The world's fourth biggest company, Google-owner Alphabet, has announced a new £5bn ($6.8bn) investment in UK artificial intelligence (AI). The money will be used for infrastructure and scientific research over the next two years - the first of several massive US investments being unveiled ahead of US President Donald Trump's state visit. Google's President and Chief Investment Officer Ruth Porat told BBC News in an exclusive interview that there were profound opportunities in the UK for its pioneering work in advanced science. The company will officially open a vast $1bn (£735m) data centre in Waltham Cross, Hertfordshire, with Chancellor Rachel Reeves on Tuesday. The investment will expand this site and also include funding for London-based DeepMind, run by British Nobel Prize winner Sir Demis Hassabis, which deploys AI to revolutionise advanced scientific research.

Traditional multi-view stereo (MVS) methods primarily depend on photometric and geometric consistency constraints. In contrast, modern learning-based algorithms often rely on the plane sweep algorithm to infer 3D geometry, applying explicit geometric consistency (GC) checks only as a post-processing step, with no impact on the learning process itself. In this work, we introduce GC MVSNet plus plus, a novel approach that actively enforces geometric consistency of reference view depth maps across multiple source views (multi view) and at various scales (multi scale) during the learning phase (see Fig. 1). This integrated GC check significantly accelerates the learning process by directly penalizing geometrically inconsistent pixels, effectively halving the number of training iterations compared to other MVS methods. Furthermore, we introduce a densely connected cost regularization network with two distinct block designs simple and feature dense optimized to harness dense feature connections for enhanced regularization. Extensive experiments demonstrate that our approach achieves a new state of the art on the DTU and BlendedMVS datasets and secures second place on the Tanks and Temples benchmark. To our knowledge, GC MVSNet plus plus is the first method to enforce multi-view, multi-scale supervised geometric consistency during learning. Our code is available.

Difficult decision-making problems abound in various disciplines and domains. The proliferation of generative techniques, especially large language models (LLMs), has excited interest in using them for decision support. However, LLMs cannot yet resolve missingness in their training data, leading to hallucinations. Retrieval-Augmented Generation (RAG) enhances LLMs by incorporating external information retrieval, reducing hallucinations and improving accuracy. Yet, RAG and related methods are only partial solutions, as they may lack access to all necessary sources or key missing information. Even everyday issues often challenge LLMs' abilities. Submitting longer prompts with context and examples is one approach to address knowledge gaps, but designing effective prompts is non-trivial and may not capture complex mental models of domain experts. For tasks with missing critical information, LLMs are insufficient, as are many existing systems poorly represented in available documents. This paper explores how LLMs can make decision-making more efficient, using a running example of evaluating whether to respond to a call for proposals. We propose a technology based on optimized human-machine dialogue and monotone Boolean and k-valued functions to discover a computationally tractable personal expert mental model (EMM) of decision-making. Our EMM algorithm for LLM prompt engineering has four steps: (1) factor identification, (2) hierarchical structuring of factors, (3) generating a generalized expert mental model specification, and (4) generating a detailed generalized expert mental model from that specification.

The first part of this paper studies the evolution of gradient flow for homogeneous neural networks near a class of saddle points exhibiting a sparsity structure. The choice of these saddle points is motivated from previous works on homogeneous networks, which identified the first saddle point encountered by gradient flow after escaping the origin. It is shown here that, when initialized sufficiently close to such saddle points, gradient flow remains near the saddle point for a sufficiently long time, during which the set of weights with small norm remain small but converge in direction. Furthermore, important empirical observations are made on the behavior of gradient descent after escaping these saddle points. The second part of the paper, motivated by these results, introduces a greedy algorithm to train deep neural networks called Neuron Pursuit (NP). It is an iterative procedure which alternates between expanding the network by adding neuron(s) with carefully chosen weights, and minimizing the training loss using this augmented network. The efficacy of the proposed algorithm is validated using numerical experiments.

This paper introduces SpaPool, a novel pooling method that combines the strengths of both dense and sparse techniques for a graph neural network. SpaPool groups vertices into an adaptive number of clusters, leveraging the benefits of both dense and sparse approaches. It aims to maintain the structural integrity of the graph while reducing its size efficiently. Experimental results on several datasets demonstrate that SpaPool achieves competitive performance compared to existing pooling techniques and excels particularly on small-scale graphs. This makes SpaPool a promising method for applications requiring efficient and effective graph processing.

