VES-Gamma adapts EI using information-theoretic principles.
problem Optimizing black-box functions using Bayesian optimization.
method Variational Entropy Search (VES) and VES-Gamma algorithm.
result VES-Gamma improves EI by incorporating information-theoretic concepts.
The paper analyzes the score field of diffusion models using Burgers dynamics.
problem Understanding the evolution of score fields in diffusion models.
method Analyzes the score field through Burgers-type evolution law for diffusion models.
result Identifies a universal \( anh\) interfacial term in the score field.
F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem …
Study on mean curvature flow in a cone, proving existence and homogenization.
problem Mean curvature flow in a cone with periodic boundary conditions.
method Construction of self-similar solutions, a priori estimates, homogenization limit analysis.
result Global existence of radially symmetric solutions and characterization of the homogenization limit.
The paper classifies functions with isolated critical points on a compact surface and develops a criterion for their global equivalence.
problem Classifying functions with isolated critical points on the boundary of a compact surface.
method Topological classification in a neighborhood of critical points, construction of chord diagrams, and development of a criterion for global equivalence.
result A criterion for global topological equivalence of functions with three critical points on a compact surface.
In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the loca…
Unified framework connects EI and information-theoretic acquisition functions.
problem Distinguish between Expected Improvement and information-theoretic acquisition functions.
method Introduces Variational Entropy Search (VES) to unify EI and information-theoretic approaches.
result EI can be seen as a variational inference approximation of Max-value Entropy Search (MES).
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incomplete, but due to recent requests from readers, I've decided to make a presentable half-finished version available here.…
A new method improves estimation of COVID-19 vaccine effectiveness.
problem Estimating vaccine effectiveness under the test-negative design.
method A doubly robust estimator (TNDDR) using cross-fitting and machine learning.
result The TNDDR estimator is n \sqrt{n} n -consistent, asymptotically normal, and doubly robust. A graph (digraph) G = ( V , E ) G=(V,E) G = ( V , E ) with a set T ⊆ V T\subseteq V T ⊆ V of terminals is called inner Eulerian if each nonterminal node v v v has even degree (resp. the numbers of edges entering and leaving v v v are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint T T T -paths in an inner Eulerian graph $G…
Lecture notes on CAT(0) cube complexes for beginners.
problem Introduction to CAT(0) cube complexes for students.
method Elementary and self-contained lectures.
result Accessible introduction to advanced topics for students.
This study compares Bitcoin and Litecoin using cryptocurrency metrics and trading strategies.
problem Valuation and trading strategies for cryptocurrencies.
method Metrics like UTXO, STXO, WAL, CDD, and trading strategies based on PU ratio.
result Bitcoin's superior store-of-value proposition compared to Litecoin validated.
Study uses neural processes to predict and classify crack patterns in moving disks.
problem Predicting and classifying crack patterns in moving disks.
method Peridynamic theory, Convolutional Neural Networks (CNNs), and Neural Processes.
result Neural Processes provide accurate predictions even with missing or insufficient data.
New metrics with constant Q-curvature created by gluing.
problem Creating metrics with constant Q-curvature on spheres with punctures.
method Gluing truncated known metrics together.
result Unmarked moduli space of solutions is nontrivial for at least four punctures.
We consider the following singularly perturbed Neumann problem \begin{eqnarray*} \ve^2 Δu -u +u^p = 0 \, \quad u>0 \quad {\mbox {in}} \quad Ω, \quad {\partial u \over \partial ν}=0 \quad {\mbox {on}} \quad \partial Ω, \end{eqnarray*} where p > 2 p>2 p > 2 and Ω Ω Ω is a smooth and bounded domain in R 2 \R^2 R 2 . We construct a new class…
We study how to communicate findings of Bayesian inference to third parties, while preserving the strong guarantee of differential privacy. Our main contributions are four different algorithms for private Bayesian inference on proba-bilistic graphical models. These include two mechanisms for adding noise to the Bayesia…
We derive a new, exact and transparent expansion for option smiles, which lends itself both to analytical approximation and, perhaps more importantly, to congenial numerical treatments. We show that the skew and the curvature of the smile can be computed as exotic options, for which the Hedged Monte Carlo method is par…
Nontrivial boundary Dehn twist found on K3#K3 manifold.
problem Proving nontriviality of a Dehn twist on a specific 4-manifold.
method Algebraic criterion and equivariant topological K-theory to show non-isotopy.
result Boundary Dehn twist is nontrivial in the smooth mapping class group.
