Relation extraction models suffer from limited qualified training data. Using human annotators to label sentences is too expensive and does not scale well especially when dealing with large datasets. In this paper, we use Auxiliary Classifier Generative Adversarial Networks (AC-GANs) to generate high-quality relational…
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48 results for “generalized relations”
Introduces Relational Privacy (RP) to control relation memorization in question answering models.
problem Relation memorization in question answering models can lead to privacy issues.
method Formalizes Relational Privacy (RP) and Differential Relational Privacy (DrP), providing bounds on relation memorization.
result DrP allows effective learning of general properties of underlying concepts while preventing relation memorization.
Study builds non-bi-orderable groups without generalized torsion.
problem Constructing non-bi-orderable groups without generalized torsion.
method Constructing specific one-relator groups.
result Demonstrates existence of non-bi-orderable groups without generalized torsion.
Bayesian weight priors improve neural network learning of identity relations.
problem Neural networks struggle to learn abstract and systematic relations, especially identity relations.
method Extended RBP approach using Bayesian weight priors as a regularization term.
result Bayesian weight priors lead to perfect generalization for identity relations and do not hinder standard neural network learning.
Zero-shot and few-shot learning aim to improve generalization to unseen concepts, which are promising in many realistic scenarios. Due to the lack of data in unseen domain, relation modeling between seen and unseen domains is vital for knowledge transfer in these tasks. Most existing methods capture seen-unseen relatio…
HIRM models noisy, sparse, heterogeneous relational data using hierarchical clustering and Dirichlet processes.
problem Modeling noisy, sparse, and heterogeneous relational data.
method Hierarchical Chinese restaurant process and Dirichlet process mixture for clustering and modeling relation values.
result HIRM generalizes standard models and discovers relational structure in real-world datasets.
Paper characterizes relation numbers for parabolic two-generator groups.
problem Determining relation numbers for parabolic two-generator groups.
method Characterized relation numbers by equivalence to roots of generalized Chebyshev polynomials.
result Deciding relation numbers can be done by checking finitely many polynomials.
CURE extracts relations without supervision by clustering similar entity pairs.
problem Extracting relations unsupervised without considering sentence correlations.
method CURE uses Encoder-Decoder architecture for self-supervised learning and clustering similar relations.
result CURE outperforms state-of-the-art models on NYT and UNPC datasets.
The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type relation satisfied by the Khovanov homology. Thanks to this relation, we are ab…
In this paper we show that to each planar line arrangement defined over the real numbers, for which no two lines are parallel, one can write down a corresponding relation on Dehn twists that can be read off from the combinatorics and relative locations of intersections. This leads to an alternate proof of Wajnryb's gen…
Uniform negative immersions prove coherence of one-relator groups.
problem Proving coherence of one-relator groups.
method Using uniform negative immersions and linear-programming techniques.
result One-relator groups with uniform negative immersions are coherent.
We study the Orchard relation for generic configurations of points in the plane (also called order types). We introduce infinitesimally-close points and analyse the relation of this notion with the Orchard relation. The second part of the paper deals with monochromatic configurations (for the Orchard relation). We give…
We prove that ``almost generically'' for a one-relator group Delzant's -invariant (which measures the smallest size of a finite presentation for a group) is comparable in magnitude with the length of the defining relator. The proof relies on our previous results regarding isomorphism rigidity of generic one-relator …
Improves neural relational inference for dynamic multi-agent trajectories.
problem Limited accuracy of NRI in short output sequences for relational inference in multi-agent trajectories.
method Proposes DYnamic multi-AgentRelational Inference (DYARI) model to handle changing interactions over time.
result DYARI model outperforms NRI in dynamic relational inference tasks.
Researchers found generators and relations for skein algebras of planar surfaces.
problem Understanding generators and relations for skein algebras of planar surfaces.
method Investigated Kauffman bracket skein algebras of -holed disks over commutative rings, identifying generators and relations of specific degrees and degrees of support.
result Generators and relations for skein algebras were identified with specific degrees and supported by certain subsurfaces.
