Study of orbifold Chern character using superconnections.
problem Chern character for orbifold settings.
method Use of flat antiholomorphic superconnections and Riemann-Roch-Grothendieck theorem.
result Uniqueness of orbifold Chern character proven.
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A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
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48 results for “character embeddings”
Unsupervised model learns word and context embeddings from character sequences.
problem Learning meaningful word and context embeddings from unlabeled data.
method Character-aware neural architecture that jointly learns word and context embeddings.
result Compact encoders achieve high performance in downstream tasks.
Utilizing Character and Word Embeddings for Text Normalization with Sequence-to-Sequence Modelscs.CL
Neural model improves text normalization for non-English languages.
problem Improving text normalization in non-English languages with limited data.
method Sequence-to-sequence model with character and word embeddings, using pre-trained word embeddings with subword information.
result Achieved state-of-the-art F1 score on Arabic language correction dataset.
AN2VEC disentangles feature and structural information in social networks.
problem Difficulty in separating feature and structural information in social networks.
method Graph Convolutional Networks (GCN) Variational Autoencoder for disentangled node embeddings.
result AN2VEC captures joint information of structure and features better than unshared information.
New surfaces found in 5D space.
problem Constructing smooth embedded special Legendrian surfaces in \(\mathbb S^5\).
method Combining implicit function theorem, loop algebra-valued meromorphic connections, and character variety analysis.
result First genus > 1 embedded special Legendrian surfaces in \(\mathbb S^5\).
A mapping bends Teichmüller spaces into character varieties, preserving symplectic structure.
problem Mapping Fricke-Teichmüller space to character variety of surface representations.
method Bending Fuchsian representations along a fixed measured lamination, proving equivariant symplectic embedding and properness.
result Continuous extension of bending map to Thurston boundary and geometric complexification.
The paper extends character varieties to marked surfaces and discovers their triangular decompositions.
problem Character varieties on marked surfaces and their properties.
method Triangulations of marked surfaces and cohomological groups.
result Stated character varieties admit triangular decompositions.
Introduces tensor product for quiver representations and applies to stable bundles and character varieties.
problem Stability and classification of quiver bundles and their subvarieties.
method Definition of tensor product for quiver representations and application to stability and character varieties.
result Tensor products of polystable quiver bundles are polystable and provide insights into character varieties.
In 1993, Bismut and Zhang establish a mod Z embedding formula of Atiyah-Patodi-Singer reduced eta invariants. In this paper, we explain the hidden mod Z term as a spectral flow and extend this embedding formula to the equivariant family case. In this case, the spectral flow is generalized to the equivariant chern chara…
New method to compute tangle sums in character varieties.
problem Computing character varieties for tangle sums.
method Cut-and-paste methods to construct perturbed character varieties.
result Bounding cochains can be used to recover differential of .
Neural Machine Translation (MT) has reached state-of-the-art results. However, one of the main challenges that neural MT still faces is dealing with very large vocabularies and morphologically rich languages. In this paper, we propose a neural MT system using character-based embeddings in combination with convolutional…
Given a 3 manifold M with torus boundary and an ideal triangulation, Yoshida and Tillmann give different methods to construct surfaces embedded in M from ideal points of the deformation variety. Yoshida builds a surface from twisted squares whereas Tillmann produces a spun-normal surface. We investigate the relation be…
Paper develops neural network for Mandarin polyphone disambiguation.
problem Homograph problem in Mandarin Chinese text-to-speech.
method Bidirectional RNN for context, prediction network for mapping embeddings to pronunciations.
result Achieves 94.69% accuracy on polyphonic character dataset.
The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this ca…
New coordinates for SL3-web graphs on surfaces defined by Fock-Goncharov.
problem Characterizing functions on SL3-character varieties of surfaces.
method Introduced tropical Fock-Goncharov coordinates based on Knutson-Tao rhombus inequalities and congruence conditions.
result Tropical coordinates naturally index the commutative algebra of functions on SL3-character varieties.
The paper solves a geometric P=W conjecture for SL(2,C) using Thurston's compactification.
problem Addressing the geometric P=W conjecture for SL(2,C) in projective compactifications of character varieties of closed surfaces.
method Using Thurston's compactification of Teichmüller space and new results, the paper constructs a projective compactification of the SL(2,C)-character variety of any closed surface of genus g>1.
result The boundary divisors are toric varieties and the dual intersection complex is a sphere.
