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1,886 results on '"Ye, Ke"'

1. Rational Curves on Real Classical Groups

Author

Li, Zijia and Ye, Ke

Subjects
Mathematics - Algebraic Geometry, Computer Science - Symbolic Computation, Mathematics - Group Theory, 14H45, 20G20, 26C15, 14L35, 14L30, 70B05
Abstract

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 curves on $\mathrm{U}_n$, $\mathrm{O}_n(\mathbb{R})$, $\mathrm{O}_{n-1,1}(\mathbb{R})$ and $\mathrm{O}_{n-2,2}(\mathbb{R})$. (ii) We prove a decomposition theorem for rational curves on real classical groups, which can be regarded as a non-commutative generalization of the fundamental theorem of algebra and partial fraction decomposition. (iii) As an application of (i) and (ii), we generalize Kempe's Universality Theorem to rational curves on homogeneous spaces., Comment: 50 pages

Published
2024

2. Apple Intelligence Foundation Language Models

Author

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, and Ren, Zhongzheng

Subjects
Computer Science - Artificial Intelligence, Computer Science - Computation and Language, Computer Science - Machine Learning
Abstract

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 models are designed to perform a wide range of tasks efficiently, accurately, and responsibly. This report describes the model architecture, the data used to train the model, the training process, how the models are optimized for inference, and the evaluation results. We highlight our focus on Responsible AI and how the principles are applied throughout the model development.

Published
2024

3. Simple matrix models for the flag, Grassmann, and Stiefel manifolds

Author

Lim, Lek-Heng and Ye, Ke

Subjects
Mathematics - Numerical Analysis, Mathematics - Differential Geometry, 14M15, 65J05, 90C48, 53Z30, 57S25, 22E70
Abstract

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 any of these manifolds is necessarily a member of the respective family, with a small number of exceptions. They have several computationally desirable features. The orthogonal equivariance allows one to obtain, for various differential geometric objects and operations, closed-form analytic expressions that are readily computable with standard numerical linear algebra. The minimal dimension aspect translates directly to a speed advantage in computations. And having an exhaustive list of all possible matrix models permits one to identify the model with the lowest matrix condition number, which translates to an accuracy advantage in computations. As an interesting aside, we will see that the family of models for the Stiefel manifold is naturally parameterized by the Cartan manifold, i.e., the positive definite cone equipped with its natural Riemannian metric., Comment: 17 pages

Published
2024

4. Minimal equivariant embeddings of the Grassmannian and flag manifold

Author

Lim, Lek-Heng and Ye, Ke

Subjects
Mathematics - Representation Theory, Mathematics - Differential Geometry, 14M15, 57R40, 57S25, 14R20, 22E46, 22E70
Abstract

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 of magnitude below the current best known result. We will show that the value $(n-1)(n+2)/2$ is the smallest possible and that any $\operatorname{SO}_n(\mathbb{R})$-equivariant embedding of $\operatorname{Flag}(k_1,\dots, k_p, \mathbb{R}^n)$ in an ambient space of minimal dimension is equivariantly equivalent to the aforementioned one., Comment: 11 pages

Published
2024

5. Grassmannian optimization is NP-hard

Author

Lai, Zehua, Lim, Lek-Heng, and Ye, Ke

Subjects
Mathematics - Optimization and Control, Mathematics - Numerical Analysis, 03D15, 90C26, 90C23, 65K10, 68Q25, 90C60
Abstract

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 at its lowest possible value $1$. We then deduce the NP-hardness of unconstrained cubic optimization over the Stiefel manifold $\operatorname{V}(k,n)$ and the orthogonal group $\operatorname{O}(n)$. As an addendum we demonstrate the NP-hardness of unconstrained quadratic optimization over the Cartan manifold, i.e., the positive definite cone $\mathbb{S}^n_{\scriptscriptstyle++}$ regarded as a Riemannian manifold, another popular example in manifold optimization. We will also establish the nonexistence of $\mathrm{FPTAS}$ in all cases., Comment: 19 pages

Published
2024

6. Simple matrix expressions for the curvatures of Grassmannian

Author

Lai, Zehua, Lim, Lek-Heng, and Ye, Ke

Subjects
Mathematics - Differential Geometry, Mathematics - Numerical Analysis, Mathematics - Optimization and Control, 15A75, 14M15
Abstract

We show that modeling a Grassmannian as symmetric orthogonal matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong\{Q \in \mathbb{R}^{n \times n} : Q^{\scriptscriptstyle\mathsf{T}} Q = I, \; Q^{\scriptscriptstyle\mathsf{T}} = Q,\; \operatorname{tr}(Q)=2k - n\}$ yields exceedingly simple matrix formulas for various curvatures and curvature-related quantities, both intrinsic and extrinsic. These include Riemann, Ricci, Jacobi, sectional, scalar, mean, principal, and Gaussian curvatures; Schouten, Weyl, Cotton, Bach, Pleba\'nski, cocurvature, nonmetricity, and torsion tensors; first, second, and third fundamental forms; Gauss and Weingarten maps; and upper and lower delta invariants. We will derive explicit, simple expressions for the aforementioned quantities in terms of standard matrix operations that are stably computable with numerical linear algebra. Many of these aforementioned quantities have never before been presented for the Grassmannian., Comment: 25 pages

Published
2024

7. Degree of the Grassmannian as an affine variety

Author

Lim, Lek-Heng and Ye, Ke

Subjects
Mathematics - Algebraic Geometry, 14E25, 14F45
Abstract

The degree of the Grassmannian with respect to the Pl\"ucker embedding is well-known. However, the Pl\"ucker embedding, while ubiquitous in pure mathematics, is almost never used in applied mathematics. In applied mathematics, the Grassmannian is usually embedded as projection matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong \{P \in \mathbb{R}^{n \times n} : P^{\scriptscriptstyle\mathsf{T}} = P = P^2,\; \operatorname{tr}(P) = k\}$ or as involution matrices $\operatorname{Gr}(k,\mathbb{R}^n) \cong \{X \in \mathbb{R}^{n \times n} : X^{\scriptscriptstyle\mathsf{T}} = X,\; X^2 = I,\; \operatorname{tr}(X)=2k - n\}$. We will determine an explicit expression for the degree of the Grassmannian with respect to these embeddings. In so doing, we resolved a conjecture of Devriendt--Friedman--Sturmfels about the degree $\operatorname{Gr}(2, \mathbb{R}^n)$ and in fact generalized it to $\operatorname{Gr}(k, \mathbb{R}^n)$. We also proved a set theoretic variant of another conjecture of Devriendt--Friedman--Sturmfels about the limit of $\operatorname{Gr}(k,\mathbb{R}^n)$ in the sense of Gr\"obner degneration., Comment: 16 pages

Published
2024

8. A quasi-optimal lower bound for skew polynomial multiplication

Author

Chen, Qiyuan and Ye, Ke

Subjects
Computer Science - Computational Complexity, Computer Science - Symbolic Computation, Mathematics - Rings and Algebras
Abstract

We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a log factor. We present algorithms for three special cases, indicating that the aforementioned lower bound is quasi-optimal. In fact, our lower bound is quasi-optimal in the sense of bilinear complexity. In addition, we discuss the average bilinear complexity of simultaneous multiplication of skew polynomials and the complexity of skew polynomial multiplication in the case of towers of extensions.

