and cross-task Discovery Skill evolution. We further ground the framework with GALILEO, a real therapeutic-discovery system in which Dry-Lab reasoning, robotic and hands-on Wet-Lab experimentation, external biological evidence, and iterative hypothesis and design revision form a closed physical discovery loop. We then formulate a unified approach to capability formation and process-centered evaluation, enabling discovery behavior to be trained, improved, and measured beyond final-answer performance. Together, these components establish discovery as a learnable, executable, and evaluable capability of foundation-model systems. We view this shift as a broader progression in intelligence scaling: from learning over existing knowledge, to learning from action outcomes, and ultimately to participating in the construction, testing, and revision of the structures through which new knowledge is discovered. Code: https://github.com/Gen-Verse/DFM-Plans