Flow and diffusion-based models have emerged as powerful tools for scientific applications, particularly for sampling non-normalized probability distributions, as exemplified by Boltzmann Generators (BGs). A critical challenge in deploying these models is their reliance on sample likelihood computations, which scale prohibitively with system size n, often rendering them infeasible for large-scale problems. To address this, we introduce HollowFlow, a flow-based generative model leveraging a novel non-backtracking graph neural network (NoBGNN). By enforcing a block-diagonal Jacobian structure, HollowFlow likelihoods are evaluated with a constant number of backward passes in n, yielding speed-ups of up to O(n2): a significant step towards scaling BGs to larger systems. Crucially, our framework generalizes: any equivariant GNN or attention-based architecture can be adapted into a NoBGNN.

Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities.

Usingourmethod weestablish anewbenchmark bycalculating the most accurate variational ground state energies ever published for a number of different atoms and molecules. Wesystematically break down and measure our improvements, focusing in particular on the effect of increasing physical prior knowledge.

Flow and diffusion-based models have emerged as powerful tools for scientific applications, particularly for sampling non-normalized probability distributions, as exemplified by Boltzmann Generators (BGs). A critical challenge in deploying these models is their reliance on sample likelihood computations, which scale prohibitively with system size $n$, often rendering them infeasible for large-scale problems. To address this, we introduce $\textit{HollowFlow}$, a flow-based generative model leveraging a novel non-backtracking graph neural network (NoBGNN). By enforcing a block-diagonal Jacobian structure, HollowFlow likelihoods are evaluated with a constant number of backward passes in $n$, yielding speed-ups of up to $\mathcal{O}(n^2)$: a significant step towards scaling BGs to larger systems. Crucially, our framework generalizes: $\textbf{any equivariant GNN or attention-based architecture}$ can be adapted into a NoBGNN. We validate HollowFlow by training BGs on two different systems of increasing size. For both systems, the sampling and likelihood evaluation time decreases dramatically, following our theoretical scaling laws. For the larger system we obtain a $10^2\times$ speed-up, clearly illustrating the potential of HollowFlow-based approaches for high-dimensional scientific problems previously hindered by computational bottlenecks.

Molecular dynamics (MD) is a broadly adopted technique to approximate such quantities.

Molecular dynamics (MD) simulations underpin modern computational drug dis- covery, materials science, and biochemistry. Recent machine learning models provide high-fidelity MD predictions without the need to repeatedly solve quantum mechanical forces, enabling significant speedups over conventional pipelines. Yet many such methods typically enforce strict equivariance and rely on sequential rollouts, thus limiting their flexibility and simulation efficiency. They are also com- monly single-task, trained on individual molecules and fixed timeframes, which restricts generalization to unseen compounds and extended timesteps. To address these issues, we propose Atomistic Transformer Operator for Molecules (ATOM), a pretrained transformer neural operator for multitask molecular dynamics. ATOM adopts a quasi-equivariant design that requires no explicit molecular graph and employs a temporal attention mechanism, allowing for the accurate parallel decod- ing of multiple future states. To support operator pretraining across chemicals and timescales, we curate TG80, a large, diverse, and numerically stable MD dataset with over 2.5 million femtoseconds of trajectories across 80 compounds. ATOM achieves state-of-the-art performance on established single-task benchmarks, such as MD17, RMD17 and MD22. After multitask pretraining on TG80, ATOM shows exceptional zero-shot generalization to unseen molecules across varying time hori- zons. We believe ATOM represents a significant step toward accurate, efficient, and transferable molecular dynamics models

We test the Platonic Representation Hypothesis (PRH) in astronomy by measuring representational convergence across a range of foundation models trained on different data types. Using spectroscopic and imaging observations from JWST, HSC, Legacy Survey, and DESI, we compare representations from vision transformers, self-supervised models, and astronomy-specific architectures via mutual $k$-nearest neighbour analysis. We observe consistent scaling: representational alignment generally increases with model capacity across our tested architectures, supporting convergence toward a shared representation of galaxy astrophysics. Our results suggest that astronomical foundation models can use pre-trained general-purpose architectures, allowing us to capitalise on the broader machine learning community's already-spent computational investment.

The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic searching techniques to simplify generating formal proofs, with a particular focus on the miniF2F dataset. We demonstrate how combining a large language model like ChatGPT with a formal language such as Lean, which has the added advantage of being verifiable, enhances the efficiency and accessibility of formal proof generation. Despite its simplicity, our best-performing Lean-based model surpasses all known benchmarks with a 31.15% pass rate. We extend our experiments to include other datasets and employ alternative language models, showcasing our models' comparable performance in diverse settings and allowing for a more nuanced analysis of our results. Our findings offer insights into AI-assisted formal proof generation, suggesting a promising direction for future research in formal mathematical proof.

1. Passive acoustic monitoring (PAM) coupled with artificial intelligence (AI) is becoming an essential tool for biodiversity monitoring. Traditional PAM systems require manual data offloading and impose substantial demands on storage and computing infrastructure. The combination of on-device AI-based processing and network connectivity enables local data analysis and transmission of only relevant information, greatly reducing storage needs. However, programming these devices for robust operation is challenging, requiring expertise in embedded systems and software engineering. Despite the increase in AI-based models for bioacoustics, their full potential remains unrealized without accessible tools to deploy them on custom hardware and tailor device behaviour to specific monitoring goals. 2. To address this challenge, we develop acoupi, an open-source Python framework that simplifies the creation and deployment of smart bioacoustic devices. acoupi integrates audio recording, AI-based data processing, data management, and real-time wireless messaging into a unified and configurable framework. By modularising key elements of the bioacoustic monitoring workflow, acoupi allows users to easily customise, extend, or select specific components to fit their unique monitoring needs. 3. We demonstrate the flexibility of acoupi by integrating two bioacoustic classifiers: BirdNET, for the classification of bird species, and BatDetect2, for the classification of UK bat species. We test the reliability of acoupi over a month-long deployment of two acoupi-powered devices in a UK urban park. 4. acoupi can be deployed on low-cost hardware such as the Raspberry Pi and can be customised for various applications. acoupi standardised framework and simplified tools facilitate the adoption of AI-powered PAM systems for researchers and conservationists. acoupi is on GitHub at https://github.com/acoupi/acoupi.