Published
2024

9. SpacTor-T5: Pre-training T5 Models with Span Corruption and Replaced Token Detection

Author

Ye, Ke, Jiang, Heinrich, Rostamizadeh, Afshin, Chakrabarti, Ayan, DeSalvo, Giulia, Kagy, Jean-François, Karydas, Lazaros, Citovsky, Gui, and Kumar, Sanjiv

Subjects
Computer Science - Machine Learning, Computer Science - Computation and Language
Abstract

Pre-training large language models is known to be extremely resource intensive and often times inefficient, under-utilizing the information encapsulated in the training text sequences. In this paper, we present SpacTor, a new training procedure consisting of (1) a hybrid objective combining span corruption (SC) and token replacement detection (RTD), and (2) a two-stage curriculum that optimizes the hybrid objective over the initial $\tau$ iterations, then transitions to standard SC loss. We show empirically that the effectiveness of the hybrid objective is tied to the two-stage pre-training schedule, and provide extensive analysis on why this is the case. In our experiments with encoder-decoder architectures (T5) on a variety of NLP tasks, SpacTor-T5 yields the same downstream performance as standard SC pre-training, while enabling a 50% reduction in pre-training iterations and 40% reduction in total FLOPs. Alternatively, given the same amount of computing budget, we find that SpacTor results in significantly improved downstream benchmark performance., Comment: 9+13 pages, 5 figures

Published
2024

10. Bundle-based similarity measurement for positive semidefinite matrices

Author

Liu, Peng and Ye, Ke

Subjects
Mathematics - Numerical Analysis
Abstract

Positive semidefinite (PSD) matrices are indispensable in many fields of science. A similarity measurement for such matrices is usually an essential ingredient in the mathematical modelling of a scientific problem. This paper proposes a unified framework to construct similarity measurements for PSD matrices. The framework is obtained by exploring the fiber bundle structure of the cone of PSD matrices and generalizing the idea of the point-set distance previously developed for linear subsapces and positive definite (PD) matrices. The framework demonstrates both theoretical advantages and computational convenience: (1) We prove that the similarity measurement constructed by the framework can be recognized either as the cost of a parallel transport or as the length of a quasi-geodesic curve. (2) We extend commonly used divergences for equidimensional PD matrices to the non-equidimensional case. Examples include Kullback-Leibler divergence, Bhattacharyya divergence and R\'enyi divergence. We prove that these extensions enjoy the same consistency property as their counterpart for geodesic distance. (3) We apply our geometric framework to further extend those in (2) to similarity measurements for arbitrary PSD matrices. We also provide simple formulae to compute these similarity measurements in most situations.

