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Awari

awari

Author:
(1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Table of Links Abstract and Intro Related Works Methods Results Discussion and Conclusions and Acknowledgements Additional Information and Declarations and References Additional Information and Declarations Competing Interests The author declares that there are no competing interests. Author Contributions Hiroki Takizawa conceived and designed the research, implemented and performed the computational experiments, analyzed the data, prepared figures and tables, authored drafts of the paper, and approved the final draft. Data Availability The source code of modified Edax is available at GitHub (https://github.com/eukaryo/edax-reversi-AVX-v446mod2), and Zenodo (https://doi.org/10.5281/zenodo.10030906). The raw outputs of analyses are available at figshare (https://doi.org/10.6084/m9.figshare.24420619). The source code for analyses are available at GitHub (https://github.com/eukaryo/reversi-scripts). Funding The author did not receive any academic funding for this study. References [1] Charles Babbage. Passages from the Life of a Philosopher. London: Longman, 1864. [2] Claude E Shannon. Xxii. programming a computer for playing chess. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(314):256–275, 1950. [3] Murray Campbell, A. Joseph Hoane, and Feng-hsiung Hsu. Deep blue. Artif. Intell., 134(1–2):57–83, January 2002. [4] David Silver, Aja Huang, Christopher J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the game of go with deep neural networks and tree search. nature, 529(7587):484–489, 2016. [5] Tomoyuki Kaneko and Takenobu Takizawa. Computer shogi tournaments and techniques. IEEE Transactions on Games, 11(3):267–274, 2019. [6] David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science, 362(6419):1140–1144, 2018. [7] Michael Buro. The othello match of the year: Takeshi murakami vs. logistello. ICGA Journal, 20(3):189–193, 1997. [8] L. V. Allis. Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Department of Computer Science, University of Limburg, 1994. [9] Hiroki Takizawa. Strongly solved ostle: calculating a strong solution helps compose high-quality puzzles for recent games. PeerJ Computer Science, 9:e1560, 2023. [10] Jonathan Schaeffer, Neil Burch, Yngvi Björnsson, Akihiro Kishimoto, Martin Müller, Robert Lake, Paul Lu, and Steve Sutphen. Checkers is solved. science, 317(5844):1518–1522, 2007. [11] Ralph Gasser. Solving nine men’s morris. Computational Intelligence, 12(1):24–41, 1996. [12] John W Romein and Henri E Bal. Solving awari with parallel retrograde analysis. Computer, 36(10):26–33, 2003. [13] Donald E Knuth and Ronald W Moore. An analysis of alpha-beta pruning. Artificial intelligence, 6(4):293–326, 1975. [14] Ken Thompson. Retrograde analysis of certain endgames. J. Int. Comput. Games Assoc., 9(3):131–139, 1986. [15] Ayumu Nagai. Df-pn algorithm for searching AND/OR trees and its applications. PhD thesis, Department of Information Science, University of Tokyo, 2002. [16] Akihiro Kishimoto, Mark HM Winands, Martin Müller, and Jahn-Takeshi Saito. Game-tree search using proof numbers: The first twenty years. Icga Journal, 35(3):131–156, 2012. [17] L.Victor Allis, Maarten van der Meulen, and H.Jaap van den Herik. Proof-number search. Artificial Intelligence, 66(1):91–124, 1994. [18] Rainer Feldmann, Burkhard Monien, Peter Mysliwietz, and Oliver Vornberger. Distributed game tree search. Parallel Algorithms for Machine Intelligence and Vision, pages 66–101, 1990. [19] Emil Fredrik Østensen. A complete chess engine parallelized using lazy smp. Master’s thesis, University of Oslo, 2016. [20] Mark Gordon Brockington. Asynchronous Parallel Garne-Tree Search. PhD thesis, University of Alberta, 1998. [21] Jean-Christophe Weill. The abdada distributed minimax search algorithm. In Proceedings of the 1996 ACM 24th Annual Conference on Computer Science, CSC ’96, page 131–138, New York, NY, USA, 1996. Association for Computing Machinery. [22] Richard Delorme. edax-reversi. https://github.com/abulmo/edax-reversi, 2021. Last retrieved 2023-07-07. [23] French Othello Federation. La base wthor. https://www.ffothello.org/informatique/la-base-wthor/, 2021. Last retrieved 2023-10-13. This paper is available on arxiv under CC 4.0 license. Author: (1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Author: Author: (1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Table of Links Abstract and Intro Abstract and Intro Related Works Related Works Methods Methods Results Results Discussion and Conclusions and Acknowledgements Discussion and Conclusions and Acknowledgements Additional Information and Declarations and References Additional Information and Declarations and References Additional Information and Declarations Competing Interests The author declares that there are no competing interests. Author Contributions Hiroki Takizawa conceived and designed the research, implemented and performed the computational experiments, analyzed the data, prepared figures and tables, authored drafts of the paper, and approved the final draft. Data Availability The source code of modified Edax is available at GitHub (https://github.com/eukaryo/edax-reversi-AVX-v446mod2), and Zenodo (https://doi.org/10.5281/zenodo.10030906). The raw outputs of analyses are available at figshare (https://doi.org/10.6084/m9.figshare.24420619). The source code for analyses are available at GitHub (https://github.com/eukaryo/reversi-scripts). Funding The author did not receive any academic funding for this study. References [1] Charles Babbage. Passages from the Life of a Philosopher. London: Longman, 1864. [2] Claude E Shannon. Xxii. programming a computer for playing chess. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 41(314):256–275, 1950. [3] Murray Campbell, A. Joseph Hoane, and Feng-hsiung Hsu. Deep blue. Artif. Intell., 134(1–2):57–83, January 2002. [4] David Silver, Aja Huang, Christopher J. Maddison, Arthur Guez, Laurent Sifre, George van den Driessche, Julian Schrittwieser, Ioannis Antonoglou, Veda Panneershelvam, Marc Lanctot, Sander Dieleman, Dominik Grewe, John Nham, Nal Kalchbrenner, Ilya Sutskever, Timothy Lillicrap, Madeleine Leach, Koray Kavukcuoglu, Thore Graepel, and Demis Hassabis. Mastering the game of go with deep neural networks and tree search. nature, 529(7587):484–489, 2016. [5] Tomoyuki Kaneko and Takenobu Takizawa. Computer shogi tournaments and techniques. IEEE Transactions on Games, 11(3):267–274, 2019. [6] David Silver, Thomas Hubert, Julian Schrittwieser, Ioannis Antonoglou, Matthew Lai, Arthur Guez, Marc Lanctot, Laurent Sifre, Dharshan Kumaran, Thore Graepel, Timothy Lillicrap, Karen Simonyan, and Demis Hassabis. A general reinforcement learning algorithm that masters chess, shogi, and go through self-play. Science, 362(6419):1140–1144, 2018. [7] Michael Buro. The othello match of the year: Takeshi murakami vs. logistello. ICGA Journal, 20(3):189–193, 1997. [8] L. V. Allis. Searching for Solutions in Games and Artificial Intelligence. PhD thesis, Department of Computer Science, University of Limburg, 1994. [9] Hiroki Takizawa. Strongly solved ostle: calculating a strong solution helps compose high-quality puzzles for recent games. PeerJ Computer Science, 9:e1560, 2023. [10] Jonathan Schaeffer, Neil Burch, Yngvi Björnsson, Akihiro Kishimoto, Martin Müller, Robert Lake, Paul Lu, and Steve Sutphen. Checkers is solved. science, 317(5844):1518–1522, 2007. [11] Ralph Gasser. Solving nine men’s morris. Computational Intelligence, 12(1):24–41, 1996. [12] John W Romein and Henri E Bal. Solving awari with parallel retrograde analysis. Computer, 36(10):26–33, 2003. [13] Donald E Knuth and Ronald W Moore. An analysis of alpha-beta pruning. Artificial intelligence, 6(4):293–326, 1975. [14] Ken Thompson. Retrograde analysis of certain endgames. J. Int. Comput. Games Assoc., 9(3):131–139, 1986. [15] Ayumu Nagai. Df-pn algorithm for searching AND/OR trees and its applications. PhD thesis, Department of Information Science, University of Tokyo, 2002. [16] Akihiro Kishimoto, Mark HM Winands, Martin Müller, and Jahn-Takeshi Saito. Game-tree search using proof numbers: The first twenty years. Icga Journal, 35(3):131–156, 2012. [17] L.Victor Allis, Maarten van der Meulen, and H.Jaap van den Herik. Proof-number search. Artificial Intelligence, 66(1):91–124, 1994. [18] Rainer Feldmann, Burkhard Monien, Peter Mysliwietz, and Oliver Vornberger. Distributed game tree search. Parallel Algorithms for Machine Intelligence and Vision, pages 66–101, 1990. [19] Emil Fredrik Østensen. A complete chess engine parallelized using lazy smp. Master’s thesis, University of Oslo, 2016. [20] Mark Gordon Brockington. Asynchronous Parallel Garne-Tree Search. PhD thesis, University of Alberta, 1998. [21] Jean-Christophe Weill. The abdada distributed minimax search algorithm. In Proceedings of the 1996 ACM 24th Annual Conference on Computer Science, CSC ’96, page 131–138, New York, NY, USA, 1996. Association for Computing Machinery. [22] Richard Delorme. edax-reversi. https://github.com/abulmo/edax-reversi, 2021. Last retrieved 2023-07-07. [23] French Othello Federation. La base wthor. https://www.ffothello.org/informatique/la-base-wthor/, 2021. Last retrieved 2023-10-13. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Othello Is Solved: But If You're Curiousity Is Still Running Rampant, Check Out These References

