Any far-reaching new technology is always uneven in its adoption, but few have been more uneven than generative AI. That makes it hard to assess its likely impact on individual businesses, let alone on productivity across the economy as a whole. At one extreme, AI coding assistants have revolutionized the work of software developers. At the other extreme, most companies are seeing little if any benefit from their initial investments. That has provided fuel for the skeptics who maintain that--by its very nature as a probabilistic technology prone to hallucinating--generative AI will never have a deep impact on business. To students of tech history, though, the lack of immediate impact is normal.

'The biggest decision yet': Jared Kaplan on allowing AI to train itself Anthropic's chief scientist says AI autonomy could spark a beneficial'intelligence explosion' - or be the moment humans lose control Humanity will have to decide by 2030 whether to take the "ultimate risk" of letting artificial intelligence systems train themselves to become more powerful, one of the world's leading AI scientists has said. Jared Kaplan, the chief scientist and co-owner of the $180bn (£135bn) US startup Anthropic, said a choice was looming about how much autonomy the systems should be given to evolve. The move could trigger a beneficial "intelligence explosion" - or be the moment humans end up losing control. In an interview about the intensely competitive race to reach artificial general intelligence (AGI) - sometimes called superintelligence - Kaplan urged international governments and society to engage in what he called "the biggest decision". Anthropic is part of a pack of frontier AI companies including OpenAI, Google DeepMind, xAI, Meta and Chinese rivals led by DeepSeek, racing for AI dominance. Its widely used AI assistant, Claude, has become particularly popular among business customers.

Masayoshi Son, chairman and chief executive officer of SoftBank Group, speaks during the Future Investment Initiative (FII) Institute Priority Asia conference in Tokyo on Monday. SoftBank Group founder Masayoshi Son said he wouldn't have sold off Nvidia shares if his company had unlimited money to bankroll its next investments in artificial intelligence, which include a big bet on OpenAI. Son, addressing for the first time the surprise November disclosure that SoftBank had unloaded its entire stake in the world's most valuable company, also slammed talk of an AI investment bubble. The Japanese company simply needed to raise capital to fund projects including data center construction, he told a forum in Tokyo Monday. I don't want to sell a single share. I just had more need for money to invest in OpenAI" and other projects, Son said during the FII Priority Asia forum.

Foundation models have become central to unifying perception and planning in robotics, yet real-world deployment exposes a mismatch between their monolithic assumption that a single model can handle all cognitive functions and the distributed, dynamic nature of practical service workflows. Vision-language models offer strong semantic understanding but lack embodiment-aware action capabilities while relying on hand-crafted skills. Vision-Language-Action policies enable reactive manipulation but remain brittle across embodiments, weak in geometric grounding, and devoid of proactive collaboration mechanisms. These limitations indicate that scaling a single model alone cannot deliver reliable autonomy for service robots operating in human-populated settings. To address this gap, we present InteractGen, an LLM-powered multi-agent framework that decomposes robot intelligence into specialized agents for continuous perception, dependency-aware planning, decision and verification, failure reflection, and dynamic human delegation, treating foundation models as regulated components within a closed-loop collective. Deployed on a heterogeneous robot team and evaluated in a three-month open-use study, InteractGen improves task success, adaptability, and human-robot collaboration, providing evidence that multi-agent orchestration offers a more feasible path toward socially grounded service autonomy than further scaling standalone models.

This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven (statistical) formalism to a constrained or ``physics-informed'' formalism, which integrates physical knowledge and methods from traditional computational engineering. In the first part, we introduce the general concepts and the statistical flavor of regression versus other forms of curve fitting. We then move to an overview of traditional methods from machine learning and their classification and ways to link these to traditional computational science. Finally, we close with a note on methods to combine machine learning and numerical methods for physics

Safety-critical environments are inherently dynamic. Distribution shifts, emerging vulnerabilities, and evolving requirements demand continuous updates to machine learning models. Yet even benign parameter updates can have unintended consequences, such as catastrophic forgetting in classical models or alignment drift in foundation models. Existing heuristic approaches (e.g., regularization, parameter isolation) can mitigate these effects but cannot certify that updated models continue to satisfy required performance specifications. We address this problem by introducing a framework for provably safe model updates. Our approach first formalizes the problem as computing the largest locally invariant domain (LID): a connected region in parameter space where all points are certified to satisfy a given specification. While exact maximal LID computation is intractable, we show that relaxing the problem to parameterized abstract domains (orthotopes, zonotopes) yields a tractable primal-dual formulation. This enables efficient certification of updates - independent of the data or algorithm used - by projecting them onto the safe domain. Our formulation further allows computation of multiple approximately optimal LIDs, incorporation of regularization-inspired biases, and use of lookahead data buffers. Across continual learning and foundation model fine-tuning benchmarks, our method matches or exceeds heuristic baselines for avoiding forgetting while providing formal safety guarantees.

