In modern neuroscience, functional magnetic resonance imaging (fMRI) has been a crucial and irreplaceable tool that provides a non-invasive window into the dynamics of whole-brain activity. Nevertheless, fMRI is limited by hemodynamic blurring as well as high cost, immobility, and incompatibility with metal implants. Electroencephalography (EEG) is complementary to fMRI and can directly record the cortical electrical activity at high temporal resolution, but has more limited spatial resolution and is unable to recover information about deep subcortical brain structures. The ability to obtain fMRI information from EEG would enable cost-effective, imaging across a wider set of brain regions. Further, beyond augmenting the capabilities of EEG, cross-modality models would facilitate the interpretation of fMRI signals. However, as both EEG and fMRI are high-dimensional and prone to artifacts, it is currently challenging to model fMRI from EEG. To address this challenge, we propose a novel architecture that can predict fMRI signals directly from multi-channel EEG without explicit feature engineering. Our model achieves this by implementing a Sinusoidal Representation Network (SIREN) to learn frequency information in brain dynamics from EEG, which serves as the input to a subsequent encoder-decoder to effectively reconstruct the fMRI signal from a specific brain region. We evaluate our model using a simultaneous EEG-fMRI dataset with 8 subjects and investigate its potential for predicting subcortical fMRI signals. The present results reveal that our model outperforms a recent state-of-the-art model, and indicates the potential of leveraging periodic activation functions in deep neural networks to model functional neuroimaging data.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder