Related papers: Transversality for Interval Translation Maps
In a feedforward network, Transfer Entropy (TE) can be used to measure the influence that one layer has on another by quantifying the information transfer between them during training. According to the Information Bottleneck principle, a…
In his 1979 paper Trotman proves, using the techniques of the Thom transversality theorem, that under some conditions on the dimensions of the manifolds under consideration, openness of the set of maps transverse to a stratification in the…
In many computer vision applications, images are acquired with arbitrary or random rotations and translations, and in such setups, it is desirable to obtain semantic representations disentangled from the image orientation. Examples of such…
A cognitive map is an internal model which encodes the abstract relationships among entities in the world, giving humans and animals the flexibility to adapt to new situations, with a strong out-of-distribution (OOD) generalization that…
The transmission matrix (TM) is a representation to describe the light scattering process through a scattering medium. The degree of control elements in TM is correlated with the capacity of evaluating enormous equations with tremendous…
Transformer-based models have demonstrated remarkable reasoning abilities, but the mechanisms underlying relational reasoning remain poorly understood. We investigate how transformers perform \textit{transitive inference}, a classic…
All wavelets can be associated to a multiresolution like structure, i.e. an incr easing sequence of subspaces of L^2(R). We consider the interaction of a wavel et and the translation operator in terms of which of the subspaces in this multi…
We explore a quantitative interpretation of 2-dimensional intuitionistic type theory (ITT) in which the identity type is interpreted as a "type of differences". We show that a fragment of ITT, that we call difference type theory (dTT),…
Circular-arc graphs are graphs that can be represented as intersection graphs of subpaths of a cycle. Interval graphs are graphs that can be represented as intersection graphs of subpaths of a path. Since cycles are locally paths, every…
Variational Neural Machine Translation (VNMT) is an attractive framework for modeling the generation of target translations, conditioned not only on the source sentence but also on some latent random variables. The latent variable modeling…
By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…
Black-box deep neural networks excel in text classification, yet their application in high-stakes domains is hindered by their lack of interpretability. To address this, we propose Text Bottleneck Models (TBM), an intrinsically…
Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond…
Transformers have revolutionized performance in Natural Language Processing and Vision, paving the way for their integration with Graph Neural Networks (GNNs). One key challenge in enhancing graph transformers is strengthening the…
The interval graph for a set of intervals on a line consists of one vertex for each interval, and an edge for each intersecting pair of intervals. A probe interval graph is a variant that is motivated by an application to genomics, where…
In-context learning (ICL) is a remarkable capability of pretrained transformers that allows models to generalize to unseen tasks after seeing only a few examples. We investigate empirically the conditions necessary on the pretraining…
Topology offers a means to formally generalize digital filtering methods based on digital linear translation-invariant (LTI) filters while also, in principle, incorporating translation-variant and nonlinear methods as well as studying large…
A generalized translational invariant noncommutative field theory is analyzed in detail, and a complete description of translational invariant noncommutative structures is worked out. The relevant gauge theory is described, and the planar…
We present a computational study of finite-time mixing of a line segment by cutting and shuffling. A family of one-dimensional interval exchange transformations is constructed as a model system in which to study these types of mixing…
The increased availability of interactive maps on the Internet and on personal mobile devices has created new challenges in computational cartography and, in particular, for label placement in maps. Operations like rotation, zoom, and…