Smooths metrics on manifolds with curvature bounds and injectivity radius constraints.
problem Smooth metrics on manifolds with curvature and injectivity constraints.
method Bi-Lipschitz smoothing with controlled smoothing and volume lower bounds.
result Proves existence of smooth metrics with curvature bounds and injectivity radius constraints.
Optimal dividend strategy with ratcheting and capital injection under Cramér-Lundberg model.
problem Optimal dividend payout for an insurance company with ratcheting constraints and capital injections.
method Systematic probabilistic and PDE-based approach to solve HJB equation, constructing strong solution and optimal strategy.
result Existence and uniqueness of strong solution, explicit optimal feedback control strategy.
This two-part work puts forth the idea of engaging power electronics to probe an electric grid to infer non-metered loads. Probing can be accomplished by commanding inverters to perturb their power injections and record the induced voltage response. Once a probing setup is deemed topologically observable by the tests o…
In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting capital. In the first pro…
Lower bounds on curvature integral for manifolds with curvature constraints.
problem Bounding curvature integrals under curvature constraints.
method Proving a lower bound for the curvature integral using dimension, upper curvature bounds, and injectivity radius.
result Uniformly bounded below integral of scalar curvature.
A novel method relaxes binary constraints to non-negative spheres for multi-matching and clustering.
problem Optimization problems over binary matrices with injectivity constraints.
method Non-negative spherical relaxation followed by conditional power iteration.
result Automatic adjustment of the continuous parameter related to universe size.
Bi-Lipschitz Autoencoder ensures robust manifold preservation.
problem Non-injective autoencoders lead to poor convergence and distorted latent representations.
method Injective regularization and bi-Lipschitz relaxation.
result BLAE consistently outperforms existing methods in manifold preservation.
This paper examines the assumptions of the derived equivalence between dropout noise injection and L2 regularisation for logistic regression with negative log loss. We show that the approximation method is based on a divergent Taylor expansion, making, subsequent work using this approximation to compare the dropout …
Despite the great achievements of deep neural networks (DNNs), the vulnerability of state-of-the-art DNNs raises security concerns of DNNs in many application domains requiring high reliability.We propose the fault sneaking attack on DNNs, where the adversary aims to misclassify certain input images into any target lab…
New method controls posterior collapse in VAEs without network architecture constraints.
problem Posterior collapse in VAEs reduces diversity of generated samples.
method Introduces Latent Reconstruction (LR) loss to control posterior collapse.
result Controls posterior collapse on various datasets without architectural constraints.
We study several geometric and group theoretical problems related to Kodaira fibrations, to more general families of Riemann surfaces, and to surface-by-surface groups. First we provide constraints on Kodaira fibrations that fiber in more than two distinct ways, addressing a question by Catanese and Salter about their …
Sharp inequalities on curved spaces with bounded curvature.
problem Establishing inequalities on curved spaces with curvature constraints.
method Using Sobolev and Moser-Trudinger inequalities on noncompact Riemannian manifolds with Ricci curvature bounded below.
result Best constants for inequalities on curved spaces with curvature constraints.
The paper optimizes dividend strategies for companies with assets and liabilities under solvency constraints.
problem Maximizing dividends while adhering to solvency requirements in the face of correlated asset and liability movements.
method Developed verification lemmas to show optimal barrier dividend strategies in two cases: with and without shareholder funding.
result Optimal dividend strategies are barrier-type, derived in closed form and illustrated.
Flexible VAEs using FIFs improve model likelihood on image datasets.
problem Limitations of diagonal Gaussian posteriors in VAEs.
method Regularized Free-form Injective Flow (FIF) for flexible posterior.
result Full covariance VAEs outperform diagonal Gaussian posteriors.
In this paper, we construct a solution to the optimal contract problem for delegated portfolio management of the fist-best (risk-sharing) type. The novelty of our result is (i) in the robustness of the optimal contract with respect to perturbations of the wealth process (interpreted as capital injections), and (ii) in …
Novel method HAO mitigates Graph Injection Attack by preserving homophily.
problem Graph Injection Attack's high flexibility can harm graph homophily.
method Introduce homophily unnoticeability constraint and Harmonious Adversarial Objective (HAO).
result GIA with HAO breaks homophily-based defenses and outperforms previous attacks.
The paper shows regularization can't always find all optimal solutions in constrained ML.
problem Finding the right balance between model accuracy and constraint satisfaction.
method Formal demonstration of the limitations of regularization-based approaches in non-convex cases.
result There are optimal solutions for constrained problems that do not correspond to any multiplier value.