Published
2023

11. Gemini: A Family of Highly Capable Multimodal Models

Author

Gemini Team, Anil, Rohan, Borgeaud, Sebastian, Alayrac, Jean-Baptiste, Yu, Jiahui, Soricut, Radu, Schalkwyk, Johan, Dai, Andrew M., Hauth, Anja, Millican, Katie, Silver, David, Johnson, Melvin, Antonoglou, Ioannis, Schrittwieser, Julian, Glaese, Amelia, Chen, Jilin, Pitler, Emily, Lillicrap, Timothy, Lazaridou, Angeliki, Firat, Orhan, Molloy, James, Isard, Michael, Barham, Paul R., Hennigan, Tom, Lee, Benjamin, Viola, Fabio, Reynolds, Malcolm, Xu, Yuanzhong, Doherty, Ryan, Collins, Eli, Meyer, Clemens, Rutherford, Eliza, Moreira, Erica, Ayoub, Kareem, Goel, Megha, Krawczyk, Jack, Du, Cosmo, Chi, Ed, Cheng, Heng-Tze, Ni, Eric, Shah, Purvi, Kane, Patrick, Chan, Betty, Faruqui, Manaal, Severyn, Aliaksei, Lin, Hanzhao, Li, YaGuang, Cheng, Yong, Ittycheriah, Abe, Mahdieh, Mahdis, Chen, Mia, Sun, Pei, Tran, Dustin, Bagri, Sumit, Lakshminarayanan, Balaji, Liu, Jeremiah, Orban, Andras, Güra, Fabian, Zhou, Hao, Song, Xinying, Boffy, Aurelien, Ganapathy, Harish, Zheng, Steven, Choe, HyunJeong, Weisz, Ágoston, Zhu, Tao, Lu, Yifeng, Gopal, Siddharth, Kahn, Jarrod, Kula, Maciej, Pitman, Jeff, Shah, Rushin, Taropa, Emanuel, Merey, Majd Al, Baeuml, Martin, Chen, Zhifeng, Shafey, Laurent El, Zhang, Yujing, Sercinoglu, Olcan, Tucker, George, Piqueras, Enrique, Krikun, Maxim, Barr, Iain, Savinov, Nikolay, Danihelka, Ivo, Roelofs, Becca, White, Anaïs, Andreassen, Anders, von Glehn, Tamara, Yagati, Lakshman, Kazemi, Mehran, Gonzalez, Lucas, Khalman, Misha, Sygnowski, Jakub, Frechette, Alexandre, Smith, Charlotte, Culp, Laura, Proleev, Lev, Luan, Yi, Chen, Xi, Lottes, James, Schucher, Nathan, Lebron, Federico, Rrustemi, Alban, Clay, Natalie, Crone, Phil, Kocisky, Tomas, Zhao, Jeffrey, Perz, Bartek, Yu, Dian, Howard, Heidi, Bloniarz, Adam, Rae, Jack W., Lu, Han, Sifre, Laurent, Maggioni, Marcello, Alcober, Fred, Garrette, Dan, Barnes, Megan, Thakoor, Shantanu, Austin, Jacob, Barth-Maron, Gabriel, Wong, William, Joshi, Rishabh, Chaabouni, Rahma, Fatiha, Deeni, Ahuja, Arun, Tomar, Gaurav Singh, Senter, Evan, Chadwick, Martin, Kornakov, Ilya, Attaluri, Nithya, Iturrate, Iñaki, Liu, Ruibo, Li, Yunxuan, Cogan, Sarah, Chen, Jeremy, Jia, Chao, Gu, Chenjie, Zhang, Qiao, Grimstad, Jordan, Hartman, Ale Jakse, Garcia, Xavier, Pillai, Thanumalayan Sankaranarayana, Devlin, Jacob, Laskin, Michael, Casas, Diego de Las, Valter, Dasha, Tao, Connie, Blanco, Lorenzo, Badia, Adrià Puigdomènech, Reitter, David, Chen, Mianna, Brennan, Jenny, Rivera, Clara, Brin, Sergey, Iqbal, Shariq, Surita, Gabriela, Labanowski, Jane, Rao, Abhi, Winkler, Stephanie, Parisotto, Emilio, Gu, Yiming, Olszewska, Kate, Addanki, Ravi, Miech, Antoine, Louis, Annie, Teplyashin, Denis, Brown, Geoff, Catt, Elliot, Balaguer, Jan, Xiang, Jackie, Wang, Pidong, Ashwood, Zoe, Briukhov, Anton, Webson, Albert, Ganapathy, Sanjay, Sanghavi, Smit, Kannan, Ajay, Chang, Ming-Wei, Stjerngren, Axel, Djolonga, Josip, Sun, Yuting, Bapna, Ankur, Aitchison, Matthew, Pejman, Pedram, Michalewski, Henryk, Yu, Tianhe, Wang, Cindy, Love, Juliette, Ahn, Junwhan, Bloxwich, Dawn, Han, Kehang, Humphreys, Peter, Sellam, Thibault, Bradbury, James, Godbole, Varun, Samangooei, Sina, Damoc, Bogdan, Kaskasoli, Alex, Arnold, Sébastien M. R., Vasudevan, Vijay, Agrawal, Shubham, Riesa, Jason, Lepikhin, Dmitry, Tanburn, Richard, Srinivasan, Srivatsan, Lim, Hyeontaek, Hodkinson, Sarah, Shyam, Pranav, Ferret, Johan, Hand, Steven, Garg, Ankush, Paine, Tom Le, Li, Jian, Li, Yujia, Giang, Minh, Neitz, Alexander, Abbas, Zaheer, York, Sarah, Reid, Machel, Cole, Elizabeth, Chowdhery, Aakanksha, Das, Dipanjan, Rogozińska, Dominika, Nikolaev, Vitaliy, Sprechmann, Pablo, Nado, Zachary, Zilka, Lukas, Prost, Flavien, He, Luheng, Monteiro, Marianne, Mishra, Gaurav, Welty, Chris, Newlan, Josh, Jia, Dawei, Allamanis, Miltiadis, Hu, Clara Huiyi, de Liedekerke, Raoul, Gilmer, Justin, Saroufim, Carl, Rijhwani, Shruti, Hou, Shaobo, Shrivastava, Disha, Baddepudi, Anirudh, Goldin, Alex, Ozturel, Adnan, Cassirer, Albin, Xu, Yunhan, Sohn, Daniel, Sachan, Devendra, Amplayo, Reinald Kim, Swanson, Craig, Petrova, Dessie, Narayan, Shashi, Guez, Arthur, Brahma, Siddhartha, Landon, Jessica, Patel, Miteyan, Zhao, Ruizhe, Villela, Kevin, Wang, Luyu, Jia, Wenhao, Rahtz, Matthew, Giménez, Mai, Yeung, Legg, Keeling, James, Georgiev, Petko, Mincu, Diana, Wu, Boxi, Haykal, Salem, Saputro, Rachel, Vodrahalli, Kiran, Qin, James, Cankara, Zeynep, Sharma, Abhanshu, Fernando, Nick, Hawkins, Will, Neyshabur, Behnam, Kim, Solomon, Hutter, Adrian, Agrawal, Priyanka, Castro-Ros, Alex, Driessche, George van den, Wang, Tao, Yang, Fan, Chang, Shuo-yiin, Komarek, Paul, McIlroy, Ross, Lučić, Mario, Zhang, Guodong, Farhan, Wael, Sharman, Michael, Natsev, Paul, Michel, Paul, Bansal, Yamini, Qiao, Siyuan, Cao, Kris, Shakeri, Siamak, Butterfield, Christina, Chung, Justin, Rubenstein, Paul Kishan, Agrawal, Shivani, Mensch, Arthur, Soparkar, Kedar, Lenc, Karel, Chung, Timothy, Pope, Aedan, Maggiore, Loren, Kay, Jackie, Jhakra, Priya, Wang, Shibo, Maynez, Joshua, Phuong, Mary, Tobin, Taylor, Tacchetti, Andrea, Trebacz, Maja, Robinson, Kevin, Katariya, Yash, Riedel, Sebastian, Bailey, Paige, Xiao, Kefan, Ghelani, Nimesh, Aroyo, Lora, Slone, Ambrose, Houlsby, Neil, Xiong, Xuehan, Yang, Zhen, Gribovskaya, Elena, Adler, Jonas, Wirth, Mateo, Lee, Lisa, Li, Music, Kagohara, Thais, Pavagadhi, Jay, Bridgers, Sophie, Bortsova, Anna, Ghemawat, Sanjay, Ahmed, Zafarali, Liu, Tianqi, Powell, Richard, Bolina, Vijay, Iinuma, Mariko, Zablotskaia, Polina, Besley, James, Chung, Da-Woon, Dozat, Timothy, Comanescu, Ramona, Si, Xiance, Greer, Jeremy, Su, Guolong, Polacek, Martin, Kaufman, Raphaël