Proposes a new method for generating better negative examples in KBC.
problem Random negative sampling generates nonsensical examples that slow down learning and decrease accuracy.
method Distributional Negative Sampling generates meaningful negative examples.
result Significant improvement in Mean Reciprocal Rank values in three benchmarks.
Improved QA system by re-ranking top-10 results using machine learning.
problem Enhance deployed QA systems without re-training.
method Learn similarity function using n-gram features; implement neural sentence embeddings.
result Mean reciprocal rank improves by 9.15%.
New model accounts for scale variation and noise in pairwise comparisons.
problem Nonreciprocal pairwise comparisons in decision analysis.
method Additive model with structured matrix and random perturbation.
result Explicit estimators and probability assessments of admissible ranking regions.
In domains like bioinformatics, information retrieval and social network analysis, one can find learning tasks where the goal consists of inferring a ranking of objects, conditioned on a particular target object. We present a general kernel framework for learning conditional rankings from various types of relational da…
Parallel deep learning architectures like fine-tuned BERT and MT-DNN, have quickly become the state of the art, bypassing previous deep and shallow learning methods by a large margin. More recently, pre-trained models from large related datasets have been able to perform well on many downstream tasks by just fine-tunin…
Study how past eon's matter affects present eon in Penrose's cyclic cosmology.
problem Determining present eon's matter content from past eon's matter.
method Use Penrose's reciprocity hypothesis to link past and present eons' matter.
result Perfect fluid matter content of past eon influences present eon's matter content.
Many information retrieval algorithms rely on the notion of a good distance that allows to efficiently compare objects of different nature. Recently, a new promising metric called Word Mover's Distance was proposed to measure the divergence between text passages. In this paper, we demonstrate that this metric can be ex…
Classifies reciprocal elements in Hecke groups, generalizing Sarnak's work.
problem Classifying reciprocal elements in Hecke groups.
method Classifying and parametrizing reciprocal classes in Hecke groups Γp for p≥3. result Generalizes Sarnak's result on reciprocal elements in the modular group.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …
Estimates growth of reciprocal classes in Hecke groups.
problem Estimating the growth of reciprocal conjugacy classes in Hecke groups.
method Using free product structure and word lengths of reciprocal elements, with tools from basic probability theory.
result Estimates the asymptotic growth of reciprocal conjugacy classes in Hecke groups.
The paper models social networks with varying levels of reciprocity.
problem Understanding diverse reciprocal behavior in social networks.
method Developed a preferential attachment model with heterogeneous reciprocity.
result Captures the heavy-tailed nature of empirical degree distributions and identifies multiple user groups.
The study calculates the growth rate of reciprocal hyperbolic elements in Hecke groups.
problem Counting reciprocal hyperbolic elements in Hecke groups.
method Analyzes conjugacy classes of hyperbolic elements associated with reciprocal geodesics.
result Determines the asymptotic growth rate and limiting constant of primitive conjugacy classes of reciprocal hyperbolic elements.
Formulates Hilbert reciprocity law on 3-manifolds.
problem Developing arithmetic topology on 3-manifolds.
method Formulated an analogue of Hilbert reciprocity law using intersection forms and Kummer extensions.
result Cyclic covers of links are analogues of Kummer extensions.
Meta-learning predicts optimal ensemble size and methods for time series forecasting.
problem Finding the best ensemble of time series forecasting methods.
method Two-step approach using meta-learning to predict ensemble size and methods.
result Meta-learning outperformed benchmarks in forecasting errors for all data types and horizons.
Minimal spectral radii found for specific matrix types.
problem Finding smallest spectral radii for certain matrix classes.
method Analyzing skew-reciprocal integer matrices of fixed even dimensions.
result Most classes of matrices have smaller spectral radii than their reciprocal counterparts.
Study on geodesics and dihedral groups in lattices.
problem Growth and distribution of conjugacy classes of dihedral subgroups.
method Generalizing earlier work on reciprocal geodesics, proving equidistribution.
result Reciprocal geodesics are equidistributed in the unit tangent bundle.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. In this paper, we provide a probabilistic graphical model for reciprocal processes. This le…
The paper models reciprocity in interbank markets using a statistical null model.
problem Understanding the importance of individual banks in financial networks.
method Developed an exponential random graph model to account for reciprocal links on both topological and weighted levels.
result Weighted reciprocity in interbank markets is more significant than network size and volume before the financial crisis.
