Simple yet Effective: Low-Rank Spatial Attention for Neural Operators

• URL: http://arxiv.org/abs/2604.03582v1
• Date: Sat, 04 Apr 2026 04:15:01 GMT
• Title: Simple yet Effective: Low-Rank Spatial Attention for Neural Operators
• Abstract summary: We introduce Low-Rank Spatial Attention (LRSA) as a clean and direct instantiation of this template.<n>Unlike prior approaches that often rely on non-standard aggregation or normalization modules, LRSA is built purely from standard Transformer primitives.<n>In our experiments, such a simple construction is sufficient to achieve high accuracy, yielding an average error reduction of over 17%.
• Score: 12.794762297826848
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural operators have emerged as data-driven surrogates for solving partial differential equations (PDEs), and their success hinges on efficiently modeling the long-range, global coupling among spatial points induced by the underlying physics. In many PDE regimes, the induced global interaction kernels are empirically compressible, exhibiting rapid spectral decay that admits low-rank approximations. We leverage this observation to unify representative global mixing modules in neural operators under a shared low-rank template: compressing high-dimensional pointwise features into a compact latent space, processing global interactions within it, and reconstructing the global context back to spatial points. Guided by this view, we introduce Low-Rank Spatial Attention (LRSA) as a clean and direct instantiation of this template. Crucially, unlike prior approaches that often rely on non-standard aggregation or normalization modules, LRSA is built purely from standard Transformer primitives, i.e., attention, normalization, and feed-forward networks, yielding a concise block that is straightforward to implement and directly compatible with hardware-optimized kernels. In our experiments, such a simple construction is sufficient to achieve high accuracy, yielding an average error reduction of over 17\% relative to second-best methods, while remaining stable and efficient in mixed-precision training.

