We develop an axiomatic theory of balance functions (future value functions) in the theory of interest that is derived from financial considerations and which applies to general regulated payment streams, including continuous payment streams. Balance functions exist and are unique up to an initial choice of deposit and…
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48 results for “Balance Theory”
In this work we apply the Poincare-Cartan formalism of the Classical Field Theory to study the systems of balance equations (balance systems). We introduce the partial k-jet bundles of the configurational bundle and study their basic properties: partial Cartan structure, prolongation of vector fields, etc. A constituti…
A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regressionstat.ML
Unified theory for causal inference using various methods.
problem Estimating causal effects in ATE estimation.
method Riesz regression, covariate balancing, DRE, TMLE, matching estimator.
result Unified theory integrating multiple methods for ATE estimation.
Regularization leads to balancedness in deep linear networks.
problem Balancedness in deep linear networks.
method Geometric invariant theory and Riemannian geometry of fibers.
result Balancing flows converge to the balanced manifold at a uniform exponential rate.
Finite presentation for a specific group in 3D handlebody topology.
problem Finding a finite presentation for a specific group in 3D handlebody topology.
method Constructed a finite presentation for the liftable Hilden group to derive the presentation for the balanced superelliptic handlebody group.
result A finite presentation was given for the balanced superelliptic handlebody group.
Paper proves non-existence of certain balanced metrics on six-manifolds.
problem Existence of balanced metrics on six-manifolds with specific properties.
method Analysis of cohomogeneity one actions and properties of balanced structures.
result Non-existence of balanced non-Kähler SU(3)-structures on six-manifolds.
Given a compact complex -fold satisfying the -lemma and supposed to have a trivial canonical bundle and to admit a balanced (=semi-Kähler) Hermitian metric , we introduce the concept of deformations of that are {\bf co-polarised} by the balanced class $[ω^{n-1}]\in H^{n-1,\,n-1…
The article studies embeddings of edge-colored graphs related to balanced 3- and 4-manifolds.
problem Investigating embeddings of edge-colored dual graphs of balanced 3- and 4-manifolds.
method Introducing the concept of balanced genus and proving lower bounds for the genus of 3- and 4-manifolds.
result Established lower bounds for the balanced genus of 3- and 4-manifolds, and conditions for homeomorphism to spheres.
A new GCN model detects cryptocurrency fraud by considering network evolution and balance theory.
problem Detecting fraud in evolving signed cryptocurrency trust networks.
method Motif-aware temporal GCN using balance theory and learnable weights.
result The model outperforms existing methods on bitcoin datasets.
New findings on 3-manifolds using Heegaard Floer theory.
problem Understanding equivalence classes of 3-manifolds.
method Heegaard Floer homology tools.
result Existence of simple balanced 3-manifolds not equivalent to .
We test a historical price time series in a financial market (the NASDAQ 100 index) for a statistical property known as detailed balance. The presence of detailed balance would imply that the market can be modeled by a stochastic process based on a Markov chain, thus leading to equilibrium. In economic terms, a positiv…
Proves a minimal generating set for a specific group of mapping classes.
problem Finding a minimal generating set for a specific group of mapping classes.
method Proved the group is generated by four elements, with minimal exceptions.
result Minimal generating set for the balanced superelliptic mapping class group.
We provide an algebraic framework for quantization of Hermitian metrics that are solutions of the Hitchin equation for Higgs bundles over a projective manifold. Using Geometric Invariant Theory, we introduce a notion of balanced metrics in this context. We show that balanced metrics converge at the quantum limit toward…
Kronheimer and Mrowka defined invariants of balanced sutured manifolds using monopole and instanton Floer homology. Their invariants assign isomorphism classes of modules to balanced sutured manifolds. In this paper, we introduce refinements of these invariants which assign much richer algebraic objects called projecti…
Paper simplifies balancing weights by relaxing outcome assumptions.
problem Estimating missing outcomes in a target population.
method Relaxes outcome assumptions to simplify balancing weights.
result Balancing weights can be simplified with convex loss and minimum worst-case bias.
In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural) configuration of the body in response to changes in mass density and "shape". We show t…
BUDS balances privacy and utility by shuffling data, achieving strong privacy with minimal loss.
problem Balancing privacy and utility in crowd-sourced statistical databases.
method One-hot encoding, iterative shuffling, loss estimation, risk minimization.
result Achieves for privacy, maintaining a privacy bound of .
