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We establish center manifold theorems that allow one to study the bifurcation of small solutions from a trivial state in systems of functional equations posed on the real line. The class of equations includes most importantly nonlinear…

Deep learning models, especially large Transformers, carry substantial "memory" in their intermediate layers -- an \emph{internal world} that encodes a wealth of relational and contextual knowledge. This work harnesses that internal world…

Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…

Local Fourier analysis is a commonly used tool for the analysis of multigrid and other multilevel algorithms, providing both insight into observed convergence rates and predictive analysis of the performance of many algorithms. In this…

Differential medical VQA models compare multiple images to identify clinically meaningful changes and rely on vision encoders to capture fine-grained visual differences that reflect radiologists' comparative diagnostic workflows. However,…

Image retrieval in realistic scenarios targets large dynamic datasets of unlabeled images. In these cases, training or fine-tuning a model every time new images are added to the database is neither efficient nor scalable. Convolutional…

While mechanistic interpretability tools like Sparse Autoencoders (SAEs) can uncover meaningful features within Large Language Models (LLMs), a critical gap remains in transforming these insights into practical actions for model…

Large Language Models (LLMs) are deployed in high-stakes settings but can show demographic, gender, and geographic biases that undermine fairness and trust. Prior debiasing methods, including embedding-space projections, prompt-based…

Researchers in functional neuroimaging mostly use activation coordinates to formulate their hypotheses. Instead, we propose to use the full statistical images to define regions of interest (ROIs). This paper presents two machine learning…

Turbulent flows are chaotic and multi-scale dynamical systems, which have large numbers of degrees of freedom. Turbulent flows, however, can be modelled with a smaller number of degrees of freedom when using the appropriate coordinate…

Learning structured task representations from human demonstrations is essential for understanding long-horizon manipulation behaviors, particularly in bimanual settings where action ordering, object involvement, and interaction geometry can…

Deformable image registration poses a challenging problem where, unlike most deep learning tasks, a complex relationship between multiple coordinate systems has to be considered. Although data-driven methods have shown promising…

Human bilinguals often use similar brain regions to process multiple languages, depending on when they learned their second language and their proficiency. In large language models (LLMs), how are multiple languages learned and encoded? In…

Cross-embodiment manipulation is crucial for enhancing the scalability of robot manipulation and reducing the high cost of data collection. However, the significant differences between embodiments, such as variations in action spaces and…

Deep neural networks process data through a cascade of representations: input features, hidden activations, logits, and loss. While perturbations at the input, logit, and label levels have been systematically studied, the intermediate…

Long-term complex activity recognition and localisation can be crucial for decision making in autonomous systems such as smart cars and surgical robots. Here we address the problem via a novel deformable, spatiotemporal scene graph…

In this paper we present a novel approach for representing and evolving deformable active contours. The method combines piecewise regular B{\'e}zier models and curve evolution defined by local Free Form Deformation. The contour deformation…

Visually-grounded language models (VLMs) are highly effective in linking visual and textual information, yet they often struggle with basic classification and localization tasks. While classification mechanisms have been studied more…

Functional connectivity (FC) derived from resting-state fMRI plays a critical role in personalized predictions such as age and cognitive performance. However, applying foundation models(FM) to fMRI data remains challenging due to its high…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…