  We propose an end-to-end trainable framework that processes large-scale
visual data tensors by looking at a fraction of their entries only. Our method
combines a neural network encoder with a tensor train decomposition to learn a
low-rank latent encoding, coupled with cross-approximation (CA) to learn the
representation through a subset of the original samples. CA is an adaptive
sampling algorithm that is native to tensor decompositions and avoids working
with the full high-resolution data explicitly. Instead, it actively selects
local representative samples that we fetch out-of-core and on-demand. The
required number of samples grows only logarithmically with the size of the
input. Our implicit representation of the tensor in the network enables
processing large grids that could not be otherwise tractable in their
uncompressed form. The proposed approach is particularly useful for large-scale
multidimensional grid data (e.g., 3D tomography), and for tasks that require
context over a large receptive field (e.g., predicting the medical condition of
entire organs). The code is available at https://github.com/aelphy/c-pic.