Lopez, Tokumine, Simon, Hu, Hexiang, Buchatskaya, Elena, Miao, Yingjie, Elhawaty, Mohamed, Siddhant, Aditya, Tomasev, Nenad, Xing, Jinwei, Greer, Christina, Miller, Helen, Ashraf, Shereen, Roy, Aurko, Zhang, Zizhao, Ma, Ada, Filos, Angelos, Besta, Milos, Blevins, Rory, Klimenko, Ted, Yeh, Chih-Kuan, Changpinyo, Soravit, Mu, Jiaqi, Chang, Oscar, Pajarskas, Mantas, Muir, Carrie, Cohen, Vered, Lan, Charline Le, Haridasan, Krishna, Marathe, Amit, Hansen, Steven, Douglas, Sholto, Samuel, Rajkumar, Wang, Mingqiu, Austin, Sophia, Lan, Chang, Jiang, Jiepu, Chiu, Justin, Lorenzo, Jaime Alonso, Sjösund, Lars Lowe, Cevey, Sébastien, Gleicher, Zach, Avrahami, Thi, Boral, Anudhyan, Srinivasan, Hansa, Selo, Vittorio, May, Rhys, Aisopos, Konstantinos, Hussenot, Léonard, Soares, Livio Baldini, Baumli, Kate, Chang, Michael B., Recasens, Adrià, Caine, Ben, Pritzel, Alexander, Pavetic, Filip, Pardo, Fabio, Gergely, Anita, Frye, Justin, Ramasesh, Vinay, Horgan, Dan, Badola, Kartikeya, Kassner, Nora, Roy, Subhrajit, Dyer, Ethan, Campos, Víctor Campos, Tomala, Alex, Tang, Yunhao, Badawy, Dalia El, White, Elspeth, Mustafa, Basil, Lang, Oran, Jindal, Abhishek, Vikram, Sharad, Gong, Zhitao, Caelles, Sergi, Hemsley, Ross, Thornton, Gregory, Feng, Fangxiaoyu, Stokowiec, Wojciech, Zheng, Ce, Thacker, Phoebe, Ünlü, Çağlar, Zhang, Zhishuai, Saleh, Mohammad, Svensson, James, Bileschi, Max, Patil, Piyush, Anand, Ankesh, Ring, Roman, Tsihlas, Katerina, Vezer, Arpi, Selvi, Marco, Shevlane, Toby, Rodriguez, Mikel, Kwiatkowski, Tom, Daruki, Samira, Rong, Keran, Dafoe, Allan, FitzGerald, Nicholas, Gu-Lemberg, Keren, Khan, Mina, Hendricks, Lisa Anne, Pellat, Marie, Feinberg, Vladimir, Cobon-Kerr, James, Sainath, Tara, Rauh, Maribeth, Hashemi, Sayed Hadi, Ives, Richard, Hasson, Yana, Noland, Eric, Cao, Yuan, Byrd, Nathan, Hou, Le, Wang, Qingze, Sottiaux, Thibault, Paganini, Michela, Lespiau, Jean-Baptiste, Moufarek, Alexandre, Hassan, Samer, Shivakumar, Kaushik, van Amersfoort, Joost, Mandhane, Amol, Joshi, Pratik, Goyal, Anirudh, Tung, Matthew, Brock, Andrew, Sheahan, Hannah, Misra, Vedant, Li, Cheng, Rakićević, Nemanja, Dehghani, Mostafa, Liu, Fangyu, Mittal, Sid, Oh, Junhyuk, Noury, Seb, Sezener, Eren, Huot, Fantine, Lamm, Matthew, De Cao, Nicola, Chen, Charlie, Mudgal, Sidharth, Stella, Romina, Brooks, Kevin, Vasudevan, Gautam, Liu, Chenxi, Chain, Mainak, Melinkeri, Nivedita, Cohen, Aaron, Wang, Venus, Seymore, Kristie, Zubkov, Sergey, Goel, Rahul, Yue, Summer, Krishnakumaran, Sai, Albert, Brian, Hurley, Nate, Sano, Motoki, Mohananey, Anhad, Joughin, Jonah, Filonov, Egor, Kępa, Tomasz, Eldawy, Yomna, Lim, Jiawern, Rishi, Rahul, Badiezadegan, Shirin, Bos, Taylor, Chang, Jerry, Jain, Sanil, Padmanabhan, Sri Gayatri Sundara, Puttagunta, Subha, Krishna, Kalpesh, Baker, Leslie, Kalb, Norbert, Bedapudi, Vamsi, Kurzrok, Adam, Lei, Shuntong, Yu, Anthony, Litvin, Oren, Zhou, Xiang, Wu, Zhichun, Sobell, Sam, Siciliano, Andrea, Papir, Alan, Neale, Robby, Bragagnolo, Jonas, Toor, Tej, Chen, Tina, Anklin, Valentin, Wang, Feiran, Feng, Richie, Gholami, Milad, Ling, Kevin, Liu, Lijuan, Walter, Jules, Moghaddam, Hamid, Kishore, Arun, Adamek, Jakub, Mercado, Tyler, Mallinson, Jonathan, Wandekar, Siddhinita, Cagle, Stephen, Ofek, Eran, Garrido, Guillermo, Lombriser, Clemens, Mukha, Maksim, Sun, Botu, Mohammad, Hafeezul Rahman, Matak, Josip, Qian, Yadi, Peswani, Vikas, Janus, Pawel, Yuan, Quan, Schelin, Leif, David, Oana, Garg, Ankur, He, Yifan, Duzhyi, Oleksii, Älgmyr, Anton, Lottaz, Timothée, Li, Qi, Yadav, Vikas, Xu, Luyao, Chinien, Alex, Shivanna, Rakesh, Chuklin, Aleksandr, Li, Josie, Spadine, Carrie, Wolfe, Travis, Mohamed, Kareem, Das, Subhabrata, Dai, Zihang, He, Kyle, von Dincklage, Daniel, Upadhyay, Shyam, Maurya, Akanksha, Chi, Luyan, Krause, Sebastian, Salama, Khalid, Rabinovitch, Pam G, M, Pavan Kumar Reddy, Selvan, Aarush, Dektiarev, Mikhail, Ghiasi, Golnaz, Guven, Erdem, Gupta, Himanshu, Liu, Boyi, Sharma, Deepak, Shtacher, Idan Heimlich, Paul, Shachi, Akerlund, Oscar, Aubet, François-Xavier, Huang, Terry, Zhu, Chen, Zhu, Eric, Teixeira, Elico, Fritze, Matthew, Bertolini, Francesco, Marinescu, Liana-Eleonora, Bölle, Martin, Paulus, Dominik, Gupta, Khyatti, Latkar, Tejasi, Chang, Max, Sanders, Jason, Wilson, Roopa, Wu, Xuewei, Tan, Yi-Xuan, Thiet, Lam Nguyen, Doshi, Tulsee, Lall, Sid, Mishra, Swaroop, Chen, Wanming, Luong, Thang, Benjamin, Seth, Lee, Jasmine, Andrejczuk, Ewa, Rabiej, Dominik, Ranjan, Vipul, Styrc, Krzysztof, Yin, Pengcheng, Simon, Jon, Harriott, Malcolm Rose, Bansal, Mudit, Robsky, Alexei, Bacon, Geoff, Greene, David, Mirylenka, Daniil, Zhou, Chen, Sarvana, Obaid, Goyal, Abhimanyu, Andermatt, Samuel, Siegler, Patrick, Horn, Ben, Israel, Assaf, Pongetti, Francesco, Chen, Chih-Wei "Louis", Selvatici, Marco, Silva, Pedro, Wang, Kathie, Tolins, Jackson, Guu, Kelvin, Yogev, Roey, Cai, Xiaochen, Agostini, Alessandro, Shah, Maulik, Nguyen, Hung, Donnaile, Noah