Unsupervised feature selection (UFS) is widely applied in machine learning and pattern recognition. However, most of the existing methods only consider a single sparsity, which makes it difficult to select valuable and discriminative feature subsets from the original high-dimensional feature set. In this paper, we propose a new UFS method called DSCOFS via embedding double sparsity constrained optimization into the classical principal component analysis (PCA) framework. Double sparsity refers to using $\ell_{2,0}$-norm and $\ell_0$-norm to simultaneously constrain variables, by adding the sparsity of different types, to achieve the purpose of improving the accuracy of identifying differential features. The core is that $\ell_{2,0}$-norm can remove irrelevant and redundant features, while $\ell_0$-norm can filter out irregular noisy features, thereby complementing $\ell_{2,0}$-norm to improve discrimination. An effective proximal alternating minimization method is proposed to solve the resulting nonconvex nonsmooth model. Theoretically, we rigorously prove that the sequence generated by our method globally converges to a stationary point. Numerical experiments on three synthetic datasets and eight real-world datasets demonstrate the effectiveness, stability, and convergence of the proposed method. In particular, the average clustering accuracy (ACC) and normalized mutual information (NMI) are improved by at least 3.34% and 3.02%, respectively, compared with the state-of-the-art methods. More importantly, two common statistical tests and a new feature similarity metric verify the advantages of double sparsity. All results suggest that our proposed DSCOFS provides a new perspective for feature selection.

Utilizing longer contexts is increasingly essential to power better AI systems. However, the cost of attending to long contexts is high due to the involved softmax computation. While the scaled dot-product attention (SDPA) exhibits token sparsity, with only a few pivotal tokens significantly contributing to attention, leveraging this sparsity effectively remains an open challenge. Previous methods either suffer from model degradation or require considerable additional resources. We propose HashAttention --a principled approach casting pivotal token identification as a recommendation problem. Given a query, HashAttention encodes keys and queries in Hamming space capturing the required semantic similarity using learned mapping functions. HashAttention efficiently identifies pivotal tokens for a given query in this Hamming space using bitwise operations, and only these pivotal tokens are used for attention computation, significantly improving overall attention efficiency. HashAttention can reduce the number of tokens used by a factor of $1/32\times$ for the Llama-3.1-8B model with LongBench, keeping average quality loss within 0.6 points, while using only 32 bits per token auxiliary memory. At $32\times$ sparsity, HashAttention is $3{-}6\times$ faster than LightLLM and $2.5{-}4.5\times$ faster than gpt-fast on Nvidia-L4 GPU.

The inference process for large language models is slow and memory-intensive, with one of the most critical bottlenecks being excessive Key-Value (KV) cache accesses. This paper introduces "Double Sparsity," a novel post-training sparse attention technique designed to alleviate this bottleneck by reducing KV cache access. Double Sparsity combines token sparsity, which focuses on utilizing only the important tokens for computing self-attention, with channel sparsity, an approach that uses important feature channels for identifying important tokens. Our key insight is that the pattern of channel sparsity is relatively static, allowing us to use offline calibration to make it efficient at runtime, thereby enabling accurate and efficient identification of important tokens. Moreover, this method can be combined with offloading to achieve significant memory usage reduction. Experimental results demonstrate that Double Sparsity can achieve $\frac{1}{16}$ token and channel sparsity with minimal impact on accuracy across various tasks, including wiki-2 perplexity, key-value retrieval, and long context benchmarks with models including Llama-2-7B, Llama-2-70B, and Mixtral-8x7B. It brings up to a 14.1$\times$ acceleration in attention operations and a 1.9$\times$ improvement in end-to-end inference on GPUs. With offloading, it achieves a decoding speed acceleration of 16.3$\times$ compared to state-of-the-art solutions at a sequence length of 256K. Our code is publicly available at https://github.com/andy-yang-1/DoubleSparse.