This work is a further study on the Generalized Constraint Neural Network (GCNN) model [1], [2]. Two challenges are encountered in the study, that is, to embed any type of prior information and to select its imposing schemes. The work focuses on the second challenge and studies a new constraint imposing scheme for equa…
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48 results for “Locality constraints”
Analyzes learning dynamics of RNNs under locality constraints.
problem Understanding learning dynamics in RNNs with locality constraints.
method Dynamical systems theory applied to data-aligned linear RNNs.
result RFLO solutions are restricted to low-rank perturbations of initial parameters.
We analyze the local convergence of proximal splitting algorithms to solve optimization problems that are convex besides a rank constraint. For this, we show conditions under which the proximal operator of a function involving the rank constraint is locally identical to the proximal operator of its convex envelope, hen…
Study Federated RL with diverse constraints, proposing new optimization methods.
problem Solving reinforcement learning with multiple constraints in federated learning.
method Federated primal-dual policy optimization methods based on policy gradient methods.
result FedNPG achieves global convergence with an rate.
This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror des…
Simple Binary Hypothesis Testing under Local Differential Privacy and Communication Constraintsmath.ST
Study binary hypothesis testing with privacy and communication constraints.
problem Binary hypothesis testing under local differential privacy and communication constraints.
method Qualifies results as minimax or instance optimal, develops instance-optimal algorithms.
result Achieves minimum possible sample complexity under both privacy and communication constraints.
In this paper we study a constraint-based representation of neural network architectures. We cast the learning problem in the Lagrangian framework and we investigate a simple optimization procedure that is well suited to fulfil the so-called architectural constraints, learning from the available supervisions. The compu…
This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical norm. This result is convenient to apply in real applications and could yield re…
VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.
problem Stochastic convex optimization under convex constraints.
method Natural variance reduced proximal gradient (VRPG) algorithm.
result VRPG achieves local minimax lower bound up to constants and log factor of .
We analyse the definition of quasi-local energy in GR based on a Hamiltonian analysis of the Einstein-Hilbert action initiated by Brown-York. The role of the constraint equations, in particular the Hamiltonian constraint on the timelike boundary, neglected in previous studies, is emphasized here. We argue that a consis…
FedCONST adapts update magnitudes to enhance feature generalization in FL.
problem Heterogeneous client data in FL leads to overfitting and distorted transferable features.
method FedCONST uses linear convex constraints to stabilize training and preserve generalization.
result FedCONST enhances feature transferability and robustness, achieving state-of-the-art performance.
A constrained informationally efficient market is defined to be one whose price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which despite its simplicity, generates new insights. In particular, it is show…
Decision Making in Changing Environments: Robustness, Query-Based Learning, and Differential Privacycs.LG
Framework for robust decision making in changing environments with privacy constraints.
problem Interactive decision making in changing environments with constraints.
method Hybrid Decision Making with Structured Observations (hybrid DMSO) framework, local differentially private decision making, query-based learning, robust and smooth decision making.
result Strong connections and bounds derived for DEC, SQ dimension, local minimax complexity, learnability, and joint differential privacy.
In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on it. If the form is closed, it is found that the constraint is (locally) holonomi…
Quantum walks blend patterns into splines when averaged.
problem Understanding the asymptotic patterns of quantum random walks.
method Averaging over quantum coins using the Haar measure.
result Patterns blend into splines, showing a unified behavior.
Unified framework for combinatorial and rounding algorithms in experimental design.
problem Designing and analyzing combinatorial and rounding algorithms for experimental design problems.
method Local search framework for combinatorial algorithms and regret minimization framework for rounding algorithms.
result Unified approach to match and improve all known results in D/A/E-design and obtain new results in unknown settings.
Efficient Federated Learning over Multiple Access Channel with Differential Privacy Constraintscs.LG
Paper addresses FL over MAC with DP constraints, proposing a novel consensus scheme.
problem Federated learning over a multiple access channel with differential privacy constraints.
method Proposes a novel consensus scheme using digital distributed stochastic gradient descent (D-DSGD) with artificial noise to preserve DP.
result Demonstrates improved convergence rate and DP level for a given MAC capacity.
