Sums along binary quartic forms

We give power saving asymptotics for \sum_{x,y<X} d(x^4+y^4). This constitutes the first case of estimates for a divisor sums along such a sparse sequence breaching the hyperbola method since 1963 work of Hooley for single variable quadratics. The techniques involve a mix of algebraic number theory, a 2d delta method, and an application of subconvexity for GL2 L-functions in the level aspect.