SOE: SO(3)-Equivariant 3D MRI Encoding

Representation learning has become increasingly important, especially as powerful models have shifted towards learning latent representations before fine-tuning for downstream tasks. This approach is particularly valuable in leveraging the structural information within brain anatomy. However, a common limitation of recent models developed for MRIs is their tendency to ignore or remove geometric information, such as translation and rotation, thereby creating invariance with respect to geometric operations. We contend that incorporating knowledge about these geometric transformations into the model can significantly enhance its ability to learn more detailed anatomical information within brain structures. As a result, we propose a novel method for encoding 3D MRIs that enforces equivariance with respect to all rotations in 3D space, in other words, SO(3)-equivariance (SOE). By explicitly modeling this geometric equivariance in the representation space, we ensure that any rotational operation applied to the input image space is also reflected in the embedding representation space. This approach requires moving beyond traditional representation learning methods, as we need a representation vector space that allows for the application of the same SO(3) operation in that space. To facilitate this, we leverage the concept of vector neurons. The representation space formed by our method captures the brain's structural and anatomical information more effectively. We evaluate SOE pretrained on the structural MRIs of two public data sets with respect to the downstream task of predicting age and diagnosing Alzheimer's Disease from T1-weighted brain scans of the ADNI data set. We demonstrate that our approach not only outperforms other methods but is also robust against various degrees of rotation along different axes. The code is available at https://github.com/shizhehe/SOE-representation-learning.

Enforcing Conditional Independence for Fair Representation Learning and Causal Image Generation

Conditional independence (CI) constraints are critical for defining and evaluating fairness in machine learning, as well as for learning unconfounded or causal representations. Traditional methods for ensuring fairness either blindly learn invariant features with respect to a protected variable (e.g., race when classifying sex from face images) or enforce CI relative to the protected attribute only on the model output (e.g., the sex label). Neither of these methods are effective in enforcing CI in high-dimensional feature spaces. In this paper, we focus on a nascent approach characterizing the CI constraint in terms of two Jensen-Shannon divergence terms, and we extend it to high-dimensional feature spaces using a novel dynamic sampling strategy. In doing so, we introduce a new training paradigm that can be applied to any encoder architecture. We are able to enforce conditional independence of the diffusion autoencoder latent representation with respect to any protected attribute under the equalized odds constraint and show that this approach enables causal image generation with controllable latent spaces. Our experimental results demonstrate that our approach can achieve high accuracy on downstream tasks while upholding equality of odds.