Invariants for 3D manifolds with boundaries using crossed modules.
problem Develop invariants for compact 3D manifolds with boundaries.
method Employ crossed modules to count correct colors over triangulations.
result Validated invariants for compact 3D manifolds with boundaries.
SAIL improves graph node representation learning by distilling knowledge between graphs.
problem Improving graph node representation learning with GNNs in unsupervised scenarios.
method SAIL framework with intra- and inter-graph knowledge distillation.
result SAIL consistently outperforms state-of-the-art baselines on various benchmark datasets.
Auto-detection system identifies safety issues in baby products from reviews.
problem Early detection of safety issues in baby products to reduce injuries and deaths.
method Text cleaning, feature extraction, dimensionality reduction, classifier analysis.
result Logistic regression model with 66% precision in identifying top 50 safety issues.
In distributed ML applications, shared parameters are usually replicated among computing nodes to minimize network overhead. Therefore, proper consistency model must be carefully chosen to ensure algorithm's correctness and provide high throughput. Existing consistency models used in general-purpose databases and moder…
iEFM trains CNF models from unnormalized densities efficiently.
problem Training generators from energy functions or unnormalized densities.
method Iterated energy-based flow matching (iEFM) with simulation-free objective.
result iEFM outperforms existing methods in probabilistic modeling.
ICYM2I corrects missingness bias in multimodal learning.
problem Missingness patterns between source and target environments affect multimodal learning performance.
method ICYM2I uses inverse probability weighting to correct missingness bias in predictive performance and information gain.
result ICYM2I improves multimodal learning performance by accounting for missingness.
Surveying strategies for making machine learning models robust against adversarial attacks.
problem Ensuring machine learning models are robust and reliable in real-world applications.
method Taxonomy of adversarial attacks and defenses, Robust Optimization problem formulation, and survey of methods.
result Surveyed recent results in adversarial example generation, defense mechanisms, and formal robustness certificates.
Paper adapts GMs for heterogeneous inference scenarios.
problem Traditional GMs struggle with non-hierarchical, heterogeneous stochastic variables.
method Adapts GAN and VAE to heterogeneous learning and inference in polynomial time.
result Proposed EAR model achieves best performance on BN datasets.
We created financial benchmarks for distribution shifts in crude oil prices and volatility.
problem Scarcity of task-labeled time-series benchmarks in finance.
method Transformed asset price data into volatility proxies, generated task labels based on distribution shifts, and made datasets publicly available.
result Inclusion of task labels improves continual learning algorithms' performance on real-world data.
Researchers describe and compare decompositions of Poincaré duality pairs.
problem Understanding and comparing different decompositions of Poincaré duality pairs.
method Developed and described edge splittings of decompositions based on group properties.
result Compared decompositions with two other related decompositions.
This paper generalizes Michell Truss to higher dimensions using geometric measure theory.
problem Finding optimal designs of k-beam structures under equilibrium forces.
method Geometric measure theory and flat chain complex.
result Existence of optimal k-beam structures has been solved completely.
The paper proposes and discusses semiorthogonal decompositions for moduli spaces of vector bundles.
problem Decompositions of moduli spaces of vector bundles with fixed determinant of odd degree.
method Semiorthogonal decompositions, Grothendieck ring of varieties, mirror symmetry, graph potentials, Fukaya category.
result Evidence for a conjectural semiorthogonal decomposition of moduli spaces of rank 2 bundles with odd determinant.
New complexity notion connects finite decomposition and asymptotic property C.
problem Understanding and connecting different properties in metric spaces.
method Introducing finite APC-decomposition complexity and proving its implications.
result Finite APC-decomposition complexity implies property A for metric spaces.
Conservation of heat in manifolds with boundary under mixed conditions.
problem Conservation of heat in manifolds with boundary and mixed conditions.
method Uniform lower bounds on the zero order piece of the Dirac Laplacian and on the endomorphism defining the mixed boundary condition.
result Conservation principle holds under suitable geometric control.
