RankSEG-RMA improves semantic segmentation efficiency and applicability.
problem Inconsistent or suboptimal semantic segmentation results due to argmax or thresholding.
method Developed RankSEG-RMA using reciprocal moment approximation to optimize Dice and IoU metrics.
result RankSEG-RMA reduces computational complexity to O(d) while maintaining comparable performance.
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.
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.
Quasispheres can be approximated by smooth spheres.
problem Characterizing quasispheres using geometric conditions.
method Proving every quasisphere is a limit of smooth spheres and providing necessary and sufficient conditions for uniform quasispheres.
result Every quasisphere can be approximated by uniform quasispheres that satisfy specific geometric conditions.
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.
Transformers use ReLUs to approximate softmax efficiently.
problem Analyzing resource usage in softmax transformer models.
method Translating ReLU approximation results to softmax attention mechanisms.
result Economic resource bounds for softmax attention mechanisms.
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 predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction accuracy or the so-called Area Under the Curve (AUC). Minimizing the reciprocals of these measures are the goals of supervised learning. However, when the models are constructed by the means of em…
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.
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.
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). Approximates discounted moments for financial products using polynomial expansions.
problem Approximating discounted moments of stochastic processes for financial applications.
method High-order power series expansion of the infinitesimal generator.
result Error decreases to around 10 to 100 times machine precision for higher orders.
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.
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.
New neural networks learn distribution functions using quantiles and moments.
problem Approximating functions of distributions in probability spaces.
method Quantile and moment neural networks, mixing quantile and moment features.
result Moment neural network outperforms others for bivariate distributions.
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.
Paper introduces new approximations for lognormal sums, matching comonotonicity and moments.
problem Approximating sums of lognormal random variables accurately.
method Introduces new approximations based on weighted distribution theory, emphasizing comonotonicity and moment matching.
result Approximations perform better than classical methods, especially in the right tail of the distribution.
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.
Develops efficient methods for approximating densities of financial models with jumps.
problem Approximating densities of affine jump diffusions with state-independent jump intensities.
method Recursive approach for deriving closed-form solutions to moments, constructing density approximations via moment matching.
result Superior computational efficiency and precision in option pricing and simulation compared to existing techniques.
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…
New KSDs control moments in approximations, improving diagnostics and tests.
problem Inability of standard KSDs to control moment convergence.
method Developed alternative diffusion KSDs under sufficient conditions.
result First KSDs to exactly characterize q-Wasserstein convergence.
New method approximates diffusion process posteriors using moment functions.
problem Approximating posteriors of stochastic differential equations.
method Constructs variational process as controlled prior, approximates posterior with moment functions, uses natural gradient descent.
result Richer variational approximations for state-dependent diffusion terms.
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.
Paper tackles non-convex optimization for higher moments in portfolio management.
problem Complexity of higher moments in optimization problems.
method Method of successive convex approximation.
result Solves mean-variance-skewness problem using non-convex optimization.
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.
Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propag…
QEM uses parallel importance weighting for fast approximate Bayesian inference.
problem Bayesian inference challenges in large models with many observations and latent variables.
method Expectation Maximization (EM) with massively parallel importance weighting.
result QEM is faster and more scalable than RWS and VI.
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 …
For a GJR-GARCH specification with a generic innovation distribution we derive analytic expressions for the first four conditional moments of the forward and aggregated returns and variances. Moment for the most commonly used GARCH models are stated as special cases. We also the limits of these moments as the time hori…
Neural operators solve families of 2BSDEs efficiently.
problem Solving infinite families of 2BSDEs on bounded domains.
method Introduces a mild generative neural operator model to approximate solutions.
result Solution operators can be approximated by neural operators with polynomial parameters.
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the relaxation of the OT problem when the marginal constraints are replaced by some mome…
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 …
New SGMM algorithm for efficient estimation of moment restriction models.
problem Estimation and inference on overidentified moment restriction models.
method Stochastic Approximation to Generalized Method of Moments (SGMM).
result SGMM offers fast and scalable implementation with streaming dataset handling.
Paper proposes an efficient algorithm to handle high-order portfolio moments.
problem Designing portfolios with high-order moments (skewness and kurtosis) is computationally challenging.
method Proposes a SCA algorithm framework for solving high-order portfolios efficiently.
result Demonstrates the efficiency of the proposed algorithm through numerical experiments.
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and replacing higher order terms with functions of lower order ones. For a give…
We reveal connections between RBMs and Bosons, explaining symmetry breaking in their energy landscapes.
problem Understanding the relationships among different deep generative models and their learning mechanisms.
method Introducing a reciprocal space formulation to RBMs, revealing connections to diffusion processes and Bosons.
result Symmetry breaking in RBM energy landscapes is characterized by singular values and weight matrix eigenvectors.