Related papers: Transversality for Interval Translation Maps

Linear probes and sparse autoencoders consistently recover meaningful structure from transformer representations -- yet why should such simple methods succeed in deep, nonlinear systems? We show this is not merely an empirical regularity…

AI is widely thought to be poised to transform business, yet current perceptions of the scope of this transformation may be myopic. Recent progress in natural language processing involving transformer language models (TLMs) offers a…

We consider the nonlinear inverse problem of learning a transition operator $\mathbf{A}$ from partial observations at different times, in particular from sparse observations of entries of its powers…

A key generative principle within social and other complex networks is transitivity, where friends of friends are more likely friends. We propose a new model for highly dense complex networks based on transitivity, called the Iterated Local…

Transformers are deep architectures that define ``in-context maps'' which enable predicting new tokens based on a given set of tokens (such as a prompt in NLP applications or a set of patches for a vision transformer). In previous work, we…

This paper uses a construction of M. Keane to show that there exists a topologically mixing interval exchange transformation.

If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…

An important development in deep learning from the earliest MLPs has been a move towards architectures with structural inductive biases which enable the model to keep distinct sources of information and routes of processing well-separated.…

Broadly speaking Information theory (IT) assumes no structure of the underlying states. But what about contexts where states do have a clear structure - how should IT cope with such situations? And if such coping is at all possible then -…

This paper introduces a new approach for solving electrical impedance tomography (EIT) problems using deep neural networks. The mathematical problem of EIT is to invert the electrical conductivity from the Dirichlet-to-Neumann (DtN) map.…

Deep neural networks are applied in more and more areas of everyday life. However, they still lack essential abilities, such as robustly dealing with spatially transformed input signals. Approaches to mitigate this severe robustness issue…

The capability to jointly process multi-modal information is becoming an essential task. However, the limited number of paired multi-modal data and the large computational requirements in multi-modal learning hinder the development. We…

Unpaired image-to-image translation is to translate an image from a source domain to a target domain without paired training data. By utilizing CNN in extracting local semantics, various techniques have been developed to improve the…

In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…

Text image machine translation (TIMT) aims to translate texts embedded in images from one source language to another target language. Existing methods, both two-stage cascade and one-stage end-to-end architectures, suffer from different…

In computational PDE-based inverse problems, a finite amount of data is collected to infer unknown parameters in the PDE. In order to obtain accurate inferences, the collected data must be informative about the unknown parameters. How to…

In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…

How can prior knowledge on the transformation invariances of a domain be incorporated into the architecture of a neural network? We propose Equivariant Transformers (ETs), a family of differentiable image-to-image mappings that improve the…

We present IMTLab, an open-source end-to-end interactive machine translation (IMT) system platform that enables researchers to quickly build IMT systems with state-of-the-art models, perform an end-to-end evaluation, and diagnose the…

Video Diffusion Transformers (DiTs) have been synthesizing high-quality video with high fidelity from given text descriptions involving motion. However, understanding how Video DiTs convert motion words into video remains insufficient.…