  Efficient compression of correlated data is essential to minimize
communication overload in multi-sensor networks. In such networks, each sensor
independently compresses the data and transmits them to a central node due to
limited communication bandwidth. A decoder at the central node decompresses and
passes the data to a pre-trained machine learning-based task to generate the
final output. Thus, it is important to compress the features that are relevant
to the task. Additionally, the final performance depends heavily on the total
available bandwidth. In practice, it is common to encounter varying
availability in bandwidth, and higher bandwidth results in better performance
of the task. We design a novel distributed compression framework composed of
independent encoders and a joint decoder, which we call neural distributed
principal component analysis (NDPCA). NDPCA flexibly compresses data from
multiple sources to any available bandwidth with a single model, reducing
computing and storage overhead. NDPCA achieves this by learning low-rank task
representations and efficiently distributing bandwidth among sensors, thus
providing a graceful trade-off between performance and bandwidth. Experiments
show that NDPCA improves the success rate of multi-view robotic arm
manipulation by 9% and the accuracy of object detection tasks on satellite
imagery by 14% compared to an autoencoder with uniform bandwidth allocation.