Study reveals structural differences in financial networks near and far from crises using balance theory.
problem Understanding the complex behavior of stocks and their collective behavior in financial crises.
method Investigates financial networks by triplet interaction in the framework of balance theory, focusing on higher-order interactions.
result Formation of an ordered structure in crisis networks makes them resistant to disorder, with a critical temperature measuring crisis strength.
Noise balance theory explains SGD's behavior in neural networks.
problem Understanding SGD's navigation in neural network loss landscapes.
method Analyzes minibatch noise and loss function symmetries.
result Derives the stationary distribution of SGD for deep networks.
New model reveals balance crucial for robust neural coding.
problem Efficient neural coding in noisy, chaotic networks.
method Analytical model of balanced predictive coding with dissociated balance and weight disorder.
result Superclassical scaling in coding accuracy, independent of balance and weight disorder.
Balanced Direction from Multifarious Choices: Arithmetic Meta-Learning for Domain Generalizationcs.LG
New meta-learning method improves domain generalization by balancing parameters closer to domain centroids.
problem Improving domain generalization by reducing overfitting to specific domains.
method Arithmetic meta-learning with arithmetic-weighted gradients to balance parameters closer to domain centroids.
result Experimental validation of improved domain generalization performance.
While the Anomaly flow was originally motivated by string theory, its zero slope case is potentially of considerable interest in non-Kahler geometry, as it is a flow of conformally balanced metrics whose stationary points are precisely Kahler metrics. We establish its convergence on Kahler manifolds for suitable initia…
Paper presents a Bayesian-decision-theory framework for long-tailed classification.
problem Heavy imbalance and asymmetric misprediction costs in long-tailed datasets.
method Bayesian-decision-theory perspective, unifying re-balancing and ensemble methods.
result Improves accuracy for all classes, especially tails, with provably optimal decisions.
In this paper, we develop a novel weighted Laplacian method, which is partially inspired by the theory of graph Laplacian, to study recent popular graph problems, such as multilevel graph partitioning and balanced minimum cut problem, in a more convenient manner. Since the weighted Laplacian strategy inherits the virtu…
Balanced Excitation and Inhibition are Required for High-Capacity, Noise-Robust Neuronal Selectivityq-bio.NC
Neurons and networks in the cerebral cortex must operate reliably despite multiple sources of noise. To evaluate the impact of both input and output noise, we determine the robustness of single-neuron stimulus selective responses, as well as the robustness of attractor states of networks of neurons performing memory ta…
The paper studies matrix normalization and graph balancing using a new functional and gradient descent.
problem Matrix normalization and graph balancing.
method A new functional called the non-normal energy, and gradient descent.
result Gradient descent of the non-normal energy converges to balanced graphs and preserves spectra and realness of weights.
Motivated from mathematical aspects of the superstring theory, we introduce a new equation on a balanced, hermitian manifold, with zero first Chern class. Solving the equation, one will obtain, in each Bott--Chern cohomology class, a balanced metric which is hermitian Ricci--flat. This can be viewed as a differential f…
Proposes a framework to balance supervised and unsupervised learning using random matrix theory.
problem Balancing supervised and unsupervised learning in high-dimensional data.
method QLDS model with quadratic margin maximization under low density separation assumption.
result Establishes a smooth bridge between supervised and unsupervised learning methods.
A modern version of Monetary Circuit Theory with a particular emphasis on stochastic underpinning mechanisms is developed. It is explained how money is created by the banking system as a whole and by individual banks. The role of central banks as system stabilizers and liquidity providers is elucidated. It is shown how…
Extends knot polynomial to knotted 4-valent graphs.
problem Constructing an invariant for knotted 4-valent graphs.
method Graphical calculus and Reidemeister moves for 4-valent graphs.
result Extension of polynomial to knotted 4-valent graphs.
The thesis tackles overconfident approximations in simulation-based inference.
problem Overconfident conclusions from machine learning approximations in statistical analyses.
method Introduces balancing and Bayesian neural networks to reduce overconfidence.
result Balancing and Bayesian neural networks lead to less overconfident approximations.
New geometric analysis of PWSPDs balances density and geometry in high-dimensional data.
problem Balancing density and geometry in high-dimensional data.
method Power-weighted shortest-path distances (PWSPDs) and their geometric and computational analyses.
result High probability guarantees on the equivalence of PWSPDs on complete and nearest neighbor graphs.
