Related papers: On the Geometric Structure of Layer Updates in Dee…

Learning dense correspondences across deformable 3D shapes remains a long-standing challenge due to structural variability, non-isometric deformation, and inconsistent topology. Existing methods typically trade off generalization, geometric…

Complex geometric tasks such as geometric modeling, physical simulation, and texture parametrization often involve the embedding of many complex sub-domains with potentially different dimensions. These tasks often require evolving the…

Large Language Models (LLMs) have demonstrated strong capabilities in natural language understanding and reasoning, while recent extensions that incorporate visual inputs enable them to process multimodal information. Despite these…

Multilingual language models (LMs) promise broader NLP access, yet current systems deliver uneven performance across the world's languages. This survey examines why these gaps persist and whether they reflect intrinsic linguistic difficulty…

Large Language Models (LLMs) drive current AI breakthroughs despite very little being known about their internal representations. In this work, we propose to shed the light on LLMs inner mechanisms through the lens of geometry. In…

Vision-language models encode continuous geometry that their text pathway fails to express: a 6,000-parameter linear probe extracts hand joint angles at 6.1 degrees MAE from frozen features, while the best text output achieves only 20.0…

In document image rectification, there exist rich geometric constraints between the distorted image and the ground truth one. However, such geometric constraints are largely ignored in existing advanced solutions, which limits the…

Triangulated meshes have become ubiquitous discrete-surface representations. In this paper we address the problem of how to maintain the manifold properties of a surface while it undergoes strong deformations that may cause topological…

A two-part affine approximation has been found to be a good approximation for transformer computations over certain subject object relations. Adapting the Bigger Analogy Test Set, we show that the linear transformation Ws, where s is a…

GPT-style language models are sensitive to single-token changes at generation points where the predicted probability distribution is spread across multiple tokens. Viewing this sensitivity as a geometric property, we derive an…

Recent research has extensively studied how large language models manipulate integers in specific arithmetic tasks, and on a more fundamental level, how they represent numeric values. These previous works have found that language model…

The advancement of large language models (LLMs) for real-world applications hinges critically on enhancing their reasoning capabilities. In this work, we explore the reasoning abilities of large language models (LLMs) through their…

Understanding how neural representations respond to geometric transformations is essential for evaluating whether learned features preserve meaningful spatial structure. Existing approaches primarily assess robustness primarily by comparing…

Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers…

Off-road semantic segmentation suffers from thick, inconsistent boundaries, sparse supervision for rare classes, and pervasive label noise. Designs that fuse only at low resolution blur edges and propagate local errors, whereas maintaining…

A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…

Deep generative models like variational autoencoders approximate the intrinsic geometry of high dimensional data manifolds by learning low-dimensional latent-space variables and an embedding function. The geometric properties of these…

We study how information propagates in decoder-only Transformers, which are the architectural backbone of most existing frontier large language models (LLMs). We rely on a theoretical signal propagation analysis -- specifically, we analyse…

We seek to understand how the representations of individual tokens and the structure of the learned feature space evolve between layers in deep neural networks under different learning objectives. We focus on the Transformers for our…

Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…