Author:
(1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Table of Links Abstract and Intro Related Works Methods Results Discussion and Conclusions and Acknowledgements Additional Information and Declarations and References 2 Related Works 2.1 Solved Games To the best of our knowledge, the latest game solved prior to this study as a grand challenge is checkers [10]. However, many nontrivial games have been solved, including Connect Four [8], Qubic [8], Go-Moku [8], Nine Men’s Morris [11], and Awari [12]. The difficulty of solving these games largely depends on the number of positions or situations in the game. Solving a game not only reveals its outcome but can also be useful in creating puzzles based on that game [9]. 2.2 Solving Technique The algorithms used to solve games have been extensively studied, and they are chosen based on the purpose and nature of the game. For weak solutions, alpha-beta search [13] is often used, while retrograde analysis [14] is frequently used for strong solutions. Additionally, algorithms like depth-first proof-number (df-pn) search [15, 16], which is based on proof-number (pn) search [17], have been developed to solve puzzles with very long solution sequences. In our study, we utilized alpha-beta search because our goal was to obtain a weak solution. 2.3 Algorithms for Parallel Search Alpha-beta search is an algorithm that sequentially performs depth-first search of a game graph, and naive parallelization does not improve search efficiency very much. Many algorithms have been developed for efficient parallelization. Young Brothers Wait Concept (YBWC) [18] and Lazy SMP [19] are popular methods for shared memory environments (e.g., a single computer). Algorithms suited for distributed memory environments (e.g., supercomputers or cloud computing) might include Asynchronous Parallel Hierarchical Iterative Deepening (APHID) [20] and ABDADA [21]. However, distributed memory environments greatly differ due to various factors including the bandwidth and latency of interconnects between nodes, and thus the appropriate algorithms may also differ. Therefore, developers who work with current or future distributed memory environments may need to choose or develop algorithms that are appropriate for those environments. This paper is available on arxiv under CC 4.0 license. Author: (1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Author: Author: (1) Hiroki Takizawa, Preferred Networks, Inc., Chiyoda-ku, Tokyo, Japan (contact@hiroki-takizawa.name). Table of Links Abstract and Intro Abstract and Intro Related Works Related Works Methods Methods Results Results Discussion and Conclusions and Acknowledgements Discussion and Conclusions and Acknowledgements Additional Information and Declarations and References Additional Information and Declarations and References 2 Related Works 2.1 Solved Games To the best of our knowledge, the latest game solved prior to this study as a grand challenge is checkers [10]. However, many nontrivial games have been solved, including Connect Four [8], Qubic [8], Go-Moku [8], Nine Men’s Morris [11], and Awari [12]. The difficulty of solving these games largely depends on the number of positions or situations in the game. Solving a game not only reveals its outcome but can also be useful in creating puzzles based on that game [9]. 2.2 Solving Technique The algorithms used to solve games have been extensively studied, and they are chosen based on the purpose and nature of the game. For weak solutions, alpha-beta search [13] is often used, while retrograde analysis [14] is frequently used for strong solutions. Additionally, algorithms like depth-first proof-number (df-pn) search [15, 16], which is based on proof-number (pn) search [17], have been developed to solve puzzles with very long solution sequences. In our study, we utilized alpha-beta search because our goal was to obtain a weak solution. 2.3 Algorithms for Parallel Search Alpha-beta search is an algorithm that sequentially performs depth-first search of a game graph, and naive parallelization does not improve search efficiency very much. Many algorithms have been developed for efficient parallelization. Young Brothers Wait Concept (YBWC) [18] and Lazy SMP [19] are popular methods for shared memory environments (e.g., a single computer). Algorithms suited for distributed memory environments (e.g., supercomputers or cloud computing) might include Asynchronous Parallel Hierarchical Iterative Deepening (APHID) [20] and ABDADA [21]. However, distributed memory environments greatly differ due to various factors including the bandwidth and latency of interconnects between nodes, and thus the appropriate algorithms may also differ. Therefore, developers who work with current or future distributed memory environments may need to choose or develop algorithms that are appropriate for those environments. This paper is available on arxiv under CC 4.0 license. This paper is available on arxiv under CC 4.0 license. available on arxiv

Solving Othello: Related Works You Should Be Aware Of

In 2021, hosted the first-ever awards!! HackerNoon Startup of the Year The goal of this campaign was to give recognition to the hardworking startups who pulled through the pandemic -- growing and thriving (despite all of the challenges). More than 44,000 startups were nominated all across the globe! They were selected from over 4,553 cities, with a total number of * cough * “4 billion” votes. Insane, right? To see who is a winner in each respective city, visit and pick a city. The name at the top of the list is the winner. (Awards, with compromised reviews, are under review.) startups.hackernoon.com The will announce the winners per region in their respective cities. Startups Winners Announcement Series Apparently, South America startups did incredibly well in that regard. With so many, until now, uncrowned jewels, it’s time we present to you... * drumroll* 🥳 The South America Startups of the Year Winners! Santiago, Chile Chile is known for being the most stable country to do business in Latin America, ranking 13th in The Economist’s Business Environment Index. Moreover, according to the Global Innovation Index, Chile ranks first in Latin America for innovation and is recognised as Chilean Silicon Valley with Santiago being the central city. The winner is…. QCObjects It is the 1st world class open-source framework made in Latin-America. São Paulo, Brazil And the winner of Brazil’s vibrant financial center is... Innvo Digital Their mission is to create the best ecosystem for a technology professional to work and undertake while sharing it with our customers and society. São Carlos The absolute leader of Sao Carlos seems to be: Predify Predify is an online software for optimizing pricing proccess and improving profits with AI and Big Data Analytics. Belo Horizonte, Brazil With a more than noble goal, Belo Horizone’s winner is: CM Tecnologia CM Tecnologia is an online scheduling system for healthcare providers in Brazil. Porto Alegre, Brazil With the focus on data protection, Porto Alegre, Brazil’s winner is…. Privacy Tools Privacy compliance platform, based on AI/Blockchain, which helps global companies to keep compliant with the data protection requirements. Brasil, Brazil With the focus on EdTech, Brasil is bringing us: Awari Awari is a YC-W21 company focusing on education for the Tech Industry. The company is growing at a fast pace and has gathered experts from all leading tech companies into a full education experience to prepare the next cohort of tech talent. Quito The capital of Ecuador, and also the closest capital to the actual equator, as the winner brings us: Agrodemanda The most comprehensive agricultural directory in Ecuador. Rio De Janeiro, Brazil Rio de Janeiro has more than 300 startups and is ranked 3rd in Brazil in terms of startup ecosystem development. The city is famous for the startups in the spheres of education, energy & environment and foodtech. Their winner is…. Bybrand Bybrand is the simplest way to save time and avoid frustration when managing your employee's email signatures. Buenos Aires, Argentina Buenos Aires, Argentina is not only the cosmopolitan capital with a vibrant history. It’s also Latin America’s most important port. Which makes their winner actually a very logical choice. Please meet: Liftit Liftit is the leading technology platform to automate and execute last-mile truck deliveries across Latin America. Curitiba, Brazil With a more noble mission and sustainability in mind, Curitiba, Brazil, as the winner brings us... Discrepante is the marketplace for a more human and sustainable economy Discrepante.com Florianópolis, Brazil Would you really be surprised one of the Brazil’s winners is related to football training? We neither. Please meet... Fútbol Fit Club Football FitClub® is a fitness training firm that gives fitness training to improve like a professional football player. Medellín, Colombia And the first Colombian Startup Winner is is a data intelligence solution powered by a high quality team. Meet... LogComex Market intelligence for international trade in Latin America Montevideo, Uruguay The host of inaugural FIFA world cup of 1930 comes through when it comes to innovation even in 2021. I’d like to introduce you to: Drop Technologies First electronic hand antiperspirant device Lima, Peru Lima, Peru, has in 2021 delivered some amazing results when it comes to blockchain technology. Their winner is very well deserved: RSK Labs RSK is the first open-source smart contract platform São Carlos Do Pinhal Well this is a unique case. The absolute unanimous winner of São Carlos Do Pinhal is: brain4care brain4care solution enables monitoring intracranial compliance noninvasively anywhere Blumenau, Brazil We’re sensing a theme here. Another stellar EdTech winner is coming from Blumenau, Brazil. Please meet... Uniasselvi Uniasselvi is a Brazilian distance-learning company that offers more than 60 undergraduate and postgraduate courses, in person and distance. Bogotá, Colombia Startups of Bogotá, Colombia definitely showed they’re not to be underestimated. With a very noble mission, let me introduce you to: Risü Risü is an online platform that links online consumption to donation to social institutions. Campina, Brazil If there’s one typo of business we’d single out as taking the biggest hit out of the pandemic, it would have to be small businesses. Thankfully, the winner of Campina, Brazil, operates with small businesses in mind Superlógica Tecnologias Ltda. Superlogica is a management system company created for small service businesses. Cerqueira César, Brazil Swooping half the points from the entire City, this year’s winners of Cerqueira César are InfoPrice INFOPRICE is a business intelligence company focused on physical retail pricing. Governador Valadares, Brazil The same can be said for the winners here. Let’s hear it for: Grupo KPG Saas, Payment, Manufacture, Pharmaceutical, E-commerce, Marketplace, Logistics Caxias Do Sul Known for wine making and Italian cultural influence, Caxias Do Sul brings as an interesting winner. Studio 360 Studio 360 is a proptech focused on easing the purchase experience for real state companies, brokers, and costumers. Sorocaba From Sorocaba, we have an interesting concept coming. Looking forward to seeing it further develop. Let’s meet: Quinto Quinto is a social network that represents the collective opinion of society—to help democracy evolve through technology Viña Del Mar To be a venue-oriented business and survive through the pandemic definitely deserves some recognition. In the name of that, let’s meet: SonicPollen SonicPollen, based in Chile, is a web-based booking platform that connects bands with venues and organizers. Lages Learn more about high-growth startups in Lages, South America. and the winner is…. Qualiall Qualiall develops technologies for training in operational processes such as work security, equipment maintenance, and more. Córdoba, Argentina Another gem from Argentina brings us unique agricultural solutions. Please meet: Kilimo Kilimo is a Big Data solution for water management in agriculture. São José Dos Campos, Brazil Another great agricultural solution comes this time from Brasil. Meet São José Dos Campos Startup winner: TerraMagna TerraMagna is a fintech company that focuses on risk mitigation for agribusinesses. São Leopoldo, Brazil Event-oriented businesses that have survived in the previous years should definitely bottle their perseverance and start selling it. One of those is definitely this winner: Wedy Wedy offers a one-stop-social marketplace for weddings. Pelotas, Brazil Medical scheduling platforms are definitely something we need to see more of. So glad Pelotos winner comes from this particular niche. Fácil Consulta Fácil Consulta is a booking platform that allows people to schedule an appointment with a Specialist Physician in their area. Santa Maria Could you believe how versatile the startups of South America are when we are only now coming across a game development studio? Let’s meet them Imgnation Studios Imgnation Studios is a game development studio that focuses on virtual reality. Asunción, Paraguay A FinTech solution coming from Paraguay. Meet Asunción Startup of the Year winner Vision Banco Vision Banco is a solid and growing financial institution serving the financial needs of the micro, small and medium enterprises. Caracas Venezualan food delivery app that seemed to have your heart. Meet Caracas Startup of the Year winner Yummy Inc. First Food Delivery App in Venezuela Recife A suitable combo between gaming and education, Recife Startup of the Year winner brings revolutionary solutions. Let’s meet them. Joy Street Joy Street offers develops video games focused on educational needs. Rosario, Argentina The winner of Rosario Startup of the Year award for 2021 is... Gbot Gbot is an autonomous robot that controls weeds without using agrochemicals. We also collect data in fields and generate precision maps. Vila Olímpia, Brazil The winner of Vila Olímpia Startup of the Year award for 2021 