Deep neural networks tend to memorize noisy labels, severely degrading their generalization performance. Although Mixup has demonstrated effectiveness in improving generalization and robustness, existing Mixup-based methods typically perform indiscriminate mixing without principled guidance on sample selection and mixing strategy, inadvertently propagating noisy supervision. To overcome these limitations, we propose SelectMix, a confidence-guided mixing framework explicitly tailored for noisy labels. SelectMix first identifies potentially noisy or ambiguous samples through confidence based mismatch analysis using K-fold cross-validation, then selectively blends identified uncertain samples with confidently predicted peers from their potential classes. Furthermore, SelectMix employs soft labels derived from all classes involved in the mixing process, ensuring the labels accurately represent the composition of the mixed samples, thus aligning supervision signals closely with the actual mixed inputs. Through extensive theoretical analysis and empirical evaluations on multiple synthetic (MNIST, Fashion-MNIST, CIFAR-10, CIFAR-100) and real-world benchmark datasets (CIFAR-N, MNIST and Clothing1M), we demonstrate that SelectMix consistently outperforms strong baseline methods, validating its effectiveness and robustness in learning with noisy labels.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, $\mathbb{E}_π[\ell(Y \mid Γ_π(X))]$, which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length $\ell(Y \mid X)$. This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as $O(\log n)$ with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows $a+b\ln n$ (Qwen2-7B $b \approx 0.377$, Llama-3.1-8B $b \approx 0.147$); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by $\sim 0.13$ per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.

Magnitude, obtained as a special case of Euler characteristic of enriched category, represents a sense of the size of metric spaces and is related to classical notions such as cardinality, dimension, and volume. While the studies have explained the meaning of magnitude from various perspectives, continuity also gives a valuable view of magnitude. Based on established results about continuity of magnitude and maximum diversity, this article focuses on continuity of weighting, a distribution whose totality is magnitude, and its variation corresponding to maximum diversity. Meanwhile, recent studies also illuminated the connection between magnitude and data analysis by applying magnitude theory to point clouds representing the data or the set of model parameters. This article will also provide an application for time series analysis by introducing a new kind of invariants of periodic time series, where the invariance follows directly from the continuity results. As a use-case, a simple machine learning experiment is conducted with real-world data, in which the suggested invariants improved the performance.

We propose FACTORS, a framework that combines design of experiments with Shapley decomposition to address performance and stability issues that are sensitive to combinations of training factors. Our approach consistently estimates main effects and two-factor interactions, then integrates them into a risk-adjusted objective function that jointly accounts for uncertainty and cost, enabling reliable selection of configurations under a fixed budget. Effect estimation is implemented through two complementary paths: a plug-in path based on conditional means, and a least-squares path that reconstructs Shapley contributions from samples. These paths are designed to work complementarily even when design density and bias levels differ. By incorporating standardization of estimates, bias correction, and uncertainty quantification, our procedure ensures comparability across heterogeneous factor spaces and designs, while a lightweight search routine yields configurations within practical time even for large factor spaces. On the theoretical side, we provide error decompositions, sample complexity analysis, and upper bounds on optimality gaps. On the interpretive side, we summarize main effects and interactions in map form, highlighting adjustment priorities and safe improvement pathways. Across diverse datasets and design conditions, our approach improves rank preservation and optimal configuration identification, reduces decision-making risks, and offers a tuning foundation that delivers interpretable justification alongside stable performance gains even under budget constraints.

Signature-based methods have recently gained significant traction in machine learning for sequential data. In particular, signature kernels have emerged as powerful discriminators and training losses for generative models on time-series, notably in quantitative finance. However, existing implementations do not scale to the dataset sizes and sequence lengths encountered in practice. We present pySigLib, a high-performance Python library offering optimised implementations of signatures and signature kernels on CPU and GPU, fully compatible with PyTorch's automatic differentiation. Beyond an efficient software stack for large-scale signature-based computation, we introduce a novel differentiation scheme for signature kernels that delivers accurate gradients at a fraction of the runtime of existing libraries.