Smoothness Errors in Dynamics Models and How to Avoid Them

Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly similar to those of its neighbors. Unitary graph convolutions, which are mathematically constrained to preserve smoothness, have been proposed to address this issue. Despite this, in many physical systems, such as diffusion processes, smoothness naturally increases and unitarity may be overconstraining. In this paper, we systematically study the smoothing effects of different GNNs for dynamics modeling and prove that unitary convolutions hurt performance for such tasks. We propose relaxed unitary convolutions that balance smoothness preservation with the natural smoothing required for physical systems. We also generalize unitary and relaxed unitary convolutions from graphs to meshes. In experiments on PDEs such as the heat and wave equations over complex meshes and on weather forecasting, we find that our method outperforms several strong baselines, including mesh-aware transformers and equivariant neural networks.

SpectraKAN: Conditioning Spectral Operators

Spectral neural operators, particularly Fourier Neural Operators (FNO), are a powerful framework for learning solution operators of partial differential equations (PDEs) due to their efficient global mixing in the frequency domain. However, existing spectral operators rely on static Fourier kernels applied uniformly across inputs, limiting their ability to capture multi-scale, regime-dependent, and anisotropic dynamics governed by the global state of the system. We introduce SpectraKAN, a neural operator that conditions the spectral operator on the input itself, turning static spectral convolution into an input-conditioned integral operator. This is achieved by extracting a compact global representation from spatio-temporal history and using it to modulate a multi-scale Fourier trunk via single-query cross-attention, enabling the operator to adapt its behaviour while retaining the efficiency of spectral mixing. We provide theoretical justification showing that this modulation converges to a resolution-independent continuous operator under mesh refinement and KAN gives smooth, Lipschitz-controlled global modulation. Across diverse PDE benchmarks, SpectraKAN achieves state-of-the-art performance, reducing RMSE by up to 49% over strong baselines, with particularly large gains on challenging spatio-temporal prediction tasks.

Pruning for Generalization: A Transfer-Oriented Spatiotemporal Graph Framework

Multivariate time series forecasting in graph-structured domains is critical for real-world applications, yet existing spatiotemporal models often suffer from performance degradation under data scarcity and cross-domain shifts. We address these challenges through the lens of structure-aware context selection. We propose TL-GPSTGN, a transfer-oriented spatiotemporal framework that enhances sample efficiency and out-of-distribution generalization by selectively pruning non-optimized graph context. Specifically, our method employs information-theoretic and correlation-based criteria to extract structurally informative subgraphs and features, resulting in a compact, semantically grounded representation. This optimized context is subsequently integrated into a spatiotemporal convolutional architecture to capture complex multivariate dynamics. Evaluations on large-scale traffic benchmarks demonstrate that TL-GPSTGN consistently outperforms baselines in low-data transfer scenarios. Our findings suggest that explicit context pruning serves as a powerful inductive bias for improving the robustness of graph-based forecasting models.

Convolution Operator Network for Forward and Inverse Problems (FI-Conv): Application to Plasma Turbulence Simulations

We propose the Convolutional Operator Network for Forward and Inverse Problems (FI-Conv), a framework capable of predicting system evolution and estimating parameters in complex spatio-temporal dynamics, such as turbulence. FI-Conv is built on a U-Net architecture, in which most convolutional layers are replaced by ConvNeXt V2 blocks. This design preserves U-Net performance on inputs with high-frequency variations while maintaining low computational complexity. FI-Conv uses an initial state, PDE parameters, and evolution time as input to predict the system future state. As a representative example of a system exhibiting complex dynamics, we evaluate the performance of FI-Conv on the task of predicting turbulent plasma fields governed by the Hasegawa-Wakatani (HW) equations. The HW system models two-dimensional electrostatic drift-wave turbulence and exhibits strongly nonlinear behavior, making accurate approximation and long-term prediction particularly challenging. Using an autoregressive forecasting procedure, FI-Conv achieves accurate forward prediction of the plasma state evolution over short times (t ~ 3) and captures the statistic properties of derived physical quantities of interest over longer times (t ~ 100). Moreover, we develop a gradient-descent-based inverse estimation method that accurately infers PDE parameters from plasma state evolution data, without modifying the trained model weights. Collectively, our results demonstrate that FI-Conv can be an effective alternative to existing physics-informed machine learning methods for systems with complex spatio-temporal dynamics.

Dynamic High-frequency Convolution for Infrared Small Target Detection

Infrared small targets are typically tiny and locally salient, which belong to high-frequency components (HFCs) in images. Single-frame infrared small target (SIRST) detection is challenging, since there are many HFCs along with targets, such as bright corners, broken clouds, and other clutters. Current learning-based methods rely on the powerful capabilities of deep networks, but neglect explicit modeling and discriminative representation learning of various HFCs, which is important to distinguish targets from other HFCs. To address the aforementioned issues, we propose a dynamic high-frequency convolution (DHiF) to translate the discriminative modeling process into the generation of a dynamic local filter bank. Especially, DHiF is sensitive to HFCs, owing to the dynamic parameters of its generated filters being symmetrically adjusted within a zero-centered range according to Fourier transformation properties. Combining with standard convolution operations, DHiF can adaptively and dynamically process different HFC regions and capture their distinctive grayscale variation characteristics for discriminative representation learning. DHiF functions as a drop-in replacement for standard convolution and can be used in arbitrary SIRST detection networks without significant decrease in computational efficiency. To validate the effectiveness of our DHiF, we conducted extensive experiments across different SIRST detection networks on real-scene datasets. Compared to other state-of-the-art convolution operations, DHiF exhibits superior detection performance with promising improvement. Codes are available at https://github.com/TinaLRJ/DHiF.

