Science & Mathematics

In recent years, physical artificial intelligence (physical AI) has experienced rapid development, capturing significant attention in academia and industry. However, the field has yet to reach consensus on its definition, technical landscape, and core challenges. To address this gap, this monograph seeks to define physical AI, present its technical landscape, and examine each key technical subfield in depth. In doing so, it establishes a unified framework for Physical AI: artificial systems that perceive, model, and act upon the physical world through continuous feedback under real-world constraints. Further, this monograph distinguishes physical AI from conventional digital AI, embodied AI, cyber-physical systems, and digital twins. It develops the foundations of physical AI across physics, control, cognition, learning, and reasoning. It reviews key methodologies, including multimodal perception, physical data and simulation, world models, embodied foundation models, motor-control systems, multi-agent coordination, and hardware-software co-design. Furthermore, it examines applications spanning robotics, manufacturing, infrastructure, scientific experimentation, and autonomous services. Particular attention is given to sim-to-real transfer, reliability, real-time execution, evaluation, safety, governance, and long-term deployment. By connecting perception, prediction, decision-making, action, and adaptation in a closed loop, this monograph identifies the technical challenges and research directions required to advance from narrow automation toward more generalizable physical AI and, ultimately, physical artificial general intelligence (Physical AGI).

Existing world models can generate action-conditioned video from a single image. Many focus on camera movement, allowing users to explore the generated scene. However, navigation alone does not ensure that an action follows persistent rules when its outcome depends on state that is invisible in the current frame. We present Stateful Harness, a framework that separates world evolution from video rendering to support stateful and rule-governed interaction. It maintains an evolving world state under specified rules, renders each resulting event with a frozen video model, and uses the generated clip to update the world state for the next turn. At each turn, the harness resolves the action selected by the user and compiles the resulting event into an instruction, while a preview clip from an editable 3D scene provides spatial and camera guidance. To evaluate rule compliance, we build WorldState-Bench, a benchmark of 50 counterfactual twin pairs that share an initial frame and action but differ in hidden state and required outcome. Under rule-only prompting, the best of the 11 evaluated video backends produces the required endings for both cases in 32% of pairs. For MiniMax-H3, specifying the required endings raises this rate from 32% to 64%, while the full harness reaches 92% with the same frozen model. These results support separating rule execution from video rendering for world interactions with hidden state.

The grid integration of large data centers poses a growing power-system stability challenge. Rapidly varying computing demand can induce oscillations, while the facilities must provide a prescribed response to grid disturbances. Existing controls address load fluctuations and grid support but do not establish their jointly achievable performance. This paper derives fundamental limits and develops a source-selective controller for simultaneous oscillation isolation and grid support. A coupled closed-loop model gives a condition for distinguishing disturbance sources and reveals a direct isolation-support conflict under grid-import-power feedback alone; additional electrical measurements can remove this pointwise conflict but leave a conditional cross-frequency sensitivity limit. Guided by these limits, we design a local residual-feedback storage controller through convex frequency-domain optimization with stability, isolation, and grid-response constraints across operating points. Tests on a single-generator interconnection and a modified nine-bus network show stronger oscillation isolation than equal-order optimized comparators while meeting the prescribed grid response across operating points.

World Action Models (WAMs) jointly predict future video and generate actions, yet remain sensitive to task-irrelevant visual perturbations, i.e., changes in visual appearance that should not affect robot behavior. We identify a gap in conventional WAM training: video prediction encourages representations to preserve appearance information, while action generation does not explicitly enforce invariance to task-irrelevant appearance. Data augmentation exposes WAMs to such perturbations but does not require perturbed and nominal observations to produce consistent action representations, and alignment with external pretrained features does not guarantee the desired invariance. To address this gap, we propose PICA-WAM, a self-supervised training framework that casts perturbation invariance as an auxiliary cross-appearance self-alignment task for WAMs. An exponential-moving-average (EMA) teacher processes the nominal observation to provide a deeper-layer target, while the online WAM processes a perturbed observation and aligns its shallower-layer action representation to this target through a lightweight projection head. Across four strong WAMs evaluated on RoboTwin 2.0, LIBERO-Plus, EBench, and a real robot, PICA-WAM consistently improves robustness under visual perturbations, preserves nominal performance in simulation, and raises the real robot success rate. PICA-WAM further reduces the sensitivity of video features to task-irrelevant appearance and its propagation into actions, as shown by paired layer-wise diagnostics. Code: https://github.com/YudeZou/PICA-WAM-release