Graph machine learning lacks a balanced theory, focusing on expressive power and optimization.
problem Insufficient theoretical understanding of GNNs' generalization behavior.
method Develop a balanced theory focusing on expressive power, generalization, and optimization.
result Theoretical advancements need to align with practical success in graph machine learning.
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane---that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory---is a cohomological field theory which describes the topology of the moduli space o…
Abstract study of HKT manifolds, proving Hodge theory and formality properties.
problem Analyzing Hodge theory and formality in HKT manifolds.
method Study of Dolbeault operators and Laplacians, proving relations and properties.
result Formality of differential graded algebra for certain HKT manifolds.
Entropy formula derived for deep linear networks using geometric analysis.
problem Thermodynamic description of learning in deep linear networks.
method Group actions, Riemannian submersion, foliation, Jacobi matrices.
result Entropy formula defined on the balanced manifold of DLN.
We propose a novel algorithm for learning fair representations that can simultaneously mitigate two notions of disparity among different demographic subgroups in the classification setting. Two key components underpinning the design of our algorithm are balanced error rate and conditional alignment of representations. …
In this paper, we generalize the work of the second author and prove a grading shifting property, in sutured monopole and instanton Floer theories, for general balanced sutured manifolds. This result has a few consequences. First, we offer an algorithm that computes the Floer homologies of a family of sutured handle-bo…
Large learning rates lead to various implicit biases in nonconvex optimization.
problem Understanding the conditions under which large learning rates yield edge of stability, balancing, and catapult phenomena.
method Developed a global convergence theory for nonconvex functions without globally Lipschitz continuous gradient, focusing on functions with good regularity.
result These implicit biases are more likely to occur in functions with good regularity, and large learning rates favor flatter regions.
In 2003, Ozsváth and Szabó defined the concordance invariant for knots in oriented 3-manifolds as part of the Heegaard Floer homology package. In 2011, Sarkar gave a combinatorial definition of for knots in and a combinatorial proof that gives a lower bound for the slice genus of a knot. Recently, Har…
Study reveals class disparities in balanced datasets through spectral imbalance.
problem Class disparities in balanced datasets are overlooked despite model performance gaps.
method Developed a theoretical framework and studied 11 encoders to diagnose spectral imbalance.
result Identified spectral imbalance as a source of class disparities in balanced datasets.
AlphaZero assesses new chess variants for balance and dynamics.
problem Designing engaging and balanced game rules, especially for chess variants.
method Used AlphaZero to learn near-optimal strategies for nine chess variants.
result AlphaZero reveals novel strategic and tactical patterns in chess variants.
We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on coming from a construction of the Geometric Invariant Theory (G.I.T). These metrics are balanced in the sense of S.K. Donaldson.…
In this paper we study 1/k-geodesics, those closed geodesics that minimize on any subinterval of length . We employ energy methods to provide a relationship between the 1/k-geodesics and what we define as the balanced points of the uniform energy. We show that classes of balanced points of the uniform energy pe…
Study on balanced Hermitian structures on Lie algebras twisted by representations.
problem Conditions for balanced and locally conformally balanced Hermitian structures on Lie algebras.
method Analysis of Hermitian structures on twisted cartesian products of Lie algebras.
result Classification of six-dimensional balanced Hermitian twisted cartesian products Lie algebras.
We study the intrinsic geometrical structure of hypersurfaces in 6-manifolds carrying a balanced Hermitian SU(3)-structure, which we call {\em balanced} SU(2)-{\em structures}. We provide conditions which imply that such a 5-manifold can be isometrically embedded as a hypersurface in a manifold with a balanced SU(3)-st…
Local and Global Balance in Financial Correlation Networks: an Application to Investment Decisionsq-fin.PM
The study identifies assets with local balance deviating from global balance to mitigate financial risk.
problem Selecting outperforming assets during financial crises.
method Investigates deviations of local balance from global balance as a criterion for asset selection.
result Assets with local balance deviating from global balance can mitigate financial risk.
Proposes -balancing for more balanced expert utilization in MoE models.
problem Balanced expert utilization in MoE models to avoid bias.
method Directly targets population-level balance by minimizing a convex potential function.
result Consistently outperforms prior methods in stability and effectiveness.