Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.

Diffusion Transformer (DiT), a promising diffusion model for visual generation, demonstrates impressive performance but incurs significant computational overhead. Intriguingly, analysis of pre-trained DiT models reveals that global selfattention is often redundant, predominantly capturing local patterns--highlighting the potential for more efficient alternatives. In this paper, we revisit convolution as an alternative building block for constructing efficient and expressive diffusion models. However, naively replacing self-attention with convolution typically results in degraded performance. Our investigations attribute this performance gap to the higher channel redundancy in ConvNets compared to Transformers. To resolve this, we introduce a compact channel attention mechanism that promotes the activation of more diverse channels, thereby enhancing feature diversity.

In this work, we explore the trade-offs of explicit structural priors, particularly group-equivariance. We address this through theoretical analysis and a comprehensive empirical study focusing on point clouds. To enable controlled and fair comparisons, we introduce Rapidash, a unified group convolutional architecture that allows for different variants of equivariant and non-equivariant models. Our results suggest that more constrained equivariant models outperform less constrained alternatives when aligned with the geometry of the task, and increasing representation capacity does not fully eliminate performance gaps. We see improved performance of models with equivariance and symmetry-breaking through tasks like segmentation, regression, and generation across diverse datasets. Explicit symmetry breaking via geometric reference frames consistently improves performance, while breaking equivariance through geometric input features can be helpful when aligned with task geometry. Our results provide task-specific performance trends that offer a more nuanced way for model selection.

Depthwise-separable convolution has emerged as a significant milestone in the lightweight development of Convolutional Neural Networks (CNNs) over the past decade. This technique consists of two key components: depthwise convolution, which captures spatial information, and pointwise convolution, which enhances channel interactions. In this paper, we propose a novel method to lightweight CNNs through the discretization of Ordinary Differential Equations (ODEs). Specifically, we optimize depthwise-separable convolution by replacing the pointwise convolution with a discrete ODE module, termed the Channelwise ODESolver (COS). The COS module is constructed by a simple yet efficient direct differentiation Euler algorithm, using learnable increment parameters. This replacement reduces parameters by over 98.36% compared to conventional pointwise convolution. By integrating COS into MobileNet, we develop a new extra lightweight network called MobileODE. With carefully designed basic and inverse residual blocks, the resulting MobileODEV1 and MobileODEV2 reduce channel interaction parameters by 71.0% and 69.2%, respectively, compared to MobileNetV1, while achieving higher accuracy across various tasks, including image classification, object detection, and semantic segmentation.

Point Cloud Few-Shot Semantic Segmentation (PC-FSS) aims to segment unknown categories in query samples using only a small number of annotated support samples. However, scene complexity and insufficient representation of local geometric structures pose significant challenges to PC-FSS. To address these issues, we propose a novel pre-training-free Visual Introspective Prototype Segmentation network (VIP-Seg). Specifically, we design a Visual Introspective Prototype (VIP) module that employs a multi-step reasoning approach to tackle intra-class diversity and domain gaps between support and query sets. The VIP module consists of a Prototype Enhancement Module (PEM) and a Prototype Difference Module (PDM), which work alternately to progressively refine prototypes. The PEM enhances prototype discriminability and reduces intra-class diversity, while the PDM learns common representations from the differences between query and support features, effectively eliminating semantic inconsistencies caused by domain gaps. To further reduce intra-class diversity and enhance point discriminative ability, we propose a Dynamic Power Convolution (DyPowerConv) that leverages learnable power functions to effectively capture local geometric structures and detailed features of point clouds. Extensive experiments on S3DIS and ScanNet demonstrate that our proposed VIP-Seg significantly outperforms current state-of-the-art methods, proving its effectiveness in PC-FSS tasks.

The advent of foundation models in AI has significantly advanced general-purpose learning, enabling remarkable capabilities in zero-shot inference and in-context learning. However, training such models on physics data, including solutions to partial differential equations (PDEs), poses a unique challenge due to varying dimensionalities across different systems. Traditional approaches either fix a maximum dimension or employ separate encoders for different dimensionalities, resulting in inefficiencies. To address this, we propose a dimension-agnostic neural network architecture, the Axial Neural Network (XNN), inspired by parametersharing structures such as Deep Sets and Graph Neural Networks.

Photorealistic Codec Avatars (PCA), which generate high-fidelity human face renderings, are increasingly being used in Virtual Reality (VR) environments to enable immersive communication and interaction through deep learning-based generative models. However, these models impose significant computational demands, making real-time inference challenging on resource-constrained VR devices such as head-mounted displays (HMDs), where latency and power efficiency are critical. To address this challenge, we propose an efficient post-training quantization (PTQ) method tailored for Codec Avatar models, enabling low-precision execution without compromising output quality. In addition, we design a custom hardware accelerator that can be integrated into the system-on-chip (SoC) of VR devices to further enhance processing efficiency. Building on these components, we introduce ESCA, a full-stack optimization framework that accelerates PCA inference on edge VR platforms. Experimental results demonstrate that ESCA boosts FovVideoVDP quality scores by up to +0.39 over the best 4-bit baseline, delivers up to 3.36 latency reduction, and sustains a rendering rate of 100 frames per second in endto-end tests, satisfying real-time VR requirements. These results demonstrate the feasibility of deploying high-fidelity codec avatars on resource-constrained devices, opening the door to more immersive and portable VR experiences. Paper website can be found at https://zmzfpc.github.io/ESCA/.

Image restoration aims to recover sharp, high-quality images from degraded, lowquality inputs. Existing methods have progressively advanced from task-specific designs to general architectures, all-in-one frameworks, and composite degradation handling. Despite these advances, computational efficiency remains a critical factor for practical deployment. In this work, we present BioIR, an efficient and universal image restoration framework inspired by the human visual system. Specifically, we design two bio-inspired modules, Peripheral-to-Foveal (P2F) and Foveal-to-Peripheral (F2P), to emulate the perceptual processes of human vision, with a particular focus on the functional interplay between foveal and peripheral pathways. P2F delivers large-field contextual signals to foveal regions based on pixel-to-region affinity, while F2P propagates fine-grained spatial details through a static-to-dynamic two-stage integration strategy. Leveraging the biologically motivated design, BioIR achieves state-of-the-art performance across three representative image restoration settings: single-degradation, all-in-one, and composite degradation. Moreover, BioIR maintains high computational efficiency and fast inference speed, making it highly suitable for real-world applications. The code and pre-trained models are available at https://github.com/c-yn/BioIR.

Spiking Neural Networks (SNNs) are distinguished from Artificial Neural Networks (ANNs) for their complex neuronal dynamics and sparse binary activations (spikes) inspired by the biological neural system. Traditional neuron models use iterative step-by-step dynamics, resulting in serial computation and slow training speed of SNNs. Recently, parallelizable spiking neuron models have been proposed to fully utilize the massive parallel computing ability of graphics processing units to accelerate the training of SNNs. However, existing parallelizable spiking neuron models involve dense floating operations and can only achieve high long-term dependencies learning ability with a large order at the cost of huge computational and memory costs. To solve the dilemma of performance and costs, we propose the mul-free channel-wise Parallel Spiking Neuron, which is hardware-friendly and suitable for SNNs' resource-restricted application scenarios.

We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.