Continues work on derived manifolds and symplectic schemes, constructing virtual classes.
problem Constructing virtual fundamental classes for derived manifolds and schemes.
method Cosection localization, reduced virtual fundamental classes, and applications to Donaldson-Thomas theory.
result Virtual fundamental classes for (−2)-shifted symplectic derived schemes are consistent with algebraic and differential geometric constructions. LD-SGD improves communication in decentralized SGD.
problem Efficiently combining local updates and decentralized communication.
method Proposes LD-SGD integrating local updates and decentralized SGD, with a convergence analysis.
result LD-SGD converges to a critical point for non-convex objectives with non-identically distributed data.
Generalizes soft noncommutative schemes to flag varieties.
problem Applying soft noncommutative schemes to flag varieties.
method Generalization via toric geometry and distinguished affine charts.
result Soft noncommutative schemes can be applied to flag varieties.
New iterative schemes solve Yamabe-type equations on closed manifolds.
problem Solving Yamabe-type equations on closed manifolds.
method Double iterative scheme and local variational method.
result Reproof of classical Yamabe problem as a consequence of Yamabe-type equations.
This paper proposes an in-depth re-thinking of neural computation that parallels apparently unrelated laws of physics, that are formulated in the variational framework of the least action principle. The theory holds for neural networks that are also based on any digraph, and the resulting computational scheme exhibits …
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…
NeLLoC improves image compression with parallel decoding.
problem Image compression with OOD generalization.
method Local autoregressive model with parallel decoding.
result Significant gains in compression runtime.
For the first time in mathematical finance field, we propose the local weak form meshless methods for option pricing; especially in this paper we select and analysis two schemes of them named local boundary integral equation method (LBIE) based on moving least squares approximation (MLS) and local radial point interpol…
New schemes improve error estimates for sampling from non-log-concave distributions.
problem Improving sampling from non-log-concave distributions with super-linear drift growth.
method Developed tamed Euler and randomized Euler schemes with error estimates.
result Near-optimal error bounds for sampling and optimization problems.
The MBO scheme for data clustering is analyzed in the large data limit, proving convergence to optimal partition problems.
problem Analyzing the MBO scheme for data clustering in the large data limit.
method Implicit gradient descent on the thresholding energy of a similarity graph.
result The MBO scheme outcomes converge to minimizers of a weighted optimal partition problem.
Implementing large-scale deep neural networks with high computational complexity on low-cost IoT devices may inevitably be constrained by limited computation resource, making the devices hard to respond in real-time. This disjunction makes the state-of-art deep learning algorithms, i.e. CNN (Convolutional Neural Networ…
Develops LSH schemes for f-divergences and mutual information loss.
problem Approximating nearest neighbors in high-dimensional probability distributions.
method General framework and specific LSH schemes for f-divergences and mutual information loss.
result Generalized Jensen-Shannon divergence can be approximated by Hellinger distance.
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.
Derives local energy equation and proves consistency of staggered finite volume schemes for Euler equations.
problem Preserving conservation and consistency in staggered finite volume methods for Euler equations.
method Staggered discretization, material velocity upwinding, internal energy balance with correction term.
result Derives local total energy equation and proves schemes are conservative and consistent.
cKAM improves adaptive sampling by incorporating a cyclical stepsize scheme.
problem Adaptive Metropolis algorithms can get stuck in local modes.
method cKAM uses a cyclical stepsize scheme to encourage exploration and escape from local modes.
result cKAM successfully escapes local modes and converges to the true posterior distribution.
Proposes a boundary detection method inspired by LLE for high-dimensional data.
problem Identifying boundary points from data on an embedded manifold.
method Inspired by locally linear embedding, uses nearest neighbor search schemes and spectral properties of local covariance matrix.
result Enhanced boundary detection in noisy data.
Federated learning improves with adaptive hyper-parameters and representation matching.
problem Heterogeneous client data leads to divergent local models in federated learning.
method Representation matching and adaptive hyper-parameters.
result Significant performance and robustness improvements in federated learning.