is... Seekr Seekr operates in the Information Technology sector, providing tools for managing and monitoring of brands. Barueri The winner of Barueri Startup of the Year award for 2021 is.... Glic Brazilian mhealth (web/app) platform for diabetes management Brasília The winner of Brasília Startup of the Year award for 2021 is... Ticies Ticies is a social network that helps people plan where to go with their friends, relatives and acquaintances, in all cities of the world. Juiz De Fora The winner of Juiz De Fora Startup of the Year award for 2021 is... Qranio Qranio is a gamified mobile learning platform for enterprises that rewards learning and stimulates users to engage with educational content. La Paz The winner of La Paz Startup of the Year award for 2021 is... Jukumari Advice 360 photo based market place for responsible tour operators Temuco The winner of Temuco Startup of the Year award for 2021 is... GoFeels GoFeels is the first independent hospitality network in the world. We promote collaborative work among hotels around the world. Vitacura The winner of Vitacura Startup of the Year award for 2021 is... MeatMe MeatMe delivers meats and accessories to have a culinary experience. Barranquilla The winner of Barranquilla Startup of the Year award for 2021 is... Mandaos Mandaos is a digital platform that connects companies and people with a network of independent messengers Ceará The winner of Ceará Startup of the Year award for 2021 is... Caroá Caroá is a cooperative that sells 34 varieties of vegetables, organic fruits, and vegetables. Chapecó The winner of Chapecó Startup of the Year award for 2021 is... HortiAgro HortiAgro is a seed and fertilizer market. Chile Chico The winner of Chile Chico Startup of the Year award for 2021 is... Gleengo Gleengo connects children with their favorite toys, through a tiny device and an application based on text-to-voice. Goiânia The winner of Goiânia Startup of the Year award for 2021 is... Auvo Auvo is an external teams management software. Itá The winner of Itá Startup of the Year award for 2021 is... TISSUELAB Tissuelab is a research and development center focused on biotechnology, and systems for reconstructive musculoskeletal surgery. Jardim Paulista The winner of Jardim Paulista Startup of the Year award for 2021 is... DiviCom DiviCom is a digital video networking company that designs, integrates, and markets complete systems. João Pessoa The winner of João Pessoa Startup of the Year award for 2021 is... YupiPlay YupiPlay develops and offers an educational gaming platform. La Reina The winner of La Reina Startup of the Year award for 2021 is... INTI-TECH INTI-TECH is the fastest growing renewable energy in Chile and the world's leading unconventional source. Leme The winner of Leme Startup of the Year award for 2021 is... EcoStart EcoStart focuses on manufacturing sustainable electric bicycles, fans, and accessories. Loja The winner of Loja Startup of the Year award for 2021 is... Enerwi Corporation Keeping people connected and secured through wireless charging novel solutions Manizales The winner of Manizales Startup of the Year award for 2021 is... Porter Metrics Porter Metrics has developed an automated solution for generating social media reports in minutes. Nova Lima The winner of Nova Lima Startup of the Year award for 2021 is... Biomimetic Solutions Biomimetic Solutions is an innovative tissue engineering company. Paraná The winner of Paraná Startup of the Year award for 2021 is... Laura Laura is a provider of artificial intelligence and predictive analytics platform for hospitala and clinics to prevent damage & reduce costs. Salvador The winner of Salvador Startup of the Year award for 2021 is... Sanar Sanar is a platform that focuses on being the doctor's guide and support, offering specialized content that helps in their development. Santa Catarina The winner of Santa Catarina Startup of the Year award for 2021 is... DrPOCKET Sunchales The winner of Sunchales Startup of the Year award for 2021 is... Eolo Pharma Eolo Pharma focuses on developing drugs targeting the molecular and cellular basis of inflammation-related diseases Valparaiso The winner of Valparaiso Startup of the Year award for 2021 is... Invitta Invitta transforms plastic waste into a high-performance construction material for manufacturing sustainable urban furniture. Vila Velha The winner of Vila Velha Startup of the Year award for 2021 is... OneGrid OneGrid is a developer of hardware and software solutions focused on energy management. Indaiatuba The winner of Indaiatuba Startup of the Year award for 2021 is... DWUL Energy Renewable Energy Campinas, Brazil The winner of Campinas Startup of the Year award for 2021 is... Ativy Ativy is an IT company specialized in cloud computing, data centers, IT outsourcing, service desk, and IT management. Las Condes, Chile The winner of Las Condes Startup of the Year award for 2021 is... # MuvPass Subscription services that allows it's users unlimited access to fitness classes in the best gyms and studios in Latin America. Pinheiros, Brazil The winner of Pinheiros Startup of the Year award for 2021 is... GuiaBolso GuiaBolso is a personal finance platform that empowers people to take control of financial well-being. Rio, Brazil The winner of Rio Startup of the Year award for 2021 is... EmCasa EmCasa is a vertically-integrated platform that helps customers buy and sell a home in Latin America, starting in Brazil. Guayaquil The winner of Guayaquil Startup of the Year award for 2021 is... Sabroso Online platform for LatAm's enterprises to order low-cost meals Jundiaí The winner of Jundiaí Startup of the Year award for 2021 is... Sintecsys Sintecsys offers a fast and effective detection, reducing losses and costs with fire brigades. Minas Gerais The winner of Minas Gerais Startup of the Year award for 2021 is... Rizoflora Biotechnology Rizoflora Biotechnology is a producer of biological product designed for nematodes control. São Caetano Do Sul The winner of São Caetano Do Sul Startup of the Year award for 2021 is... Wevo 1 iPaaS in Latam - Enabling companies to be truly digital companies with APIs, systems and data integrated into a single platform Canoas The winner of Canoas Startup of the Year award for 2021 is... ContaÁgil ContaÁgil facilitates and reduces bureaucracy in accounting routines of companies. Chile The winner of Chile Startup of the Year award for 2021 is... Unight Unight is the future of nightlife social media. Israelândia The winner of Israelândia Startup of the Year award for 2021 is... Matchpool Matchpool is a platform that creates human connections. La Plata The winner of La Plata Startup of the Year award for 2021 is... Pixivus Pixivus offers a community-based application that enables its users to collect, store, and share pictures of events. Novo Hamburgo The winner of Novo Hamburgo Startup of the Year award for 2021 is... Devorando Devorando offers an online food ordering system and menus available in restaurants based in Brazil. Pernambuco The winner of Pernambuco Startup of the Year award for 2021 is... Redu Redu is a distant learning platform which is built on a social networking structure. Providencia The winner of Providencia Startup of the Year award for 2021 is... # TrainFES TrainFES is a medical Devices for the rehabilitation of people with paralysis. Ribeirão Prêto The winner of Ribeirão Prêto Startup of the Year award for 2021 is... AllyHub Ally is a sales distribution channel technology that connects Schools and Service Providers with Education Agencies. Santa Cruz De La Sierra The winner of Santa Cruz De La Sierra Startup of the Year award for 2021 is... Mobi Latam Mobi Latam is a clean energy startup that focuses on transportation systems based on electric mobility. Santana De Parnaíba The winner of Santana De Parnaíba Startup of the Year award for 2021 is... MercadoLivre.com is an e-commerce technology company providing solutions to individuals and companies buying, selling, and more online. MercandoLivre.com More Information If you’re a winner, please answer ! If you’re a reader, participant, just a curious individual, consider answering one of our interviews . this interview here Read the FAQs about or . Startups here here To see all of the winners you may visit , pick any city and view the name that appears at the top. this site If you’re interested in partnering with us, we invite you to look through some of these or reach out to our business department. unique sponsorship options Perhaps creating your very own tickles your fancy or maybe you have a whole new idea for how we can partner! writing contest Thank you to all of our sponsors! We truly appreciate your contribution to the tech world and thus the future! The Startups Awards are sponsored by: , , , , , , , , , , Blockster Brex FreeCodeCamp LaunchDarkly Coil Udacity Udemy Vercel Asia Pacific Transgender Network Bybit Everscale Network This post was written/compiled by Shreya Kundu and Katarina Andrejević! If you have any questions or concerns or would like to report a discrepancy please email ellen@hackernoon.com.

