State Space Models (SSMs) have emerged as promising alternatives to attention mechanisms, with the Mamba architecture demonstrating impressive performance and linear complexity for processing long sequences. However, the fundamental differences between Mamba and Transformer architectures remain incompletely understood. In this work, we use carefully designed synthetic tasks to reveal Mamba's inherent limitations. Through experiments, we identify that Mamba's nonlinear convolution introduces an asymmetry bias that significantly impairs its ability to recognize symmetrical patterns and relationships. Using composite function and inverse sequence matching tasks, we demonstrate that Mamba strongly favors compositional solutions over symmetrical ones and struggles with tasks requiring the matching of reversed sequences. We show these limitations stem not from the SSM module itself but from the nonlinear convolution preceding it, which fuses token information asymmetrically. These insights provide a new understanding of Mamba's constraints and suggest concrete architectural improvements for future sequence models.

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.

Data arrives at our senses as a continuous stream, smoothly transforming from one instant to the next. These smooth transformations can be viewed as continuous symmetries of the environment that we inhabit, defining equivalence relations between stimuli over time. In machine learning, neural network architectures that respect symmetries of their data are called equivariant and have provable benefits in terms of generalization ability and sample efficiency. To date, however, equivariance has been considered only for static transformations and feed-forward networks, limiting its applicability to sequence models, such as recurrent neural networks (RNNs), and corresponding time-parameterized sequence transformations. In this work, we extend equivariant network theory to this regime of'flows' - one-parameter Lie subgroups capturing natural transformations over time, such as visual motion. We begin by showing that standard RNNs are generally not flow equivariant: their hidden states fail to transform in a geometrically structured manner for moving stimuli. We then show how flow equivariance can be introduced, and demonstrate that these models significantly outperform their non-equivariant counterparts in terms of training speed, length generalization, and velocity generalization, on both next step prediction and sequence classification. We present this work as a first step towards building sequence models that respect the time-parameterized symmetries which govern the world around us.

Classical image filters, such as those for averaging or differencing, are carefully normalized to ensure consistency, interpretability, and to avoid artifacts like intensity shifts, halos, or ringing. In contrast, convolutional filters learned end-to-end in deep networks lack such constraints. Although they may resemble wavelets and blob/edge detectors, they are not normalized in the same or any way. Consequently, when images undergo atmospheric transfer, their responses become distorted, leading to incorrect outcomes. We address this limitation by proposing filter normalization, followed by learnable scaling and shifting, akin to batch normalization. This simple yet effective modification ensures that the filters are atmosphere-equivariant, enabling co-domain symmetry. By integrating classical filtering principles into deep learning (applicable to both convolutional neural networks and convolution-dependent vision transformers), our method achieves significant improvements on artificial and natural intensity variation benchmarks. Our ResNet34 could even outperform CLIP by a large margin. Our analysis reveals that unnormalized filters degrade performance, whereas filter normalization regularizes learning, promotes diversity, and improves robustness and generalization.

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/.