We study the Heston-Cox-Ingersoll-Ross++ stochastic-local volatility model in the context of foreign exchange markets and propose a Monte Carlo simulation scheme which combines the full truncation Euler scheme for the stochastic volatility component and the stochastic domestic and foreign short interest rates with the …
ISALT uses inference to simulate SDEs with large time-steps, improving efficiency.
problem Efficiently simulating ergodic SDEs with large time-steps.
method Inference-based schemes adaptive to large time-steps (ISALT) from data.
result ISALT achieves significant time reduction and optimal accuracy.
New boundary treatment improves accuracy for complex PDEs.
problem Order reduction in high-order IMEX schemes for multidimensional PDEs.
method Novel boundary treatment algorithms for Cartesian meshes, treating implicit-explicit stages similarly to interior points.
result Recovery of designed order of convergence by numerical verification.
Develops locally private methods for nonparametric contextual bandits.
problem Privacy concerns in sequential decision-making on sensitive data.
method Uniform-confidence-bound-type estimator and jump-start scheme.
result Minimax optimality of proposed methods supported by lower bounds.
Paper studies particle method for LSV model calibration, proving convergence and error bounds.
problem Calibration of local-stochastic volatility models with open well-posedness question.
method Regularized Euler--Maruyama scheme for particle approximation of McKean--Vlasov dynamics.
result Strong convergence of the Euler--Maruyama scheme with rate 1/2 in step-size.
AMP regularization improves deep learning models by favoring flat minima.
problem Improving deep learning model generalization and avoiding overfitting.
method AMP regularization uses adversarial model perturbation to minimize a norm-bounded perturbation of the empirical risk.
result AMP regularization leads to state-of-the-art performance across various deep architectures.
The aim of this paper is to provide new theoretical and computational understanding on two loss regularizations employed in deep learning, known as local entropy and heat regularization. For both regularized losses we introduce variational characterizations that naturally suggest a two-step scheme for their optimizatio…
Study simulates Heston-type local stochastic volatility model using particle method.
problem Simulate calibrated Heston-type local stochastic volatility model with non-standard coefficients.
method Monte Carlo particle method, Euler-Maruyama scheme, full truncation Euler scheme.
result Strong convergence of Euler-Maruyama scheme with rate 1/2 in time, up to a logarithmic factor.
Adaptive importance sampling for estimating point process statistics.
problem Estimating the expected value of a statistic of a locally stable point process.
method Adaptive importance sampling with Poisson point processes and cross-entropy minimization.
result The proposed estimator converges to the target value almost surely and is asymptotically normal.
Proposes ContSup to boost local learning by supplying context between isolated modules.
problem Local learning's performance degrades with more isolated modules.
method Theoretical analysis and ContSup scheme to supply context between modules.
result Significant performance improvement with minimal overhead.
This work extends stochastic localization to joint probability measures for data analysis.
problem Data distributional analysis in high-dimensional probability.
method Unified stochastic localization under Eldan's α-scheme, coupled probability measures via shared Brownian motion.
result Eldan's α-distance as a scalable surrogate for Wasserstein distance.
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate. Under some regularity and integrability conditions, we obtain the opt…
We relate two notions of local error for integration schemes on Riemannian homogeneous spaces, and show how to derive global error estimates from such local bounds. In doing so, we prove for the first time that the Lie-Butcher theory of Lie group integrators leads to global error estimates.
This paper introduces a new method for semi-supervised learning on high dimensional nonlinear manifolds, which includes a phase of unsupervised basis learning and a phase of supervised function learning. The learned bases provide a set of anchor points to form a local coordinate system, such that each data point x on…
It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme an…
Paper solves local well-posedness for Schrödinger flow into sphere with natural boundary conditions.
problem Local well-posedness of Schrödinger flow into S2 with natural boundary conditions. method Developed a new approximation scheme to solve the problem.
result Solved the local well-posedness problem for the Schrödinger flow into S2 with natural boundary conditions. Paper proposes efficient privacy-preserving matrix encryption for secure collaborative learning against malicious adversaries.
problem Secure collaborative learning of sensitive data across different agencies is challenging with malicious adversaries.
method The paper applies matrix encryption to secure data against chosen plaintext attack, known plaintext attack, and collusion attack, achieving local differential privacy and high computation efficiency.
result The proposed schemes are computationally efficient and secure against malicious adversaries compared to existing techniques.