Meet the Winners of Startups in South America

Admit it! Startups are hard, why? Because in startup space we are looking at a problem that no one is solving or an incumbent is making lives miserable there and we improve the state, we add value, we find a new business model while doing so and somehow make that startup - now turned into a business - ! self sustainable Of course! You know all of that stuff then why am I repeating it? To give you context! Start-ups are hard because of the uncertainty of new - the unavailability of examples of business models, what to charge, how to charge, who will pay, whether customer wants it or not, etc. Apply that context to the dapps now - being born out of layer 1 blockchains, the first one of whom is merely 10 years old, we are in a nascent industry. The community is small, - on one side we see Bitcoin OGs whom you will rarely find (and imaginably they are well-funded because they were there when BTC was of $1 so don't need to show their face to anyone) self-righteousness is out of proportions On the other side you will see youngsters who just got into Ethereum development right in college or as first job and are ok with going about propagating the means of decentralisation, attending hackathons and just work for the common public good! Then there are some 35+ years olds who never made money as part of core-devs group, are dapp developers and you will find a tweet every now and then from them telling the world that how their kids are living without medical insurance and how hard it is to put food on the table with what is being offered as a salary or a grant in this space - mind you - these are the same developers who could go into mainstream tech at anytime and earn decent but they are also infected with decentralisation bug, enjoy the community and social bonding and don't want to leave the space. The point that I am raising here is that everyone has to find an earning source, everyone has to sustain themselves first and then they also need to sustain the project they are working on! Without positive cash-flows no one is going to pay for the electricity that you burn to power your laptop or to buy that black cup of coffee! Here I will dissect various funding sources that I am aware of and also would dissect them candidly, just so you can be aware of all the pitfalls (if you are not agreed with me, you can always reach out to me, I will be happy to listen your point of view). General Observations about funding avenues Let me start from hard to digest observations: Off-loading the deal with regulations - most layer 1 projects want to declare themselves decentralised, eat up most of the investor money and push the responsibility of dealing with regulators to the front-end dapp developers Almost all of the I pay dapp developers from the tokens minted from thin-air CO'ed projects Poorly designed dapp developer programs eventually hurt the end retail investor who are holding these tokens and developers eventually get paid on the investor's expense The grants/money on offer is too low for dapp developers to sustain themselves; as opposed to sustaining their projects and cover development and market costs I can keep filling this observation list but I am assuming I have set the stage, let's move on to some of the funding avenues available: Developer Grant Programs Nearly every project has them. They typically have the RFQs that you can choose from and afterwards you will fill in a grant application, give them a well-defined scope and they approve your application in 2-4 weeks. The funding available for these types of grants was still relatively good until the start of 2019 but bear market of last year has dented here the hardest. Let's say a grant that was coming around $5-$7k for a project, is now down to $1-$2k - yes, this is for a project whose MVP can take couple of months for a single developer. While we live in a an open world now, this range can be good for a fresh grad - this is however, not attracting any quality developers anymore - and from dapp developers to grant approvers, everyone is suffering in the process! The easiest way to find these grant programs is to write the name of the project in google along with developer grants keyword, you will find Polkadot, Nervos, Binance DEX, Aave, etc. - what you choose is up-to-you, these can be good or bad! Hackathons I attended about 4-6 online and in-person hackathons last year. While, these hackathons were once seen a good opportunity to on-board beginner developers to a specific blockchain by offering bounties - these are never the avenue for earning a living for the developer or finding a good future project for bounty sponsors (although I know several good projects came out of hackathons but these were usually pre-formed teams, who knew what and when to do and just used hackathon as an accelerator). For the starters, most developers at the hackathons are beginners who do not possess good knowledge or subject matter grasp to learn and execute a project in a domain that is entirely new while the cherry on top is most sponsors also don't know what they want from a project. The end result is, contrary to popular belief, a good developer only has 50% chance of earning a bounty at a hackathon that also merely covers his/her traveling cost to the hackathon. The average bounty in these hackathons is $200 to $1000 range. While EOS tried running their own hackathons, only successful ones are in Ethereum ecosystem being run by and . ETHGlobal Gitcoin Gitcoin CLR Grants is an Ethereum project that allows other blockchain projects to post bounties in their monthly hackathons, however, their other program Gitcoin CLR grants is just available for Ethereum projects at the moment. Gitcoin The program started in 2019 and just concluded its 4th round. This round was the craziest as for the first time everyone was allowed to participate (of course the application was to be approved by the Gitcoin team itself) but given the context of distributing development funds that Ethereum Foundation holds and wants someone else to come forward and manage the distribution process, this project actually ticked many of the boxes - not perfect - but better than others! Gitcoin CLR grants work on a concept called Quadratic funding, Vitalik wrote about the technical details in depth in his article . From the top, the concept is that public vote for projects with their hard-earned tokens, either DAI or ETH or any other supported tokens - the emphasis of Gitcoin is to give projects a style subscription, means if you are pledging to support a project by giving them 1 DAI, you can put that on subscription and project will get paid 1 DAI every month. here patreon You can also provide one time sponsorship.  The project is designed in such a way that most number of fundings is given higher weight in the algorithm as opposed to the amount of the funding. Gitcoin then matches your funding with its own pool of sponsored funds - sometimes up to 4x. 4th round of CLR funding saw some Twitter brawls as well since media projects were also allowed to put in applications and some opponents also accused the community to just use their friends to increase their bag of total funded amount. However, I never participated but dug into how hard it was to game the system and found an that could be used to find which projects were susceptible for gaming the system. I can safely say it wasn't that easy but since the system is not bulletproof yet, gaming could happen and should have happened. analysis project You can find the result of 4th round of Gitcoin CLR grants and information about upcoming 5th round . here Blockstack's App Mining Program If you ever want to run a developer program, what follows is a classic example of what not to do! On technical and conceptual grounds, I liked Blockstack since the beginning and even wrote a great promoting them on hackernoon. However, it's time to introduce their and equally run program called App Mining. blog post bold poorly App Mining is a program that is conceptually formed to release a developer from the burden of running ads or selling user-data in order to sustain their app. The idea is that protocol somehow will keep the dapps supported while developers can focus on their work - so no monetisation is required, developers can just go on to build great software - perfect utopia - but how? You may remember hearing Blockstack's name as part of first ever SEC approved token sale. The project, however, is operating on a turf much difficult than Bitcoin and Ethereum. Instead of democratising finance, Blockstack went after democratising the social media, auth and storage space. This is difficult because first of all, even after Cambridge Analytica, there are still billions of users who log-in to Facebook every month, hence privacy and owning your data (and paying for its storage) does not resonate with general public yet! With App Mining, the project went into even much tougher turf by thinking of ranking apps against each other, something that Apple and Google struggle with despite being old, in possession of full analytics, having hundreds of thousands of apps, in access of thousands of thousands of dollars and running full fledge app quality teams. Blockstack's version of ranking the apps was to: Delegate the review process from day one to 3rd parties in the name of decentralisation They couldn't create any categories of apps because total submissions were low - so imagine, Slack being scored against Bitcoin memes website Employed a academic formula to stop developers from gaming the system Blockstack's App Mining program started it's pilot in October 2018 and my app was included in the second run of the program in November 2018. Timski The 3rd party reviewers at the time were: TryMyUI DemocracyEarth ProductHunt The problem with DemocracyEarth at the time was that Blockstack was expecting accredited private investors (by definition each with net worth of above $1M to log in each month and review 50+ apps and vote - not even with their own money!). The second problem was with ProductHunt that despite the claims is too easy to manipulate especially when someone is offering you money to do so - (literally you just had to buy upvotes from regular members of the PH). App mining discontinued DemocracyEarth after 5 months and discontinued using ProductHunt upvotes after a whole year. Instead Awario was introduced in the mean time to quantify social and web/news mentions. Current app mining reviewers and process can be seen . here The pilot program offered $25,000 in grant money at the start and has recently been giving away $400,000 every month, however, app number still remains under 300. There were great apps as part of the project initially, such as and who also believed on the vision of the Blockstack, however, I believe as the team behind App Mining refused to iterate quickly, these projects left the program as well. Stealthy Graphite Docs I also pulled Timski just after 1st month, there was no way to keep pounding my head against the wall while the effort on a decentralised group chat iOS app was 4x higher than a normal Firebase powered app while the competition that I would need to go in was with Discord and Slack, both of which were already unicorns in this category. As Blockstack's STX tokens are now on Binance, the Blockstack PBC now wants to outsource App Mining program to a 3rd party. Only 2 years worth of STX tokens were pre-mined for App Mining. It's a tough task for anyone in the world to run a program like this where you are actually giving away money to improve the apps - as this becomes a honey-pot for developers to just game the system and draw as much money as they can! Also, the biggest task is to bake App Mining into the protocol itself, so imagine protocol deciding which app should get the money based on user statistics, domain its operating in, user profiles, etc. To be fair to Blockstack PBC, while trying to close all the gates of gaming, they went on to declare the iOS and Android (subsequently penalising everyone who had already invested in making those apps). native apps are not good for digital rights This makes me wonder if Tor was a better alternate choice than making a whole other blockchain if we do not want to include mainstream in the fight for digital privacy. After Timski that was 100% decentralised app (even the notifications were decentralised), I re-entered the App Mining program in November 2019 with my iOS app. Vegan Scanner - Is it Vegan? This time I am just testing the water and doing what everyone is doing, as I said doing a startup is hard, doing a dapp is hardest especially if you are operating in a wild-west kind of environment. The App Mining program was due to grow to $1M by May, 2020, however, since no good apps were coming up, Blockstack PBC is deciding to pause the program from February 1, 2020 and has asked the community for suggestions on how to go forward from here. EOS Block Producer Developer Programs I will just mention EOS here as I am not a subject matter expert in the world of EOS, however, I have met block producers coming to meet-ups to recruit developers. EOS seems heavily gamified and each block producer is required to come up with quality dapps as well. What you deal with that block producer is up to you but these are mostly service projects and be-aware of the fact that you are dealing with a full-fledge business here, instead of a startup or layer 1 blockchain project. NEAR Protocol I will just put in the name of another developer program here, NEAR protocol is helping dapp developers to raise from VCs and a few of them are already able to raise. This again brings us back to the philosophy of what we are doing here? Are we making self-sustainable business apps or are we creating thin-clients on top of blockchains and distributing them for free? I would rather go with the former, no amount of funding can manage the load of sustaining hundred of thousands of dapps for the foreseeable future! Funding from DAOs This also came into light with-in 2019 by the rise of different DAOs. I wouldn't name them, you know where they are, again a much novel concept. I only had the pleasure of pitching one of my apps to the founder of a DAO and also met a few founders whose apps were actually bought by these DAOs. That deal would go through like this that some one had made a mixer on Ethereum, a DAO approached them and asked if they can re-skin the mixer for the DAO and the guys did that, so it was actually a software sale! We will have to wait and see how DAOs can improve the funding landscape of the dapps. Conclusion Dapp funding is an interesting space, of course we are all experimenting and still fighting if sharding works or if PoS is better than PoW, similarly, dapp funding is a much harder nut to crack as well. However, utopia or dystopia, do think about your bills every now and then as well and keep things in perspective. For me I have now moved into core development of tendermint/cosmos sdk and learned to use elliptic-curve cryptography. This is quite an important skill to grasp if you want to stay in blockchain for long and this is where you get to do most exciting work as well. If you would want to discuss anything, you can reach out to me on or find me at one of the crypto conferences. Twitter

