We present a differentiable framework to automatically learn view-dependent 2D kernels in a splatting-based pipeline to improve reconstruction quality and representation efficiency for novel 3D view synthesis. Our volumetric primitive is defined as a bounding ellipsoid and a 3D-kernel latent vector. We first learn a projection network to output a 2D-kernel latent, taking the attributes of the ellipsoid and the 3D-kernel latent as input. Next, the result is sent to a decoder to produce a radially symmetric 2D kernel in terms of Mahalanobis distance, bounded by the projected ellipsoid. The neural networks along with per-primitive attributes are jointly optimized. The effectiveness of our approach is demonstrated on standard benchmarks, comparing favorably against state-of-the-art techniques on both analytical and learned kernels. Finally, we extend the idea to learn general 2D kernels for 2D splatting as well as image representation.