News from the AI & ML world
DeeperML - #math
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Michael Weiss@Diagonal Argument
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Diagonal Argument
Recent discussions in mathematical concepts and programming tools cover a range of topics, including theoretical foundations and practical applications. Peter Cameron highlighted the Compactness Theorem for first-order logic, explaining its consequences and connections to topology. Also, a beginner's guide to sets has been published to explain how they work and some applications.
Noel Welsh presented a talk at Imperial College on dualities in programming, exploring the relationships between data and codata, calls and returns, and ASTs and stack machines. The use of adjoints in boolean operations was justified, and Daniel Lemire published an overview of parallel programming using Go. These discussions bridge the gap between abstract mathematical principles and their concrete uses in software development and programming paradigms. Recommended read:
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@phys.org
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mathoverflow.net
, medium.com
Recent mathematical research is pushing the boundaries of theoretical understanding across various domains. One area of focus involves solving the least squares problem, particularly with rank constraints. A specific problem involves minimizing a function with a rank constraint and the quest for efficient solutions to these constrained optimization challenges remains a significant area of investigation.
This also involves a three-level exploration into a "mathematics-driven universe," questioning whether math is discovered or invented, and delving into the philosophical implications of mathematics in modern physics. Furthermore, mathematicians are employing topology to investigate the shape of the universe. This includes exploring possible 2D and 3D spaces to better understand the cosmos we inhabit, hinting at intriguing and surprising possibilities that could change our understanding of reality. Recommended read:
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@www.marktechpost.com
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DeepMind's AlphaGeometry2, an AI system, has achieved a remarkable milestone by surpassing the average performance of gold medalists in the International Mathematical Olympiad (IMO) geometry problems. This significant upgrade to the original AlphaGeometry demonstrates the potential of AI in tackling complex mathematical challenges that require both high-level reasoning and strategic problem-solving abilities. The system leverages advanced AI techniques to solve these intricate geometry problems, marking a notable advancement in AI's capabilities.
Researchers from Google DeepMind, alongside collaborators from the University of Cambridge, Georgia Tech, and Brown University, enhanced the system with a Gemini-based language model, a more efficient symbolic engine, and a novel search algorithm with knowledge sharing. These improvements have significantly boosted its problem-solving rate to 84% on IMO geometry problems from 2000-2024. AlphaGeometry2 represents a step towards a fully automated system capable of interpreting problems from natural language and devising solutions, underscoring AI's growing potential in fields demanding high mathematical reasoning skills, such as research and education. Recommended read:
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@the-decoder.com
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OpenAI's o3 model is facing scrutiny after achieving record-breaking results on the FrontierMath benchmark, an AI math test developed by Epoch AI. It has emerged that OpenAI quietly funded the development of FrontierMath, and had prior access to the benchmark's datasets. The company's involvement was not disclosed until the announcement of o3's unprecedented performance, where it achieved a 25.2% accuracy rate, a significant jump from the 2% scores of previous models. This lack of transparency has drawn comparisons to the Theranos scandal, raising concerns about potential data manipulation and biased results. Epoch AI's associate director has admitted the lack of transparency was a mistake.
The controversy has sparked debate within the AI community, with questions being raised about the legitimacy of o3's performance. While OpenAI claims the data wasn't used for model training, concerns linger as six mathematicians who contributed to the benchmark said that they were not aware of OpenAI's involvement or the company having exclusive access. They also indicated that had they known, they might not have contributed to the project. Epoch AI has said that an "unseen-by-OpenAI hold-out set" was used to verify the model's capabilities. Now, Epoch AI is working on developing new hold-out questions to retest the o3 model's performance, ensuring OpenAI does not have prior access. Recommended read:
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