#mathematical-foundations News & Analysis

2 articles tagged with #mathematical-foundations. AI-curated summaries with sentiment analysis and key takeaways from 50+ sources.

2 articles

AINeutralarXiv – CS AI · 9h ago6/10

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A Generalized Singular Value Theory for Neural Networks

Researchers prove that modern neural networks can be represented using a Generalized Singular Value Decomposition that makes them left-invertible before a final linear layer while preserving norm properties. This mathematical framework enables distance calibration between feature space and input space, with demonstrated applications to adversarial perturbation detection and potential future use in addressing model bias and invertibility.

AINeutralarXiv – CS AI · 9h ago6/10

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Generalized Euler Logarithm and its Applications in Machine Learning: Natural Gradient, Backpropagation, Generalized EG, Mirror Descent and OLPS

Researchers present a comprehensive mathematical framework unifying generalized Euler logarithms with applications to machine learning optimization. The work establishes theoretical foundations for deformed exponential functions and introduces new algorithms—Generalized Exponentiated Gradient and Mirror Descent schemes—alongside an Euler-based loss function for neural networks that integrates with natural gradient descent.