Can quantum annealing be used for training convolutional neural networks?

Question

Simulated annealing is applied for deep learning using convolutional neural networks. Likewise, can quantum annealing be used?

These two papers:

• Simulated Annealing Algorithm for Deep Learning (Rere et al., 2015)

• Application of Quantum Annealing to Training of Deep Neural Networks (Adachi & Henderson, 2015)

have both used the annealing technique for optimization of the problems but with different learning types. Therefore, my concern is whether quantum annealing can be applied for convolutional neural networks as well as or not.

If yes, then how? If no, then why not?

Any reference or related theories or work will be a great help.

Answer 1

I will assume you are asking about D-Wave's quantum annealer.

If there is a part of the learning process that can fit the QUBO (Quadratic Unconstrained Binary Optimization) formulation, then yes.

The problem however is what to consider as binary variables of your problem. In CNN, we have in general real-valued parameters that we tweak for training (using Stochastic Gradient Descent for instance). At first glance, considering the cost function would not fit the requirements, especially because you have nonlinear functions applied to the real weights so it does not look like a QUBO.

The second paper you mention used it especially because the energy function of Restricted Boltzmann machines is a QUBO and they were using the machine as a Boltzmann-like sampler for estimating an intractable part in the gradient (the negative part). So it's a different setup than CNNs.