arXiv:2607. 19378v1 Announce Type: new Abstract: Subquadratic alternatives to attention require compromises when applied to multi-dimensional data: standard convolutions lack global receptive fields and input dependency, while recurrent models require rasterizing data such as images, volumes, and partial differential equation (PDE) into an ad-hoc $1\rm D$ scan order that violates their spatial structure.
arXiv:2606. 01172v1 Announce Type: new Abstract: Modeling unknown latent functions from finite, irregularly sampled measurements is a recurring challenge across science and engineering.
LoopVAE introduces a recurrent depth architecture that reuses a scale‑ and loop‑conditioned core across different spatial scales while keeping resolution‑changing transitions separate. The four‑block core applies 28 block operations per encoder or decoder, enabling a 29M‑parameter convolutional model to achieve 0.28 rFID and 32.54 dB PSNR on ImageNet‑256 with roughly 65% fewer parameters than comparable VAEs. Experiments with both convolutional and Transformer operators, as well as ablations on parameter sharing, demonstrate competitive image quality metrics and reveal how targeted loop interventions and truncation affect reconstruction quality and computational trade‑offs.
The paper investigates how different attention mechanisms affect the performance of DeepONet neural operators. Five variants—varying in cross‑attention, self‑attention, tokenization, and attention depth—are trained in both data‑driven and physics‑informed settings on one‑ and two‑dimensional PDE benchmarks. Results show that per‑sensor tokenization with cross‑attention consistently reduces error, while branch self‑attention helps only in complex spatial problems, and deeper cross‑attention yields diminishing returns with higher cost.
arXiv:2606. 00746v1 Announce Type: cross Abstract: Vision foundation models are bottlenecked by the quadratic cost of self-attention, which limits usable resolution and increases the cost of large-scale pretraining.
The paper introduces Gated Token Recurrence (GTR), a softmax‑free recurrent vision backbone that replaces global softmax attention with gated linear attention, alternating scan directions, and enhanced SwiGLU blocks. GTR is distilled from a DINOv3 teacher using only final‑layer patch‑token alignment, and achieves strong performance on COCO object detection (58.9 box AP) with very low latency (1.908 ms on an RTX 4090). The backbone also transfers to multiple dense prediction tasks and runs efficiently on edge hardware via a specialized CUDA operator and TensorRT deployment.
The paper introduces two multi-stage neural operator learning frameworks—Deep Collocation Neural Operator (DCNO) and Deep Galerkin Neural Operator (DGNO)—for efficiently computing convolution integrals. DCNO is a supervised method that iteratively refines operator approximations by learning residuals from data pairs, while DGNO is an unsupervised approach that uses the weak form of a PDE residual when the operator can be represented by a PDE. Both frameworks build basis operators across multiple training stages, yielding markedly higher accuracy than one-shot learning and achieving near machine‑precision results for convolution problems, with significant efficiency gains for repeated queries or parametric variations.
The paper introduces the Cluster Attention Neural Operator (CANO), a neural operator that uses a novel cross‑attention mechanism to dynamically cluster queries while keeping full‑resolution keys and values. This design eliminates the slice compression and weight‑sharing limitations of previous Transformer‑based operators, maintaining fast computation and global interactions. Experiments on a range of fluid and solid dynamics benchmarks—including Navier‑Stokes, Airfoil, Plasticity, Pipe Turbulence, and Composites—show that CANO achieves lower errors than existing baselines and demonstrates strong geometric adaptability and temporal consistency.
The paper introduces Cubit, a Transformer‑style architecture that replaces the standard attention mechanism with Kernel Ridge Regression (KRR). By interpreting attention as Nadaraya‑Watson regression, Cubit incorporates the closed‑form KRR solution, combining kernel‑based value aggregation with normalization via the inverse kernel matrix. The authors also propose a Limited‑Range Rescale (LRR) to stabilize training and report that Cubit shows improved long‑sequence modeling, with gains increasing as training sequence length grows.
arXiv:2609.38348v1 Announce Type: new Abstract: Many forms of data, including physical fields, geometric shapes, and visual signals, are naturally described by functions over continuous domains but a...
HiLNO is a hierarchical latent neural operator that builds a fine‑to‑coarse‑to‑fine latent space and incorporates multi‑scale supervision and anisotropic Gaussian attention to preserve spatial information in PDE solutions with multiscale structures. The hierarchy reduces information loss during compression, while multi‑scale supervision aligns intermediate predictions with downsampled targets, and anisotropic attention facilitates feature transfer across scales. Experiments on standard PDE benchmarks and a large‑scale automotive aerodynamics task show that HiLNO achieves competitive accuracy while cutting parameter count by 84.4% and FLOPs by 69.2% compared with LinearNO, and it generalizes effectively to unseen spatial resolutions.
arXiv:2606. 14597v1 Announce Type: new Abstract: Transformer-based neural operators have shown remarkable performance for approximating solution operators of partial differential equations on complex geometries.
arXiv:2608.21677v1 Announce Type: cross Abstract: Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route informat...