Scaling Density Functional Theory with Gaussian Splatting

Density functional theory (DFT) strikes a practical balance between accuracy and computational cost in many problems of computational chemistry and materials science. However, many DFT calculations are limited by fixed atom-centered basis sets, which dictate how accuracy and cost scale with system size. We propose Gaussian Splatting for Density Functional Theory (GS-DFT), which represents molecular orbitals as a cloud of Gaussians whose positions, shapes, and mixing coefficients are optimized jointly by gradient descent to minimize the energy without training data. Conceptually, GS-DFT is 3D Gaussian splatting with the renderer replaced by quantum mechanics. We introduce two key solver components: adaptive density fitting with screening for efficient evaluation of two-electron integrals, and a regularized differentiable orthogonalization of the molecular orbitals. Empirically, the optimized basis reaches the accuracy of the largest conventional basis sets with a fraction of the parameters, converging systematically in energy, density, and nuclear forces. At equal parameter count, it captures the stretched-bond and anion physics that fixed bases only recover with specialized basis augmentation. The resulting solver exhibits quadratic peak memory scaling in the cloud size, allowing us to simulate systems of up to 2,742 atoms (10,406 electrons) without any modifications at triple-zeta scale using a single four-GPU node.

Mais de arXiv AI Papers

Entre para seguir esta fonte

arXiv AI Papers·há 14 horas☆

Near Minimax Rate for Quantile Distributional Reinforcement Learning↗

In this paper, we study quantile distributional policy evaluation, where the return distribution under a given policy is approximated by the quantile Bellman fixed point η_m. We investigate the statistical accuracy of estimating η_m across quantile resolutions under Wasserstein distances. Assuming access to a generative model, we construct a quantile fixed point estimator η_m^{(n)} from an empirical Markov decision process and establish non-asymptotic error bounds under Wasserstein distances. When reward densities are uniformly bounded away from zero, we obtain a root-n high-probability bound simultaneously over all resolutions m and all Wasserstein orders 1p. When reward densities vanish at the support endpoints, we show that continuity and endpoint monotonicity suffice to preserve the same resolution-independent rate for 1p2. For p>2, we establish a root-n bound with coefficient m^{1/2-1/p}, together with a slower, resolution-independent n^{-1/p} bound for every finite p>2. We further obtain resolution-independent W_consistency governed by the continuity modulus of reward quantile functions. To investigate the sharpness of these bounds, we characterize the exact local asymptotic minimax risk at each fixed resolution as the expected Wasserstein-coordinate norm of the efficient Gaussian limit and prove that our estimator attains it. We then examine the resolution dependence of this optimal local risk. A regular one-state instance has resolution-independent local risk constants, whereas a single endpoint-vanishing two-state instance exhibits growth of order m^{1/2-1/p}, up to logarithmic factors along a resolution subsequence, for every p>2.

en

arXiv AI Papers·há 14 horas☆

A Transfer Learning-Driven Methodology for Efficient and Sustainable Indoor Localization Using VLC↗

The rapid expansion of the Internet of Things enables seamless collaboration among connected devices, making indoor localization a critical component of industrial automation. However, conventional localization techniques struggle in dynamic environments. These methods depend on extensive, frequent data collection and environment-specific calibration, limiting scalability, interoperability, and effective use of prior research while imposing significant energy penalties that hinder practical deployment. To address these challenges, we propose an energy-efficient transfer learning (TL) based approach for visible light communication based indoor localization. Our method leverages TL to tackle environmental variability, including lighting fluctuations and physical obstacles that typically degrade localization performance, while simultaneously reducing computational overhead and energy consumption compared to conventional approaches. We also introduce a novel model efficiency (ME) metric, designed to integrate localization accuracy, energy efficiency, data efficiency, and transfer gain into a single evaluative measure for comprehensive optimization. Evaluations on a real-world dataset collected from a BOSCH factory demonstrate that our model achieves a 47% improvement in localization accuracy compared to a conventional model that does not utilize TL, and achieves up to 67.5% ME with TL models, compared to only 10.4% in conventional models under high-noise conditions. These results underscore the potential of our approach to deliver a highly efficient and scalable indoor localization system suitable for energy-constrained industrial applications.

en

arXiv AI Papers·há 15 horas☆

Fragment-Level Graph Encoding for Interpretable Molecular Property Prediction↗

Graph neural networks (GNNs) are among the standard tools for molecular property prediction, but the atom-level explanations of their predictions are hard for medicinal chemists to act on. We propose a change of input representation rather than a new model: molecules are encoded as fragment-level graphs from BRICS decomposition, where each node is a synthetically meaningful fragment whose features are the element-wise sum of its atoms' features. Because only the representation changes, any message-passing GNN and any post-hoc attribution method produces explanations at the resolution of functional groups instead of single atoms. Across four architectures, four prediction tasks, and two explainers under scaffold splits, fragment-level encoding matches atom-level test accuracy on roughly five-fold smaller graphs. Integrated-Gradients attributions recover known pharmacophores above chance on two enzyme targets, namely BACE at 1.5 times the chance rate, and PTR1 at 3.2 times. A like-for-like comparison against an aggregated atom-level baseline shows that post-hoc aggregation is not a stable substitute: its BACE hit rate range both exceeds and falls below the fragment model's hit rate depending on two arbitrary aggregation choices, whereas fragment-level training yields a single convention-free attribution at no predictive cost. The code is available at: https://github.com/4D-Lab/frame

en

arXiv AI Papers·há 15 horas☆

Unlocking Spatial Grounding in Flow-Matching Models via SNR Tuning↗

Despite the success of foundation models in image synthesis, achieving fine-grained spatial control remains a significant challenge, typically requiring auxiliary structural adapters or complex inference-time steering. While modern vision-language (VLM) text encoders possess the latent capacity to represent spatial coordinates, generative models often fail to leverage this information. We demonstrate that the signal-to-noise ratio (SNR) distribution is a critical determinant of spatial grounding in flow-matching models. Using a novel synthetic benchmark of geometric primitives, we isolate structural mechanics from textural complexity inherent in natural imagery and introduce a rigorous color-aware layout metric to quantify spatial fidelity. We show that training on a centered SNR distribution results in poor layout adherence (25.9%). Instead, we identify high-noise regimes as a "critical learning phase" for spatial grounding. Shifting the training focus toward these stages increases layout adherence to 80.8%, effectively reaching the 83.6% reconstruction ceiling of the underlying variational autoencoder. We find that the necessity for this shift scales with resolution and aspect ratio variance, and that the conservative noise schedules employed by models like FLUX.1 are insufficient for precise layout adherence. Finally, we show that these findings translate to real-world imagery via the COCO dataset (1.0 vs. 57.3 Average Precision), where state-of-the-art layout adherence is unlocked through distribution tuning alone, without architectural modifications.

en