Reciprocal learning unifies various machine learning algorithms.
problem Understanding the convergence of machine learning algorithms.
method Introducing reciprocal learning as a generalization of various algorithms using decision theory.
result Reciprocal learning algorithms converge at linear rates to an approximately optimal model under certain conditions.
Study geodesics entering a fixed cusp neighborhood multiple times.
problem Understanding geodesics entering a specific cusp neighborhood multiple times.
method Investigate reciprocal geodesics entering a fixed cusp neighborhood a fixed number of times.
result Characterized the class of reciprocal geodesics entering a fixed cusp neighborhood a fixed number of times.
New method reconstructs interbank networks enforcing reciprocity to improve stability and risk prediction.
problem Lack of public interbank network data and difficulty in replicating cycles.
method Proposes a new network reconstruction method enforcing sparsity and link reciprocity from aggregate data.
result Adding reciprocity improves prediction of network properties, including largest real eigenvalue and eccentricity of eigenvalues.
Growth rates of geodesics on modular orbifolds are studied.
problem Understanding growth rates of geodesics on modular orbifolds.
method Exhaustion of modular orbifold by compact subsurfaces, analysis of low lying geodesics and reciprocal geodesics.
result Growth rates of low lying geodesics and reciprocal geodesics converge to the full set's growth rate.
The paper proves generalization bounds and stopping rules for self-selected data in reciprocal learning.
problem Generalization of learning algorithms using self-selected data.
method Proves universal generalization bounds using covering numbers and Wasserstein ambiguity sets.
result Provides stopping rules for reciprocal learning algorithms to ensure out-of-sample performance.
The abstract discusses conjectures about Chern-Simons invariants of 3-manifolds.
problem Conjectures about the reciprocity of Chern-Simons invariants of 3-manifolds.
method Supporting evidence through Galois descent of a K3-group. result The conjectures hold under the condition of Galois descent of a K3-group. Given a knot and an SL(n,C) representation of its group that is conjugate to its dual, the representation that replaces each matrix with its inverse-transpose, the associated twisted Reidemeister torsion is reciprocal. An example is given of a knot group and SL(3,Z) representation that is not conjugate to its dual for …
Reciprocity laws for line bundles on circle fibrations over complex manifolds.
problem Analytic reciprocity laws for complex line bundles on fibrations in oriented circles.
method Study of Gysin maps and first Chern classes in cohomology.
result Sum of Gysin maps of Chern classes equals zero in H3(B,Z) under specific conditions. We reformulate Lehmer's question from 1933 and a question due to Schinzel and Zassenhaus from 1965 in terms of a comparison of the Mahler measures and the houses, respectively, of monic integer reciprocal and skew-reciprocal polynomials of the same degree. This entails that understanding the difference between orientat…
We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is right-angled and the nerve is Eulerian. As corollaries we obtain many of the known rationality and reciprocity results for the growth series…
Wide neural networks learn features under μP, identifying weights and decomposing support.
problem Feature learning in wide neural networks under μP. method Proving mean-field limit, characterizing identifiability, sparse-dictionary decomposition, and feature-learning-error decomposition.
result The triple (w∗,Dorb∗,S∗) identifies the natural learning cell of the architecture-data pair (σ,ρ). We prove a reciprocity formula between Gauss sums that is used in the computation of certain quantum invariants of 3-manifolds. Our proof uses the discriminant construction applied to the tensor product of lattices.
This paper gives a new definition of the Contou-Carrere symbol in terms of an exponential of a Chen iterated integral and proves the corresponding reciprocity law.
We prove that under certain linear reciprocal transformation, an evolutionary PDE of hydrodynamic type that admits a bihamiltonian structure is transformed to a system of the same type which is still bihamiltonian.
Develops Bayesian inference methods for gamma models.
problem Challenges in inference for models with gamma functions.
method Data augmentation scheme using Exponential Reciprocal Gamma distributions.
result Scalable EM and MCMC algorithms developed.
