Random features (RF) are a technique used in machine learning to approximate kernel methods, introduced by Ali Rahimi and Ben Recht in their 2007 paper "Random Features for Large-Scale Kernel Machines", and extended by. RF uses a Monte Carlo approximation to kernel functions by randomly sampled feature maps. It is used for datasets that are too large for traditional kernel methods like support vector machine, kernel ridge regression, and gaussian process. == Mathematics == === Kernel method === Given a feature map ϕ : R d → V {\textstyle \phi :\mathbb {R} ^{d}\to V} , where V {\textstyle V} is a Hilbert space (more specifically, a reproducing kernel Hilbert space), the kernel trick replaces inner products in feature space ⟨ ϕ ( x i ) , ϕ ( x j ) ⟩ V {\displaystyle \langle \phi (x_{i}),\phi (x_{j})\rangle _{V}} by a kernel function k ( x i , x j ) : R d × R d → R {\displaystyle k(x_{i},x_{j}):\mathbb {R} ^{d}\times \mathbb {R} ^{d}\to \mathbb {R} } Kernel methods replaces linear operations in high-dimensional space by operations on the kernel matrix: K X := [ k ( x i , x j ) ] i , j ∈ 1 : N {\displaystyle K_{X}:=[k(x_{i},x_{j})]_{i,j\in 1:N}} where N {\textstyle N} is the number of data points. === Random kernel method === The problem with kernel methods is that the kernel matrix K X {\textstyle K_{X}} has size N × N {\textstyle N\times N} . This becomes computationally infeasible when N {\textstyle N} reaches the order of a million. The random kernel method replaces the kernel function k {\textstyle k} by an inner product in low-dimensional feature space R D {\textstyle \mathbb {R} ^{D}} : k ( x , y ) ≈ ⟨ z ( x ) , z ( y ) ⟩ {\displaystyle k(x,y)\approx \langle z(x),z(y)\rangle } where z {\textstyle z} is a randomly sampled feature map z : R d → R D {\textstyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{D}} . This converts kernel linear regression into linear regression in feature space, kernel SVM into SVM in feature space, etc. Since we have K X ≈ Z X T Z X {\displaystyle K_{X}\approx Z_{X}^{T}Z_{X}} where Z X = [ z ( x 1 ) , … , z ( x N ) ] {\displaystyle Z_{X}=[z(x_{1}),\dots ,z(x_{N})]} , these methods no longer involve matrices of size O ( N 2 ) {\textstyle O(N^{2})} , but only random feature matrices of size O ( D N ) {\textstyle O(DN)} . == Random Fourier feature == === Radial basis function kernel === The radial basis function (RBF) kernel on two samples x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} is defined as k ( x i , x j ) = exp ( − ‖ x i − x j ‖ 2 2 σ 2 ) {\displaystyle k(x_{i},x_{j})=\exp \left(-{\frac {\|x_{i}-x_{j}\|^{2}}{2\sigma ^{2}}}\right)} where ‖ x i − x j ‖ 2 {\displaystyle \|x_{i}-x_{j}\|^{2}} is the squared Euclidean distance and σ {\displaystyle \sigma } is a free parameter defining the shape of the kernel. It can be approximated by a random Fourier feature map z : R d → R 2 D {\displaystyle z:\mathbb {R} ^{d}\to \mathbb {R} ^{2D}} : z ( x ) := 1 D [ cos ⟨ ω 1 , x ⟩ , sin ⟨ ω 1 , x ⟩ , … , cos ⟨ ω D , x ⟩ , sin ⟨ ω D , x ⟩ ] T {\displaystyle z(x):={\frac {1}{\sqrt {D}}}[\cos \langle \omega _{1},x\rangle ,\sin \langle \omega _{1},x\rangle ,\ldots ,\cos \langle \omega _{D},x\rangle ,\sin \langle \omega _{D},x\rangle ]^{T}} where ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are IID samples from the multidimensional normal distribution N ( 0 , σ − 2 I ) {\displaystyle N(0,\sigma ^{-2}I)} . Since cos , sin {\displaystyle \cos ,\sin } are bounded, there is a stronger convergence guarantee by Hoeffding's inequality. === Random Fourier features === By Bochner's theorem, the above construction can be generalized to arbitrary positive definite shift-invariant kernel k ( x , y ) = k ( x − y ) {\displaystyle k(x,y)=k(x-y)} . Define its Fourier transform p ( ω ) = 1 2 π ∫ R d e − j ⟨ ω , Δ ⟩ k ( Δ ) d Δ {\displaystyle p(\omega )={\frac {1}{2\pi }}\int _{\mathbb {R} ^{d}}e^{-j\langle \omega ,\Delta \rangle }k(\Delta )d\Delta } then ω 1 , . . . , ω D {\displaystyle \omega _{1},...,\omega _{D}} are sampled IID from the probability distribution with probability density p {\displaystyle p} . This applies for other kernels like the Laplace kernel and the Cauchy kernel. === Neural network interpretation === Given a random Fourier feature map z {\displaystyle z} , training the feature on a dataset by featurized linear regression is equivalent to fitting complex parameters θ 1 , … , θ D ∈ C {\displaystyle \theta _{1},\dots ,\theta _{D}\in \mathbb {C} } such that f θ ( x ) = R e ( ∑ k θ k e i ⟨ ω k , x ⟩ ) {\displaystyle f_{\theta }(x)=\mathrm {Re} \left(\sum _{k}\theta _{k}e^{i\langle \omega _{k},x\rangle }\right)} which is a neural network with a single hidden layer, with activation function t ↦ e i t {\displaystyle t\mapsto e^{it}} , zero bias, and the parameters in the first layer frozen. In the overparameterized case, when 2 D ≥ N {\displaystyle 2D\geq N} , the network linearly interpolates the dataset { ( x i , y i ) } i ∈ 1 : N {\displaystyle \{(x_{i},y_{i})\}_{i\in 1:N}} , and the network parameters is the least-norm solution: θ ^ = arg min θ ∈ C D , f θ ( x k ) = y k ∀ k ∈ 1 : N ‖ θ ‖ {\displaystyle {\hat {\theta }}=\arg \min _{\theta \in \mathbb {C} ^{D},f_{\theta }(x_{k})=y_{k}\forall k\in 1:N}\|\theta \|} At the limit of D → ∞ {\displaystyle D\to \infty } , the L2 norm ‖ θ ^ ‖ → ‖ f K ‖ H {\displaystyle \|{\hat {\theta }}\|\to \|f_{K}\|_{H}} where f K {\displaystyle f_{K}} is the interpolating function obtained by the kernel regression with the original kernel, and ‖ ⋅ ‖ H {\displaystyle \|\cdot \|_{H}} is the norm in the reproducing kernel Hilbert space for the kernel. == Other examples == === Random binning features === A random binning features map partitions the input space using randomly shifted grids at randomly chosen resolutions and assigns to an input point a binary bit string that corresponds to the bins in which it falls. The grids are constructed so that the probability that two points x i , x j ∈ R d {\displaystyle x_{i},x_{j}\in \mathbb {R} ^{d}} are assigned to the same bin is proportional to K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . The inner product between a pair of transformed points is proportional to the number of times the two points are binned together, and is therefore an unbiased estimate of K ( x i , x j ) {\displaystyle K(x_{i},x_{j})} . Since this mapping is not smooth and uses the proximity between input points, Random Binning Features works well for approximating kernels that depend only on the L 1 {\displaystyle L_{1}} distance between datapoints. === Orthogonal random features === Orthogonal random features uses a random orthogonal matrix instead of a random Fourier matrix. == Historical context == In NIPS 2006, deep learning had just become competitive with linear models like PCA and linear SVMs for large datasets, and people speculated about whether it could compete with kernel SVMs. However, there was no way to train kernel SVM on large datasets. The two authors developed the random feature method to train those. It was then found that the O ( 1 / D ) {\displaystyle O(1/D)} variance bound did not match practice: the variance bound predicts that approximation to within 0.01 {\displaystyle 0.01} requires D ∼ 10 4 {\displaystyle D\sim 10^{4}} , but in practice required only ∼ 10 2 {\displaystyle \sim 10^{2}} . Attempting to discover what caused this led to the subsequent two papers.
