Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries

A recent study has explored the application of differential privacy (DP) in the context of dependent data, which is prevalent in social and health sciences. The research highlights the challenges posed by dependence in data, particularly when individuals provide multiple observations, and demonstrates that Winsorized mean estimators can be effective for both bounded and unbounded data under these conditions.

A new approach called Corrective Unlearning in Task Space (CUTS) has been introduced to address the challenge of removing the influence of corrupted training data in machine learning without needing access to the original data. This method utilizes a small proxy set of corrupted samples to guide the unlearning process, marking a significant advancement in Corrective Machine Unlearning (CMU).

Recent research has established an upper bound for the box-counting dimension of pullback attractors in recurrent neural networks, particularly those utilizing reservoir computing. This study builds on the conjecture that these networks can effectively learn and reconstruct chaotic system dynamics, including Lyapunov exponents and fractal dimensions.

A recent study published on arXiv explores the relationship between model capacity and the number of visual tokens necessary to maintain image semantics, introducing a method called Orthogonal Filtering to cluster redundant tokens into a compact set of orthogonal bases. This research demonstrates that larger Vision Transformer (ViT) models can operate effectively with fewer tokens, enhancing efficiency in representation learning.

A recent study has introduced a semantic distribution-guided reconstruction framework that leverages a vision-language foundation model to improve undersampled MRI reconstruction. This approach encodes both the reconstructed images and auxiliary information into high-level semantic features, enhancing the quality of MRI images, particularly for knee and brain datasets.

UltraViCo has been introduced as a novel approach to address the challenges of video length extrapolation in video diffusion transformers, identifying issues such as periodic content repetition and quality degradation due to attention dispersion. This work proposes a fundamental rethinking of attention maps to improve model performance beyond training lengths.

The recent introduction of Agent0-VL marks a significant advancement in vision-language reasoning, enabling self-evaluation and self-repair through tool-integrated reasoning. This self-evolving agent aims to overcome the limitations of human-annotated supervision by allowing the model to introspect and refine its reasoning based on evidence-grounded analysis.

ReDirector has been introduced as a novel method for generating video retakes of any length using Rotary Camera Encoding (RoCE), which improves the alignment of spatiotemporal positions in dynamically captured videos. This method addresses previous misapplications of RoPE, enhancing dynamic object localization and preserving static backgrounds across varying camera trajectories and video lengths.