A new GAN model uses characteristic functions to improve image generation.
problem Improving stability and diversity in GANs for complex distributions.
method Integrates characteristic functions to compare distributions directly, stabilizes training, and uses auto-encoder structure.
result Proposes RCF-GAN achieving superior image generation and reconstruction.
The study examines the growth of reciprocal classes in Hecke groups, proving an asymptotic formula.
problem Analyzing the growth of reciprocal classes in Hecke groups.
method Utilizes the free product structure of Hecke groups, combinatorial counting, and recurrence relations.
result Proves an asymptotic formula for the number of reciprocal classes in Hecke groups.
This paper characterizes hierarchical clustering methods that abide by two previously introduced axioms -- thus, denominated admissible methods -- and proposes tractable algorithms for their implementation. We leverage the fact that, for asymmetric networks, every admissible method must be contained between reciprocal …
This work improves KG embeddings by integrating hyperbolic and attention mechanisms.
problem Preserving hierarchical and logical patterns in KGs with low-dimensional embeddings.
method Combines hyperbolic reflections/rotations with attention mechanisms to capture complex relational patterns.
result Improves MRR by up to 6.1% on standard benchmarks and new state-of-the-art results in high dimensions.
We exploit the symmetry concepts developed in the companion review of this article to introduce a stochastic version of link reversal symmetry, which leads to an improved understanding of the reciprocity of directed networks. We apply our formalism to the international trade network and show that a strong embedding in …
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
Study foliations of hyperbolic 3-manifolds with constant Gaussian curvature.
problem Understanding foliations of hyperbolic 3-manifolds with constant Gaussian curvature.
method Analyzing Thurston and Schwarzian parametrizations, proving Kleinian reciprocity, and describing foliations as Hamiltonian vector fields.
result Generalization of McMullen's Kleinian reciprocity theorem and description of constant curvature foliations.
Develops a duality for graphs in Riemannian and Lorentzian spaces with prescribed mean curvature.
problem Finding graphs with prescribed mean curvature in Riemannian and Lorentzian spaces.
method Introduces a conformal duality that swaps mean curvature and bundle curvature, invariant to base surface and reciprocal of the Killing vector field length.
result Entire graphs in Lorentz-Minkowski space with prescribed mean curvature a bounded function H.
Empirical study shows carriers ignore past shippers' behavior, focusing only on current actions.
problem Opportunistic behavior by shippers and carriers in dynamic freight markets.
method Empirical analysis of carrier reciprocity in US truckload transportation sector.
result Carriers do not remember shippers' past behaviors but respond to current actions.
This article investigates local properties of the further generalized Weierstrass relations for a spin manifold S immersed in a higher dimensional spin manifold M from viewpoint of study of submanifold quantum mechanics. We show that kernel of a certain Dirac operator defined over S, which we call submanifold Dir…
SEM-DNN learns reciprocal interactions from observational data without external instruments.
problem Estimating bidirectional interactions from endogenous data.
method Heteroscedastic neural simultaneous-equation estimator (SEM-DNN) that learns reciprocal structural interactions.
result SEM-DNN recovers structural effects more reliably than other methods under increasing information.
Schrödinger and Onsager's ideas linked in nonequilibrium thermodynamics.
problem Linking Schrödinger's variational problem with Onsager's nonequilibrium statistical mechanics.
method Analyzing the historical context and comparing the two approaches.
result Schrödinger's ideas have not yet been fully integrated into the classical context of Onsager's work.
Efficiently reduces tensor ranks using mean-field approximation.
problem Low-rank approximation of non-negative tensors.
method Mean-field approximation of tensor rank reduction.
result Our algorithm achieves faster and competitive tensor rank reduction.
This paper evaluates knowledge graph completion models under the open-world assumption, revealing unexpected behavior of metrics.
problem Evaluation of knowledge graph completion models often assumes a closed-world assumption, which can lead to misleading results.
method The paper studies KGC evaluation under the open-world assumption, analyzing the behavior of metrics like MRR and Hits@K.
result Metrics like MRR and Hits@K can show significant degradation under the open-world assumption, leading to incorrect model comparisons.
NMF and PCC linked, improving data denoising and feature stability.
problem Improving NMF's rank estimation and feature stability.
method Combining NMF and PCC for robust rank estimation and feature stability.
result NMF features are stable against noise and optimization seeds.