Robust scene understanding under varying environmental conditions is essential for safe autonomous driving. While cameras and LiDAR degrade in adverse weather and poor lighting, Frequency-Modulated Continuous-Wave (FMCW) spinning radar provides dependable 360° perception at extended ranges with minimal compute cost. However, real-time FMCW radar scene understanding is challenging due to complex signal returns, limited temporal resolution, and scarce annotated datasets. We introduce StreamRPS, a novel framework for streaming FMCW radar panoptic segmentation, comprising an automated label-generation pipeline via LiDAR scene completion and a real-time streaming network for semantic and panoptic segmentation. Our encoder-decoder streaming architecture comprises a radar-specific hierarchical Transformer encoder and task-specific decoders for semantic or panoptic prediction. Our encoder introduces a stem to capture range-dependent signatures, anisotropic patch embeddings to preserve angular resolution, and axial polar attention to separately model the periodic azimuth and bounded range axes. We further introduce azimuth roll rotation augmentation to simulate ego-vehicle rotation during training. Comprehensive experiments on the SAX and BOREAS datasets validate both our auto-labeling methodology and streaming segmentation network against established baselines. We outperform the strongest baseline by at least 1.4pp while processing sectors at over 400 FPS in a 4-sector streaming setting. We additionally provide manual annotations for 100 SAX radar scans, enabling independent evaluation of the entire framework.

Next Best Action (NBA) systems must select among customer interventions (e.g., discounts, promotions, and lifecycle actions), maximize long-term economic value, satisfy complex operational constraints, and remain causally grounded. Existing approaches lack a rigorous framework for meeting these requirements jointly. We address this gap by formulating NBA as a Constrained Markov Decision Process (CMDP). We then integrate off-policy causal correction of the estimated customer dynamics directly into the Linear Programming (LP) formulation of the CMDP. The resulting policy selects actions based on customer states to maximize long-term value while explicitly enforcing business guardrails. Furthermore, the LP formulation yields shadow prices that quantify the economic trade-offs of operational constraints (e.g., fairness and user welfare), enhancing policy interpretability. We validate our proposed offline Reinforcement Learning (RL) framework on an industry case study involving rideshare coupon targeting, where customer states are defined by Recency, Frequency, and Monetary (RFM) stages. We evaluate performance using model-based off-policy evaluation, with causal dynamics estimated from a temporal holdout. Under the observed coupon budget and RFM state representation, our optimized policy improves customer lifetime value (LTV) by 19% over the estimated behavior policy and 8% over a myopic baseline. Although the demonstrated action space is binary, the proposed framework is action-agnostic, yielding a general-purpose decision module for targeting systems that manage multiple interventions.

As AI systems begin to resolve open research problems, reliable verification becomes increasingly important. Formal mathematics provides a trusted framework for mathematical reasoning, enabling agents to produce machine-checkable proofs while conducting mathematical exploration. Existing formal mathematics benchmarks often focus on known results or a small set of prominent open problems, which can become difficult to evaluate reliably once solutions are discovered and widely disseminated. Existing evaluation protocols are also not always aligned with how modern coding agents operate. We therefore introduce ReuF2F, a Lean 4 benchmark of 244 formalized open problems drawn from Research Experiences for Undergraduates (REU), spanning entry-level open research problems across a broad range of mathematical subfields. We expect these less prominent open problems, which tend to attract less attention and may remain unsolved for longer, to be better suited for held-out evaluation of end-to-end open problem resolution in Lean. We adopt a standard coding-agent evaluation setting, placing each problem and its logical negation into a Lean project in a Docker container. We also build Leanimum-agent on mini-SWE-agent to provide a unified harness for fair comparisons across models. Our evaluation finds that even the best-performing model resolves only ~40% of the problems, leaving substantial room for improvement on formalized open research problems.

