Related papers: Transversality for Interval Translation Maps
Although piecewise isometries (PWIs) are higher dimensional generalizations of one dimensional interval exchange transformations (IETs), their generic dynamical properties seem to be quite different. In this paper we consider embeddings of…
Transformers have emerged as a competitive alternative to convnets in vision tasks, yet they lack the architectural inductive bias of convnets, which may hinder their potential performance. Specifically, Vision Transformers (ViTs) are not…
Any continuous, transitive, piecewise monotonic map is determined up to a binary choice by its dimension module with the associated finite sequence of generators. The dimension module by itself determines the topological entropy of any…
Variational models are widely used in image segmentation, with various models designed to address different types of images by optimizing specific objective functionals. However, traditional segmentation models primarily focus on the visual…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…
Vision Transformers (ViTs) have become prominent models for solving various vision tasks. However, the interpretability of ViTs has not kept pace with their promising performance. While there has been a surge of interest in developing {\it…
Attention-based neural networks such as transformers have demonstrated a remarkable ability to exhibit in-context learning (ICL): Given a short prompt sequence of tokens from an unseen task, they can formulate relevant per-token and…
Learning transformation invariant representations of visual data is an important problem in computer vision. Deep convolutional networks have demonstrated remarkable results for image and video classification tasks. However, they have…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
Transformers have emerged as the dominant architecture in the field of deep learning, with a broad range of applications and remarkable in-context learning (ICL) capabilities. While not yet fully understood, ICL has already proved to be an…
Traffic flow prediction (TFP) is a fundamental problem of the Intelligent Transportation System (ITS), as it models the latent spatial-temporal dependency of traffic flow for potential congestion prediction. Recent graph-based models with…
Unlike literal expressions, idioms' meanings do not directly follow from their parts, posing a challenge for neural machine translation (NMT). NMT models are often unable to translate idioms accurately and over-generate compositional,…
Large language models (LLMs) face inherent performance bottlenecks under parameter constraints, particularly in processing critical tokens that demand complex reasoning. Empirical analysis reveals challenging tokens induce abrupt gradient…
Vision Transformer (ViT) architectures represent images as collections of high-dimensional vectorized tokens, each corresponding to a rectangular non-overlapping patch. This representation trades spatial granularity for embedding…
A fundamental problem in object recognition is the development of image representations that are invariant to common transformations such as translation, rotation, and small deformations. There are multiple hypotheses regarding the source…
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear…
Transport-Based Morphometry (TBM) has emerged as a new framework for 3D medical image analysis. By embedding images into a transport domain via invertible transformations, TBM facilitates effective classification, regression, and other…
The remarkable understanding and generation capabilities of large language models (LLMs) have greatly improved translation performance. However, incorrect understanding of the sentence to be translated can degrade translation quality. To…
Effective spatiotemporal feature representation is crucial to the video-based action recognition task. Focusing on discriminate spatiotemporal feature learning, we propose Information Fused Temporal Transformation Network (IF-TTN) for…
We say that $f:[0,1]\to [0,1]$ is a {\it piecewise continuous interval map} if there exists a partition $0=x_0<x_1<\cdots<x_{d}<x_{d+1}=1$ of $[0,1]$ such that $f\vert_{(x_{i-1},x_i)}$ is continuous and the lateral limits $w_0^+=\lim_{x\to…