Cherry-Picking Gradients: Learning Low-Rank Embeddings of Visual Data via Differentiable Cross-Approximation
This method addresses the challenge of processing large-scale multidimensional grid data, such as 3D tomography, for tasks requiring extensive context, like medical condition prediction of entire organs, but it is incremental as it builds on existing tensor decomposition and sampling techniques.
The authors tackled the problem of processing large-scale visual data tensors by proposing an end-to-end trainable framework that learns low-rank embeddings using only a fraction of the data entries, achieving logarithmic sample growth with input size and enabling handling of previously intractable large grids.
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.