Jive (software)
Jive (formerly known as Clearspace, then Jive SBS, then Jive Engage) is a commercial Java EE-based Enterprise 2.0 collaboration and knowledge management tool produced by Jive Software. It was first released as "Clearspace" in 2006, then renamed SBS (for "Social Business Software") in March 2009, then renamed "Jive Engage" in 2011, and renamed simply to "Jive" in 2012. Jive integrates the functionality of online communities, microblogging, social networking, discussion forums, blogs, wikis, and IM under one unified user interface. Content placed into any of the systems (blog, wiki, documentation, etc.) can be found through a common search interface. Other features include RSS capability, email integration, a reputation and reward system for participation, personal user profiles, JAX-WS web service interoperability, and integration with the Spring Framework. The product is a pure-Java server-side web application and will run on any platform where Java (JDK 1.5 or higher) is installed. It does not require a dedicated server - users have reported successful deployment in both shared environments and multiple machine clusters. As of Jive 8, released March 30, 2015, there is a Jive-n version which is for internal use (hosted by the consumer or hosted by Jive as a service) and a Jive-x version which is an external version hosted as a service. Jive no longer supports wiki markup language. == Server requirements for Jive 8-n == The following are the server requirements for Jive 8-n Operating systems: RHEL version 6 or 7 for x86_64, CentOS version 6 or 7 for x86_64 or SuSE Enterprise Linux Server (SLES) 11 and 12 for x86_64 Application Servers: Jive ships with its own embedded Apache HTTPD and Tomcat servers as part of the install package. It is not possible to deploy the application onto other appservers. Databases: MySQL (5.1, 5.5, 5.6) Oracle (11gR2, 12c) Postgres (9.0, 9.1, 9.2, 9.3, 9.4 - 9.2 or higher recommended) Microsoft SQL Server (2008R2, 2012, 2014) Environment: Jive recommends a server with at least 4GB of RAM and a dual-core 2 GHz processor with x86_64 architecture The product integrates with an LDAP repository or Active Directory For optimal deployment with a large community Jive Software recommends: using dedicated cache and document-conversion servers hosting the application and database servers separately == Releases == Jive 8, released on March 30, 2015 Jive 7, released in October 2013 Jive 9.0.x, released in November 2016 Jive 9, released in November 2016, supported now
Jiaya Jia
Jiaya Jia (Chinese: 贾佳亚) is a Chair Professor of the Department of Computer Science and Engineering at The Hong Kong University of Science and Technology (HKUST). He is an IEEE Fellow, the associate editor-in-chief of one of IEEE’s flagship and premier journals- Transactions on Pattern Analysis and Machine Intelligence (TPAMI), as well as on the editorial board of International Journal of Computer Vision (IJCV). == Early life and education == Jiaya Jia joined CUHK in 2004 as an assistant professor, and was promoted to full professor in 2015. He obtained his PhD degree in computer science jointly from Hong Kong University of Science and Technology and Microsoft Research in 2004. From March 2003 to August 2004, he was a visiting scholar at Microsoft. He conducted collaborative research at Adobe Research in 2007. == Career == Jiaya Jia is a distinguished scientist in the fields of computer vision and artificial intelligence. His research team at HKUST, DV Lab, is one of the largest vision AI research teams in the world and has been making significant contribution to advanced development of computer vision algorithms and technologies with focuses on image/video understanding, detection and segmentation, multi-modal AI, computational imaging, practical optimization, and advanced learning for visual content since 2000. Jiaya Jia has published 200+ top papers and was cited 80,000+ times on Google Scholar with H-Index 110+. 