Diffusion Transformers (DiT) have become a leading architecture in image generation. However, the quadratic complexity of attention mechanisms, which are responsible for modeling token-wise relationships, results in significant latency when generating high-resolution images. To address this issue, we aim at a linear attention mechanism in this paper that reduces the complexity of pre-trained DiTs to linear. We begin our exploration with a comprehensive summary of existing efficient attention mechanisms and identify four key factors crucial for successful linearization of pre-trained DiTs: locality, formulation consistency, high-rank attention maps, and feature integrity. Based on these insights, we introduce a convolution-like local attention strategy termed CLEAR, which limits feature interactions to a local window around each query token, and thus achieves linear complexity. Our experiments indicate that, by fine-tuning the attention layer on merely 10K self-generated samples for 10K iterations, we can effectively transfer knowledge from a pre-trained DiT to a student model with linear complexity, yielding results comparable to the teacher model. Simultaneously, it reduces attention computations by 99.5% and accelerates generation by 6.3 times for generating 8K-resolution images. Furthermore, we investigate favorable properties in the distilled attention layers, such as zero-shot generalization across various models and plugins, and improved support for multi-GPU parallel inference. Models and codes will be available.

Domain Generalization (DG) aims to enable models to generalize to unseen target domains by learning from multiple source domains. Existing DG methods primarily rely on convolutional neural networks (CNNs), which inherently learn texture biases due to their limited receptive fields, making them prone to overfitting source domains. While some works have introduced transformer-based methods (ViTs) for DG to leverage the global receptive field, these methods incur high computational costs due to the quadratic complexity of self-attention. Recently, advanced state space models (SSMs), represented by Mamba, have shown promising results in supervised learning tasks by achieving linear complexity in sequence length during training and fast RNN-like computation during inference. Inspired by this, we investigate the generalization ability of the Mamba model under domain shifts and find that input-dependent matrices within SSMs could accumulate and amplify domain-specific features, thus hindering model generalization. To address this issue, we propose a novel SSM-based architecture with saliency-based token-aware transformation (namely START), which achieves state-of-the-art (SOTA) performances and offers a competitive alternative to CNNs and ViTs. Our START can selectively perturb and suppress domain-specific features in salient tokens within the input-dependent matrices of SSMs, thus effectively reducing the discrepancy between different domains. Extensive experiments on five benchmarks demonstrate that START outperforms existing SOTA DG methods with efficient linear complexity.

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention.

Transformer is a transformative framework for deep learning which models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention mechanism. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way. Based on the equivalence between the inner product of binary codes and the Hamming distance as well as the associative property of matrix multiplication, we can approximate the attention in linear complexity by expressing it as a dot-product of binary codes. Moreover, the compact binary representations of queries and keys in EcoFormer enable us to replace most of the expensive multiply-accumulate operations in attention with simple accumulations to save considerable on-chip energy footprint on edge devices. Extensive experiments on both vision and language tasks show that EcoFormer consistently achieves comparable performance with standard attentions while consuming much fewer resources. For example, based on PVTv2-B0 and ImageNet-1K, EcoFormer achieves a 73% reduction in on-chip energy footprint with only a slight performance drop of 0.33% compared to the standard attention.

Large-scale Gaussian process inference has long faced practical challenges due to time and space complexity that is superlinear in dataset size. While sparse variational Gaussian process models are capable of learning from large-scale data, standard strategies for sparsifying the model can prevent the approximation of complex functions. In this work, we propose a novel variational Gaussian process model that decouples the representation of mean and covariance functions in reproducing kernel Hilbert space. We show that this new parametrization generalizes previous models. Furthermore, it yields a variational inference problem that can be solved by stochastic gradient ascent with time and space complexity that is only linear in the number of mean function parameters, regardless of the choice of kernels, likelihoods, and inducing points. This strategy makes the adoption of large-scale expressive Gaussian process models possible. We run several experiments on regression tasks and show that this decoupled approach greatly outperforms previous sparse variational Gaussian process inference procedures.

According to the eigenfunction's definition, we can get: null k (y,x)φ Li Zhang (lizhangfd@fudan.edu.cn) is the corresponding author with School of Data Science, Fudan In our formulation, instead of directly calculating the Gaussian kernel weights, they are approximated. More specifically, the relation between any two tokens is reconstructed via sampled bottleneck tokens. However, it turns out to suffer from a similar failure. For each model, we show the output from the first two attention heads (up and down row). Attention is all you need.

Domain Generalization (DG) aims to enable models to generalize to unseen target domains by learning from multiple source domains. Existing DG methods primarily rely on convolutional neural networks (CNNs), which inherently learn texture biases due to their limited receptive fields, making them prone to overfitting source domains. While some works have introduced transformer-based methods (ViTs) for DG to leverage the global receptive field, these methods incur high computational costs due to the quadratic complexity of self-attention. Recently, advanced state space models (SSMs), represented by Mamba, have shown promising results in supervised learning tasks by achieving linear complexity in sequence length during training and fast RNN-like computation during inference. Inspired by this, we investigate the generalization ability of the Mamba model under domain shifts and find that input-dependent matrices within SSMs could accumulate and amplify domain-specific features, thus hindering model generalization.

Transformers have demonstrated remarkable performance across diverse domains. The key component of Transformers is self-attention, which learns the relationship between any two tokens in the input sequence. Recent studies have revealed that the self-attention can be understood as a normalized adjacency matrix of a graph. Notably, from the perspective of graph signal processing (GSP), the self-attention can be equivalently defined as a simple graph filter, applying GSP using the value vector as the signal. However, the self-attention is a graph filter defined with only the first order of the polynomial matrix, and acts as a low-pass filter preventing the effective leverage of various frequency information. Consequently, existing self-attention mechanisms are designed in a rather simplified manner. Therefore, we propose a novel method, called A ttentive G raph F ilter (AGF), interpreting the self-attention as learning the graph filter in the singular value domain from the perspective of graph signal processing for directed graphs with the linear complexity w.r.t. the input length n, i.e., O p nd

Vision transformers (ViTs) have pushed the state-of-the-art for various visual recognition tasks by patch-wise image tokenization followed by self-attention. Various attempts on approximating the self-attention computation with linear complexity have been made in Natural Language Processing. However, an in-depth analysis in this work shows that they are either theoretically flawed or empirically ineffective for visual recognition. We further identify that their limitations are rooted in keeping the softmax self-attention during approximations. Specifically, conventional self-attention is computed by normalizing the scaled dot-product between token feature vectors.

Transformer is a transformative framework for deep learning which models sequential data and has achieved remarkable performance on a wide range of tasks, but with high computational and energy cost. To improve its efficiency, a popular choice is to compress the models via binarization which constrains the floating-point values into binary ones to save resource consumption owing to cheap bitwise operations significantly. However, existing binarization methods only aim at minimizing the information loss for the input distribution statistically, while ignoring the pairwise similarity modeling at the core of the attention mechanism. To this end, we propose a new binarization paradigm customized to high-dimensional softmax attention via kernelized hashing, called EcoFormer, to map the original queries and keys into low-dimensional binary codes in Hamming space. The kernelized hash functions are learned to match the ground-truth similarity relations extracted from the attention map in a self-supervised way.