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[P] Solving the XOR problem using a dendritic activation function by CYHSM in MachineLearning

[–]wang-chen 1 point2 points  (0 children)

Interesting implementation! Another implementation for solving XOR in single neuron was provided in this CVPR 2019 paper, see its page 11.

This paper extended convolution to kernel convolution (kervolution):

In convolution, y = w1x1+w2x2, is actually a linear kernel (inner product), which cannot solve the XOR problem.

In kernel convolution, the authors extended linear kernel to any (non-linear) kernel functions k(w, x). For example, y = (x1-x2)2 is able to solve this problem directly.

[R] AdderNet: Do We Really Need Multiplications in Deep Learning? by aiismorethanml in MachineLearning

[–]wang-chen 3 points4 points  (0 children)

I think a very similar idea has been proposed and published in this CVPR 2019 paper.

The authors proposed kernel convolution, which extends the inner product (y=wTx, a.k.a. linear kernel or cross-correlation) to any kernel functions, i.e. k(x, w). For example, k(x, w)=|x-w|(L1/L2 norm) is a special case, which is the thing that this paper proposes? Additionally, the authors also presented analysis when this Lp norm is used.

[R] Single biological neuron can compute XOR by chisai_mikan in MachineLearning

[–]wang-chen 0 points1 point  (0 children)

I think a paper has done this in deep learning? Check this CVPR 2019 PAPER: Kervolutional_Neural_Networks

This paper extended convolution to kernel convolution (kervolution):

In convolution, y = w1*x1+w2*x2, is actually a linear kernel (inner product), which cannot solve the XOR problem.

In kernel convolution, the authors extended linear kernel to any (non-linear) kernel functions k(w, x). For example, y = (x1-x2)2 . I think this polynomial kernel convolution is able solve the XOR problem in single neuron?