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Tag: universal

  • From Universal Approximation Theorem to Tropical Geometry of Multi-Layer Perceptrons

    From Universal Approximation Theorem to Tropical Geometry of Multi-Layer Perceptrons arXiv:2510.15012v1 Announce Type: new Abstract: We revisit the Universal Approximation Theorem(UAT) through the lens of the tropical geometry of neural networks and introduce a constructive, geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs). Tropical geometry shows that Rectified Linear Unit (ReLU) networks admit decision functions with…

  • The Theory of Universal Computation: Bayesian Optimality, Solomonoff Induction & AIXI

    The Theory of Universal Computation: Bayesian Optimality, Solomonoff Induction & AIXI Is it possible to build a perfect induction machine? The post The Theory of Universal Computation: Bayesian Optimality, Solomonoff Induction & AIXI appeared first on Towards Data Science. Angjelin Hila Go to original source

  • Universal Architectures for the Learning of Polyhedral Norms and Convex Regularization Functionals

    Universal Architectures for the Learning of Polyhedral Norms and Convex Regularization Functionals arXiv:2503.19190v1 Announce Type: new Abstract: This paper addresses the task of learning convex regularizers to guide the reconstruction of images from limited data. By imposing that the reconstruction be amplitude-equivariant, we narrow down the class of admissible functionals to those that can be…

  • Universal Rates of Empirical Risk Minimization

    Universal Rates of Empirical Risk Minimization arXiv:2412.02810v1 Announce Type: new Abstract: The well-known empirical risk minimization (ERM) principle is the basis of many widely used machine learning algorithms, and plays an essential role in the classical PAC theory. A common description of a learning algorithm’s performance is its so-called “learning curve”, that is, the decay…