A geometric style learned from one family of shapes is typically applied to new shapes from the same family. We consider a more challenging setting: learning the geometric design language of a stylized Latin alphabet and applying it to new forms, from Greek glyphs to entirely different structures such as human poses. We introduce Open-Form Geometric Style Transfer, where the forms to which a learned geometric style can be applied are not restricted to the shape family in which that style was observed. This setting is deceptively challenging: the difficulty is not merely learning a style, but learning the style without learning the shape family in which it was observed. We represent target forms by structural sketches and disentangle structural adherence from style realization using a Geometry LoRA and a style-specific LoRA. Critically, open-form transfer requires the Geometry LoRA to be universal. To achieve this, we devise a geometry-enrichment strategy that constructs a large and purposefully diverse collection of synthetic structural sketches spanning a broad range of unfamiliar geometries. Our experiments and ablations demonstrate the importance of both disentanglement and this universal geometry prior, enabling geometric styles learned from glyphs, pictograms, and other shape families to be transferred to substantially different, unseen forms.

Despite advancements in automatic speech recognition systems (ASR), current systems exhibit speaker-attribute bias, i.e., their speech recognition performance is biased against certain speakers based on their demographic attributes such as gender, accents, and speaker type. However, accurately assessing speaker attribute bias in a given ASR system requires the availability of a bias evaluation dataset with comparable speech across subgroups of a speaker attribute. In this paper, we introduce African speech Bias Evaluation Dataset (AfriBED), a novel speech recognition bias evaluation dataset for two low resource African languages, Bemba and Nyanja, to detect and estimate gender and speaker-type bias for ASR systems. The dataset comprises 9 hours of speech with 3928 utterances recorded by 80 speakers for Bemba, while the Nyanja set includes 6260 utterances with approximately 18 hours of speech recorded by 127 speakers. The results of our baseline experiments demonstrate that the datasets are useful for examining gender and speaker-type attribute bias in the target languages.

Matryoshka Representation Learning (MRL) is designed to support flexible representation sizes by jointly optimizing nested prefixes. While effective, this design lacks an explicit constraint to ensure that the leading portion provides a suitable compact encoding. To address this, we propose SpecMRL, which reorganizes the feature space to enable more effective prefix readout. Specifically, we extend MRL with a parameter-derived spectral basis organized with feature importance. SpecMRL otherwise follows standard MRL, with prefix readout performed in the learned spectral space. Experiments on MTEB show that SpecMRL outperforms MRL at all evaluated reduced dimensions, with larger gains under more aggressive compression. These results suggest that the learned spectral basis better prioritizes informative directions, enabling more effective representation compression. Notably, SpecMRL extends the performance frontier of MRL, surpassing full-dimensional MRL with only half the embedding dimensions.

Memory-native evolution requires making memory an intrinsic capability of foundation models, enabling them to continuously accumulate and utilize information. To this end, we introduce MemT-1.0, a new architecture of memory foundation models that internalize memory as part of model computation. Building on Metis, MemT-1.0 employs Gated DeltaNet-2 with a stable token-level memory update mechanism within each turn. We further introduce Mixture-of-Storage to scale native memory capacity. Following a deliberate backbone preparation, we develop a two-stage training pipeline consisting of continued pre-training and post-training, supported by 34B tokens of training data and efficient training and inference infrastructure. We release a model family comprising MemT-1.0-Nano and MemT-1.0-Flash, and conduct a comprehensive evaluation of memory and general capabilities. The results show that they outperform the parametric memory baselines on average and remain competitive with retrieval-augmented methods, while largely preserving general capabilities. At a history length of 128K tokens, MemT-1.0-Nano achieves approximately $1.86\times$ end-to-end inference speedup and a $66\times$ reduction in persistent storage relative to full context KV cache. By internalizing retrieved procedural experience, MemT-1.0 improves task success on agentic tasks, providing a practical step toward memory-native evolution.

Beyond basic tool use and coding skills, effectively incorporating visual references into agentic generation is equally essential for applying AI agents to real-world productivity tasks. We study this crucial capability through webpage development, a practical and readily evaluable setting in which existing benchmarks remain largely idealized: they typically focus on reconstructing visual targets or generating webpages from textual instructions alone, overlooking the more common workflow of developing from visual examples. Specifically, we introduce RefCraft, a benchmark comprising 300 realistic multimodal webpage-development tasks that combine natural-language instructions with screenshots from one to five reference webpages. Agents must selectively interpret and utilize these references while rendering, visually inspecting, and iteratively refining their outputs. We evaluate the resulting open-ended artifacts using independently verifiable keypoints and complementary programmatic and VLM judges. Across nine frontier (M)LLMs, the strongest system achieves an overall score of only 52.12 out of 100, revealing that visual-reference-conditioned agentic generation remains a substantial challenge for current models in practical webpage-development settings.

