w4c_neural_net_more_fit.pdf - More on fitting neural...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
More on fitting neural networks This note is a continuation of our high-level introduction to neural networks. Local optima The cost function for neural networks is not unimodal, and so is certainly not convex (a stronger property). It’s easy to see why by considering a neural network with two hidden units. Assume we’ve fitted the network to a (local) optimum of a cost function, so that any small change in parameters will make the network worse. Then we can find another parameter vector that will represent exactly the same function, showing that the optimum is only a local one. To create the second parameter vector, we simply take all of the parameters associated with hidden unit one, and replace them with the corresponding parameters associated with hidden unit two. Then we take all of the parameters associated with hidden unit two and replace them with the parameters that were associated with hidden unit one. The network is really the same as before, with the hidden units labelled differently, so will have the same cost. It’s a common difficulty with “hidden” or “latent” representations of data, that there are usually many equivalent ways to represent the same model. As machine learning is usually concerned about making predictions, it doesn’t matter that the parameters aren’t well- specified. But it’s worth remembering that the values of individual parameters are often completely arbitrary, and can’t be interpreted in isolation.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern