Building The Ph(ysical)AI Layer Of Machine Intelligence

Recent physics foundation models claim general spatiotemporal forecasting ability, yet their evaluations often collapse performance into a single average score under a fixed training distribution. This makes it difficult to determine whether a model has learned generalizable physical dynamics or only performs well under particular settings. We construct a benchmark with 8 physical dynamics, 3 training-data mixtures, and 25 test regimes induced by dynamic-scale and initial-condition complexity shifts, covering in-distribution, distribution-shift, and out-of-distribution settings. We evaluate five physics foundation model architectures and four model variants per architecture (scratch and three pretrained sizes), resulting in 60,000 measurements. Our results show that current physics foundation models behave as conditional rather than universal generalists: their generality depends on the physical regime, temporal scale, initial-condition setting, pretraining, model size, and architecture. Improving the training data distribution only partially mitigates this limitation. Pretraining and scaling are also unable to reliably remove their ability biases. We argue that improving physics foundation models requires moving beyond scaling models or expanding data, toward learning mechanisms that better capture transferable physical knowledge across regimes, temporal scales, and distribution shifts.

Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited data, yet this practice does not always improve downstream performance and can sometimes lead to a loss of performance, known as negative transfer. We propose RADAR, a simple, geometrically grounded metric for estimating cross-domain transferability in foundation models. RADAR analyzes the layer-wise evolution of representations by measuring angular alignments and relative changes in distance along layer-to-layer displacement trajectories, and by comparing empirical distributions of within-domain and cross-domain dynamics. We hypothesize that domain transferability is related to the divergence between these trajectory distributions. We evaluate the metric across multiple modalities, including cross-lingual sentiment classification with text embedding models and cross-domain image classification with foundation vision models. Across several settings, RADAR provides competitive predictive performance relative to existing transferability metrics on several vision and text benchmarks, with particularly strong results when domain transitions are smooth or cleanly separated. Our ablations further suggest that the effectiveness of transferability estimation depends on the geometry of the model's internal representation space, with different modalities favoring different topological formulations.

Foundation models are deep neural networks (such as GPT-5, Gemini3, and Opus4) trained on large datasets that can perform diverse downstream tasks -- text and code generation, question answering, summarization, image classification, and so on. The philosophy of foundation models is to put effort into a single, large (${\sim}10^{12}$-parameter) general-purpose model that can be adapted to many downstream tasks with no or minimal additional training. We argue that the rise of foundation models presents an opportunity for hardware engineers: in contrast to when different models were used for different tasks, it now makes sense to build special-purpose, fixed hardware implementations of neural networks, manufactured and released at the roughly 1-year cadence of major new foundation-model versions. Beyond conventional digital-electronic inference hardware with read-only weight memory, we advocate a more radical re-thinking: hardware in which the neural network is realized directly at the level of the physical design and operates via the hardware's natural physical dynamics -- \textit{Physical Foundation Models} (PFMs). PFMs could enable orders-of-magnitude advantages in energy efficiency, speed, and parameter density. For ${\sim}10^{12}$-parameter models, this would both reduce the high energy burden of AI in datacenters and enable AI in edge devices that today are power-constrained to far smaller models. PFMs could also enable inference hardware for models much larger than current ones: $10^{15}$- or even $10^{18}$-parameter PFMs seem plausible by some measures. We present back-of-the-envelope calculations illustrating PFM scaling using an optical example -- a 3D nanostructured glass medium -- and discuss prospects in nanoelectronics and other physical platforms. We conclude with the major research challenges that must be resolved for trillion-parameter PFMs and beyond to become reality.