Related papers: Embeddings into outer models
Given graphs $G$ and $H$, we propose a method to implicitly enumerate topological-minor-embeddings of $H$ in $G$ using decision diagrams. We show a useful application of our method to enumerating subgraphs characterized by forbidden…
A recent body of work has demonstrated that Transformer embeddings can be linearly decomposed into well-defined sums of factors, that can in turn be related to specific network inputs or components. There is however still a dearth of work…
Recent advances in self-supervised learning and neural network scaling have enabled the creation of large models, known as foundation models, which can be easily adapted to a wide range of downstream tasks. The current paradigm for…
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that…
We give a simple, low resource method to produce order embeddings from ontologies. Such embeddings map words to vectors so that order relations on the words, such as hypernymy/hyponymy, are represented in a direct way. Our method uses…
We propose a new method for determining the elementary paths and elementary circuits in a directed graph. Also, the Hamiltonian paths and Hamiltonian circuits are enumerated.
In this paper, we prove a theorem about embedding of some partially ordered topological spaces in topological hyperspaces equipped with Fell topology. Then we give some examples to show that the map defining the embedding may not be…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
We discuss some highlights of our computer-verified proof of the construction, given a countable transitive set-model $M$ of $\mathit{ZFC}$, of generic extensions satisfying $\mathit{ZFC}+\neg\mathit{CH}$ and $\mathit{ZFC}+\mathit{CH}$.…
For a relational structure ${\mathbb X}$ we investigate the partial order $\langle {\mathbb P} ({\mathbb X}) ,\subset \rangle$, where ${\mathbb P} ({\mathbb X}):=\{ f[X]: f\in \mathop{\rm Emb}\nolimits ({\mathbb X})\}$. Here we consider…
Representation learning on graphs has been gaining attention due to its wide applicability in predicting missing links, and classifying and recommending nodes. Most embedding methods aim to preserve certain properties of the original graph…
Network embedding maps the nodes of a given network into a low-dimensional space such that the semantic similarities among the nodes can be effectively inferred. Most existing approaches use inner-product of node embedding to measure the…
We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the…
Word embedding is an essential building block for deep learning methods for natural language processing. Although word embedding has been extensively studied over the years, the problem of how to effectively embed numerals, a special subset…
Metric data structures (distance oracles, distance labeling schemes, routing schemes) and low-distortion embeddings provide a powerful algorithmic methodology, which has been successfully applied for approximation algorithms \cite{llr},…
This paper is a sequel to \cite{Tz10}, where a local version of ZFC, LZFC, was introduced and examined and transitive models of ZFC with properties that resemble large cardinal properties, namely Mahlo and $\Pi_1^1$-indescribable models,…
The Homeomorphic Embedding relation has been amply used for defining termination criteria of symbolic methods for program analysis, transformation, and verification. However, homeomorphic embedding has never been investigated in the context…
We study the spaces of embeddings $S^m\hookrightarrow R^n$ and those of long embeddings $R^m\hookrightarrow R^n$, i.e. embeddings of a fixed behavior outside a compact set. More precisely we look at the homotopy fiber of the inclusion of…
We investigate the structure of fixed point sets of self-embeddings of models of arithmetic. In particular, given a countable nonstandard model M of a modest fragment of Peano arithimetic, we provide complete characterizations of (a) the…
This paper frames a general prediction system as an observer traveling around a continuous space, measuring values at some locations, and predicting them at others. The observer is completely agnostic about any particular task being solved;…