40+ PhDs and fellows from this group are now active in academia and industry, and have become prominent AI tech leaders as professors, directors in major research labs, and founders of several successful startups. Jiaya Jia assumes the position of associate editor-in-chief of IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) since 2021. He is also on the editorial board of International Journal of Computer Vision (IJCV). Jiaya Jia has served as the area chair of ICCV, CVPR, AAAI, ECCV, and several other premium international AI conferences for years. He was on program committees of major conferences in graphics and computational imaging, including ICCP, SIGGRAPH, and SIGGRAPH Asia. == Research == The research areas of Jiaya Jia are computer vision, large X models, and deep learning. Jiaya Jia has made outstanding contributions to computer vision technology, algorithms and engineering, and is among the world's leading experts in the field. His research partners include numerous renowned multinational technology companies, such as Microsoft, Qualcomm, Adobe, Intel, NVIDIA, Amazon, and Lenovo. Jia has cultivated a number of outstanding talents with Master's and PhDs who continue to engage in scientific research and development in computer vision. Many technologies in image analysis and processing developed by Jiaya Jia are still leading in the field worldwide. Wherein, his achievements in image deblurring, filtering, image sparse processing, multi-band image signal fusion and enhancement, large range motion estimation, texture and structure-based layering, etc. have been published in the industry's most influential conferences and publications, and implemented in the real-world applications. These achievements have demonstrated outstanding performance in established systems, and most of which are open source so as to enable wider applications across industries such as aviation, medical imaging, safety management, robotic design, meteorological analysis and many more. == Selected publications == In his over 20 years of research experience, Jiaya Jia has published 200+ top papers that have been cited more than 80,000 times. According to HKUST Website in August 2024, Jiaya Jia has accumulatively published over 200 scientific papers in books, journals and conferences, such as IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), International Journal of Computer Vision (IJCV) "Computer Vision and Pattern Recognition (CVPR)", and "International Conference on Computer Vision (ICCV)". Representative papers include: Jiaya Jia: Mathematical Models and Practical Solvers for Uniform Motion Deblurring (in Motion Deblurring: Algorithms and Systems), Cambridge University Press, ISBN 9781107044364, 2014; Jiaya Jia: “Matte Extraction” Book: Computer Vision - A Reference Guide, Springer, ISBN 9780387307718 Editor-in-chief: Ikeuchi, Katsushi; Jiaya Jia, Chi-Keung Tang：Image Stitching Using Structure Deformation，IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), Vol. 30, No. 4, 2008; Jiaya Jia, Jian Sun, Chi-Keung Tang, Heung-Yeung Shum：Drag-and-Drop Pasting，ACM Transactions on Graphics (also in SIGGRAPH 2006), Vol. 25, No. 3, 2006. Xiaojuan Qi, Zheng zhe Liu, Renjie Liao, Philip HS Torr, Raquel Urtasun, Jiaya Jia：GeoNet++: Iterative Geometric Neural Network with Edge-Aware Refinement for Joint Depth and Surface Normal Estimation，IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI). Accepted. == Selected honors and awards == ACM Fellow. 1st Place of WAD Drivable Area Segmentation Challenge 2018; 1st Place of LSUN'17 Instance and Semantic Segmentation Challenges; 1st Place of COCO Instance Segmentation Challenge 2017; 2nd Place in COCO Detection Challenge 2017; 1st Place of ImageNet Scene Parsing Challenge 2016 with the paper PSPNet presented in CVPR 2017.
Danqi Chen
Danqi Chen (Chinese: 陈丹琦; pinyin: Chén Dānqí, IPA: [ʈ͡ʂʰə̌n tan t͡ɕʰǐ]; born in Changsha, China) is a Chinese computer scientist and assistant professor at Princeton University specializing in the AI field of natural language processing (NLP). In 2019, she joined the Princeton NLP group, alongside Sanjeev Arora, Christiane Fellbaum, and Karthik Narasimhan. She was previously a visiting scientist at Facebook AI Research (FAIR). She earned her Ph.D. at Stanford University and her BS from Tsinghua University. Chen is the author of Neural Reading Comprehension and Beyond, a dissertation on using artificial intelligence to access knowledge in ordinary and structured documents. She is the author or co-author of a number of journal articles, including Reading Wikipedia to Answer Open-Domain Questions. Google's SyntaxNet is based on algorithms developed by Danqi Chen and Christopher Manning at Stanford. Her primary research interests are in text understanding and knowledge representation and reasoning. She won a gold medal at the 2008 International Informatics Olympiad. She is known among friends as CDQ. A well known algorithm in competitive programming, CDQ Divide and Conquer, is named after this acronym. She is married to Huacheng Yu, an assistant professor in theoretical computer science at Princeton University.