Hybrid model learns novel handwritten characters better than neural or symbolic models alone.
problem Generating novel yet structured concepts.
method Neuro-symbolic model combining neural networks and probabilistic programs.
result Hybrid model outperforms alternative models in learning and generalizing novel handwritten characters.
The traceless character variety of a -punctured 2-sphere is the symplectic reduction of a Hamiltonian -torus action on the character variety of a closed surface of genus . It is stratified with a finite singular stratum and a top smooth symplectic stratum of dimens…
Paper studies invariants of knots using logarithmic Gauss maps and character varieties.
problem Understanding invariants of knots using logarithmic Gauss maps and character varieties.
method Develops a homological point of view on the slope using non-abelian representations.
result Defines a rational function on the character variety that unifies various known invariants.
Byte-level machine translation outperforms embedding-based methods.
problem Improving machine translation without embedding layers.
method Replacing embedding layers with one-hot representations of bytes, and using decoder-input dropout.
result Byte-to-byte machine translation achieves BLEU scores comparable to character-level and subword-level models.
A differential topology proof that the character variety of the genus two surface is homeomorphic to math.GT
Proof that character variety of genus 2 surface is .
problem Character variety structure of genus 2 surface.
method Differential topology, algebraic topology, representations.
result Character variety is homeomorphic to .
The moduli space of stable rank 2 parabolic bundles over an elliptic curve with 3 marked pointsmath.AG
We describe the moduli space of stable rank 2 parabolic bundles over an elliptic curve with 3 marked points.
problem Characterize the moduli space of stable rank 2 parabolic bundles over an elliptic curve with marked points.
method Explicitly describe the moduli space as a blow-up of an embedded elliptic curve in and interpret it as the character variety of the 3-punctured torus.
result The moduli space can be described as a blow-up of an embedded elliptic curve in and interpreted as the character variety of the 3-punctured torus.
New knot homology theory from symplectic geometry.
problem Developing a symplectic counterpart to instanton knot homology.
method Using symplectic character varieties and Floer homology, a new invariant for knots in 3-manifolds is constructed.
result Symplectic instanton knot homology (SIK) is a new invariant of knots and links in 3-manifolds.
We propose several ways of reusing subword embeddings and other weights in subword-aware neural language models. The proposed techniques do not benefit a competitive character-aware model, but some of them improve the performance of syllable- and morpheme-aware models while showing significant reductions in model sizes…
Quantum hyperbolic geometrymath.GT
We construct a new family, indexed by the odd integers , of -dimensional quantum field theories called {\it quantum hyperbolic field theories} (QHFT), and we study its main structural properties. The QHFT are defined for (marked) -bordisms supported by compact oriented 3-manifolds with a prop…
We construct a new family of exact quantum field theories modeled on hyperbolic geometry, called {\it quantum hyperbolic field theories} (QHFTs). The QHFTs are defined for a -bordism category based on the set of compact oriented 3-manifolds , equipped with properly embedded framed links $L_\Ff$ and with flat …
The theory of differential characters is developed completely from a de Rham - Federer viewpoint. Characters are defined as equivalence classes of special currents, called sparks, which appear naturally in the theory of singular connections. There are many different spaces of currents which yield the character groups. …
Character scheme of small Seifert 3-manifolds is reduced if and only if no exceptional abelian character exists.
problem Character scheme of small Seifert 3-manifolds and its reduction condition.
method Complete description of the SL2(C)-character scheme of small Seifert 3-manifolds.
result Character scheme is reduced if and only if no exceptional abelian character exists, and exceptional abelian character has multiplicity 2.
Quantum character varietiesmath.QA
Quantum character varieties unify four construction methods.
problem No specific problem stated; unification of approaches.
method Four different approaches to construction.
result Unified understanding of quantum character varieties.
We show that for any knot there exist only finitely many irreducible metabelian characters in the -character variety of the knot group, and the number is given explicitly by using the determinant of the knot. Then it turns out that for any 2-bridge knot a section of the -character va…
Character varieties get a natural Poisson structure.
problem Character varieties of surfaces.
method Natural Poisson structure.
result Character varieties have a Poisson structure.