Optimal portfolio tracking with dynamic capital injection into a ratcheting benchmark.
problem Optimizing a portfolio's performance by dynamically adding capital to a non-decreasing benchmark.
method Formulated as an unconstrained control problem with a running maximum cost, transformed into an auxiliary problem with a nonlinear HJB equation, solved using probabilistic representation and stochastic flow analysis.
result Established the existence of a unique classical solution to the HJB equation, providing feedback optimal portfolio strategies.
Synthesizes sensor likelihoods to enforce accuracy constraints in uncertain systems.
problem Designing sensing architectures for systems with uncertain or unavailable sensor models and accuracy requirements.
method Inverts the design flow, synthesizing measurement likelihoods that minimize Kullback-Leibler divergence from the prior while enforcing an accuracy bound.
result The method synthesizes a maximum-entropy posterior and induced likelihood, accommodating various discrepancy metrics.
In this paper, the extension of the framework of Learning from Constraints (LfC) to a distributed setting where multiple parties, connected over the network, contribute to the learning process is studied. LfC relies on the generic notion of "constraint" to inject knowledge into the learning problem and, due to its gene…
This paper studies the optimal dividend problem with capital injection under the constraint that the cumulative dividend strategy is absolutely continuous. We consider an open problem of the general spectrally negative case and derive the optimal solution explicitly using the fluctuation identities of the refracted-ref…
Study optimal consumption with relaxed benchmarks and drawdown constraints.
problem Optimal consumption under relaxed benchmark tracking and consumption drawdown constraint.
method Transformed stochastic control problem into regular control problem with state-control constraints, then solved using dual transform and optimal consumption behavior.
result Closed-form solution for optimal investment and consumption in feedback form.
Arguments in favor of injecting symbolic knowledge into neural architectures abound. When done right, constraining a sub-symbolic model can substantially improve its performance and sample complexity and prevent it from predicting invalid configurations. Focusing on deep probabilistic (logical) graphical models -- i.e.…
In this paper, we propose a scalable algorithm for spectral embedding. The latter is a standard tool for graph clustering. However, its computational bottleneck is the eigendecomposition of the graph Laplacian matrix, which prevents its application to large-scale graphs. Our contribution consists of reformulating spect…
Domain knowledge helps detect adversarial examples in multi-label classification.
problem Detecting adversarial examples in multi-label classification.
method Convert domain knowledge into constraints and inject them into a semi-supervised learning problem.
result Domain-knowledge constraints help detect adversarial examples effectively.
Survey of integrating domain knowledge into DL models.
problem Improving DL model performance with limited data or complex functions.
method Five categories of approaches to inject domain knowledge into DL models.
result Survey identifies five main categories of approaches.
The paper extends Merton's problem by adding benchmark tracking, finding optimal strategies.
problem Maximizing consumption utility with a trade-off against benchmark performance.
method Developed a convex duality theorem and derived optimal strategies for specific cases.
result Found optimal portfolio and consumption strategies for CRRA utility and geometric Brownian motion benchmarks.
Injectivity of ReLU networks is characterized for generative models and inverse problems.
problem Injectivity in ReLU networks for generative models and inverse problems.
method Layerwise analysis, worst-case Lipschitz constants, differential topology, random projections.
result Global injectivity of ReLU networks requires expansivity between 3.4 and 10.5 for Gaussian matrices.
Classifies π1-injective maps between non-compact surfaces.
problem Characterizing maps with injective fundamental groups.
method Proper homotopy classification of maps.
result All π1-injective proper maps are classified. Positive injectivity radius for manifolds with Lie structure at infinity.
problem Injectivity radius positivity for manifolds with specific boundary conditions.
method Lie groupoids to prove injectivity radius positivity.
result Injectivity radius is positive for manifolds with Lie structure at infinity.
High throughput sequencing techniques have highly impactedon modern biology, widening the gap between sequenced andannotated data. Automatic annotation tools are thereforeof the foremost importance to guide biologists' experiments. However, most of the state-of-the-art methods rely on annotation transfer, offering reli…
Geometric analysis improves noise injection in GANs.
problem Unclear mechanism of noise injection in GANs.
method Geometric framework based on Riemannian geometry.
result A new strategy for noise injection is devised.
