Spotlight
Surfing: Iterative Optimization Over Incrementally Trained Deep Networks
Ganlin Song · Zhou Fan · John Lafferty

Thu Dec 12th 04:20 -- 04:25 PM @ West Ballroom C

We investigate a sequential optimization procedure to minimize the empirical risk functional $f{\hat\theta}(x) = \frac{1}{2}\|G{\hat\theta}(x) - y\|^2$ for certain families of deep networks $G{\theta}(x)$. The approach is to optimize a sequence of objective functions that use network parameters obtained during different stages of the training process. When initialized with random parameters $\theta0$, we show that the objective $f{\theta0}(x)$ is ``nice'' and easy to optimize with gradient descent. As learning is carried out, we obtain a sequence of generative networks $x \mapsto G{\thetat}(x)$ and associated risk functions $f{\thetat}(x)$, where $t$ indicates a stage of stochastic gradient descent during training. Since the parameters of the network do not change by very much in each step, the surface evolves slowly and can be incrementally optimized. The algorithm is formalized and analyzed for a family of expansive networks. We call the procedure {\it surfing} since it rides along the peak of the evolving (negative) empirical risk function, starting from a smooth surface at the beginning of learning and ending with a wavy nonconvex surface after learning is complete. Experiments show how surfing can be used to find the global optimum and for compressed sensing even when direct gradient descent on the final learned network fails.

Author Information

Ganlin Song (Yale University)
Zhou Fan (Yale Univ)
John Lafferty (Yale University)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors