# coVariance Neural Networks

In two-view data, each view has its own covariance and a cross-view covariance links them, yet covariance neural networks handled only single-view data and could not distinguish these structures once the views were concatenated. CANE splits the model into an in-view covariance filtering stage and a cross-view covariance filtering stage, replacing the whitening and singular-vector selection of canonical correlation analysis with learnable polynomial responses on the covariance spectrum, and trains directly on the downstream task. Across seven brain-imaging and motion-sensing datasets, CANE is best or tied for best on six, reaching a mean absolute error of 4.97 years for age prediction on ADNI1, often with fewer parameters than a two-view VNN.

In two-view data, each view has its own covariance and a cross-view covariance links them, yet covariance neural networks handled only single-view data and could not distinguish these structures once the views were concatenated. CANE splits the model into an in-view covariance filtering stage and a cross-view covariance filtering stage, replacing the whitening and singular-vector selection of canonical correlation analysis with learnable polynomial responses on the covariance spectrum, and trains directly on the downstream task. Across seven brain-imaging and motion-sensing datasets, CANE is best or tied for best on six, reaching a mean absolute error of 4.97 years for age prediction on ADNI1, often with fewer parameters than a two-view VNN.