We extend Donaldson's diagonalization theorem to intersection forms with certain local coefficients, under some constraints. This provides new examples of non-smoothable topological 4-manifolds.
The paper classifies energy-minimizing sets in specific domains.
problem Classifying volume-constraint local energy-minimizing sets.
method Proved a Poincaré-type inequality for stable sets.
result Relative boundary of energy-minimizing sets is smooth.
We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condit…
Proposes a method to generate text that adheres to logical constraints.
problem Generating text that respects logical constraints is hard for autoregressive models.
method Bayesian conditioning to draw samples subject to a constraint, considering the entire sequence and inducing a local, factorized distribution.
result Our approach generates samples that closely approximate the target distribution and are guaranteed to satisfy the constraints.
Local Linear embedding (LLE) is a popular dimension reduction method. In this paper, we first show LLE with nonnegative constraint is equivalent to the widely used Laplacian embedding. We further propose to iterate the two steps in LLE repeatedly to improve the results. Thirdly, we relax the kNN constraint of LLE and p…
Using the theory of group action, we first introduce the concept of the automorphism group of an exponential family or a graphical model, thus formalizing the general notion of symmetry of a probabilistic model. This automorphism group provides a precise mathematical framework for lifted inference in the general expone…
Local LMO optimizes constrained problems using local linear minimization.
problem Constrained optimization problems with complex feasible sets.
method Designs a new projection-free gradient method using local linear minimization.
result Transfers convergence rates of Projected Gradient Descent to the projection-free world.
New methods test discrete distributions faster with local privacy constraints.
problem Testing discrete distributions under local differential privacy constraints.
method Efficient randomized algorithms and test procedures, both non-interactive and interactive.
result Faster separation rates in interactive privacy mechanisms.
Two ML approaches learn local volatility surfaces from option prices, with GP being arbitrage-free.
problem Interpolating European vanilla option prices to create a local volatility surface.
method Gaussian process regression and neural net with arbitrage penalties.
result GP approach is arbitrage-free and yields best out-of-sample calibration error.
New approach approximates c-space geometry of multi-loop linkages.
problem Higher-order mobility analysis of multi-loop linkages.
method Higher-order Taylor series expansion of geometric constraint mapping using joint screws.
result Local approximation of c-space and configurations with certain rank.
A lens cluster minimizes perimeter in the plane with given area constraints.
problem Minimizing perimeter in the plane with given area constraints.
method Analyzing lens clusters consisting of circular arcs with specific geometric properties.
result Lens clusters are local minimizers of the total perimeter functional.
Data processing inequalities link Fisher information to local differential privacy constraints.
problem Understanding how Fisher information scales with local differential privacy constraints.
method Developed data processing inequalities for Fisher information under local differential privacy.
result Implications for private estimation with optimal bounds and error rates.
FedSGM tackles constrained federated learning with unified framework.
problem Functional constraints, communication bottlenecks, local updates, and partial client participation in federated learning.
method Unified framework based on switching gradient method, incorporating bi-directional error feedback, and soft switching for stability.
result Achieves convergence rate with high-probability bounds decoupling from sampling noise.
DePAint solves MARL for agents with local constraints, privacy, and no central controller.
problem Training multi-agent systems to optimize rewards while adhering to safety constraints in a decentralized setting.
method Formulated as a decentralized constrained multi-agent Markov Decision Problem, proposed DePAint method using momentum-based decentralized policy gradient.
result First privacy-preserving fully decentralized MARL algorithm considering both peak and average constraints.
Deep Local Volatilityq-fin.CP
Develops a deep learning method for enforcing no-arbitrage in local volatility surfaces.
problem No-arbitrage conditions not enforced in deep learning approaches for local volatility.
method Jointly interpolates European vanilla option prices, enforcing no-arbitrage through modified loss functions or network architectures.
result Demonstrates the effectiveness of enforcing no-arbitrage in local volatility surfaces using deep learning.
FLIX simplifies federated learning with efficient communication.
problem Handling constraints specific to federated learning.
method Introduces FLIX, a new framework for federated learning that addresses communication and personalization challenges.
result FLIX achieves dissimilarity regularization similar to local methods without requiring local steps.
