Related papers: A Guide to the Bott Index and Localizer Index
Which spaces look like an n-sphere through the eyes of the n-th Postnikov section functor and the n-connected cover functor? The answer is what we call the Postnikov genus of the n-sphere. We define in fact the notion of localization genus…
Vision Transformers have emerged as powerful, scalable and versatile representation learners. To capture both global and local features, a learnable [CLS] class token is typically prepended to the input sequence of patch tokens. Despite…
We derive the expression for the local Hall conductivity for systems that lack translation symmetry and use it to study the local fluctuations of the Hall signal around disordered patches in magnetic insulators. We find that the regime in…
Circuit analysis of any certain model behavior is a central task in mechanistic interpretability. We introduce our circuit discovery pipeline with Sparse Autoencoders (SAEs) and a variant called Transcoders. With these two modules inserted…
It is shown that the Mott insulating and superfluid phases of bosons in an optical lattice may be distinguished by a non-local 'parity order parameter' which is directly accessible via single site resolution imaging. In one dimension, the…
Dyson insulators with random hoppings in a lattice approach localization faster compared to the usual Anderson insulators with site disorder. For even-$N$ lattice sites the Dyson insulators mimic topological insulators with a pseudo-gap at…
In this paper, we investigate a coupled polar code architecture that supports both local and global decoding. This local-global construction is motivated by practical applications in data storage and transmission where reduced-latency…
We study topological insulators under dephasing noise. With examples of both a $2d$ Chern insulator and a $3d$ topological insulator protected by time-reversal symmetry, we demonstrate that there is a phase transition at finite dephasing…
Edge states of chiral topologically ordered phases are commonly described by chiral Luttinger liquids, effective theories that are exact only in the hydrodynamic limit. Motivated by recent bulk observations of fractional Chern insulators…
Autonomous robotics is critically affected by the robustness of its scene understanding algorithms. We propose a two-axis pipeline based on polarization indices to analyze dynamic urban scenes. As robots evolve in unknown environments, they…
Topological states of matter were first introduced for non-interacting fermions on an infinite uniform lattice. Since then, substantial effort has been made to generalize these concepts to more complex settings. Recently, local markers have…
An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by…
We investigate the existence of sufficient local conditions under which poset representations decompose as direct sums of indecomposables from a given class. In our work, the indexing poset is the product of two totally ordered sets,…
The transformer is the most popular neural architecture for language modeling. The cornerstone of the transformer is its global attention mechanism, which lets the model aggregate information from all preceding tokens before generating the…
Locally exact integrators preserve linearization of the original system at every point. We construct energy-preserving locally exact discrete gradient schemes for arbitrary multidimensional canonical Hamiltonian systems by modifying…
Indoor location-based services (LBS), such as POI search and routing, are often built on top of typical indoor spatial queries. To support such queries and indoor LBS, multiple techniques including model/indexes and search algorithms have…
Commonly, a two-dimensional topological insulator is characterized by non-zero Chern numbers associated with its band structure. In our work, we present the experimental demonstration of an anomalous topological insulator, for which the…
We study the local functor of points (which we call the Weil-Berezin functor) for smooth supermanifolds, providing a characterization, representability theorems and applications to differential calculus.
The discovery that the band structure of electronic insulators may be topologically non-trivial has unveiled distinct phases of electronic matter with novel properties. Recently, mechanical lattices have been found to have similarly rich…
For a given autonomous time-dependent system that generates either a global, in time, semigroup or else only a local, in time, semigroup, a test involving a linear eigenvalue problem is given which determines which of 'global' or 'local'…