Alternative Avenues to Raise Funds as a DApp Developer in 2020

The ftNFT YoCerebrum Awards 2024 invites everyone to participate in the final voting phase to celebrate excellence in the NFT space.The voting period runs from November 6-10, 2024. The jury voting took place from November 1 to November 5, where a group of distinguished experts meticulously evaluated the submissions. During the jury phase, three nominees were selected from each category to move forward to the public voting stage. Now, it’s time for the blockchain voting phase. Meet the Jury Rahim Mahtab: Investor and Art Collector | Social Link: https://x.com/Rahim_mahtab
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pukerainbow (Amos): Founder of Pukecast & Rug Radio Asia  | Social Link: https://x.com/pukerrainbrow
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Vote: Select your preferred nominees and submit your vote Join us in this exciting journey and support your favorite artists and projects! For more details and to stay updated on the Awards, please visit our website. Cast your vote today to celebrate innovation and creativity in the Web3 community and shape the future of digital art! About the ftNFT YoCerebrum Awards Now in its third edition, the ftNFT YoCerebrum Awards is an international event recognizing the most creative achievements in NFTs. Organized by ftNFT, the awards celebrate advancements in digital art, blockchain technology, and the NFT industry. This year, the event will be held on November 14 at Fort Manoel on Manoel Island, Malta—a location that merges historical ambiance with the forward-thinking NFT community spirit. The awards will honor talent across 15 categories, including NFT Project of the Year, Best Phygital NFT, and Most Innovative NFT Collection. Winners will be selected through public blockchain voting and data from the ftNFT.com marketplace, with winning projects receiving 2024 Fasttokens (FTN) as a prize. About ftNFT and Its Phygital Spaces Founded in 2022, ftNFT is a platform that combines a digital NFT marketplace with physical “phygital” spaces. As part of the Fastex Web3 ecosystem, ftNFT operates on the Bahamut and Ethereum blockchains, ensuring a secure and transparent environment for NFT transactions. In addition to its digital marketplace, ftNFT has opened four phygital spaces in Dubai, Yerevan, and Venice. These spaces offer visitors unique experiences with NFT art through 3D scanners and virtual galleries, blending physical and digital interactions. As the organizer of the YoCerebrum Awards, ftNFT is at the forefront of celebrating innovation within the NFT community. The ftNFT YoCerebrum Awards 2024 invites everyone to participate in the final voting phase to celebrate excellence in the NFT space.The voting period runs from November 6-10, 2024. voting phase voting phase The jury voting took place from November 1 to November 5, where a group of distinguished experts meticulously evaluated the submissions. During the jury phase, three nominees were selected from each category to move forward to the public voting stage. Now, it’s time for the blockchain voting phase. Meet the Jury Meet the Jury Rahim Mahtab: Investor and Art Collector | Social Link: https://x.com/Rahim_mahtab Sarah Scribner: Digital Collections Curator at 6529 Museum  | Social Link: https://x.com/foncedechic pukerainbow (Amos): Founder of Pukecast & Rug Radio Asia  | Social Link: https://x.com/pukerrainbrow Demetrio Paparoni: Art Critic, Curator, and Writer  | Social Link: https://www.demetriopaparoni.com Rahim Mahtab : Investor and Art Collector | Social Link: https://x.com/Rahim_mahtab Rahim Mahtab https://x.com/Rahim_mahtab Sarah Scribner : Digital Collections Curator at 6529 Museum  | Social Link: https://x.com/foncedechic Sarah Scribner https://x.com/foncedechic pukerainbow (Amos) : Founder of Pukecast & Rug Radio Asia  | Social Link: https://x.com/pukerrainbrow pukerainbow (Amos) https://x.com/pukerrainbrow Demetrio Paparoni : Art Critic, Curator, and Writer  | Social Link: https://www.demetriopaparoni.com Demetrio Paparoni https://www.demetriopaparoni.com During this period, NFT enthusiasts and the wider community will have the opportunity to cast their votes via the blockchain, ensuring a transparent voting process. This innovative approach reflects the core values of the NFT ecosystem, emphasizing fairness and community involvement. The results will play a pivotal role in determining the winners of the ftNFT YoCerebrum Awards 2024 in Malta. How to Vote How to Vote Download Fastex Wallet Go to the Website: Visit voting.ftnft.com Connect Wallet: Click "Connect Wallet" or scan the QR code Vote: Select your preferred nominees and submit your vote Download Fastex Wallet Go to the Website: Visit voting.ftnft.com voting.ftnft.com voting.ftnft.com Connect Wallet: Click "Connect Wallet" or scan the QR code Vote: Select your preferred nominees and submit your vote Join us in this exciting journey and support your favorite artists and projects! For more details and to stay updated on the Awards, please visit our website . our website our website Cast your vote today to celebrate innovation and creativity in the Web3 community and shape the future of digital art! Cast your vote today to celebrate innovation and creativity in the Web3 community and shape the future of digital art! About the ftNFT YoCerebrum Awards About the ftNFT YoCerebrum Awards Now in its third edition, the ftNFT YoCerebrum Awards is an international event recognizing the most creative achievements in NFTs. Organized by ftNFT , the awards celebrate advancements in digital art, blockchain technology, and the NFT industry. This year, the event will be held on November 14 at Fort Manoel on Manoel Island, Malta—a location that merges historical ambiance with the forward-thinking NFT community spirit. The awards will honor talent across 15 categories, including NFT Project of the Year, Best Phygital NFT, and Most Innovative NFT Collection. 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Hey Hackers, Quatfit has been nominated in HackerNoon's annual Startups of The Year awards in Telangana, India! Please vote for us here: https://hackernoon.com/startups/asia/asia-jaipur-rj-india?stup=66f325bd6ea4677e23e2d501&embedable=true Meet Quatfit Quatfit is an AI startup at the forefront of creating cutting-edge solutions to help businesses optimize operations and achieve unparalleled efficiency. Our core mission is to democratize access to advanced AI technologies, providing tools that are both powerful and easy to integrate across industries. Whether it's healthcare, urban planning, or environmental sustainability, Quatfit is shaping the future of AI by addressing the most pressing needs of today’s world. Our team is deeply committed to developing Artificial Super Intelligence (ASI) that enhances human life. We believe in building AI that serves people, communities, and industries with a focus on safety, ethics, and long-term benefit. As a startup based in Telangana, we are proud to contribute to the region’s thriving tech ecosystem, bringing innovative solutions to the global stage. How Quatfit Achieved Product-Market Fit Achieving product-market fit is a critical milestone for any startup, and for Quatfit, this journey has been both exciting and rewarding. We realized that businesses across sectors faced an increasing demand for AI tools that are scalable, reliable, and customizable. By offering solutions that address the unique challenges of industries like healthcare, urban planning, and logistics, we found our sweet spot in the market. The indicators of our product-market fit are clear. We've seen a rapid adoption of our AI tools among medium to large enterprises, which tells us that there is a significant demand for our technology. Additionally, the positive feedback we’ve received from early adopters and industry experts reaffirms that our products solve real-world problems, leading to increased efficiency, reduced operational costs, and more informed decision-making. The Evolution of Quatfit Quatfit’s journey has been one of constant evolution and learning. Like most startups, we started with a broad vision, but over time, user feedback and market trends shaped our path. Initially, we focused on offering AI tools primarily for healthcare, but as we engaged with more clients and understood their diverse needs, we broadened our scope to include industries like urban planning, supply chain management, and environmental sustainability. One of the pivotal moments in our journey was when we decided to expand our product offering beyond niche industries and target a wider market. This decision was informed by the growing demand for scalable AI solutions that could be applied across multiple sectors. Our ability to adapt and pivot based on market insights has been a key driver of our growth. We also incorporated user feedback into every iteration of our platform, which helped us refine the user experience and ensure that our AI tools were easy to integrate into existing workflows. Milestones and Achievements Quatfit has reached several important milestones on its path to success. Some of the highlights include: Expanding from a single industry focus to a multi-industry platform that serves healthcare, urban planning, and more.
Securing partnerships with leading enterprises and institutions in India and abroad.
Launching our AI platform internationally, allowing businesses globally to benefit from our innovative tools.
Being recognized as a leader in AI innovation, both within India and on the global stage, through numerous awards and nominations, such as this nomination for HackerNoon’s Startups of The Year. Lessons Learned Building a startup is never easy, and Quatfit has faced its fair share of challenges. One of the biggest lessons we’ve learned is the importance of listening to our users. Early in our journey, we discovered that while our technology was impressive, it needed to be more user-friendly and accessible to non-technical professionals. By making our platform more intuitive, we were able to reach a wider audience and provide real value to businesses that previously struggled with AI adoption. Another lesson is the necessity of staying agile. The tech landscape evolves rapidly, and we’ve learned to anticipate changes and pivot when needed. Whether it’s adjusting our product offerings or responding to new market demands, our ability to remain flexible has been crucial to our success. What Startups of The Year Means to Us Being nominated for HackerNoon’s Startups of The Year is an incredible honor for Quatfit. It not only validates the hard work and dedication of our team but also gives us an opportunity to showcase our innovations to a global audience. We believe that participating in this initiative will help us build stronger connections within the tech community, attract new partners, and inspire future AI innovations. Conclusion Quatfit is on a mission to revolutionize the AI industry, and we need your support! Please vote for us and help us continue our journey to make AI accessible, ethical, and impactful for all. Our Founder says At Quatfit, we believe in harnessing the power of AI to empower businesses and enhance human potential. Our journey is driven by innovation, collaboration, and a commitment to creating solutions that make a meaningful impact on society. Vote for us today! Hey Hackers, Quatfit has been nominated in HackerNoon's annual Startups of The Year awards in Telangana, India! Please vote for us here: https://hackernoon.com/startups/asia/asia-jaipur-rj-india?stup=66f325bd6ea4677e23e2d501&embedable=true https://hackernoon.com/startups/asia/asia-jaipur-rj-india?stup=66f325bd6ea4677e23e2d501&embedable=true Meet Quatfit Quatfit is an AI startup at the forefront of creating cutting-edge solutions to help businesses optimize operations and achieve unparalleled efficiency. Our core mission is to democratize access to advanced AI technologies, providing tools that are both powerful and easy to integrate across industries. Whether it's healthcare, urban planning, or environmental sustainability, Quatfit is shaping the future of AI by addressing the most pressing needs of today’s world. Our team is deeply committed to developing Artificial Super Intelligence (ASI) that enhances human life. We believe in building AI that serves people, communities, and industries with a focus on safety, ethics, and long-term benefit. As a startup based in Telangana, we are proud to contribute to the region’s thriving tech ecosystem, bringing innovative solutions to the global stage. How Quatfit Achieved Product-Market Fit Achieving product-market fit is a critical milestone for any startup, and for Quatfit, this journey has been both exciting and rewarding. We realized that businesses across sectors faced an increasing demand for AI tools that are scalable, reliable, and customizable. By offering solutions that address the unique challenges of industries like healthcare, urban planning, and logistics, we found our sweet spot in the market. The indicators of our product-market fit are clear. We've seen a rapid adoption of our AI tools among medium to large enterprises, which tells us that there is a significant demand for our technology. Additionally, the positive feedback we’ve received from early adopters and industry experts reaffirms that our products solve real-world problems, leading to increased efficiency, reduced operational costs, and more informed decision-making. The Evolution of Quatfit Quatfit’s journey has been one of constant evolution and learning. Like most startups, we started with a broad vision, but over time, user feedback and market trends shaped our path. Initially, we focused on offering AI tools primarily for healthcare, but as we engaged with more clients and understood their diverse needs, we broadened our scope to include industries like urban planning, supply chain management, and environmental sustainability. One of the pivotal moments in our journey was when we decided to expand our product offering beyond niche industries and target a wider market. This decision was informed by the growing demand for scalable AI solutions that could be applied across multiple sectors. Our ability to adapt and pivot based on market insights has been a key driver of our growth. We also incorporated user feedback into every iteration of our platform, which helped us refine the user experience and ensure that our AI tools were easy to integrate into existing workflows. Milestones and Achievements Quatfit has reached several important milestones on its path to success. Some of the highlights include: Expanding from a single industry focus to a multi-industry platform that serves healthcare, urban planning, and more. Securing partnerships with leading enterprises and institutions in India and abroad. Launching our AI platform internationally, allowing businesses globally to benefit from our innovative tools. Being recognized as a leader in AI innovation, both within India and on the global stage, through numerous awards and nominations, such as this nomination for HackerNoon’s Startups of The Year. Expanding from a single industry focus to a multi-industry platform that serves healthcare, urban planning, and more. Securing partnerships with leading enterprises and institutions in India and abroad. Launching our AI platform internationally, allowing businesses globally to benefit from our innovative tools. Being recognized as a leader in AI innovation, both within India and on the global stage, through numerous awards and nominations, such as this nomination for HackerNoon’s Startups of The Year. Lessons Learned Building a startup is never easy, and Quatfit has faced its fair share of challenges. One of the biggest lessons we’ve learned is the importance of listening to our users. Early in our journey, we discovered that while our technology was impressive, it needed to be more user-friendly and accessible to non-technical professionals. By making our platform more intuitive, we were able to reach a wider audience and provide real value to businesses that previously struggled with AI adoption. Another lesson is the necessity of staying agile. The tech landscape evolves rapidly, and we’ve learned to anticipate changes and pivot when needed. Whether it’s adjusting our product offerings or responding to new market demands, our ability to remain flexible has been crucial to our success. What Startups of The Year Means to Us Being nominated for HackerNoon’s Startups of The Year is an incredible honor for Quatfit. It not only validates the hard work and dedication of our team but also gives us an opportunity to showcase our innovations to a global audience. We believe that participating in this initiative will help us build stronger connections within the tech community, attract new partners, and inspire future AI innovations. Conclusion Quatfit is on a mission to revolutionize the AI industry, and we need your support! Please vote for us and help us continue our journey to make AI accessible, ethical, and impactful for all. Our Founder says At Quatfit, we believe in harnessing the power of AI to empower businesses and enhance human potential. Our journey is driven by innovation, collaboration, and a commitment to creating solutions that make a meaningful impact on society. At Quatfit, we believe in harnessing the power of AI to empower businesses and enhance human potential. Our journey is driven by innovation, collaboration, and a commitment to creating solutions that make a meaningful impact on society. At Quatfit, we believe in harnessing the power of AI to empower businesses and enhance human potential. Our journey is driven by innovation, collaboration, and a commitment to creating solutions that make a meaningful impact on society. Vote for us today ! Vote for us today

Meet Quatfit, The AI Innovator in HackerNoon’s Startups of the Year Awards!

Understanding the Generalization Performance of GNNs: Topology Awareness and Future Directions