Ó, Pereira, Sébastien, Friso, Linda, Stambler, Adam, Kuang, Chenkai, Romanikhin, Yan, Geller, Mark, Yan, ZJ, Jang, Kane, Lee, Cheng-Chun, Fica, Wojciech, Malmi, Eric, Tan, Qijun, Banica, Dan, Balle, Daniel, Pham, Ryan, Huang, Yanping, Avram, Diana, Shi, Hongzhi, Singh, Jasjot, Hidey, Chris, Ahuja, Niharika, Saxena, Pranab, Dooley, Dan, Potharaju, Srividya Pranavi, O'Neill, Eileen, Gokulchandran, Anand, Foley, Ryan, Zhao, Kai, Dusenberry, Mike, Liu, Yuan, Mehta, Pulkit, Kotikalapudi, Ragha, Safranek-Shrader, Chalence, Goodman, Andrew, Kessinger, Joshua, Globen, Eran, Kolhar, Prateek, Gorgolewski, Chris, Ibrahim, Ali, Song, Yang, Eichenbaum, Ali, Brovelli, Thomas, Potluri, Sahitya, Lahoti, Preethi, Baetu, Cip, Ghorbani, Ali, Chen, Charles, Crawford, Andy, Pal, Shalini, Sridhar, Mukund, Gurita, Petru, Mujika, Asier, Petrovski, Igor, Cedoz, Pierre-Louis, Li, Chenmei, Chen, Shiyuan, Santo, Niccolò Dal, Goyal, Siddharth, Punjabi, Jitesh, Kappaganthu, Karthik, Kwak, Chester, LV, Pallavi, Velury, Sarmishta, Choudhury, Himadri, Hall, Jamie, Shah, Premal, Figueira, Ricardo, Thomas, Matt, Lu, Minjie, Zhou, Ting, Kumar, Chintu, Jurdi, Thomas, Chikkerur, Sharat, Ma, Yenai, Yu, Adams, Kwak, Soo, Ähdel, Victor, Rajayogam, Sujeevan, Choma, Travis, Liu, Fei, Barua, Aditya, Ji, Colin, Park, Ji Ho, Hellendoorn, Vincent, Bailey, Alex, Bilal, Taylan, Zhou, Huanjie, Khatir, Mehrdad, Sutton, Charles, Rzadkowski, Wojciech, Macintosh, Fiona, Shagin, Konstantin, Medina, Paul, Liang, Chen, Zhou, Jinjing, Shah, Pararth, Bi, Yingying, Dankovics, Attila, Banga, Shipra, Lehmann, Sabine, Bredesen, Marissa, Lin, Zifan, Hoffmann, John Eric, Lai, Jonathan, Chung, Raynald, Yang, Kai, Balani, Nihal, Bražinskas, Arthur, Sozanschi, Andrei, Hayes, Matthew, Alcalde, Héctor Fernández, Makarov, Peter, Chen, Will, Stella, Antonio, Snijders, Liselotte, Mandl, Michael, Kärrman, Ante, Nowak, Paweł, Wu, Xinyi, Dyck, Alex, Vaidyanathan, Krishnan, R, Raghavender, Mallet, Jessica, Rudominer, Mitch, Johnston, Eric, Mittal, Sushil, Udathu, Akhil, Christensen, Janara, Verma, Vishal, Irving, Zach, Santucci, Andreas, Elsayed, Gamaleldin, Davoodi, Elnaz, Georgiev, Marin, Tenney, Ian, Hua, Nan, Cideron, Geoffrey, Leurent, Edouard, Alnahlawi, Mahmoud, Georgescu, Ionut, Wei, Nan, Zheng, Ivy, Scandinaro, Dylan, Jiang, Heinrich, Snoek, Jasper, Sundararajan, Mukund, Wang, Xuezhi, Ontiveros, Zack, Karo, Itay, Cole, Jeremy, Rajashekhar, Vinu, Tumeh, Lara, Ben-David, Eyal, Jain, Rishub, Uesato, Jonathan, Datta, Romina, Bunyan, Oskar, Wu, Shimu, Zhang, John, Stanczyk, Piotr, Zhang, Ye, Steiner, David, Naskar, Subhajit, Azzam, Michael, Johnson, Matthew, Paszke, Adam, Chiu, Chung-Cheng, Elias, Jaume Sanchez, Mohiuddin, Afroz, Muhammad, Faizan, Miao, Jin, Lee, Andrew, Vieillard, Nino, Park, Jane, Zhang, Jiageng, Stanway, Jeff, Garmon, Drew, Karmarkar, Abhijit, Dong, Zhe, Lee, Jong, Kumar, Aviral, Zhou, Luowei, Evens, Jonathan, Isaac, William, Irving, Geoffrey, Loper, Edward, Fink, Michael, Arkatkar, Isha, Chen, Nanxin, Shafran, Izhak, Petrychenko, Ivan, Chen, Zhe, Jia, Johnson, Levskaya, Anselm, Zhu, Zhenkai, Grabowski, Peter, Mao, Yu, Magni, Alberto, Yao, Kaisheng, Snaider, Javier, Casagrande, Norman, Palmer, Evan, Suganthan, Paul, Castaño, Alfonso, Giannoumis, Irene, Kim, Wooyeol, Rybiński, Mikołaj, Sreevatsa, Ashwin, Prendki, Jennifer, Soergel, David, Goedeckemeyer, Adrian, Gierke, Willi, Jafari, Mohsen, Gaba, Meenu, Wiesner, Jeremy, Wright, Diana Gage, Wei, Yawen, Vashisht, Harsha, Kulizhskaya, Yana, Hoover, Jay, Le, Maigo, Li, Lu, Iwuanyanwu, Chimezie, Liu, Lu, Ramirez, Kevin, Khorlin, Andrey, Cui, Albert, LIN, Tian, Wu, Marcus, Aguilar, Ricardo, Pallo, Keith, Chakladar, Abhishek, Perng, Ginger, Abellan, Elena Allica, Zhang, Mingyang, Dasgupta, Ishita, Kushman, Nate, Penchev, Ivo, Repina, Alena, Wu, Xihui, van der Weide, Tom, Ponnapalli, Priya, Kaplan, Caroline, Simsa, Jiri, Li, Shuangfeng, Dousse, Olivier, Piper, Jeff, Ie, Nathan, Pasumarthi, Rama, Lintz, Nathan, Vijayakumar, Anitha, Andor, Daniel, Valenzuela, Pedro, Lui, Minnie, Paduraru, Cosmin, Peng, Daiyi, Lee, Katherine, Zhang, Shuyuan, Greene, Somer, Nguyen, Duc Dung, Kurylowicz, Paula, Hardin, Cassidy, Dixon, Lucas, Janzer, Lili, Choo, Kiam, Feng, Ziqiang, Zhang, Biao, Singhal, Achintya, Du, Dayou, McKinnon, Dan, Antropova, Natasha, Bolukbasi, Tolga, Keller, Orgad, Reid, David, Finchelstein, Daniel, Raad, Maria Abi, Crocker, Remi, Hawkins, Peter, Dadashi, Robert, Gaffney, Colin, Franko, Ken, Bulanova, Anna, Leblond, Rémi, Chung, Shirley, Askham, Harry, Cobo, Luis C., Xu, Kelvin, Fischer, Felix, Xu, Jun, Sorokin, Christina, Alberti, Chris, Lin, Chu-Cheng, Evans, Colin, Dimitriev, Alek, Forbes, Hannah, Banarse, Dylan, Tung, Zora, Omernick, Mark, Bishop, Colton, Sterneck, Rachel, Jain, Rohan, Xia, Jiawei, Amid, Ehsan, Piccinno, Francesco, Wang, Xingyu, Banzal, Praseem, Mankowitz, Daniel J., Polozov, Alex, Krakovna, Victoria, Brown, Sasha, Bateni, MohammadHossein, Duan, Dennis, Firoiu, Vlad, Thotakuri, Meghana, Natan, Tom, Geist, Matthieu, Girgin, Ser tan, Li, Hui, Ye, Jiayu, Roval, Ofir, Tojo, Reiko, Kwong, Michael, Lee-Thorp, James, Yew, Christopher, Sinopalnikov, Danila, Ramos, Sabela, Mellor, John, Sharma, Abhishek, Wu, Kathy, Miller, David, Sonnerat, Nicolas, Vnukov, Denis, Greig, Rory, Beattie, Jennifer, Caveness, Emily, Bai, Libin, Eisenschlos, Julian, Korchemniy, Alex, Tsai, Tomy, Jasarevic, Mimi, Kong, Weize, Dao, Phuong, Zheng, Zeyu, Liu, Frederick, Zhu, Rui, Teh, Tian