Context compression improves long-context efficiency but may introduce faithfulness issues through an information bottleneck. Existing evaluations rely on QA metrics, but a reader can still answer correctly from an unfaithful compression, so these metrics underestimate such loss. To bridge this gap, we introduce KEEP-Bench, a diagnostic benchmark that directly assesses compression faithfulness with 4,102 cases across three challenging settings that require keeping evidence for plausible reference resolutions, explicit qualifiers, and minority perspectives. Experiments show that even with tailored prompting, the strongest models remain unreliable: despite context windows exceeding 100K tokens and inputs averaging only 3.1K tokens, the best open-weight model (31B) preserves all required evidence in only 66.8% of cases, and the best proprietary model in only 61.6%. Performance also varies sharply across evidence structures, so conclusions from limited structures may be biased. We further introduce a metric, Evidence Preservation Return (EPR), to relate evidence recall to inference FLOPs, and find that it peaks at moderate scales (4B-8B), where recall remains low. Additional output budget mainly benefits already strong models and widens capability gaps, yet the stronger preservation of these models comes at a steep computational cost. These findings highlight the importance for future work to investigate compressors with strong information preservation under a small computation budget, rather than relying on a large output budget or model scaling.

Agent learning is shifting from learning from human data toward learning through interaction with the world. However, scaling such learning directly in real-world computer systems is challenging and can introduce substantial security risks. We therefore propose Agent World Model in the Wild (WildAWM), a scalable pipeline for synthesizing controllable environments and tasks for training general computer-use agents (CUAs). Whereas existing approaches typically specialize in a single agent interaction interface, we construct executable environments that jointly support graphical user interfaces, model context protocol services, and command-line interfaces, allowing agents to flexibly combine visual interaction, tool use, and code execution. WildAWM is entirely powered by open-source models, demonstrating that high-quality computer-use environments can be generated without proprietary frontier models. Beyond environments, we address three recurring challenges in task synthesis: ensuring solvability, maintaining sufficient difficulty, and producing reliable verifiers, by introducing execution-based quality gates that combine heterogeneous agent rollouts, cross-judge consistency checks, and counterfactual probes of judgment robustness. The resulting pipeline synthesizes 341 long-horizon environment-task pairs that can require over 100 agent steps to solve and remain challenging even for frontier models, with GPT-6-Astra solving only 60% of them. We train two Qwen models of different sizes exclusively in these synthetic worlds. Both models achieve substantial gains across 8 out-of-distribution benchmarks spanning web, claw, and computer-use agents, demonstrating that learning in WildAWM's synthesized worlds generalizes broadly to unseen computer-use tasks. The code is publicly available at https://github.com/MSR-Orchard/WildAWM.

Frontier agents retrieve structural metadata well and compute geometry from coordinates less reliably. We ask how much of a benchmark score reflects that gap and how much reflects the evaluation configuration around the model. We study ProteinGeoBench, a suite of 131 protein-structure tasks, using 4,249 rollouts from four frontier models and 4,486 further trials across 26 models. Three of the four frontier models fall within 0.031 of one another (0.785 to 0.816) with no difference between them resolved, while the fourth scores 0.707 and all three gaps to it exclude zero. Three of the four do better on metadata lookup than on numeric calculation. The fourth is slightly better on numeric. Numeric tasks are 28 of the 131 but half of the twelve tasks that all four models fail. The ranking also depends on the evaluation budget: with one run per task, 23.9% of bootstrap replicates put a different model first. On a selected 15-task slice, removing network access lowers scores more than blocking eight structural-database domains, but the two contrasts were graded in different passes and cannot be cleanly decomposed. Swapping in each model's own command-line agent changes scores by -0.071 to +0.086, a comparison too small to rule out moderate harness effects. Across 26 models, numeric performance rises with non-numeric performance rather than staying flat. The experiments use different task subsets, so they cannot rank model, harness, access and task composition against one another. Evaluations should report results by task family, along with the number of runs, the harness and the access conditions.