It is known that holomorphic Poisson structures are closely related to theories of generalized Kähler geometry and bi-Hermitian structures. In this article, we introduce quantization of holomorphic Poisson structures which are closely related to generalized Kähler structures /bi-Hermitian structures. By resulting nonco…
Study challenges neural models in compositional learning tasks.
problem Challenges in neural models for compositional and relational learning.
method Introduced ConceptWorld environment for generating images from compositional concepts, tested various neural architectures.
result Neural models struggle with longer compositional chains and substitutivity tests.
Traditional sequential multi-object attention models rely on a recurrent mechanism to infer object relations. We propose a relational extension (R-SQAIR) of one such attention model (SQAIR) by endowing it with a module with strong relational inductive bias that computes in parallel pairwise interactions between inferre…
We solve the problem on flat extensions of a generic surface with boundary in Euclidean 3-space, relating it to the singularity theory of the envelope generated by the boundary. We give related results on Legendre surfaces with boundaries via projective duality and observe the duality on boundary singularities. Moreove…
In the field of Natural Language Processing (NLP), we revisit the well-known word embedding algorithm word2vec. Word embeddings identify words by vectors such that the words' distributional similarity is captured. Unexpectedly, besides semantic similarity even relational similarity has been shown to be captured in word…
DARE uses GPT-2 to generate relation examples, improving RE performance.
problem Challenges in Relation Extraction, especially limited data and class imbalance.
method Data augmentation with GPT-2 fine-tuning to generate relation examples.
result Improves RE performance by up to 11 F1 score points.
We extend several results of Helfer, Wise, Louder and Wilton related to coherence in one-relator groups to the more general setting of one-relator products of locally indicable groups. The methods developed to do so also give rise to a new proof of a theorem of Brodsky.
Defines relations between Dirac structures and spinors using Courant algebroid relations.
problem Defines relations between Dirac structures and spinors using Courant algebroid relations.
method Uses Courant algebroid relations to define relations between Dirac structures and spinors.
result Proves existence results for T-dual structures and demonstrates compatibility with Type II supergravity equations.
Proves divisibility relations for symplectic curve polynomials.
problem Divisibility relations for symplectic curve polynomials.
method New proofs of divisibility relations for Oka and Alexander polynomials of symplectic curves.
result Proves Libgober's divisibility relations for symplectic curves.
We construct a 2-generated 2-related group without non-trivial finite factors. That answers a question of J. Button.
Legendre transformations link related integrable hierarchies.
problem Understanding relationships between integrable hierarchies.
method Legendre-type transformations of generalized Frobenius manifolds.
result Linear reciprocal transformations link related hierarchies.
Abstractor enhances Transformers for relational reasoning, improving sample efficiency and performance.
problem Improving sample efficiency and performance in relational tasks.
method Introduces Abstractor module with relational cross-attention to enable explicit relational reasoning.
result Dramatic improvements in sample efficiency and performance on various relational tasks.
Generic groups satisfy a chain condition for subgroups.
problem Understanding subgroup structures in generic groups.
method Proving for fixed integers in generic -generator -relator groups.
result Generic groups satisfy the Ascending Chain Condition for -generated subgroups.
Courant algebroids provide a useful mathematical tool (not only) in string theory. It is thus important to define and examine their morphisms. To some extent, this was done before using an analogue of canonical relations known from symplectic geometry. However, it turns out that applications in physics require a more g…
Language helps RL agents learn complex relational and causal structures.
problem Learning relational and causal structure in complex environments.
method Training RL agents to predict language descriptions and explanations.
result Language aids agents in learning challenging relational and causal tasks.
Graph Convolutional Networks (GCNs) have recently been shown to be quite successful in modeling graph-structured data. However, the primary focus has been on handling simple undirected graphs. Multi-relational graphs are a more general and prevalent form of graphs where each edge has a label and direction associated wi…
Speed-accuracy relations for diffusion models: Wisdom from nonequilibrium thermodynamics and optimal transportcond-mat.stat-mech
Diffusion models' speed-accuracy relations derived from thermodynamics.
problem Understanding the trade-off between model speed and accuracy.
method Connecting diffusion models to thermodynamics and optimal transport.
result Speed-accuracy relations derived, providing insights into optimal learning protocols.
