Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route information through a small set of latent tokens, and local models that perform message passing across mesh edges. Consistent with both classes is the inability to perform beyond low-dimensional problems and small-scale or oversimplified meshes, the simulation regimes where industrial problems reside. Our work shows this explicitly and presents a unified formulation. In global approaches, latent-token attention acts as a spatial low-pass filter, while local message passing lacks the global reach necessary to propagate information across large mesh spaces. Viewed through the error, the two operators are the halves of a multigrid cycle: one corrects errors at the lower end of the spectrum, the other at the higher end, and neither can do the other's job. We introduce Read-Write-Relax (RWR), which interleaves latent attention with message-passing relaxation under a unified formulation. The interleaved processor lowers error across the entire spectrum, making RWR the most accurate model in nearly every comparison across our industrial and public benchmarks. It is also markedly data-efficient in the scarce-data regimes, accurate on the engineering quantities of interest, and scales full-field predictions to challenging, large-scale problems.
Autonomous laparoscopic camera control requires continuous understanding of the surgeon's operative intent in dynamic surgical scenes, where the target operative region is not a stable physical object but a latent and temporally evolving attention state. In this work, we present Surgical Latent Attention Tracking (SurgLAT), a causal online framework for latent surgical attention modeling and autonomous laparoscopic view control. SurgLAT uses a frozen DINOv3 encoder and a state-conditioned spatial token mixer to extract operative evidence under a memory-guided spatial prior, while a selective causal latent memory module jointly models short-term motion continuity and long-horizon surgical intent evolution through dynamic retrieval of current, recent, and historical latent states. The learned latent surgical attention state is decoded into a probabilistic attention heatmap and operative region for downstream endoscope guidance. Beyond perception, we further introduce a robotic deployment framework with explicit laparoscopic Remote Center of Motion (RCM) constrained control based on virtual-axis formulation, together with redundancy-aware null-space initialization for stable and smooth manipulator motion. We validate the full system on real laparoscopic surgical videos and a physical robotic laparoscope platform. Experimental results demonstrate robust online operative-region tracking and stable autonomous endoscopy adjustment under occlusion, rapid motion, and target transitions, highlighting the effectiveness of latent surgical intent modeling for surgical autonomy.