We thank the reviewers for insightful remarks and comments that help to considerably improve our manuscript. We1 address the most important ones in detail below. Before doing so, we highlight a comment from R3 in order to make an2 important clarification about the scope of our contribution. "It is well known that an attention mechanism would reduce3 gradient vanishing. It feels trivial to me as there is a direct connection for gradients to pass. We are in complete agreement and recognize that the very mechanism of (self-)attention was designed to improve6 gradient propagation over long sequences, and that sparsity is a good way to keep complexity costs low. Much like work from the '90s established formal results for gradient exploding/vanishing in deep/recurrent networks, we9 believe it is crucial to establish similar theoretical tools for attention mechanisms, as these methods are under intense10 development where scalability and complexity are important issues. The proposed relevancy mechanism and accompanying experiments,14 building on established work, are meant to illustrate how our theorems can be concretely exploited. We chose simple15 tasks for their ease of interpretation, and their variety of computational demands (memorization, prediction, RL, etc.).16 As is clearly indicated in the text, it is not our goal to propose this method "as is" in a race for state-of-the-art. Werecognize thatreviewersmay have basedtheir evaluation asthey wouldhavein amethod paper, and we20 kindly invite them to reconsider the value of our experiments in the broader context of our theoretical contributions. We21 also thank reviewers for their additional minor comments not explicitly addressed here and agree to implement them.22 R1: Q"The authors didn't spell out the relation between κ and d: higher κ tends to have smaller d.

We collected about 30 million text-image pairs from multiple channels, and built a 2.5TB new dataset (after tokenization, the size becomes about 250GB). The sources of data are basically classified into the following categories: (1) Professional image websites (both English and Chinese). The images in the websites are usually with captions. We have already introduced tokenizers in section 2.2, and here are some details. Colored grids are all the tokens attended to by the token marked "O".

Wireframe parsing aims to recover line segments and their junctions to form a structured geometric representation useful for downstream tasks such as Simultaneous Localization and Mapping (SLAM). Existing methods predict lines and junctions separately and reconcile them post-hoc, causing mismatches and reduced robustness. We present Co-PLNet, a point-line collaborative framework that exchanges spatial cues between the two tasks, where early detections are converted into spatial prompts via a Point-Line Prompt Encoder (PLP-Encoder), which encodes geometric attributes into compact and spatially aligned maps. A Cross-Guidance Line Decoder (CGL-Decoder) then refines predictions with sparse attention conditioned on complementary prompts, enforcing point-line consistency and efficiency. Experiments on Wireframe and YorkUrban show consistent improvements in accuracy and robustness, together with favorable real-time efficiency, demonstrating our effectiveness for structured geometry perception.

Emergence is a fascinating property of large language models and neural networks more broadly: as models scale and train for longer, they sometimes develop new abilities in sudden ways. Despite initial studies, we still lack a comprehensive understanding of how and when these abilities emerge. To address this gap, we study the emergence over training of sparse attention, a critical and frequently observed attention pattern in Transformers. By combining theoretical analysis of a toy model with empirical observations on small Transformers trained on a linear regression variant, we uncover the mechanics driving sparse attention emergence and reveal that emergence timing follows power laws based on task structure, architecture, and optimizer choice. We additionally find that repetition can greatly speed up emergence. Finally, we confirm these results on a well-studied in-context associative recall task. Our findings provide a simple, theoretically grounded framework for understanding how data distributions and model design influence the learning dynamics behind one form of emergence.

Long video generation is fundamentally a long context memory problem: models must retain and retrieve salient events across a long range without collapsing or drifting. However, scaling diffusion transformers to generate long-context videos is fundamentally limited by the quadratic cost of self-attention, which makes memory and computation intractable and difficult to optimize for long sequences. We recast long-context video generation as an internal information retrieval task and propose a simple, learnable sparse attention routing module, Mixture of Contexts (MoC), as an effective long-term memory retrieval engine. In MoC, each query dynamically selects a few informative chunks plus mandatory anchors (caption, local windows) to attend to, with causal routing that prevents loop closures. As we scale the data and gradually sparsify the routing, the model allocates compute to salient history, preserving identities, actions, and scenes over minutes of content. Efficiency follows as a byproduct of retrieval (near-linear scaling), which enables practical training and synthesis, and the emergence of memory and consistency at the scale of minutes.

