Traveling Waves Integrate Spatial Information Into Spectral Representations

Traveling waves are widely observed in the brain, but their precise computational function remains unclear. One prominent hypothesis is that they enable the transfer and integration of spatial information across neural populations. However, few computational models have explored how traveling waves might be harnessed to perform such integrative processing. Drawing inspiration from the famous ``Can one hear the shape of a drum?'' problem -- which highlights how spectral modes encode geometric information -- we introduce a set of convolutional recurrent neural networks that learn to produce traveling waves in their hidden states in response to visual stimuli. By applying a spectral decomposition to these wave-like activations, we obtain a powerful new representational space that outperforms equivalently local feed-forward networks on tasks requiring global spatial context. In particular, we observe that traveling waves effectively expand the receptive field of locally connected neurons, supporting long-range encoding and communication of information. We demonstrate that models equipped with this mechanism and spectral readouts solve visual semantic segmentation tasks demanding global integration, where local feed-forward models fail. As a first step toward traveling-wave-based representations in artificial networks, our findings suggest potential efficiency benefits and offer a new framework for connecting to biological recordings of neural activity.