Huey, Sanmiya, Jason, Gladchenko, Evgeny, Trdin, Nejc, Toyama, Daniel, Rosen, Evan, Tavakkol, Sasan, Xue, Linting, Elkind, Chen, Woodman, Oliver, Carpenter, John, Papamakarios, George, Kemp, Rupert, Kafle, Sushant, Grunina, Tanya, Sinha, Rishika, Talbert, Alice, Wu, Diane, Owusu-Afriyie, Denese, Thornton, Chloe, Pont-Tuset, Jordi, Narayana, Pradyumna, Li, Jing, Fatehi, Saaber, Wieting, John, Ajmeri, Omar, Uria, Benigno, Ko, Yeongil, Knight, Laura, Héliou, Amélie, Niu, Ning, Gu, Shane, Pang, Chenxi, Li, Yeqing, Levine, Nir, Stolovich, Ariel, Santamaria-Fernandez, Rebeca, Goenka, Sonam, Yustalim, Wenny, Strudel, Robin, Elqursh, Ali, Deck, Charlie, Lee, Hyo, Li, Zonglin, Levin, Kyle, Hoffmann, Raphael, Holtmann-Rice, Dan, Bachem, Olivier, Arora, Sho, Koh, Christy, Yeganeh, Soheil Hassas, Põder, Siim, Tariq, Mukarram, Sun, Yanhua, Ionita, Lucian, Seyedhosseini, Mojtaba, Tafti, Pouya, Liu, Zhiyu, Gulati, Anmol, Liu, Jasmine, Ye, Xinyu, Chrzaszcz, Bart, Wang, Lily, Sethi, Nikhil, Li, Tianrun, Brown, Ben, Singh, Shreya, Fan, Wei, Parisi, Aaron, Stanton, Joe, Koverkathu, Vinod, Choquette-Choo, Christopher A., Li, Yunjie, Lu, TJ, Shroff, Prakash, Varadarajan, Mani, Bahargam, Sanaz, Willoughby, Rob, Gaddy, David, Desjardins, Guillaume, Cornero, Marco, Robenek, Brona, Mittal, Bhavishya, Albrecht, Ben, Shenoy, Ashish, Moiseev, Fedor, Jacobsson, Henrik, Ghaffarkhah, Alireza, Rivière, Morgane, Walton, Alanna, Crepy, Clément, Parrish, Alicia, Zhou, Zongwei, Farabet, Clement, Radebaugh, Carey, Srinivasan, Praveen, van der Salm, Claudia, Fidjeland, Andreas, Scellato, Salvatore, Latorre-Chimoto, Eri, Klimczak-Plucińska, Hanna, Bridson, David, de Cesare, Dario, Hudson, Tom, Mendolicchio, Piermaria, Walker, Lexi, Morris, Alex, Mauger, Matthew, Guseynov, Alexey, Reid, Alison, Odoom, Seth, Loher, Lucia, Cotruta, Victor, Yenugula, Madhavi, Grewe, Dominik, Petrushkina, Anastasia, Duerig, Tom, Sanchez, Antonio, Yadlowsky, Steve, Shen, Amy, Globerson, Amir, Webb, Lynette, Dua, Sahil, Li, Dong, Bhupatiraju, Surya, Hurt, Dan, Qureshi, Haroon, Agarwal, Ananth, Shani, Tomer, Eyal, Matan, Khare, Anuj, Belle, Shreyas Rammohan, Wang, Lei, Tekur, Chetan, Kale, Mihir Sanjay, Wei, Jinliang, Sang, Ruoxin, Saeta, Brennan, Liechty, Tyler, Sun, Yi, Zhao, Yao, Lee, Stephan, Nayak, Pandu, Fritz, Doug, Vuyyuru, Manish Reddy, Aslanides, John, Vyas, Nidhi, Wicke, Martin, Ma, Xiao, Eltyshev, Evgenii, Martin, Nina, Cate, Hardie, Manyika, James, Amiri, Keyvan, Kim, Yelin, Xiong, Xi, Kang, Kai, Luisier, Florian, Tripuraneni, Nilesh, Madras, David, Guo, Mandy, Waters, Austin, Wang, Oliver, Ainslie, Joshua, Baldridge, Jason, Zhang, Han, Pruthi, Garima, Bauer, Jakob, Yang, Feng, Mansour, Riham, Gelman, Jason, Xu, Yang, Polovets, George, Liu, Ji, Cai, Honglong, Chen, Warren, Sheng, XiangHai, Xue, Emily, Ozair, Sherjil, Angermueller, Christof, Li, Xiaowei, Sinha, Anoop, Wang, Weiren, Wiesinger, Julia, Koukoumidis, Emmanouil, Tian, Yuan, Iyer, Anand, Gurumurthy, Madhu, Goldenson, Mark, Shah, Parashar, Blake, MK, Yu, Hongkun, Urbanowicz, Anthony, Palomaki, Jennimaria, Fernando, Chrisantha, Durden, Ken, Mehta, Harsh, Momchev, Nikola, Rahimtoroghi, Elahe, Georgaki, Maria, Raul, Amit, Ruder, Sebastian, Redshaw, Morgan, Lee, Jinhyuk, Zhou, Denny, Jalan, Komal, Li, Dinghua, Hechtman, Blake, Schuh, Parker, Nasr, Milad, Milan, Kieran, Mikulik, Vladimir, Franco, Juliana, Green, Tim, Nguyen, Nam, Kelley, Joe, Mahendru, Aroma, Hu, Andrea, Howland, Joshua, Vargas, Ben, Hui, Jeffrey, Bansal, Kshitij, Rao, Vikram, Ghiya, Rakesh, Wang, Emma, Ye, Ke, Sarr, Jean Michel, Preston, Melanie Moranski, Elish, Madeleine, Li, Steve, Kaku, Aakash, Gupta, Jigar, Pasupat, Ice, Juan, Da-Cheng, Someswar, Milan, M., Tejvi, Chen, Xinyun, Amini, Aida, Fabrikant, Alex, Chu, Eric, Dong, Xuanyi, Muthal, Amruta, Buthpitiya, Senaka, Jauhari, Sarthak, Khandelwal, Urvashi, Hitron, Ayal, Ren, Jie, Rinaldi, Larissa, Drath, Shahar, Dabush, Avigail, Jiang, Nan-Jiang, Godhia, Harshal, Sachs, Uli, Chen, Anthony, Fan, Yicheng, Taitelbaum, Hagai, Noga, Hila, Dai, Zhuyun, Wang, James, Hamer, Jenny, Ferng, Chun-Sung, Elkind, Chenel, Atias, Aviel, Lee, Paulina, Listík, Vít, Carlen, Mathias, van de Kerkhof, Jan, Pikus, Marcin, Zaher, Krunoslav, Müller, Paul, Zykova, Sasha, Stefanec, Richard, Gatsko, Vitaly, Hirnschall, Christoph, Sethi, Ashwin, Xu, Xingyu Federico, Ahuja, Chetan, Tsai, Beth, Stefanoiu, Anca, Feng, Bo, Dhandhania, Keshav, Katyal, Manish, Gupta, Akshay, Parulekar, Atharva, Pitta, Divya, Zhao, Jing, Bhatia, Vivaan, Bhavnani, Yashodha, Alhadlaq, Omar, Li, Xiaolin, Danenberg, Peter, Tu, Dennis, Pine, Alex, Filippova, Vera, Ghosh, Abhipso, Limonchik, Ben, Urala, Bhargava, Lanka, Chaitanya Krishna, Clive, Derik, Li, Edward, Wu, Hao, Hongtongsak, Kevin, Li, Ianna, Thakkar, Kalind, Omarov, Kuanysh, Majmundar, Kushal, Alverson, Michael, Kucharski, Michael, Patel, Mohak, Jain, Mudit, Zabelin, Maksim, Pelagatti, Paolo, Kohli, Rohan, Kumar, Saurabh, Kim, Joseph, Sankar, Swetha, Shah, Vineet, Ramachandruni, Lakshmi, Zeng, Xiangkai, Bariach, Ben, Weidinger, Laura, Vu, Tu, Andreev, Alek, He, Antoine, Hui, Kevin, Kashem, Sheleem, Subramanya, Amar, Hsiao, Sissie, Hassabis, Demis, Kavukcuoglu, Koray, Sadovsky, Adam, Le, Quoc, Strohman, Trevor, Wu, Yonghui, Petrov, Slav, Dean, Jeffrey, and Vinyals, Oriol