The paper analyzes optimal dividend and capital injection strategies under time-inconsistent preferences.
problem Optimal dividend and capital injection strategies under time-inconsistent preferences.
method Diffusion risk model with general discount functions, weak equilibrium definition, HJB equation system.
result Explicit solutions and threshold types of optimal strategies derived under different discount functions.
A quasi-geodesic is Morse if and only if it is strongly contracting in injective spaces.
problem Characterizing Morse quasi-geodesics in injective spaces.
method Proving equivalence between Morse and strongly contracting quasi-geodesics.
result Injective metric spaces have the Morse local-to-global property and acylindrically hyperbolic groups with Morse elements.
This paper connects noise injection to Bayesian inference for neural networks, improving model uncertainty.
problem Improving the reliability and confidence of neural network predictions through uncertainty quantification.
method Introducing noise into neural network parameters during training and inference to estimate prediction uncertainty.
result The MCNI method outperforms baseline models in regression and classification tasks.
Compact theorem for minimal surfaces with lower injectivity radius.
problem Proving compactness of minimal surfaces with lower injectivity radius.
method Variant of Choi--Schoen compactness theorem, focusing on injectivity radius.
result Proved compactness theorem for minimal surfaces.
Lecture notes on group actions on injective spaces and Helly graphs.
problem Understanding group actions on specific metric spaces.
method Review of injective metric spaces and Helly graphs, elementary properties, constructions, and exercises.
result Presentation of various constructions of injective metric spaces and Helly graphs with interesting group actions.
Proves polynomial injectivity of Fubini-Study map for ample line bundles.
problem Injectivity of Fubini-Study map for ample line bundles.
method Polynomial injectivity proof with polynomial dependence on ample line bundle exponent.
result Quantitative version of injectivity proved, polynomial in ample line bundle exponent.
Lower bound on boundary injectivity radius for specific tubes.
problem Estimating the boundary injectivity radius of Margulis tubes.
method Using curvature bounds to derive a lower bound.
result A lower bound on the boundary injectivity radius is provided.
Reservoir subspace injection improves online ICA by preserving injected features.
problem Discarding injected features in top-n whitening can degrade performance. method Formalized reservoir subspace injection (RSI) and developed diagnostics (IER, SSO, ρ_x) to identify and mitigate the failure mode.
result RSI controller preserves passthrough retention, improving performance by up to 2.2 dB.
Injective and surjective neural operators for function spaces.
problem Tackles injective and surjective neural operators in function spaces.
method Combines prior work in ReLU and operator learning, uses Fredholm theory and Leray-Schauder degree theory.
result Injective and surjective neural operators are universal approximators and maintain their properties in finite-rank implementations.
Proposes a method to enhance graph models by injecting unseen connections.
problem Enhancing graph models to utilize unseen connections.
method Parametric link injection layer to find and inject weak connections.
result Improves performance on node classification and link prediction tasks.
The paper proves that certain spaces are injective and Helly graphs.
problem Understanding the structure of certain geometric and algebraic spaces.
method Building Helly graphs and injective metric spaces from lattices.
result The natural piecewise ℓ∞ metric on Euclidean buildings and Deligne complexes is injective. Nonuniform tubular neighborhoods of curves in Euclidean n-space are studied by using weighted distance functions and generalizing the normal exponential map. Different notions of injectivity radii are introduced to investigate singular but injective exponential maps. A generalization of the thickness formula is obtaine…
In this paper, we obtain two-sided bounds for the volumes of the Aloff-Wallach spaces W(p,q), compute maximal and minimal sectional curvature for the spaces W(n,n+1), and use this information to estimate the injectivity radii: We derive an upper bound for the injectivity radii of W(p,q) and a lower bound for the …
Injectivity of geodesic ray transform on specific Finsler manifolds proven.
problem Injectivity of geodesic ray transform on spherically symmetric reversible Finsler manifolds.
method Reduction to invertibility of generalized Abel transforms using angular Fourier series and Taylor expansions of geodesics.
result Injectivity of geodesic ray transform proven on specified Finsler manifolds.
Noise Injection probes deep learning dynamics during training phases.
problem Understanding the learning mechanism of deep neural networks.
method Noise Injection Nodes (NINs) are used to perturb DNN architectures without altering the optimization algorithm.
result Distinct training phases are observed based on the scale of injected noise.
Generalizes a soul-bound for noncompact Alexandrov spaces.
problem Finding a lower bound for injectivity radius in Alexandrov spaces.
method Introduces the soul of Alexandrov spaces and applies a generalized bound.
result Injectivity radius is at least πK⁻¹/² if not equal to the soul's.