Paper presents a novel neural network method for topic detection in micro-blogs.
problem Challenging topic detection without known topic count.
method Unsupervised neural sentence embedding model with attention mechanism.
result Improved clustering algorithm (RADBSCAN) discovers topics based on dataset character.
In this paper, we give a quantum interpretation of the Bismut-Chern character form (the loop space lifting of the Chern character form) as well as the Chern character form associated to a complex vector bundle with connection over a smooth manifold in the framework of supersymmetric quantum field theories developed by …
Study shows how certain knots and tori are detected by ideal points in character varieties.
problem Detecting essential twice-punctured tori in character varieties.
method Extending Tillmann's limiting character method to new families of knots and tori.
result Explicit determination of limiting characters at ideal points for specific knots and tori.
Study SL(2,C) character schemes for finitely generated groups.
problem Characterize SL(2,C) representations of finitely generated groups.
method Define coordinate rings and equations for SL(2,C) character schemes.
result Explicit equations for character schemes of finitely presented groups.
Background elimination for noisy character images or character images from real scene is still a challenging problem, due to the bewildering backgrounds, uneven illumination, low resolution and different distortions. We propose a stroke-based character reconstruction(SCR) method that use a weighted quadratic Bezier cur…
Character variety of Borromean link solved, Alexander polynomial formula found.
problem Character variety of Borromean link
method Determined irreducible SL(2,C) character variety, found Alexander polynomial formula
result Formula for twisted Alexander polynomial on character variety
Character varieties of 2-bridge knots and links explained using Farey recursion.
problem Understanding character varieties of 2-bridge knots and links.
method Using Farey recursion to define polynomials for character varieties.
result Character varieties described in terms of polynomials defined by Farey recursion.
Computes dimensions of representation and character varieties for 2 and 3-dimensional orbifolds.
problem Computing dimensions of representation and character varieties for orbifolds.
method Analyzes varieties of representations and characters of hyperbolic and non-hyperbolic orbifolds, provides tools for computation.
result Shows that the dimension of a specific component of characters equals half the dimension of the variety of characters of the boundary.
Paper generates personalized fonts from a few characters.
problem Creating personalized fonts from a limited set of characters.
method Designs a network framework to extract and recombine character content and style using various neural networks.
result Generated characters are structurally similar to real characters.
WEST compresses word embeddings and softmax layers for memory efficiency.
problem Memory constraints in large vocabulary models.
method WEST encodes words with sequences of sub-units, improving compression without performance loss.
result WEST achieves significant compression without sacrificing performance.
We study some basic properties of the variety of characters in PSL(2,C) of a finitely generated group. In particular we give an interpretation of its points as characters of representations. We construct 3-manifolds whose variety of characters has arbitrarily many components that do not lift to SL(2,C). We also study t…
Study of quantum decorated character stacks and their quantizations.
problem Quantization of decorated character stacks and their compatibility with cutting and gluing.
method Using stratified factorization homology, extend Fock and Goncharov's construction to include stacky points.
result Construction of categorical charts and flips on quantum decorated character stacks.
Let K be a knot in an integral homology 3-sphere and let B denote the 2-fold branched cover of the integral homology sphere branched along K. We construct a map from the slice of characters with trace free along meridians in the SL(2, C)-character variety of the knot exterior to the SL(2, C)-character variety of 2-fold…
Study character varieties of hyperbolic 3-manifolds using bundle methods.
problem Character varieties of hyperbolic 3-manifolds in once-punctured torus bundles.
method Restrict characters to the fibre and analyze branched covering maps.
result Infinite family of hyperbolic once-punctured bundles with unbounded genus.
Finite automorphisms of SL(2,C) character varieties identified.
problem Character varieties of surfaces with negative Euler characteristic.
method Algebraic automorphisms and mapping class groups studied.
result Finite extension of mapping class group identified.
Researchers describe character varieties for Hopf links, proving geometric properties.
problem Character variety geometry of Hopf links with twists.
method Geometric descriptions of irreducible and totally reducible representations.
result Complete geometric description of -character variety for .
Study of SU(2,1) character varieties on one-holed torus.
problem Characterize representations of mapping class group on SU(2,1) character variety.
method Explicit description of SU(2,1) character variety, use of Farey graph adaptation, and mapping class group action analysis.
result Description of an open domain of discontinuity for mapping class group action.