3 ms·
Theorem demonstrates that CNNs can always be trained on quantum computers
- prof-dr-ir 5y agoSuggested background music: "if I were a rich man" https://youtu.be/j5fCqKbSC7M https://youtu.be/j5fCqKbSC7M If I had a quantum computer, I could do all these wonderful things... it's interesting theoretical research but we do not have the machines yet.
- miguelmurca 5y agoI am very suspicious of free lunches; almost surely this means the expressibility of QCNNs is limited (as opposed to a sufficient depth VQE)? (Disclaimer: I didn't Google for known results w.r.t. the expressibility of QCNNs)
- deleted 5y ago[deleted]
- rp1 5y agoSlightly unrelated, but does anyone think we'll ever discover a closed-form solution to neural network optimization? If you think about it, the network is known, the initial weights are known, the training data is known, and the objective function is known. All of the work spent "training" is spent computing the solution to an optimization problem that could (theoretically) have a closed-form solution.
- Nevermark 5y agoSince we can't find general closed form solutions for simpler equations such as 5th order polynomials, general closed form NN solvers (vs optimizers) do not look likely. However, constraints on the general class of polynomials of 5th order and higher can result in subclasses that are solvable in closed form. So there may be a long tail of closed form solvable classes of NN architectures waiting to be discovered. Whether non-trivial closed-form subclasses of neural networks exist, and whether any of those classes is actually useful ... seems an area worth exploring.
- archibaldJ 5y agoDigressing back to qc.. If you look at how Shor's algorithm works, it's more like manipulating some kind of embeded values (that we have no direct access to) eg via Hadamard gates and eventually collapsing the entanglement into the solution. So maybe we can have something closed-form-ish that solves NN by arranging some q gates some way