The paper classifies decompositions of 3-sphere and lens spaces with handlebodies.
problem Classifying decompositions of 3-manifolds with handlebodies.
method Studied decompositions of 3-sphere and lens spaces with three handlebodies, using stabilizations.
result Determined whether decompositions are stabilized.
This paper generalizes octahedral decomposition to links in thickened surfaces.
problem Understanding the geometry of links in thickened surfaces.
method Octahedral decomposition of links in thickened surfaces.
result Nonpositive curvature of the complement and essential-ness of edges proved.
A new tensor decomposition method using a dictionary for better interpretability.
problem Ensuring interpretability in tensor decomposition models.
method Dictionary-based tensor canonical polyadic decomposition with sparse coding.
result Improves parameter identifiability and estimation accuracy in tensor decomposition.
A new tensor decomposition method that minimizes KL divergence.
problem Tensor reconstruction accuracy.
method Legendre decomposition, based on information geometry.
result Minimizes KL divergence and improves tensor reconstruction accuracy.
Systematizes blockchain decentralization taxonomy and metrics.
problem Lack of a unified definition for blockchain decentralization.
method Formulated a taxonomy of five facets and developed metrics.
result Provided comprehensive insights into blockchain decentralization.
Study of Quillen metric on Riemann surfaces with cusps and compactification.
problem Behavior of Quillen metric on Riemann surfaces with cusps.
method Continuous extension of Quillen metric over singular curves and explicit universal constant.
result Compatibility of Quillen metric with clutching morphisms and analytic torsion.
Researchers compute Goeritz groups for all (1,1)-link decompositions.
problem Computing Goeritz groups for all (1,1)-link decompositions.
method Analyzing surface decompositions and isotopy classes of homeomorphisms.
result Computed Goeritz groups for all (1,1)-link decompositions.
Study concordance of decompositions from defining sequences in 3-sphere.
problem Understanding concordance and bordism of decompositions from defining sequences.
method Relate to invariants of toroidal decompositions and cobordism of homology manifolds.
result At least uncountably many concordance classes of decompositions in 3-sphere.
Characterizes conditions for quotient spaces of decompositions to be manifolds.
problem Conditions for quotient spaces of decompositions to be manifolds.
method Generalized characterizations of upper semi-continuity for decomposition into one for a class decomposition.
result Characterizations of necessary and sufficient conditions for quotient spaces of decompositions to be k k k -manifolds ( k = 1 , 2 k = 1, 2 k = 1 , 2 ). Study shows OAT decomposition generates unexplained profit and loss, while SU decompositions depend on risk factor order.
problem Understanding profit and loss attribution in financial markets.
method Used financial market data from 2003 to 2022 to compare OAT, SU, and ASU decompositions.
result SU decompositions are sensitive to risk factor order and cannot identify all relevant risk factors.
Given a Delaunay decomposition of a compact hyperbolic surface, one may record the topological data of the decomposition, together with the intersection angles between the `empty disks' circumscribing the regions of the decomposition. The main result of this paper is a characterization of when a given topological decom…
New tensor network decompositions improve CNN performance.
problem Limited exploration of tensor network decompositions for CNNs.
method Characterized a new class of CNN modules and experimentally compared various decompositions.
result Some nonlinear decompositions outperform existing ones in terms of accuracy and efficiency.
A new algorithm speeds up CP decomposition for large tensors.
problem Efficiently processing large-scale tensors in real-time.
method Randomized online CP decomposition (ROCP) algorithm.
result ROCP reduces computing time and memory usage significantly.
Paper characterizes optimization landscape of Tucker decomposition.
problem Finding exact Tucker decomposition is a nonconvex optimization problem.
method Characterized the optimization landscape and provided a local search algorithm.
result All local minima are globally optimal if tensor has an exact Tucker decomposition.
A double pants decomposition of a 2-dimensional surface is a collection of two pants decomposition of this surface introduced in arXiv:1005.0073v2. There are two natural operations acting on double pants decompositions: flips and handle twists. It is shown in arXiv:1005.0073v2 that the groupoid generated by flips and h…
Smooth 4-manifolds have simple horizontal decompositions.
problem Classifying smooth, closed, orientable 4-manifolds.
method Horizontal handlebody decomposition.
result Simplest horizontal decompositions classify closed 4-manifolds.