Subjects
Computer Science - Computation and Language, Computer Science - Artificial Intelligence, Computer Science - Computer Vision and Pattern Recognition
Abstract

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

Published
2023

14. FFINet: Future Feedback Interaction Network for Motion Forecasting

Author

Kang, Miao, Wang, Shengqi, Zhou, Sanping, Ye, Ke, Jiang, Jingjing, and Zheng, Nanning

Subjects
Computer Science - Computer Vision and Pattern Recognition, Computer Science - Artificial Intelligence
Abstract

Motion forecasting plays a crucial role in autonomous driving, with the aim of predicting the future reasonable motions of traffic agents. Most existing methods mainly model the historical interactions between agents and the environment, and predict multi-modal trajectories in a feedforward process, ignoring potential trajectory changes caused by future interactions between agents. In this paper, we propose a novel Future Feedback Interaction Network (FFINet) to aggregate features the current observations and potential future interactions for trajectory prediction. Firstly, we employ different spatial-temporal encoders to embed the decomposed position vectors and the current position of each scene, providing rich features for the subsequent cross-temporal aggregation. Secondly, the relative interaction and cross-temporal aggregation strategies are sequentially adopted to integrate features in the current fusion module, observation interaction module, future feedback module and global fusion module, in which the future feedback module can enable the understanding of pre-action by feeding the influence of preview information to feedforward prediction. Thirdly, the comprehensive interaction features are further fed into final predictor to generate the joint predicted trajectories of multiple agents. Extensive experimental results show that our FFINet achieves the state-of-the-art performance on Argoverse 1 and Argoverse 2 motion forecasting benchmarks., Comment: 11 pages, 8 figures, 12 tables

Published
2023

16. Generalizing Frobenius Inversion to Quaternion Matrices

Author

Chen, Qiyuan, Uhlmann, J., and Ye, Ke

Subjects
Mathematics - Numerical Analysis
Abstract

In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient that other existing methods. Moreover, our algorithm is optimal in the sense of the least number of complex inversions. On the practice side, our algorithm outperforms existing algorithms on randomly generated matrices. We argue that this algorithm can be used to improve the practical utility of recursive Strassen-type algorithms by providing the fastest possible base case for the recursive decomposition process when applied to quaternion matrices.

Published
2023

18. Influence Analysis of Damp Defect of Composite Insulated Zinc Oxide Arrester Based on Finite Element Calculation

Author

Li, Wenyan, Liu, Jiangming, Sun, Lintao, Liu, Changbiao, Ai, Yunfei, Wang, Zhi, Zhou, Jie, Ye, Ke, Angrisani, Leopoldo, Series Editor, Arteaga, Marco, Series Editor, Chakraborty, Samarjit, Series Editor, Chen, Jiming, Series Editor, Chen, Shanben, Series Editor, Chen, Tan Kay, Series Editor, Dillmann, Rüdiger, Series Editor, Duan, Haibin, Series Editor, Ferrari, Gianluigi, Series Editor, Ferre, Manuel, Series Editor, Jabbari, Faryar, Series Editor, Jia, Limin, Series Editor, Kacprzyk, Janusz, Series Editor, Khamis, Alaa, Series Editor, Kroeger, Torsten, Series Editor, Li, Yong, Series Editor, Liang, Qilian, Series Editor, Martín, Ferran, Series Editor, Ming, Tan Cher, Series Editor, Minker, Wolfgang, Series Editor, Misra, Pradeep, Series Editor, Mukhopadhyay, Subhas, Series Editor, Ning, Cun-Zheng, Series Editor, Nishida, Toyoaki, Series Editor, Oneto, Luca, Series Editor, Panigrahi, Bijaya Ketan, Series Editor, Pascucci, Federica, Series Editor, Qin, Yong, Series Editor, Seng, Gan Woon, Series Editor, Speidel, Joachim, Series Editor, Veiga, Germano, Series Editor, Wu, Haitao, Series Editor, Zamboni, Walter, Series Editor, Zhang, Junjie James, Series Editor, Tan, Kay Chen, Series Editor, Dong, Xuzhu, editor, and Cai, Li, editor

Published
2024
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19. Lower Bounds of Functions on Finite Abelian Groups

Author

Yang, Jianting, Ye, Ke, Zhi, Lihong, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Wu, Weili, editor, and Tong, Guangmo, editor

Published
2024
Full Text
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20. Lower Bounds of Functions on Finite Abelian Groups

Author

Yang, Jiangting, Ye, Ke, and Zhi, Lihong

Subjects
Mathematics - Optimization and Control
Abstract

The problem of computing the optimum of a function on a finite set is an important problem in mathematics and computer science. Many combinatorial problems such as MAX-SAT and MAXCUT can be recognized as optimization problems on the hypercube $C_2^n = \{-1,1\}^n$ consisting of $2^n$ points. It has been noticed that if a finite set is equipped with an abelian group structure, then one can efficiently certify nonnegative functions on it by Fourier sum of squares (FSOS). Motivated by these works, this paper is devoted to developing a framework to find a lower bound of a function on a finite abelian group efficiently. We implement our algorithm by the SDP solver SDPNAL+ for computing the verified lower bound of $f$ on $G$ and test it on the MAX-2SAT and MAX-3SAT benchmark problems from the Max-SAT competitions in 2009 and 2016. Beyond that, we also test our algorithm on random functions on $C_3^n$. These experiments demonstrate the advantage of our algorithm over previously known methods.

Published
2023

21. Simpler flag optimization

Author

Lai, Zehua, Lim, Lek-Heng, and Ye, Ke

Subjects
Mathematics - Optimization and Control, 14M15, 90C30, 90C53, 49Q12, 65F25, 62H12
Abstract

We study the geometry of flag manifolds under different embeddings into a product of Grassmannians. We show that differential geometric objects and operations -- tangent vector, metric, normal vector, exponential map, geodesic, parallel transport, gradient, Hessian, etc -- have closed-form analytic expressions that are computable with standard numerical linear algebra. Furthermore, we are able to derive a coordinate descent method in the flag manifold that performs well compared to other gradient descent methods., Comment: 26 pages

Published
2022

22. The Lazy Neuron Phenomenon: On Emergence of Activation Sparsity in Transformers

Author

Li, Zonglin, You, Chong, Bhojanapalli, Srinadh, Li, Daliang, Rawat, Ankit Singh, Reddi, Sashank J., Ye, Ke, Chern, Felix, Yu, Felix, Guo, Ruiqi, and Kumar, Sanjiv

