A carefully designed two-layer neural network with channel attention trained by gradient descent achieves the minimax optimal sample complexity Theta(d to the ell_0 over epsilon) for learning degree-ell_0 spherical polynomials.
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RNCRNs are proven to universally approximate any dynamics with enough chemical neurons and fast reactions, with small instances trained for biological behaviors and shown realizable via DNA technologies.
The Binary Principle treats zero and one as the primitive units from which complex mathematical theories and applications emerge.
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Shallow Neural Networks Learn Low-Degree Spherical Polynomials with Feature Learning by Learnable Channel Attention
A carefully designed two-layer neural network with channel attention trained by gradient descent achieves the minimax optimal sample complexity Theta(d to the ell_0 over epsilon) for learning degree-ell_0 spherical polynomials.
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Recurrent neural chemical reaction networks that approximate arbitrary dynamics
RNCRNs are proven to universally approximate any dynamics with enough chemical neurons and fast reactions, with small instances trained for biological behaviors and shown realizable via DNA technologies.
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The Universal Language of Mathematics (Introduction to Binary Principle)
The Binary Principle treats zero and one as the primitive units from which complex mathematical theories and applications emerge.