Recent research has shown that Transformers with linear attention are capable of in-context learning (ICL) by implementing a linear estimator through gradient descent steps. However, the existing results on the optimization landscape apply under stylized settings where task and feature vectors are assumed to be IID and the attention weights are fully parameterized. In this work, we develop a stronger characterization of the optimization and generalization landscape of ICL through contributions on architectures, low-rank parameterization, and correlated designs: (1) We study the landscape of 1-layer linear attention and 1-layer H3, a state-space model. Under a suitable correlated design assumption, we prove that both implement 1-step preconditioned gradient descent. We show that thanks to its native convolution filters, H3 also has the advantage of implementing sample weighting and outperforming linear attention in suitable settings.

Vision transformer model (ViT) is widely used and performs well in vision tasks due to its ability to capture long-range dependencies. However, the time complexity and memory consumption increase quadratically with the number of input patches which limits the usage of ViT in real-world applications. Previous methods have employed linear attention to mitigate the complexity of the original self-attention mechanism at the expense of effectiveness. In this paper, we propose QT-ViT models that improve the previous linear self-attention using quadratic Taylor expansion. Specifically, we substitute the softmax-based attention with second-order Taylor expansion, and then accelerate the quadratic expansion by reducing the time complexity with a fast approximation algorithm. The proposed method capitalizes on the property of quadratic expansion to achieve superior performance while employing linear approximation for fast inference. Compared to previous studies of linear attention, our approach does not necessitate knowledge distillation or high-order attention residuals to facilitate the training process. Extensive experiments demonstrate the efficiency and effectiveness of the proposed QT-ViTs, showcasing the state-of-the-art results. Particularly, the proposed QT-ViTs consistently surpass the previous SOTA EfficientViTs under different model sizes, and achieve a new Pareto-front in terms of accuracy and speed.

Widely adopted in modern Vision Transformer designs, Softmax attention can effectively capture long-range visual information; however, it incurs excessive computational cost when dealing with high-resolution inputs. In contrast, linear attention naturally enjoys linear complexity and has great potential to scale up to higher-resolution images. Nonetheless, the unsatisfactory performance of linear attention greatly limits its practical application in various scenarios. In this paper, we take a step forward to close the gap between the linear and Softmax attention with novel theoretical analyses, which demystify the core factors behind the performance deviations. Specifically, we present two key perspectives to understand and alleviate the limitations of linear attention: the injective property and the local modeling ability. Firstly, we prove that linear attention is not injective, which is prone to assign identical attention weights to different query vectors, thus adding to severe semantic confusion since different queries correspond to the same outputs. Secondly, we confirm that effective local modeling is essential for the success of Softmax attention, in which linear attention falls short. The aforementioned two fundamental differences significantly contribute to the disparities between these two attention paradigms, which is demonstrated by our substantial empirical validation in the paper. In addition, more experiment results indicate that linear attention, as long as endowed with these two properties, can outperform Softmax attention across various tasks while maintaining lower computation complexity.

Softmax attention is a central component of transformer architectures, yet its nonlinear structure poses significant challenges for theoretical analysis. We develop a unified, measure-based framework for studying single-layer softmax attention under both finite and infinite prompts. For i.i.d. Gaussian inputs, we lean on the fact that the softmax operator converges in the infinite-prompt limit to a linear operator acting on the underlying input-token measure. Building on this insight, we establish non-asymptotic concentration bounds for the output and gradient of softmax attention, quantifying how rapidly the finite-prompt model approaches its infinite-prompt counterpart, and prove that this concentration remains stable along the entire training trajectory in general in-context learning settings with sub-Gaussian tokens. In the case of in-context linear regression, we use the tractable infinite-prompt dynamics to analyze training at finite prompt length. Our results allow optimization analyses developed for linear attention to transfer directly to softmax attention when prompts are sufficiently long, showing that large-prompt softmax attention inherits the analytical structure of its linear counterpart. This, in turn, provides a principled and broadly applicable toolkit for studying the training dynamics and statistical behavior of softmax attention layers in large prompt regimes.

