Restricted Boltzmann Machines (RBMs) are widely used as building blocks for deep learning models. Learning typically proceeds by using stochastic gradient descent, and the gradients are estimated with sampling methods. However, the gradient estimation is a computational bottleneck, so better use of the gradients will speed up the descent algorithm.To this end, we rst derive upper bounds on the RBM cost function, then show that descent methods can have natural advantages by operating in the `1 and Shatten-1 norm. We introduce a new method called \Stochastic Spectral Descent" that updates parameters in the normed space. Empirical results show dramatic improvements over stochastic gradient descent, and have only have a fractional increase on the per-iteration cost.