Related papers

• Scalable Lindblad Noise Learning via Stochastic Tensor-Network Simulation [48.887627688666974]
  Learning dissipation rates in large-scale open quantum systems is a major obstacle for near-term quantum technologies.<n>Here, we propose a scalable noise-learning framework for Lindblad dissipation rates that combines a simulation method, the Jump Method (TJM)<n>We demonstrate the approach on two noise models in the Ising model, in which independent dissipation rates are learned for each site up to $N_mathrmsite=16$.<n>This combination of scalable numerics and rigorous theoretical guarantees positions TJM-based noise learning as a practical foundation for characterizing dissipation in large quantum devices.
  arXiv  Detail & Related papers  (2026-08-25T15:07:11Z)
• LCPNet: Latent Consistent Proximal Unfolding Network for Infrared Small Target Detection [50.3892176822492]
  Infrared small target detection (IRSTD) aims to identify long distance small targets from complex infrared backgrounds.<n>Deep learning methods have improved IRSTD by learning discriminative image-to-mask mappings.<n>Deep unfolding methods partially address this issue by embedding model-driven iterations into neural networks.<n>We propose Latent Consistent Proximal unfolding network (LCPNet) to address these limitations.
  arXiv  Detail & Related papers  (2026-07-06T02:15:09Z)
• UniRank: Unified Rank Allocation for Low-Rank LLM Compression [9.742379971053806]
  We formulate global low-rank allocation as a sorting-and-truncation pipeline.<n>We verify the strong correlation between high input-output cosine similarity and low effective rank.<n>We propose rank-preserving fine-tuning, which performs direct LoRA tuning on decomposed weights.
  arXiv  Detail & Related papers  (2026-06-20T03:10:33Z)
• Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems [10.89646305625521]
  Operator learning is an emerging field that integrates machine learning with scientific computing.<n>We propose the Starter-Iterator Neural Operator (SINO) for spectral-spatiotemporal collaborative modeling.<n>SINO achieves outstanding performance in numerical accuracy, capability, generalization, and robustness.
  arXiv  Detail & Related papers  (2026-06-16T06:54:39Z)
• PILIR: Physics-Informed Local Implicit Representation [10.009790673923789]
  We introduce the Physics-Informed Local Implicit Representation (PILIR)<n>Our approach separates the global physical domain into a discrete latent feature space and a continuous generative decoder.<n>A generative neural operator then synthesizes these local latent features into continuous physical fields, allowing accurate reconstruction of fine-scale structures.
  arXiv  Detail & Related papers  (2026-05-01T04:07:39Z)
• Monotone Optimisation with Learned Projections [0.0]
  Monotone optimisation problems admit specialised global solvers such as the Polyblock Outer Approximation (POA) algorithm.<n>We introduce an algorithm-aware learning approach that integrates learned models into POA by directly predicting its projection primitive via the radial inverse.
  arXiv  Detail & Related papers  (2026-01-28T19:32:04Z)
• Towards Globally Predictable k-Space Interpolation: A White-box Transformer Approach [9.242448133816037]
  We propose GPI-WT, a white-box Transformer framework based on Globally Predictable Interpolation (GPI) for k-space.<n> Experimental results demonstrate that the proposed method significantly outperforms state-of-the-art approaches in k-space accuracy while providing superior interpretability.
  arXiv  Detail & Related papers  (2025-08-06T03:24:28Z)
• Generalization error of min-norm interpolators in transfer learning [2.7309692684728617]
  Min-norm interpolators emerge naturally as implicit regularized limits of modern machine learning algorithms. In many applications, a limited amount of test data may be available during training, yet properties of min-norm in this setting are not well-understood. We establish a novel anisotropic local law to achieve these characterizations.
  arXiv  Detail & Related papers  (2024-06-20T02:23:28Z)
• Stable Nonconvex-Nonconcave Training via Linear Interpolation [51.668052890249726]
  This paper presents a theoretical analysis of linearahead as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss landscape and show how linear can help by leveraging the theory of nonexpansive operators.
  arXiv  Detail & Related papers  (2023-10-20T12:45:12Z)
• Quantize Once, Train Fast: Allreduce-Compatible Compression with Provable Guarantees [53.950234267704]
  We introduce Global-QSGD, an All-reduce gradient-compatible quantization method.<n>We show that it accelerates distributed training by up to 3.51% over baseline quantization methods.
  arXiv  Detail & Related papers  (2023-05-29T21:32:15Z)
• Low-rank Optimal Transport: Approximation, Statistics and Debiasing [51.50788603386766]
  Low-rank optimal transport (LOT) approach advocated in citescetbon 2021lowrank LOT is seen as a legitimate contender to entropic regularization when compared on properties of interest. We target each of these areas in this paper in order to cement the impact of low-rank approaches in computational OT.
  arXiv  Detail & Related papers  (2022-05-24T20:51:37Z)
• Hyperspectral Image Denoising Using Non-convex Local Low-rank and Sparse Separation with Spatial-Spectral Total Variation Regularization [49.55649406434796]
  We propose a novel non particular approach to robust principal component analysis for HSI denoising. We develop accurate approximations to both rank and sparse components. Experiments on both simulated and real HSIs demonstrate the effectiveness of the proposed method.
  arXiv  Detail & Related papers  (2022-01-08T11:48:46Z)
• Probabilistic partition of unity networks: clustering based deep approximation [0.0]
  Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs. We enrich POU-Nets with a Gaussian noise model to obtain a probabilistic generalization amenable to gradient-based generalizations of a maximum likelihood loss. We provide benchmarks quantifying performance in high/low-dimensions, demonstrating that convergence rates depend only on the latent dimension of data within high-dimensional space.
  arXiv  Detail & Related papers  (2021-07-07T08:02:00Z)
• Faster Non-Convex Federated Learning via Global and Local Momentum [57.52663209739171]
  textttFedGLOMO is the first (first-order) FLtexttFedGLOMO algorithm. Our algorithm is provably optimal even with communication between the clients and the server.
  arXiv  Detail & Related papers  (2020-12-07T21:05:31Z)
• DessiLBI: Exploring Structural Sparsity of Deep Networks via Differential Inclusion Paths [45.947140164621096]
  We propose a new approach based on differential inclusions of inverse scale spaces. We show that DessiLBI unveils "winning tickets" in early epochs.
  arXiv  Detail & Related papers  (2020-07-04T04:40:16Z)
• Log-Likelihood Ratio Minimizing Flows: Towards Robust and Quantifiable Neural Distribution Alignment [52.02794488304448]
  We propose a new distribution alignment method based on a log-likelihood ratio statistic and normalizing flows. We experimentally verify that minimizing the resulting objective results in domain alignment that preserves the local structure of input domains.
  arXiv  Detail & Related papers  (2020-03-26T22:10:04Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.