Recent advances in diffusion models have enabled high-quality video generation, but the additional temporal dimension significantly increases computational costs, making training and inference on long videos prohibitively expensive. In this paper, we identify a phenomenon we term Spatiotemporal Energy Decay in video diffusion models: post-softmax attention scores diminish as spatial and temporal distance between tokens increase, akin to the physical decay of signal or waves over space and time in nature. Motivated by this, we propose Radial Attention, a scalable sparse attention mechanism with $\mathcal{O}(n \log n)$ complexity that translates energy decay into exponentially decaying compute density, which is significantly more efficient than standard $\mathcal{O}(n^2)$ dense attention and more expressive than linear attention. Specifically, Radial Attention employs a simple, static attention mask where each token attends to spatially nearby tokens, with the attention window size shrinking with temporal distance. Moreover, it allows pre-trained video diffusion models to extend their generation length with efficient LoRA-based fine-tuning. Extensive experiments show that Radial Attention maintains video quality across Wan2.1-14B, HunyuanVideo, and Mochi 1, achieving up to a 1.9$\times$ speedup over the original dense attention. With minimal tuning, it enables video generation up to 4$\times$ longer while reducing training costs by up to 4.4$\times$ compared to direct fine-tuning and accelerating inference by up to 3.7$\times$ compared to dense attention inference. Code is released at \href{https://github.com/mit-han-lab/radial-attention}{https://github.com/mit-han-lab/radial-attention}.

The computational demands of modern Deep Neural Networks (DNNs) are immense and constantly growing. While training costs usually capture public attention, inference demands are also contributing in significant computational, energy and environmental footprints. Sparsity stands out as a critical mechanism for drastically reducing these resource demands. However, its potential remains largely untapped and is not yet fully incorporated in production AI systems. To bridge this gap, this work provides the necessary knowledge and insights for performance engineers keen to get involved in deep learning inference optimization. In particular, in this work we: a) discuss the various forms of sparsity that can be utilized in DNN inference, b) explain how the original dense computations translate to sparse kernels, c) provide an extensive bibliographic review of the state-of-the-art in the implementation of these kernels for CPUs and GPUs, d) discuss the availability of sparse datasets in support of sparsity-related research and development, e) explore the current software tools and frameworks that provide robust sparsity support, and f) present evaluation results of different implementations of the key SpMM and SDDMM kernels on CPU and GPU platforms. Ultimately, this paper aims to serve as a resource for performance engineers seeking to develop and deploy highly efficient sparse deep learning models in productions.

In remote sensing applications, such as disaster detection and response, real-time efficiency and model lightweighting are of critical importance. Consequently, existing remote sensing image super-resolution methods often face a trade-off between model performance and computational efficiency. In this paper, we propose a lightweight super-resolution framework for remote sensing imagery, named HIMOSA. Specifically, HIMOSA leverages the inherent redundancy in remote sensing imagery and introduces a content-aware sparse attention mechanism, enabling the model to achieve fast inference while maintaining strong reconstruction performance. Furthermore, to effectively leverage the multi-scale repetitive patterns found in remote sensing imagery, we introduce a hierarchical window expansion and reduce the computational complexity by adjusting the sparsity of the attention. Extensive experiments on multiple remote sensing datasets demonstrate that our method achieves state-of-the-art performance while maintaining computational efficiency.

Reasoning language models have demonstrated remarkable capabilities on challenging tasks by generating elaborate chain-of-thought (CoT) solutions. However, such lengthy generation shifts the inference bottleneck from compute-bound to memory-bound. To generate each token, the model applies full attention to all previously generated tokens, requiring memory access to an increasingly large KV-Cache. Consequently, longer generations demand more memory access for every step, leading to substantial pressure on memory bandwidth. To address this, we introduce SparseSpec, a speculative decoding framework that reuses the same model as the draft and target models (i.e., self-speculation). SparseSpec features a novel sparse attention mechanism, PillarAttn, as the draft model, which accurately selects critical tokens via elegantly reusing information from the verification stage. Furthermore, SparseSpec co-designs self-speculation with three system innovations: (1) a unified scheduler to batch token drafting and verification, (2) delayed verification for CPU/GPU overlap, and (3) dynamic KV-Cache management to maximize memory utilization. Across various models and datasets, SparseSpec outperforms state-of-the-art solutions, with an up to 2.13x throughput speedup.

This work explores the challenge of building "Machines that Can Remember", framing long-term memory as the problem of efficient ultra-long context modeling. We argue that this requires three key properties: sparsity, random-access flexibility, and length generalization. To address ultra-long-context modeling, we leverage Hierarchical Sparse Attention (HSA), a novel attention mechanism that satisfies all three properties. We integrate HSA into Transformers to build HSA-UltraLong, which is an 8B-parameter MoE model trained on over 8 trillion tokens and is rigorously evaluated on different tasks with in-domain and out-of-domain context lengths to demonstrate its capability in handling ultra-long contexts. Results show that our model performs comparably to full-attention baselines on in-domain lengths while achieving over 90% accuracy on most in-context retrieval tasks with contexts up to 16M. This report outlines our experimental insights and open problems, contributing a foundation for future research in ultra-long context modeling. Figure 1: Despite being pre-trained with an 8K context window and mid-trained up to 32K, HSA-UltraLong achieves near-perfect accuracy on S-NIAH even at a 16M-token context length. The red dashed line at 32K marks the boundary between in-domain (left) and out-of-domain (right).