We prove in this article that the local image of each conformal -curvature operator of arbitrary order on the sphere admits no scalar constraint. However, we prove that identities of Kazdan--Warner type hold for its graph.
Locally-adapted convolution-based super-resolution of irregularly-sampled ocean remote sensing datastat.ML
Super-resolution is a classical problem in image processing, with numerous applications to remote sensing image enhancement. Here, we address the super-resolution of irregularly-sampled remote sensing images. Using an optimal interpolation as the low-resolution reconstruction, we explore locally-adapted multimodal conv…
Estimates Kähler metrics with noncollapsing volume under complex Monge-Ampère constraints.
problem Volume noncollapsing for Kähler metrics induced by complex Monge-Ampère equations.
method Proves local volume noncollapsing estimate with Ricci curvature lower bound.
result Establishes diameter and gradient estimates for Kähler metrics.
Variational properties of the total inverse mean curvature in the plane under boundary constraintsmath.DG
Study variational properties of curves in half-plane with area constraints.
problem Characterize critical points of inverse mean curvature.
method Variational analysis of curves with boundary constraints.
result Existence and stability of critical points with prescribed area.
We study the Einstein-Dirac equation as well as the weak Killing equation on Riemannian spin manifolds with codimension one foliation. We prove that, for any manifold admitting real Killing spinors (resp. parallel spinors), there exist warped product metrics on such that $(M^n \ti…
We study local complexity measures for stochastic convex optimization problems, providing a local minimax theory analogous to that of Hájek and Le Cam for classical statistical problems. We give complementary optimality results, developing fully online methods that adaptively achieve optimal convergence guarantees. Our…
Theory for gravity coupled with fields on manifolds with null-boundary.
problem Formulating a theory for gravity coupled with scalar, SU(n), and spinor fields on manifolds with null-boundary.
method Symplectic reduction of boundary fields and constraints analysis.
result The set of constraints does not form a first class system for the three couplings.
We study distributed estimation of a Gaussian mean under communication constraints in a decision theoretical framework. Minimax rates of convergence, which characterize the tradeoff between the communication costs and statistical accuracy, are established in both the univariate and multivariate settings. Communication-…
The paper proposes modern computational methods for optimizing reinsurance contracts.
problem Optimizing catastrophe excess-of-loss reinsurance contracts with realistic constraints and risk measures.
method Two approaches: simulated annealing for local search and quantum branch & bound for future potential.
result Quantum branch & bound approach shows potential for future optimization with quantum computers.
Finding anonymization mechanisms to protect personal data is at the heart of recent machine learning research. Here, we consider the consequences of local differential privacy constraints on goodness-of-fit testing, i.e. the statistical problem assessing whether sample points are generated from a fixed density , o…
A new pricing controller handles resource constraints to infer target prices effectively.
problem Resource constraints prevent fixed-price inference, leading to support exclusion.
method Formalizes support-exclusion failure, designs a target-aware controller, and uses a realized information clock.
result The controller can certify feasible target bands and log continuous local densities, leading to polynomial rates of inference.
LCBO tackles constrained optimization in high dimensions, offering a polynomial convergence rate.
problem Bayesian optimization for high-dimensional constrained problems.
method LCBO uses local descent and uncertainty-driven exploration, proving polynomial convergence rate.
result LCBO achieves a polynomial convergence rate for KKT residuals in high dimensions.
New method uses public data to achieve optimal nonparametric classification with privacy constraints.
problem Optimal nonparametric classification under local differential privacy constraints.
method Locally differentially private classification tree with data-driven pruning.
result Achieves mini-max optimal convergence rate with public data.
Complex textual information extraction tasks are often posed as sequence labeling or \emph{shallow parsing}, where fields are extracted using local labels made consistent through probabilistic inference in a graphical model with constrained transitions. Recently, it has become common to locally parametrize these models…
We propose a general method for deformation quantization of any second-class constrained system on a symplectic manifold. The constraints determining an arbitrary constraint surface are in general defined only locally and can be components of a section of a non-trivial vector bundle over the phase-space manifold. The c…