Zobrazeno 1 - 10
of 1 842
pro vyhledávání: '"YE, KE"'
Autor:
Lu, Jingyu, Ye, Ke
The classical Cayley transform is a birational map between a quadratic matrix group and its Lie algebra, which was first discovered by Cayley in 1846. Because of its essential role in both pure and applied mathematics, the classical Cayley transform
Externí odkaz:
http://arxiv.org/abs/2411.02071
The g-convexity of functions on manifolds is a generalization of the convexity of functions on Rn. It plays an essential role in both differential geometry and non-convex optimization theory. This paper is concerned with g-convex smooth functions on
Externí odkaz:
http://arxiv.org/abs/2409.14434
Autor:
Chen, Qiyuan, Ye, Ke
This paper studies the stability of tensor ranks under field extensions. Our main contributions are fourfold: (1) We prove that the analytic rank is stable under field extensions. (2) We establish the equivalence between the partition rank vs. analyt
Externí odkaz:
http://arxiv.org/abs/2409.04034
Autor:
Ma, Yiwei, Ji, Jiayi, Ye, Ke, Lin, Weihuang, Wang, Zhibin, Zheng, Yonghan, Zhou, Qiang, Sun, Xiaoshuai, Ji, Rongrong
Significant progress has been made in the field of Instruction-based Image Editing (IIE). However, evaluating these models poses a significant challenge. A crucial requirement in this field is the establishment of a comprehensive evaluation benchmark
Externí odkaz:
http://arxiv.org/abs/2408.14180
This paper is concerned with rational curves on real classical groups. Our contributions are three-fold: (i) We determine the structure of quadratic rational curves on real classical groups. As a consequence, we completely classify quadratic rational
Externí odkaz:
http://arxiv.org/abs/2408.04453
Autor:
Gunter, Tom, Wang, Zirui, Wang, Chong, Pang, Ruoming, Narayanan, Andy, Zhang, Aonan, Zhang, Bowen, Chen, Chen, Chiu, Chung-Cheng, Qiu, David, Gopinath, Deepak, Yap, Dian Ang, Yin, Dong, Nan, Feng, Weers, Floris, Yin, Guoli, Huang, Haoshuo, Wang, Jianyu, Lu, Jiarui, Peebles, John, Ye, Ke, Lee, Mark, Du, Nan, Chen, Qibin, Keunebroek, Quentin, Wiseman, Sam, Evans, Syd, Lei, Tao, Rathod, Vivek, Kong, Xiang, Du, Xianzhi, Li, Yanghao, Wang, Yongqiang, Gao, Yuan, Ahmed, Zaid, Xu, Zhaoyang, Lu, Zhiyun, Rashid, Al, Jose, Albin Madappally, Doane, Alec, Bencomo, Alfredo, Vanderby, Allison, Hansen, Andrew, Jain, Ankur, Anupama, Anupama Mann, Kamal, Areeba, Wu, Bugu, Brum, Carolina, Maalouf, Charlie, Erdenebileg, Chinguun, Dulhanty, Chris, Moritz, Dominik, Kang, Doug, Jimenez, Eduardo, Ladd, Evan, Shi, Fangping, Bai, Felix, Chu, Frank, Hohman, Fred, Kotek, Hadas, Coleman, Hannah Gillis, Li, Jane, Bigham, Jeffrey, Cao, Jeffery, Lai, Jeff, Cheung, Jessica, Shan, Jiulong, Zhou, Joe, Li, John, Qin, Jun, Singh, Karanjeet, Vega, Karla, Zou, Kelvin, Heckman, Laura, Gardiner, Lauren, Bowler, Margit, Cordell, Maria, Cao, Meng, Hay, Nicole, Shahdadpuri, Nilesh, Godwin, Otto, Dighe, Pranay, Rachapudi, Pushyami, Tantawi, Ramsey, Frigg, Roman, Davarnia, Sam, Shah, Sanskruti, Guha, Saptarshi, Sirovica, Sasha, Ma, Shen, Ma, Shuang, Wang, Simon, Kim, Sulgi, Jayaram, Suma, Shankar, Vaishaal, Paidi, Varsha, Kumar, Vivek, Wang, Xin, Zheng, Xin, Cheng, Walker, Shrager, Yael, Ye, Yang, Tanaka, Yasu, Guo, Yihao, Meng, Yunsong, Luo, Zhao Tang, Ouyang, Zhi, Aygar, Alp, Wan, Alvin, Walkingshaw, Andrew, Lin, Antonie, Farooq, Arsalan, Ramerth, Brent, Reed, Colorado, Bartels, Chris, Chaney, Chris, Riazati, David, Yang, Eric Liang, Feldman, Erin, Hochstrasser, Gabriel, Seguin, Guillaume, Belousova, Irina, Pelemans, Joris, Yang, Karen, Vahid, Keivan Alizadeh, Cao, Liangliang, Najibi, Mahyar, Zuliani, Marco, Horton, Max, Cho, Minsik, Bhendawade, Nikhil, Dong, Patrick, Maj, Piotr, Agrawal, Pulkit, Shan, Qi, Fu, Qichen, Poston, Regan, Xu, Sam, Liu, Shuangning, Rao, Sushma, Heeramun, Tashweena, Merth, Thomas, Rayala, Uday, Cui, Victor, Sridhar, Vivek Rangarajan, Zhang, Wencong, Zhang, Wenqi, Wu, Wentao, Zhou, Xingyu, Liu, Xinwen, Zhao, Yang, Xia, Yin, Ren, Zhile, Ren, Zhongzheng
We present foundation language models developed to power Apple Intelligence features, including a ~3 billion parameter model designed to run efficiently on devices and a large server-based language model designed for Private Cloud Compute. These mode
Externí odkaz:
http://arxiv.org/abs/2407.21075
Autor:
Lim, Lek-Heng, Ye, Ke
We derive three families of orthogonally-equivariant matrix submanifold models for the Grassmann, flag, and Stiefel manifolds respectively. These families are exhaustive -- every orthogonally-equivariant submanifold model of the lowest dimension for
Externí odkaz:
http://arxiv.org/abs/2407.13482
Autor:
Lim, Lek-Heng, Ye, Ke
We show that the flag manifold $\operatorname{Flag}(k_1,\dots, k_p, \mathbb{R}^n)$, with Grassmannian the special case $p=1$, has an $\operatorname{SO}_n(\mathbb{R})$-equivariant embedding in an Euclidean space of dimension $(n-1)(n+2)/2$, two orders
Externí odkaz:
http://arxiv.org/abs/2407.12546
We show that unconstrained quadratic optimization over a Grassmannian $\operatorname{Gr}(k,n)$ is NP-hard. Our results cover all scenarios: (i) when $k$ and $n$ are both allowed to grow; (ii) when $k$ is arbitrary but fixed; (iii) when $k$ is fixed a
Externí odkaz:
http://arxiv.org/abs/2406.19377
We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\; \operatorname{tr}(Q)=2k
Externí odkaz:
http://arxiv.org/abs/2406.11821