Support Vector Machines as Neural Nets?
An SVM with a linear kernel has the same expressive power as a single perceptron in a neural net, since both are linear classifiers. If you think of the kernel function as mapping your input to a higher dimensional feature space then the SVM is still a linear decision boundary in that high dimensional kernel space. You could theoretically use the high dimensional kernel space features as input to a neural network as well as long as the kernel space is finite. Again the linear SVM behaves similarly to a single perceptron.

However, this only applies to linear SVMs.  In practice SVMs are typically used with a non-linear kernel, and then no such equivalence applies.  So this claimed equivalence might be a bit misleading, if you are comparing how SVMs tend to be used in practice to how neural nets tend to be used in practice.

Summary: Think of an linear SVM as being similar to a single perceptron instead of a neural network.