Related papers: Jamming as Information: a Geometric Approach
How to understand deep learning systems remains an open problem. In this paper we propose that the answer may lie in the geometrization of deep networks. Geometrization is a bridge to connect physics, geometry, deep network and quantum…
Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously…
Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and…
We consider an inverse scattering problem for time-harmonic acoustic or electromagnetic waves. The goal is to localize several small penetrable objects embedded inside an otherwise homogeneous background medium from observations of far…
Last two decades, the problem of robotic mapping has made a lot of progress in the research community. However, since the data provided by the sensor still contains noise, how to obtain an accurate map is still an open problem. In this…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible…
We present a heuristic strategy for marginal MAP (MMAP) queries in graphical models. The algorithm is based on a reduction of the task to a polynomial number of marginal inference computations. Given an input evidence, the marginals mass…
We expose a relationship between jamming and a generalization of Tutte's barycentric embedding. This provides a basis for the systematic treatment of jamming and maximal packing problems on two-dimensional surfaces.
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
We design polynomial time schemes for secure message transmission over arbitrary networks, in the presence of an eavesdropper, and where each edge corresponds to an erasure channel with public feedback. Our schemes are described through…
In many real-world applications data come as discrete metric spaces sampled around 1-dimensional filamentary structures that can be seen as metric graphs. In this paper we address the metric reconstruction problem of such filamentary…
The problem of jam formation during the discharge by gravity of granular material through a two-dimensional silo has a number of practical applications. In many problems the estimation of the minimum outlet size which guarantees that the…
We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…
We form a "map of tournaments" by adapting the map framework from the world of elections. By a tournament we mean a complete directed graph where the nodes are the players and an edge points from a winner of a game to the loser (with no…
Conventional anti-jamming methods mainly focus on preventing single jammer attacks with an invariant jamming policy or jamming attacks from multiple jammers with similar jamming policies. These anti-jamming methods are ineffective against a…
This paper proposes a novel approach to analyzing multi-hop reasoning in language models through Hamiltonian mechanics. We map reasoning chains in embedding spaces to Hamiltonian systems, defining a function that balances reasoning…
This article studies the robust version of persistent homology based on trimming methodology to capture the geometric feature through support of the data in presence of outliers. Precisely speaking, the proposed methodology works when the…
The graph-navigability problem concerns how one can find as short paths as possible between a pair of vertices, given an incomplete picture of a graph. We study the navigability of graphs where the vertices are tagged by a number (between 1…
This paper develops a novel framework to defeat a super-reactive jammer, one of the most difficult jamming attacks to deal with in practice. Specifically, the jammer has an unlimited power budget and is equipped with the self-interference…
Minimax distance measure extracts the underlying patterns and manifolds in an unsupervised manner. The existing methods require a quadratic memory with respect to the number of objects. In this paper, we investigate efficient sampling…