Top 10 AI Text-to-video Tools Compared (2026)
Trying to pick the best AI text-to-video tool? An AI text-to-video tool is software that uses machine learning to help you get more done — it scales effortlessly from a single task to thousands. The best picks balance beginner-friendly simplicity with the depth power users need, and they ship updates often. Whether you are a beginner or a pro, the right AI text-to-video tool slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
You.com
You.com is an artificial intelligence search startup that has pivoted away from consumer search engine operations toward business-focused AI tools and APIs. The company was founded in 2020 by Richard Socher, the former chief scientist at Salesforce, and Bryan McCann, a former NLP researcher at Salesforce. == History == Following its 2020 founding, You.com opened its public beta on November 9, 2021, and received $20 million in funding led by Salesforce founder and CEO Marc Benioff. Other investors include Breyer Capital, Sound Ventures, and Day One Ventures. The domain You.com was initially purchased in 1996 by Benioff. Benioff invested in You.com and transferred ownership of the You.com domain name to the company. In July 2022, You.com announced its $25 million Series A funding round led by Radical Ventures with participation from Time Ventures, Breyer Capital, Norwest Venture Partners and Day One Ventures. In September 2024, You.com raised $50 million in Series B funding led by Georgian. In September 2025, You.com raised $100 million in Series C funding led by Cox Enterprises at a $1.5 billion valuation, achieving unicorn status. == Business model == You.com generates revenue primarily through enterprise sales of search APIs and AI tools. The platform provides web search capabilities that can be integrated into enterprise applications and AI agents. == Features == On December 23, 2022, You.com was the first search engine to launch an LLM chatbot with live web results alongside its responses. Initially known as YouChat, the chatbot was primarily based on the GPT-3.5 large language model and could answer questions, suggest ideas, translate text, summarize articles, compose emails, and write code snippets, while staying up-to-date with current events and citing sources. Several further versions of YouChat were released. The second version, called YouChat 2.0, was released on February 7, 2023, incorporated improved conversational AI and community-built applications by blending a large language model named C-A-L (Chat, Apps, and Links). This update enabled YouChat to provide results in various formats, such as charts, photos, videos, tables, graphs, text or code, so users can find answers without leaving the search results page. YouChat 3.0, unveiled on May 4, 2023, combined chat functionality with results from Reddit, TikTok, Stack Overflow and Wikipedia. === YouPro === On June 21, 2023, You.com introduced YouPro, a paid subscription. Both free and paid versions provide access to large language models connected to the internet with citation capabilities. === ARI === In February 2025, You.com launched ARI (Advanced Research and Insights), a deep research agent that scans over 400 sources simultaneously to produce research reports with verified citations and interactive graphs, charts, and visualizations. The platform targets regulated industries where comprehensive source verification is critical, with customers including healthcare publishers and advisory firms. == Reception == You.com was named one of TIME's Best Inventions of 2022. You.com's ARI (Advanced Research & Insights) feature was named one of TIME's Best Inventions of 2025.
Lillian Lee (computer scientist)
Lillian Lee is a computer scientist whose research involves natural language processing, sentiment analysis, and computational social science. She is a professor of computer science and information science at Cornell University, and co-editor-in-chief of the journal Transactions of the Association for Computational Linguistics. == Education == Lee graduated from Cornell University in 1993 with an undergraduate degree in math and science. She completed her Ph.D. at Harvard University in 1997. Her dissertation, Similarity-Based Approaches to Natural Language Processing, was supervised by Stuart M. Shieber. == Career == Lee has been a member of the Cornell faculty since 1997. == Recognition == Lee has been a fellow of the Association for the Advancement of Artificial Intelligence since 2013, and of the Association for Computational Linguistics since 2017. Lee was elected as an ACM Fellow in 2018 for "contributions to natural language processing, sentiment analysis, and computational social science".