Authors:
(1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk;
(2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction 2 Related Work 3 Framework 4 Main Results 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 11 Other Potential Applications 4 Main Results In this section, we present the main results derived from our proposed framework for studying the generalization and fairness of GNNs with respect to different structural groups in a graph. We start by demonstrating the relationship between the generalization performance of the model and the structural distance between the subgroups and the training set (Theorem 1). We then show that such a structural relation can induce disparities in the generalization performance across different subgroups (Theorem 2). Finally, we connect these theoretical results to the recent deep learning spline line theory [2] to provide additional insights. Detailed proof of the results presented in this paper can be found in the supplementary material. 4.1 Generalization Performance and Structural Distance Theorem 1 states that the generalization risk of a classifier with respect to a structural subgroup depends on the empirical training loss of the classifier, the structural distance between the subgroup and the training set, and the distortion (topology awareness) of GNNs. Such a relation provides a new perspective on understanding the link between topology awareness and generalization performance in GNNs. Prior research in this area has mainly focused on the connection between GNNs and the Weisfeiler-Lehman algorithm, emphasizing the ability of GNNs to differentiate various graph structures. However, Theorem 1 highlights a direct link between topology awareness and generalization performance, and a potential issue of fairness in GNNs, as it shows that the model’s performance on different structural subgroups is influenced by their distance to the training set. Next, we extend the result of Theorem 1 to analyze the relation between the generalization of different structural subgroups and their distance to the training set. 4.2 Unfair Generalization Performance on Structural Subgroups Theorem 2 states that when comparing two subgroups, if the difference in their structural distance to the training set is larger than the threshold (δα), then GNNs exhibit unfair generalization performance with respect to these groups. Specifically, the theorem states that GNNs generalize better on subgroups that are structurally closer to the training set, which leads to accuracy disparities among different subgroups. Additionally, the theorem notes that the topology awareness of GNNs (measured by the distortion rate α) plays a key role in determining the strength of this accuracy disparity. This has important implications for the use of GNNs in critical applications, as it suggests that increased topology awareness in GNNs can lead to improved generalization performance but also a greater potential for unfairness in terms of accuracy disparities among different structural subgroups. As such, it is important to carefully consider the trade-offs between topology awareness and fairness when designing new GNNs and applying them to real-world problems. 4.3 Connection with Deep Learning Spline Theory Our theoretical findings reveal that when considering the performance of the model from the viewpoint of the embedding space, the training set creates a “valley” effect on generalization performance, with the training vertex at the bottom of the valley. Representations that are closer to the embedding of the training set perform better, while those farther away perform worse. This pattern has an interesting connection with deep learning spline theory [2]. This theory suggests that in DNNs, the learning process for classification divides the input/latent space into small circles (referred to as power diagrams), where representations within each circle are grouped, and representations closer to the centre of the circle are predicted with more confidence. Our findings suggest that in GNNs, the mapping of test data to these power diagrams is related to the structural similarity between test and training data in the graph. This connection provides further validation for our derived results. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Authors: Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Framework 3 Framework 4 Main Results 4 Main Results 5 A Case Study on Shortest-Path Distance 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 7 Proof of Theorem 1 8 Proof of Theorem 2 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 10 Additional Experiments Details and Results 11 Other Potential Applications 11 Other Potential Applications 4 Main Results In this section, we present the main results derived from our proposed framework for studying the generalization and fairness of GNNs with respect to different structural groups in a graph. We start by demonstrating the relationship between the generalization performance of the model and the structural distance between the subgroups and the training set (Theorem 1). We then show that such a structural relation can induce disparities in the generalization performance across different subgroups (Theorem 2). Finally, we connect these theoretical results to the recent deep learning spline line theory [2] to provide additional insights. Detailed proof of the results presented in this paper can be found in the supplementary material. 4.1 Generalization Performance and Structural Distance Theorem 1 states that the generalization risk of a classifier with respect to a structural subgroup depends on the empirical training loss of the classifier, the structural distance between the subgroup and the training set, and the distortion (topology awareness) of GNNs. Such a relation provides a new perspective on understanding the link between topology awareness and generalization performance in GNNs. Prior research in this area has mainly focused on the connection between GNNs and the Weisfeiler-Lehman algorithm, emphasizing the ability of GNNs to differentiate various graph structures. However, Theorem 1 highlights a direct link between topology awareness and generalization performance, and a potential issue of fairness in GNNs, as it shows that the model’s performance on different structural subgroups is influenced by their distance to the training set. Next, we extend the result of Theorem 1 to analyze the relation between the generalization of different structural subgroups and their distance to the training set. 4.2 Unfair Generalization Performance on Structural Subgroups Theorem 2 states that when comparing two subgroups, if the difference in their structural distance to the training set is larger than the threshold (δα), then GNNs exhibit unfair generalization performance with respect to these groups. Specifically, the theorem states that GNNs generalize better on subgroups that are structurally closer to the training set, which leads to accuracy disparities among different subgroups. Additionally, the theorem notes that the topology awareness of GNNs (measured by the distortion rate α) plays a key role in determining the strength of this accuracy disparity. This has important implications for the use of GNNs in critical applications, as it suggests that increased topology awareness in GNNs can lead to improved generalization performance but also a greater potential for unfairness in terms of accuracy disparities among different structural subgroups. As such, it is important to carefully consider the trade-offs between topology awareness and fairness when designing new GNNs and applying them to real-world problems. 4.3 Connection with Deep Learning Spline Theory Our theoretical findings reveal that when considering the performance of the model from the viewpoint of the embedding space, the training set creates a “valley” effect on generalization performance, with the training vertex at the bottom of the valley. Representations that are closer to the embedding of the training set perform better, while those farther away perform worse. This pattern has an interesting connection with deep learning spline theory [2]. This theory suggests that in DNNs, the learning process for classification divides the input/latent space into small circles (referred to as power diagrams), where representations within each circle are grouped, and representations closer to the centre of the circle are predicted with more confidence. Our findings suggest that in GNNs, the mapping of test data to these power diagrams is related to the structural similarity between test and training data in the graph. This connection provides further validation for our derived results. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

On the Topology Awareness and Generalization Performance of Graph Neural Networks: Main Results

Authors:
(1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk;
(2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction 2 Related Work 3 Framework 4 Main Results 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 11 Other Potential Applications 3 Framework In this section, we introduce our proposed framework, which aims to investigate the intricate relationship between topology awareness and generalization performance in GNNs. The main idea of the framework is to use metric distortion to characterize the topology awareness of GNNs. With this characterization, we are able to show the relation between topology awareness of GNNs and their generalization performance. 3.1 GNN Preliminaries Let G = (V, E, X) be an undirected graph where V = {1, 2, ..., n} is the set of n nodes and E ⊆ V × V is the set of edges. Let X = {x1, x2, ..., xn} denote the set of node attribute vectors corresponding to all the nodes in V. More specifically, xv ∈ X is an m-dimensional vector which captures the attribute values of node v ∈ V. In addition, each vertex v ∈ V is associated with a node label yv ∈ {1, ..., c}, where c is the total number of classes. For our analysis, we focus on the transductive node classification setting [47], where the graph G are observed prior to learning and labels are only available for a small subset of nodes V0 ⊂ V. Without loss of generality, we treat G as fixed throughout our analysis and the randomness comes from the labels y. Given a small set of the labelled nodes, V0 ⊂ V, the task of node-level semi-supervised learning is to learn a classifier f, such that yˆv = f(v), from a hypothesis space F and perform it on the remaining unlabeled nodes. Let L(., .) 7→ R+ be a bounded continuous loss function. We denote by RL(f, V) the generalization risk of the classifier f with respect to L and V and it is defined as follows, In our case, the hypothesis space is captured by a GNN and an additional read-out function. GNNs are commonly used as an embedding function and adopt a neighbourhood aggregation scheme, where the representation of a node is learnt iteratively by aggregating representations of its neighbours. After k iterations of aggregation, a node’s representation captures the information within its k-hop neighbourhood in the graph. Formally, the k-th layer of a GNN can be written as follows, It should be noted that the distance function in Def. 2 is not symmetrical, and Eq. 4 captures the maximal structural difference of vertices in V1 to V2. To provide further insight into the concept of a structural subgroup, let’s consider a scenario where V0 ⊂ V represents the training set and ds(.) represents the shortest-path distance. In this context, we can partition the remaining vertices V\V0 into different structural subgroups based on their shortest-path distance to the nearest vertex in the training set. Specifically, we can define Vk = {v ∈ V\V0|Ds(v, V0) = k}. However, it is important to emphasize that our analysis does not assume a specific partition scheme, and the framework remains adaptable to various scenarios. 3.3 Topology Awareness To characterize and formalize the topology awareness of GNNs, we introduce the concept of distortion, which measures the degree to which the graph structure is preserved in the embedding space. Mathematically, the distortion of a function between two general metric spaces is defined as, The definition above captures the maximum expansion and minimum contraction between the two metric spaces. In the extreme case when α = 1, the mapping γ is the so-called isometric mapping that perfectly preserves the distance between any two points in the space. In other words, for any two points x and y in the domain of the function, their distance d(x, y) in the original metric space is equal to the distance d ′ (γ(x), γ(y)) in the target metric space (up to a constant scaling factor). If the distortion rate of the mapping is close to 1, then this mapping is said to have a low distortion rate. In the context of GNNs, evaluating distortion involves a straightforward comparison of embeddings in the embedding domain with the structural measures on the graph, as demonstrated in the case study. If the distortion rate between the graph domain and the embedding domain is close to 1, the resulting embedding would largely preserve the corresponding structural information from the graph space, thereby indicating high topology awareness. Consequently, distortion can be employed to measure the topology awareness of GNNs concerning the corresponding structural properties (e.g., shortest-path distance) measured in the graph domain. Consequently, distortion can be employed to measure the topology awareness of GNNs concerning the corresponding structural properties (e.g., shortest-path distance) measured in the graph domain. This concept of distortion is agnostic to specific structural configurations, enabling the study of diverse graph structures using appropriate distance functions. Moreover, its estimation can be readily achieved by comparing the embedding with the original structural measure, as illustrated later in the case study This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Authors: Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Framework 3 Framework 4 Main Results 4 Main Results 5 A Case Study on Shortest-Path Distance 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 7 Proof of Theorem 1 8 Proof of Theorem 2 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 10 Additional Experiments Details and Results 11 Other Potential Applications 11 Other Potential Applications 3 Framework In this section, we introduce our proposed framework, which aims to investigate the intricate relationship between topology awareness and generalization performance in GNNs. The main idea of the framework is to use metric distortion to characterize the topology awareness of GNNs. With this characterization, we are able to show the relation between topology awareness of GNNs and their generalization performance. 3.1 GNN Preliminaries Let G = (V, E, X) be an undirected graph where V = {1, 2, ..., n} is the set of n nodes and E ⊆ V × V is the set of edges. Let X = {x1, x2, ..., xn} denote the set of node attribute vectors corresponding to all the nodes in V. More specifically, xv ∈ X is an m-dimensional vector which captures the attribute values of node v ∈ V. In addition, each vertex v ∈ V is associated with a node label yv ∈ {1, ..., c}, where c is the total number of classes. For our analysis, we focus on the transductive node classification setting [47], where the graph G are observed prior to learning and labels are only available for a small subset of nodes V0 ⊂ V. Without loss of generality, we treat G as fixed throughout our analysis and the randomness comes from the labels y. Given a small set of the labelled nodes, V0 ⊂ V, the task of node-level semi-supervised learning is to learn a classifier f, such that yˆv = f(v), from a hypothesis space F and perform it on the remaining unlabeled nodes. Let L(., .) 7→ R+ be a bounded continuous loss function. We denote by RL(f, V) the generalization risk of the classifier f with respect to L and V and it is defined as follows, In our case, the hypothesis space is captured by a GNN and an additional read-out function. GNNs are commonly used as an embedding function and adopt a neighbourhood aggregation scheme, where the representation of a node is learnt iteratively by aggregating representations of its neighbours. After k iterations of aggregation, a node’s representation captures the information within its k-hop neighbourhood in the graph. Formally, the k-th layer of a GNN can be written as follows, It should be noted that the distance function in Def. 2 is not symmetrical, and Eq. 4 captures the maximal structural difference of vertices in V1 to V2. To provide further insight into the concept of a structural subgroup, let’s consider a scenario where V0 ⊂ V represents the training set and ds(.) represents the shortest-path distance. In this context, we can partition the remaining vertices V\V0 into different structural subgroups based on their shortest-path distance to the nearest vertex in the training set. Specifically, we can define Vk = {v ∈ V\V0|Ds(v, V0) = k}. However, it is important to emphasize that our analysis does not assume a specific partition scheme, and the framework remains adaptable to various scenarios. 3.3 Topology Awareness To characterize and formalize the topology awareness of GNNs, we introduce the concept of distortion, which measures the degree to which the graph structure is preserved in the embedding space. Mathematically, the distortion of a function between two general metric spaces is defined as, The definition above captures the maximum expansion and minimum contraction between the two metric spaces. In the extreme case when α = 1, the mapping γ is the so-called isometric mapping that perfectly preserves the distance between any two points in the space. In other words, for any two points x and y in the domain of the function, their distance d(x, y) in the original metric space is equal to the distance d ′ (γ(x), γ(y)) in the target metric space (up to a constant scaling factor). If the distortion rate of the mapping is close to 1, then this mapping is said to have a low distortion rate. In the context of GNNs, evaluating distortion involves a straightforward comparison of embeddings in the embedding domain with the structural measures on the graph, as demonstrated in the case study. If the distortion rate between the graph domain and the embedding domain is close to 1, the resulting embedding would largely preserve the corresponding structural information from the graph space, thereby indicating high topology awareness. Consequently, distortion can be employed to measure the topology awareness of GNNs concerning the corresponding structural properties (e.g., shortest-path distance) measured in the graph domain. Consequently, distortion can be employed to measure the topology awareness of GNNs concerning the corresponding structural properties (e.g., shortest-path distance) measured in the graph domain. This concept of distortion is agnostic to specific structural configurations, enabling the study of diverse graph structures using appropriate distance functions. Moreover, its estimation can be readily achieved by comparing the embedding with the original structural measure, as illustrated later in the case study This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