Subjects
Computer Science - Machine Learning, Computer Science - Computation and Language, Computer Science - Computer Vision and Pattern Recognition, Statistics - Machine Learning
Abstract

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence., Comment: A short version was presented at ICLR 2023. Previous title: Large Models are Parsimonious Learners: Activation Sparsity in Trained Transformers

Published
2022

24. Complex matrix inversion via real matrix inversions

Author

Dai, Zhen, Lim, Lek-Heng, and Ye, Ke

Subjects
Mathematics - Numerical Analysis, Computer Science - Computational Complexity, 65F05, 15B33, 68W30
Abstract

We study the inversion analog of the well-known Gauss algorithm for multiplying complex matrices. A simple version is $(A + iB)^{-1} = (A + BA^{-1}B)^{-1} - i A^{-1}B(A+BA^{-1} B)^{-1}$ when $A$ is invertible, which may be traced back to Frobenius but has received scant attention. We prove that it is optimal, requiring fewest matrix multiplications and inversions over the base field, and we extend it in three ways: (i) to any invertible $A + iB$ without requiring $A$ or $B$ be invertible; (ii) to any iterated quadratic extension fields, with $\mathbb{C}$ over $\mathbb{R}$ a special case; (iii) to Hermitian positive definite matrices $A + iB$ by exploiting symmetric positive definiteness of $A$ and $A + BA^{-1}B$. We call all such algorithms Frobenius inversions, which we will see do not follow from Sherman--Morrison--Woodbury type identities and cannot be extended to Moore--Penrose pseudoinverse. We show that a complex matrix with well-conditioned real and imaginary parts can be arbitrarily ill-conditioned, a situation tailor-made for Frobenius inversion. We prove that Frobenius inversion for complex matrices is faster than standard inversion by LU decomposition and Frobenius inversion for Hermitian positive definite matrices is faster than standard inversion by Cholesky decomposition. We provide extensive numerical experiments, applying Frobenius inversion to solve linear systems, evaluate matrix sign function, solve Sylvester equation, and compute polar decomposition, showing that Frobenius inversion can be more efficient than LU/Cholesky decomposition with negligible loss in accuracy. A side result is a generalization of Gauss multiplication to iterated quadratic extensions, which we show is intimately related to the Karatsuba algorithm for fast integer multiplication and multidimensional fast Fourier transform., Comment: 29 pages, 8 figures

Published
2022

25. Fourier sum of squares certificates

Author

Yang, Jianting, Ye, Ke, and Zhi, Lihong

Subjects
Mathematics - Optimization and Control
Abstract

The non-negativity of a function on a finite abelian group can be certified by its Fourier sum of squares (FSOS). In this paper, we propose a method of certifying the non-negativity of an integer-valued function by an FSOS certificate, which is defined to be an FSOS with a small error. We prove the existence of exponentially sparse polynomial and rational FSOS certificates and we provide two methods to validate them. As a consequence of the aforementioned existence theorems, we propose a semidefinite programming (SDP)-based algorithm to efficiently compute a sparse FSOS certificate. For applications, we consider certificate problems for maximum satisfiability (MAX-SAT) and maximum k-colorable subgraph (MkCS) and demonstrate our theoretical results and algorithm by numerical experiments.

Published
2022

27. Skew-sparse matrix multiplication

Author

Huang, Qiao-Long, Ye, Ke, and Gao, Xiao-Shan

Subjects
Computer Science - Computational Complexity, Computer Science - Symbolic Computation, Mathematics - Numerical Analysis
Abstract

Based on the observation that $\mathbb{Q}^{(p-1) \times (p-1)}$ is isomorphic to a quotient skew polynomial ring, we propose a new method for $(p-1)\times (p-1)$ matrix multiplication over $\mathbb{Q}$, where $p$ is a prime number. The main feature of our method is the acceleration for matrix multiplication if the product is skew-sparse. Based on the new method, we design a deterministic algorithm with complexity $O(T^{\omega-2} p^2)$, where $T\le p-1$ is a parameter determined by the skew-sparsity of input matrices and $\omega$ is the asymptotic exponent of matrix multiplication. Moreover, by introducing randomness, we also propose a probabilistic algorithm with complexity $O^\thicksim(t^{\omega-2}p^2+p^2\log\frac{1}{\nu})$, where $t\le p-1$ is the skew-sparsity of the product and $\nu$ is the probability parameter.

Published
2022

29. When geometry meets optimization theory: partially orthogonal tensors

Author

Ye, Ke and Hu, Shenglong

Subjects
Mathematics - Optimization and Control, Mathematics - Numerical Analysis
Abstract

Due to the multi-linearity of tensors, most algorithms for tensor optimization problems are designed based on the block coordinate descent method. Such algorithms are widely employed by practitioners for their implementability and effectiveness. However, these algorithms usually suffer from the lack of theoretical guarantee of global convergence and analysis of convergence rate. In this paper, we propose a block coordinate descent type algorithm for the low rank partially orthogonal tensor approximation problem and analyse its convergence behaviour. To achieve this, we carefully investigate the variety of low rank partially orthogonal tensors and its geometric properties related to the parameter space, which enable us to locate KKT points of the concerned optimization problem. With the aid of these geometric properties, we prove without any assumption that: (1) Our algorithm converges globally to a KKT point; (2) For any given tensor, the algorithm exhibits an overall sublinear convergence with an explicit rate which is sharper than the usual $O(1/k)$ for first order methods in nonconvex optimization; {(3)} For a generic tensor, our algorithm converges $R$-linearly., Comment: 60 pages

Published
2022

30. Computing sparse Fourier sum of squares on finite abelian groups in quasi-linear time

Author

Yang, Jianting, Ye, Ke, and Zhi, Lihong

Subjects
Mathematics - Optimization and Control
Abstract

The problem of verifying the nonnegativity of a function on a finite abelian group is a long-standing challenging problem. The basic theory of representation theory of finite groups indicates that a function $f$ on a finite abelian group $G$ can be written as a linear combination of characters of irreducible representations of $G$ by $ f(x)=\sum_{\chi \in \widehat{G}} \widehat{f} (\chi)\chi(x)$, where $\widehat{G}$ is the dual group of $G$ consisting of all characters of $G$ and $ \widehat{f} (\chi)$ is the Fourier coefficient of $f$ at $\chi \in \widehat{G}$. In this paper, we show that by performing the fast (inverse) Fourier transform, we are able to compute a sparse Fourier sum of squares (FSOS) certificate of $f$ on a finite abelian group $G$ with complexity \if $\operatorname{O}\left(|G| \log(|G|)+\log(k_{\min})\operatorname{SDP}(2k_{\min})\right)$,\fi that is quasi-linear in the order of $G$ and polynomial in the FSOS sparsity \if $k_{\min}$\fi of $f$. Moreover, for a nonnegatvie function $f$ on a finite abelian group $G$ and a set $S \subset \widehat{G}$, we give a lower bound of the constant $M$ such that $f+M$ admits an FSOS supported on} $S$. We demonstrate the efficiency of the proposed algorithm by numerical experiments on various abelian groups of orders up to $10^7$. As applications, we also solve some combinatorial optimization problems and the sum of Hermitian squares (SOHS) problem \if on $\mathbb{T}^n$\fi by sparse FSOS.

Published
2022

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