Decision trees and random forest remain highly competitive for classification on medium-sized, standard datasets due to their robustness, minimal preprocessing requirements, and interpretability. However, a single tree suffers from high estimation variance, while large ensembles reduce this variance at the cost of substantial computational overhead and diminished interpretability. In this paper, we propose Decision Tree Embedding (DTE), a fast and effective method that leverages the leaf partitions of a trained classification tree to construct an interpretable feature representation. By using the sample means within each leaf region as anchor points, DTE maps inputs into an embedding space defined by the tree's partition structure, effectively circumventing the high variance inherent in decision-tree splitting rules. We further introduce an ensemble extension based on additional bootstrap trees, and pair the resulting embedding with linear discriminant analysis for classification. We establish several population-level theoretical properties of DTE, including its preservation of conditional density under mild conditions and a characterization of the resulting classification error. Empirical studies on synthetic and real datasets demonstrate that DTE strikes a strong balance between accuracy and computational efficiency, outperforming or matching random forest and shallow neural networks while requiring only a fraction of their training time in most cases. Overall, the proposed DTE method can be viewed either as a scalable decision tree classifier that improves upon standard split rules, or as a neural network model whose weights are learned from tree-derived anchor points, achieving an intriguing integration of both paradigms.

Post-training quantization (PTQ) aims to preserve model-level behavior; however, most methods focus on individual linear layers. Even recent extensions, such as QEP and LoaQ, which mitigate error propagation or target specific submodules, still rely on layer-wise formulations and fail to capture the behavior of larger submodules. We introduce Layer-Projected Coordinate Descent (LPCD), a unified framework that extends PTQ beyond layers by optimizing relaxed objectives across arbitrary submodules and projecting the solutions with layer-wise quantizers. LPCD generalizes existing methods and provides a principled approach to quantizing complex submodules while maintaining the efficiency and compatibility of layer-wise PTQ pipelines. Across diverse LLM architectures and bit-widths, LPCD-based submodule quantization consistently enhances both layer-wise PTQ methods and existing submodule approaches.

Diffusion-based solvers for partial differential equations (PDEs) are often bottle-necked by slow gradient-based test-time optimization routines that use PDE residuals for loss guidance. They additionally suffer from optimization instabilities and are unable to dynamically adapt their inference scheme in the presence of noisy PDE residuals. To address these limitations, we introduce PRISMA (PDE Residual Informed Spectral Modulation with Attention), a conditional diffusion neural operator that embeds PDE residuals directly into the model's architecture via attention mechanisms in the spectral domain, enabling gradient-descent free inference. We show that PRISMA has competitive accuracy, at substantially lower inference costs, compared to previous methods across five benchmark PDEs especially with noisy observations, while using 10x to 100x fewer denoising steps, leading to 15x to 250x faster inference. Given the ubiquitous presence of partial differential equations (PDEs) in almost every scientific discipline, there is a rapidly growing literature on using neural networks for solving PDEs (Raissi et al., 2019a; Lu et al., 2019). This includes seminal works in operator learning methods such as the Fourier Neural Operator (FNO) Li et al. (2020) that learns resolution-independent mappings between function spaces of input parameters a and solution fields u. However, a major limitation of these methods is their reliance on complete and clean observations of either a or u, a condition rarely met in real-world applications where data is inherently noisy and sparse. The rise of generative models has inspired another class of methods for solving PDEs by modeling the joint distribution of a and u using diffusion-based backbones (Huang et al., 2024; Y ao et al., 2025; Lim et al., 2023; Shu et al., 2023; Bastek et al., 2024; Jacobsen et al., 2025). These methods offer two key advantages over operator learning methods: (i) they generate full posterior distributions of a and/or u, enabling principled uncertainty quantification crucial for ill-posed inverse problems, and (ii) they naturally accommodate sparse observations during inference using likelihood-based and PDE residual-based loss guidance, termed diffusion posterior sampling or test-time optimization.

Mean-field games (MFGs) study the Nash equilibrium of systems with a continuum of interacting agents, which can be formulated as the fixed-point of optimal control problems. They provide a unified framework for a variety of applications, including optimal transport (OT) and generative models. Despite their broad applicability, solving high-dimensional MFGs remains a significant challenge due to fundamental computational and analytical obstacles. In this work, we propose a particle-based deep Flow Matching (FM) method to tackle high-dimensional MFG computation. In each iteration of our proximal fixed-point scheme, particles are updated using first-order information, and a flow neural network is trained to match the velocity of the sample trajectories in a simulation-free manner. Theoretically, in the optimal control setting, we prove that our scheme converges to a stationary point sublinearly, and upgrade to linear (exponential) convergence under additional convexity assumptions. Our proof uses FM to induce an Eulerian coordinate (density-based) from a Lagrangian one (particle-based), and this also leads to certain equivalence results between the two formulations for MFGs when the Eulerian solution is sufficiently regular. Our method demonstrates promising performance on non-potential MFGs and high-dimensional OT problems cast as MFGs through a relaxed terminal-cost formulation.