Nonlocal operator learning for fMRI encoding and decoding tasks

Functional MRI data exhibit high-dimensional spatiotemporal structure, making both prediction and decoding challenging. In this work, we investigate neural integral-operator-based models for encoding and decoding tasks in fMRI, with particular emphasis on the role of nonlocal spatiotemporal context. We implement a latent neural integral operator framework that performs fixed point iterations in an auxiliary space from which classification and stimuli prediction is performed via a decoder. We evaluate our model on two open-source fMRI datasets. Our experiments examine both decoding of stimuli from fMRI recordings and encoding of fMRI dynamics from stimulus representations. A main focus is the effect of spatiotemporal context: we systematically compare short and long temporal windows, as well as the use of visual cortex vs whole brain recordings, and analyze their influence on performance and latent-space geometry. Across tasks and datasets, larger temporal windows generally improve results and produce more structured learned representations. In decoding experiments, the learned latent space often provides clearer class separation than the raw data. In encoding experiments, although absolute performance remains moderate due to the difficulty of the task, longer temporal windows still yield consistent gains. These findings suggest that neural integral operators provide a promising framework for modeling fMRI dynamics and that broader spatiotemporal context can be beneficial for both prediction and representation learning. More broadly, the results indicate that exploiting distributed nonlocal structure in brain dynamics requires model architectures specifically designed to capture such dependencies.

Neural Integral Operators for Inverse problems in Spectroscopy

Deep learning has shown high performance on spectroscopic inverse problems when sufficient data is available. However, it is often the case that data in spectroscopy is scarce, and this usually causes severe overfitting problems with deep learning methods. Traditional machine learning methods are viable when datasets are smaller, but the accuracy and applicability of these methods is generally more limited. We introduce a deep learning method for classification of molecular spectra based on learning integral operators via integral equations of the first kind, which results in an algorithm that is less affected by overfitting issues on small datasets, compared to other deep learning models. The problem formulation of the deep learning approach is based on inverse problems, which have traditionally found important applications in spectroscopy. We perform experiments on real world data to showcase our algorithm. It is seen that the model outperforms traditional machine learning approaches such as decision tree and support vector machine, and for small datasets it outperforms other deep learning models. Therefore, our methodology leverages the power of deep learning, still maintaining the performance when the available data is very limited, which is one of the main issues that deep learning faces in spectroscopy, where datasets are often times of small size.