Framework for Analyzing Topology Awareness and Generalization in Graph Neural Networks

Authors:
(1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk;
(2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction 2 Related Work 3 Framework 4 Main Results 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 11 Other Potential Applications 2 Related Work 2.1 Topology Awareness of GNNs Modern GNN architectures take inspiration from the Weisfeiler-Lehman isomorphism test [12,19], which employs the graph structure to propagate information. Consequently, a significant portion of existing literature on GNNs concentrates on understanding their ability to differentiate various graph structures, known as the expressive power of GNNs [28–30, 44, 48, 50]. Inspired by the expressiveness studies, it is commonly believed that increasing topology awareness is universally beneficial and many studies focus on enabling GNNs to preserve more structural properties in the learned representation [29, 33, 48]. Nevertheless, the precise ramifications of heightened topology awareness on GNNs’ generalization performance remain shrouded in ambiguity. The intricate variations within structures across different domains and tasks further compound this complexity, underscoring the necessity for a unified framework—akin to the one proposed in this paper—to shed light on these intricacies. 2.2 Generalization of GNNs Relatively few studies focus on understanding the generalization performance of GNNs in node-level tasks. [3, 9, 18, 23, 25, 34, 39, 41, 45] extend the conventional statistical learning or information-theoretic framework to GNNs, providing different generalization bounds based on concepts such as Vapnik–Chervonenkis dimension, mutual information, and algorithm stability. In light of this, despite empirical indications highlighting the critical role of GNNs’ topology awareness in generalization performance [20,29,48], there remains limited understanding of the relationship between topology awareness of GNNs and their generalization. Our proposed framework addresses this gap by utilizing the distortion concept in the approximate metric embedding to connect the topology awareness of GNNs and their generalization performance. 2.3 Active Learning in Graph Active Learning (AL) seeks to enhance model performance within a limited labeling budget by identifying the most representative samples for annotation [32]. The AL methodology generally involves two phases: 1) selecting a small, preliminary subset of samples for labeling; 2) utilizing this labeled subset to iteratively discover the most informative sample for future labeling. The initial selection of an effective subset represents the cold-start problem in AL [11]. While AL has proven effective in settings with independent and identically distributed (i.i.d.) data, such as images and text, applying it to Graph Neural Networks (GNNs) poses unique challenges. These challenges stem from the necessity to account for node interdependencies and the computational complexity of iterative sample selection and retraining, especially when considering multi-hop neighbors. Recent AL methodologies for GNNs, such as AGE [5], FeatProp [42], and GraphPart [26], aim to overcome these obstacles by leveraging the graph structure and initial node features to boost efficiency and efficacy, although their success may significantly hinge on the quality of the initial features. In this work, we focus on the cold-start problem of graph active learning and introduce a novel approach (based on our analysis) that relies exclusively on graph structure, thus eliminating the reliance on feature quality at the onset of learning. This paper is available on arxiv under CC BY 4.0 DEED license. Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Authors: Authors: (1) Junwei Su, Department of Computer Science, the University of Hong Kong and jwsu@cs.hku.hk; (2) Chuan Wu, Department of Computer Science, the University of Hong Kong and cwu@cs.hku.hk. Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Related Work 2 Related Work 3 Framework 3 Framework 4 Main Results 4 Main Results 5 A Case Study on Shortest-Path Distance 5 A Case Study on Shortest-Path Distance 6 Conclusion and Discussion, and References 6 Conclusion and Discussion, and References 7 Proof of Theorem 1 7 Proof of Theorem 1 8 Proof of Theorem 2 8 Proof of Theorem 2 9 Procedure for Solving Eq. (6) 9 Procedure for Solving Eq. (6) 10 Additional Experiments Details and Results 10 Additional Experiments Details and Results 11 Other Potential Applications 11 Other Potential Applications 2 Related Work 2.1 Topology Awareness of GNNs Modern GNN architectures take inspiration from the Weisfeiler-Lehman isomorphism test [12,19], which employs the graph structure to propagate information. Consequently, a significant portion of existing literature on GNNs concentrates on understanding their ability to differentiate various graph structures, known as the expressive power of GNNs [28–30, 44, 48, 50]. Inspired by the expressiveness studies, it is commonly believed that increasing topology awareness is universally beneficial and many studies focus on enabling GNNs to preserve more structural properties in the learned representation [29, 33, 48]. Nevertheless, the precise ramifications of heightened topology awareness on GNNs’ generalization performance remain shrouded in ambiguity. The intricate variations within structures across different domains and tasks further compound this complexity, underscoring the necessity for a unified framework—akin to the one proposed in this paper—to shed light on these intricacies. 2.2 Generalization of GNNs Relatively few studies focus on understanding the generalization performance of GNNs in node-level tasks. [3, 9, 18, 23, 25, 34, 39, 41, 45] extend the conventional statistical learning or information-theoretic framework to GNNs, providing different generalization bounds based on concepts such as Vapnik–Chervonenkis dimension, mutual information, and algorithm stability. In light of this, despite empirical indications highlighting the critical role of GNNs’ topology awareness in generalization performance [20,29,48], there remains limited understanding of the relationship between topology awareness of GNNs and their generalization. Our proposed framework addresses this gap by utilizing the distortion concept in the approximate metric embedding to connect the topology awareness of GNNs and their generalization performance. 2.3 Active Learning in Graph Active Learning (AL) seeks to enhance model performance within a limited labeling budget by identifying the most representative samples for annotation [32]. The AL methodology generally involves two phases: 1) selecting a small, preliminary subset of samples for labeling; 2) utilizing this labeled subset to iteratively discover the most informative sample for future labeling. The initial selection of an effective subset represents the cold-start problem in AL [11]. While AL has proven effective in settings with independent and identically distributed (i.i.d.) data, such as images and text, applying it to Graph Neural Networks (GNNs) poses unique challenges. These challenges stem from the necessity to account for node interdependencies and the computational complexity of iterative sample selection and retraining, especially when considering multi-hop neighbors. Recent AL methodologies for GNNs, such as AGE [5], FeatProp [42], and GraphPart [26], aim to overcome these obstacles by leveraging the graph structure and initial node features to boost efficiency and efficacy, although their success may significantly hinge on the quality of the initial features. In this work, we focus on the cold-start problem of graph active learning and introduce a novel approach (based on our analysis) that relies exclusively on graph structure, thus eliminating the reliance on feature quality at the onset of learning. This paper is available on arxiv under CC BY 4.0 DEED license. This paper is available on arxiv under CC BY 4.0 DEED license. available on arxiv

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