Miami-based AI startup Subquadratic came out of stealth mode last month with a huge claim. It announced that it had solved a mathematical bottleneck that had been holding back large language models for almost a decade. The details were thin, and many people were unconvinced. But Subquadratic has started to bring the receipts, sharing the results of an independent evaluation of its new tech. The results suggest that the company's claims might be worth paying attention to.

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 quadratic cost of attention hinders the scalability of long-context LLMs, especially in resource-constrained settings. Existing static sparse methods such as sliding windows or global tokens utilizes the sparsity of attention to reduce the cost of attention, but poorly adapts to the content-dependent variations in attention due to their staticity. While previous work has proposed several dynamic approaches to improve flexibility, they still depend on predefined templates or heuristic mechanisms. Such strategies reduce generality and prune tokens that remain contextually important, limiting their accuracy across diverse tasks. To tackle these bottlenecks of existing methods for long-context modeling, we introduce Dynamic Hierarchical Sparse Attention (DHSA), a data-driven framework that dynamically predicts attention sparsity online without retraining. Our proposed DHSA adaptively segments sequences into variable-length chunks, then computes chunk representations by aggregating the token embeddings within each chunk. To avoid the bias introduced by varying chunk lengths, we apply length-normalized aggregation that scales the averaged embeddings by the square root of the chunk size. Finally, DHSA upsamples the chunk-level similarity scores to token level similarities to calculate importance scores that determine which token-level interactions should be preserved. Our experiments on Gemma2 with Needle-in-a-Haystack Test and LongBench show that DHSA matches dense attention in accuracy, while reducing prefill latency by 20-60% and peak memory usage by 35%. Compared to other representative baselines such as block sparse attention, DHSA achieves consistently higher accuracy (6-18% relative gains) with comparable or lower cost, offering an efficient and adaptable solution for long-context on-device LLMs.

Large Language Models (LLMs) incur quadratic attention complexity with input length, creating a major time bottleneck in the prefilling stage. Existing acceleration methods largely exploit attention score sparsity by estimating blocks with high attention scores and applying dynamic sparse attention. In this work, we identify another untapped form of sparsity in the prefilling stage, namely decoding-time contribution sparsity, where many attention blocks exhibit nontrivial attention scores during prefilling yet contribute negligibly to subsequent decoding, as indicated by gradient-based analysis. Building on this observation, we propose TriangleMix, a training-free static attention pattern that uses dense attention in a subset of layers and switches to Triangle attention in the others. Extensive experiments show that TriangleMix preserves nearly lossless performance relative to dense attention while substantially reducing attention overhead in Triangle layers. For 128K inputs, Triangle attention achieves a 15.3x speedup in attention computation, significantly exceeding the acceleration of typical dynamic sparse methods (1.9x to 3.4x). Furthermore, TriangleMix can be seamlessly combined with dynamic sparsity approaches, delivering an additional 6% to 19% reduction in TTFT over using dynamic sparsity alone.

We propose a novel type of balanced clustering algorithm to approximate attention.

Efficient long-sequence generation is a critical challenge for Large Language Models. While recent sparse decoding methods improve efficiency, they suffer from KV cache misalignment, where approximation errors accumulate and degrade generation quality. In this work, we propose Rectified Sparse Attention (ReSA), a simple yet effective method that combines block-sparse attention with periodic dense rectification. By refreshing the KV cache at fixed intervals using a dense forward pass, ReSA bounds error accumulation and preserves alignment with the pretraining distribution. Experiments across math reasoning, language modeling, and retrieval tasks demonstrate that ReSA achieves near-lossless generation quality with significantly improved efficiency. Notably, ReSA delivers up to 2.42$\times$ end-to-end speedup under decoding at 256K sequence length, making it a practical solution for scalable long-context inference. Code is available at https://aka.ms/ReSA-LM.

The integration of hardware accelerators has significantly advanced the capabilities of modern recommendation systems, enabling the exploration of complex ranking paradigms previously deemed impractical. However, the GPU-based computational costs present substantial challenges. In this paper, we demonstrate our development of an efficiency-driven approach to explore these paradigms, moving beyond traditional reliance on native PyTorch modules. We address the specific challenges posed by ranking models' dependence on categorical features, which vary in length and complicate GPU utilization. We introduce Jagged Feature Interaction Kernels, a novel method designed to extract fine-grained insights from long categorical features through efficient handling of dynamically sized tensors. We further enhance the performance of attention mechanisms by integrating Jagged tensors with Flash Attention. Our novel Jagged Flash Attention achieves up to 9x speedup and 22x memory reduction compared to dense attention. Notably, it also outperforms dense flash attention, with up to 3x speedup and 53% more memory efficiency. In production models, we observe 10% QPS improvement and 18% memory savings, enabling us to scale our recommendation systems with longer features and more complex architectures.