Scaling attention faces a critical bottleneck: the $\mathcal{O}(n^2)$ quadratic computational cost of softmax attention, which limits its application in long-sequence domains. While linear attention mechanisms reduce this cost to $\mathcal{O}(n)$, they typically rely on fixed random feature maps, such as random Fourier features or hand-crafted functions. This reliance on static, data-agnostic kernels creates a fundamental trade-off, forcing practitioners to sacrifice significant model accuracy for computational efficiency. We introduce \textsc{LUNA}, a kernelized linear attention mechanism that eliminates this trade-off, retaining linear cost while matching and surpassing the accuracy of quadratic attention. \textsc{LUNA} is built on the key insight that the kernel feature map itself should be learned rather than fixed a priori. By parameterizing the kernel, \textsc{LUNA} learns a feature basis tailored to the specific data and task, overcoming the expressive limitations of fixed-feature methods. \textsc{Luna} implements this with a learnable feature map that induces a positive-definite kernel and admits a streaming form, yielding linear time and memory scaling in the sequence length. Empirical evaluations validate our approach across diverse settings. On the Long Range Arena (LRA), \textsc{Luna} achieves state-of-the-art average accuracy among efficient Transformers under compute parity, using the same parameter count, training steps, and approximate FLOPs. \textsc{Luna} also excels at post-hoc conversion: replacing softmax in fine-tuned BERT and ViT-B/16 checkpoints and briefly fine-tuning recovers most of the original performance, substantially outperforming fixed linearizations.

Window attention and linear attention represent two principal strategies for mitigating the quadratic complexity and ever-growing KV cache in Vision-Language Models (VLMs). However, we observe that window-based VLMs suffer performance degradation when sequence length exceeds the window size, while linear attention underperforms on information-intensive tasks such as OCR and document understanding. To overcome these limitations, we propose InfiniteVL, a linear-complexity VLM architecture that synergizes sliding window attention (SWA) with Gated DeltaNet. For achieving competitive multimodal performance under constrained resources, we design a three-stage training strategy comprising distillation pretraining, instruction tuning, and long-sequence SFT. Remarkably, using less than 2\% of the training data required by leading VLMs, InfiniteVL not only substantially outperforms previous linear-complexity VLMs but also matches the performance of leading Transformer-based VLMs, while demonstrating effective long-term memory retention. Compared to similar-sized Transformer-based VLMs accelerated by FlashAttention-2, InfiniteVL achieves over 3.6\times inference speedup while maintaining constant latency and memory footprint. In streaming video understanding scenarios, it sustains a stable 24 FPS real-time prefill speed while preserving long-term memory cache. Code and models are available at https://github.com/hustvl/InfiniteVL.

Traditional Transformers face a major bottleneck in long-sequence time series forecasting due to their quadratic complexity $(\mathcal{O}(T^2))$ and their limited ability to effectively exploit frequency-domain information. Inspired by RWKV's $\mathcal{O}(T)$ linear attention and frequency-domain modeling, we propose FRWKV, a frequency-domain linear-attention framework that overcomes these limitations. Our model integrates linear attention mechanisms with frequency-domain analysis, achieving $\mathcal{O}(T)$ computational complexity in the attention path while exploiting spectral information to enhance temporal feature representations for scalable long-sequence modeling. Across eight real-world datasets, FRWKV achieves a first-place average rank. Our ablation studies confirm the critical roles of both the linear attention and frequency-encoder components. This work demonstrates the powerful synergy between linear attention and frequency analysis, establishing a new paradigm for scalable time series modeling. Code is available at this repository: https://github.com/yangqingyuan-byte/FRWKV.

Experimental results corroborate our theoretical findings.

Recurrent Neural Networks (RNNs) have been considered as more efficient alternatives.

Mamba is an effective state space model with linear computation complexity.