High-Resolution Underwater Camouflaged Object Detection: GBU-UCOD Dataset and Topology-Aware and Frequency-Decoupled Networks

Underwater Camouflaged Object Detection (UCOD) is a challenging task due to the extreme visual similarity between targets and backgrounds across varying marine depths. Existing methods often struggle with topological fragmentation of slender creatures in the deep sea and the subtle feature extraction of transparent organisms. In this paper, we propose DeepTopo-Net, a novel framework that integrates topology-aware modeling with frequency-decoupled perception. To address physical degradation, we design the Water-Conditioned Adaptive Perceptor (WCAP), which employs Riemannian metric tensors to dynamically deform convolutional sampling fields. Furthermore, the Abyssal-Topology Refinement Module (ATRM) is developed to maintain the structural connectivity of spindly targets through skeletal priors. Specifically, we first introduce GBU-UCOD, the first high-resolution (2K) benchmark tailored for marine vertical zonation, filling the data gap for hadal and abyssal zones. Extensive experiments on MAS3K, RMAS, and our proposed GBU-UCOD datasets demonstrate that DeepTopo-Net achieves state-of-the-art performance, particularly in preserving the morphological integrity of complex underwater patterns. The datasets and codes will be released at https://github.com/Wuwenji18/GBU-UCOD.

DMS2F-HAD: A Dual-branch Mamba-based Spatial-Spectral Fusion Network for Hyperspectral Anomaly Detection

Hyperspectral anomaly detection (HAD) aims to identify rare and irregular targets in high-dimensional hyperspectral images (HSIs), which are often noisy and unlabelled data. Existing deep learning methods either fail to capture long-range spectral dependencies (e.g., convolutional neural networks) or suffer from high computational cost (e.g., Transformers). To address these challenges, we propose DMS2F-HAD, a novel dual-branch Mamba-based model. Our architecture utilizes Mamba's linear-time modeling to efficiently learn distinct spatial and spectral features in specialized branches, which are then integrated by a dynamic gated fusion mechanism to enhance anomaly localization. Across fourteen benchmark HSI datasets, our proposed DMS2F-HAD not only achieves a state-of-the-art average AUC of 98.78%, but also demonstrates superior efficiency with an inference speed 4.6 times faster than comparable deep learning methods. The results highlight DMS2FHAD's strong generalization and scalability, positioning it as a strong candidate for practical HAD applications.

Causal Graph Spatial-Temporal Autoencoder for Reliable and Interpretable Process Monitoring

To improve the reliability and interpretability of industrial process monitoring, this article proposes a Causal Graph Spatial-Temporal Autoencoder (CGSTAE). The network architecture of CGSTAE combines two components: a correlation graph structure learning module based on spatial self-attention mechanism (SSAM) and a spatial-temporal encoder-decoder module utilizing graph convolutional long-short term memory (GCLSTM). The SSAM learns correlation graphs by capturing dynamic relationships between variables, while a novel three-step causal graph structure learning algorithm is introduced to derive a causal graph from these correlation graphs. The algorithm leverages a reverse perspective of causal invariance principle to uncover the invariant causal graph from varying correlations. The spatial-temporal encoder-decoder, built with GCLSTM units, reconstructs time-series process data within a sequence-to-sequence framework. The proposed CGSTAE enables effective process monitoring and fault detection through two statistics in the feature space and residual space. Finally, we validate the effectiveness of CGSTAE in process monitoring through the Tennessee Eastman process and a real-world air separation process.

On the Spatiotemporal Dynamics of Generalization in Neural Networks

Why do neural networks fail to generalize addition from 16-digit to 32-digit numbers, while a child who learns the rule can apply it to arbitrarily long sequences? We argue that this failure is not an engineering problem but a violation of physical postulates. Drawing inspiration from physics, we identify three constraints that any generalizing system must satisfy: (1) Locality -- information propagates at finite speed; (2) Symmetry -- the laws of computation are invariant across space and time; (3) Stability -- the system converges to discrete attractors that resist noise accumulation. From these postulates, we derive -- rather than design -- the Spatiotemporal Evolution with Attractor Dynamics (SEAD) architecture: a neural cellular automaton where local convolutional rules are iterated until convergence. Experiments on three tasks validate our theory: (1) Parity -- demonstrating perfect length generalization via light-cone propagation; (2) Addition -- achieving scale-invariant inference from L=16 to L=1 million with 100% accuracy, exhibiting input-adaptive computation; (3) Rule 110 -- learning a Turing-complete cellular automaton without trajectory divergence. Our results suggest that the gap between statistical learning and logical reasoning can be bridged -- not by scaling parameters, but by respecting the physics of computation.

LoopViT: Scaling Visual ARC with Looped Transformers

Recent advances in visual reasoning have leveraged vision transformers to tackle the ARC-AGI benchmark. However, we argue that the feed-forward architecture, where computational depth is strictly bound to parameter size, falls short of capturing the iterative, algorithmic nature of human induction. In this work, we propose a recursive architecture called Loop-ViT, which decouples reasoning depth from model capacity through weight-tied recurrence. Loop-ViT iterates a weight-tied Hybrid Block, combining local convolutions and global attention, to form a latent chain of thought. Crucially, we introduce a parameter-free Dynamic Exit mechanism based on predictive entropy: the model halts inference when its internal state ``crystallizes" into a low-uncertainty attractor. Empirical results on the ARC-AGI-1 benchmark validate this perspective: our 18M model achieves 65.8% accuracy, outperforming massive 73M-parameter ensembles. These findings demonstrate that adaptive iterative computation offers a far more efficient scaling axis for visual reasoning than simply increasing network width. The code is available at https://github.com/WenjieShu/LoopViT.