
On the Generalization Properties of Minimumnorm Solutions for Overparameterized Neural Network Models
We study the generalization properties of minimumnorm solutions for thr...
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PhysicsGuided Recurrent Graph Networks for Predicting Flow and Temperature in River Networks
This paper proposes a physicsguided machine learning approach that comb...
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Set2Graph: Learning Graphs From Sets
Many problems in machine learning (ML) can be cast as learning functions...
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A Shooting Formulation of Deep Learning
Continuousdepth neural networks can be viewed as deep limits of discret...
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Reconciled Polynomial Machine: A Unified Representation of Shallow and Deep Learning Models
In this paper, we aim at introducing a new machine learning model, namel...
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A brief introduction to the Grey Machine Learning
This paper presents a brief introduction to the key points of the Grey M...
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Geometric Formulation for Discrete Points and its Applications
We introduce a novel formulation for geometry on discrete points. It is ...
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Machine Learning from a Continuous Viewpoint
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differentialintegral equations, very much in the spirit of classical numerical analysis and statistical physics. We demonstrate that conventional machine learning models and algorithms, such as the random feature model, the shallow neural network model and the residual neural network model, can all be recovered as particular discretizations of different continuous formulations. We also present examples of new models, such as the flowbased random feature model, and new algorithms, such as the smoothed particle method and spectral method, that arise naturally from this continuous formulation. We discuss how the issues of generalization error and implicit regularization can be studied under this framework.
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