There has been a lot of recent interest in trying to characterize the error surface of deep models. This stems from a long standing question. Given that deep networks are highly nonlinear systems optimized by local gradient methods, why do they not seem to be affected by bad local minima? It is widely believed that tra…
We propose different schemes for option hedging when asset returns are modeled using a general class of GARCH models. More specifically, we implement local risk minimization and a minimum variance hedge approximation based on an extended Girsanov principle that generalizes Duan's (1995) delta hedge. Since the minimal m…
Enhances CEV model pricing with high-order scheme and adaptive time stepping.
problem Improving accuracy in pricing American CEV models with irregularities.
method High-order time adapted scheme, local mesh refinement, adaptive time stepping, fifth-order 5(4) Dormand-Prince method.
result Highly accurate solution with reduced computational runtime.
Proves heat expansion for Laplacian on a singularity.
problem Analytic hypersurface with isolated singularity and Laplacian heat expansion.
method Local parametrization, Newton scheme, quasihomogeneous tangent cone, local models with irregular singularities.
result Existence of small time heat expansion for Laplace operator.
A new dynamic learning-rate scheme for optimization.
problem Manual tuning of learning rates in optimization is time-consuming and error-prone.
method Locally optimal stepsize estimation for dynamic learning-rate scheduling.
result Our method achieves comparable performance with minimal tuning.
We break dimension dependence in sparse distribution estimation with communication constraints.
problem Estimating sparse distributions with limited communication.
method Novel localization schemes and tree-based estimation.
result Achieve dimension-free convergence rate independent of dimension d. New method uses randomized sparse neural networks to solve time-dependent PDEs more accurately and efficiently.
problem Numerical challenges in training neural networks sequentially in time to solve time-dependent PDEs.
method Introduces Neural Galerkin schemes that update randomized sparse subsets of network parameters at each time step.
result Up to two orders of magnitude more accurate and two orders of magnitude faster than dense update schemes.
In this paper, we propose hybrid building/floor classification and floor-level two-dimensional location coordinates regression using a single-input and multi-output (SIMO) deep neural network (DNN) for large-scale indoor localization based on Wi-Fi fingerprinting. The proposed scheme exploits the different nature of th…
Optimizes convergence time of federated learning over wireless networks.
problem Limited resource blocks in wireless networks affect federated learning convergence time and performance.
method Formulates an optimization problem to minimize convergence time while optimizing performance, proposes a probabilistic user selection scheme and uses ANNs for estimation.
result Improves convergence time and performance of federated learning over wireless networks.
This work improves local differential privacy by considering context to make it more effective.
problem Local differential privacy often sacrifices utility, especially for sensitive data.
method Introduces context-aware local differential privacy, optimizing privacy and utility.
result Contextual information can reduce the number of samples needed for privacy compared to classical LDP.
We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic model that takes this structure into account by generalizi…
Formula for sections on complex manifolds with non-isolated components.
problem Localization of sections on complex manifolds with non-isolated zero varieties.
method Logarithmic Bott localization formula, current-theoretic formulation.
result Established a formula for sections on compact complex manifolds with non-isolated components.
This paper is dedicated to the construction of high-order (in both space and time) finite-difference schemes for both forward and backward PDEs and PIDEs, such that option prices obtained by solving both the forward and backward equations are consistent. This approach is partly inspired by Andreasen & Huge, 2011 who re…
Constructs initial data for Einstein vacuum equations involving multiple localized gravitational sources.
problem Modeling the interaction of distant gravitational systems in general relativity.
method Time-symmetric initial data construction using gluing schemes and localized sources.
result Produces initial data sets with finite ADM mass and multiple Einstein-Rosen bridges.