Dependent MMD coresets help compare multiple related datasets.
problem Comparing multiple related datasets for insights into model generalization.
method Dependent MMD coresets for collections of datasets.
result Dependent MMD coresets facilitate comparison and understanding of multiple related datasets.
Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a re…
Bayesian meta-learning on relation graphs improves few-shot relation extraction.
problem Predicting relations in sentences with limited labeled examples.
method Bayesian meta-learning on a global relation graph, using graph neural networks and Langevin dynamics.
result Framework effectively learns and generalizes to new relations.
TaRP predicts missing relations in KGs using type and instance-level info.
problem Missing relations in KGs.
method Type-augmented relation prediction (TaRP) combining type and instance-level info.
result Significantly better performance on benchmark datasets.
Generalizes Collins' theorem to products of locally indicable groups.
problem Intersection of conjugates of Magnus subgroups in one-relator groups.
method Generalization to one-relator products of locally indicable groups.
result Result holds for a broader class of groups.
Generic properties of Whitehead's Algorithm and isomorphism rigidity of random one-relator groupsmath.GR
We prove that Whitehead's algorithm for solving the automorphism problem in a fixed free group has strongly linear time generic-case complexity. This is done by showing that the ``hard'' part of the algorithm terminates in linear time on an exponentially generic set of input pairs. We then apply these results to …
Generators and relations found for foam categories.
problem Understanding categories of framed tangled webs and foams.
method Multijet transversality techniques.
result Presentation by generators and relations of categories.
In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.
The paper extends graph embedding models to handle multiple relations.
problem Link prediction in multi-relational networks.
method Generalized pseudo-Riemannian embedding models to multi-relational networks, considering relations as submanifolds.
result Validation of the approach in link prediction tasks, including knowledge graph completion and biological domain analysis.
In this work, we introduce a new method for imitation learning from video demonstrations. Our method, Relational Mimic (RM), improves on previous visual imitation learning methods by combining generative adversarial networks and relational learning. RM is flexible and can be used in conjunction with other recent advanc…
We consider equivalence relations among smooth map germs with respect to geometry of G-structures on the target space germ. These equivalence relations are natural generalization of right-left equivalence (i.e., A-equivalence) in the sense of Thom-Mather depending on geometric structures on the target space germ. Unfor…
Study super cluster algebras from super Plücker and Ptolemy relations.
problem Developing super cluster algebra structure in super Grassmannians.
method Analyzing super Plücker and Ptolemy relations, developing super cluster structure.
result New simple form of super Plücker relations for $\Gr_{r|1}(n|1)$.
Study proves existence of Kähler-Einstein metrics and Ricci flat Kähler metrics in 4-manifolds.
problem Existence of Kähler-Einstein metrics and Ricci flat Kähler metrics in 4-manifolds.
method Proves existence through cohomogeneity one triaxial Kähler-Einstein metrics and generalized PDEs for Ricci flat Kähler metrics.
result Proves existence of complete cohomogeneity one triaxial Kähler-Einstein metrics and local existence of Ricci flat Kähler metrics.
The relation between open topological strings and representation theory of symmetric quivers is explored beyond the original setting of the knot-quiver correspondence. Multiple cover generalizations of the skein relation for boundaries of holomorphic disks on a Lagrangian brane are observed to generate dual quiver desc…
Using a simple recurrence relation we give a new method to compute Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for Jones polynomials. The method is used to estimate degree of Jones polynomials for some families of braids and to obtain general qualitative re…
We introduce and study the notion of a biholomorphic gerbe with connection. The biholomorphic gerbe provides a natural geometrical framework for generalized Kahler geometry in a manner analogous to the way a holomorphic line bundle is related to Kahler geometry. The relation between the gerbe and the generalized Kahler…