Study constructs non-funnel foliations in 3D manifolds.
problem Does the funnel property follow from leafwise quasigeodesic foliations?
method Constructs 1D foliations within 2D subfoliations in 3-manifolds.
result Not all quasigeodesics share a common ideal point in most leaves.
A new layer, funnel, reduces dimensionality in flows for better performance.
problem Training high-dimensional models efficiently and accurately.
method Constructing dimension-reducing surjective flows using the funnel layer.
result The funnel layer improves model performance with a smaller latent space.
The paper tackles decision making problems with funnel structure in email marketing campaigns.
problem Decision making challenges in systems with funnel structure, where fewer observations are received from deeper layers.
method Formulated as a contextual bandit with funnel structure and developed a multi-task learning algorithm.
result Our algorithms offer significant improvement over previous methods in email marketing campaigns.
Funnel-Transformer reduces computation by compressing sequence data.
problem Redundant token-level representations in language processing.
method Gradually compresses sequence of hidden states to a shorter one.
result Funnel-Transformer outperforms standard Transformer with fewer FLOPs.
Paper uses Shapley values to identify key confounders in product funnel data.
problem Identifying important confounders in product funnel data.
method Applies Shapley values for scalable coarsened exact matching.
result Shapley values provide robust importance-ranking for confounders.
We establish a sharp geometric constant for the upper bound on the resonance counting function for surfaces with hyperbolic ends. An arbitrary metric is allowed within some compact core, and the ends may be of hyperbolic planar, funnel, or cusp type. The constant in the upper bound depends only on the volume of the cor…
Cross-lingual Text Classification (CLC) consists of automatically classifying, according to a common set C of classes, documents each written in one of a set of languages L, and doing so more accurately than when naively classifying each document via its corresponding language-specific classifier. In order to obtain an…
Descending phase retrieval algorithms show a phase transition with increasing sample complexity.
problem Theoretical limits of descending phase retrieval algorithms.
method Utilizing Random duality theory (RDT), the study develops a generic program to characterize algorithm performance.
result As sample complexity increases, the parametric manifold transitions from multi to single funneling points, leading to a phase transition in algorithm success.
In this paper we prove that any Riemannian surface, with no restriction of curvature at all, can be decomposed into blocks belonging just to some of these types: generalized Y-pieces, generalized funnels and halfplanes.
Multidimensional time series are sequences of real valued vectors. They occur in different areas, for example handwritten characters, GPS tracking, and gestures of modern virtual reality motion controllers. Within these areas, a common task is to search for similar time series. Dynamic Time Warping (DTW) is a common di…
Adaptive-stepsize MCMC sampling inspired by Adam optimizer.
problem Improving numerical stability and convergence speed in MCMC sampling.
method Time-rescaled Langevin dynamics with an auxiliary relaxation equation and adaptive stepsize control.
result Automatic stepsize control improves accuracy and stability in numerical experiments.
WALNUTS improves sampling efficiency and robustness for multi-scale distributions.
problem Adapting leapfrog step size for multi-scale posterior distributions.
method Adapts leapfrog step size at fixed intervals of simulated time, selecting the largest step size to keep energy error below a threshold.
result Substantial improvements in sampling efficiency and robustness compared to standard NUTS.
We propose and document the evidence for an analogy between the dynamics of granular counter-flows in the presence of bottlenecks or restrictions and financial price formation processes. Using extensive simulations, we find that the counter-flows of simulated pedestrians through a door display many stylized facts obser…
Improves classifier performance in multi-stage selection processes.
problem Difficulty in training classifiers in multi-stage selection processes due to varying sample sizes and information.
method Multi-Stage Transfer Learning (MSGTL) approach that uses knowledge from simpler classifiers trained in early stages to improve later stages.
result MSGTL outperforms other transfer learning methods in real-world selection process data.
On compact surfaces with or without boundary, Osgood, Phillips and Sarnak proved that the maximum of the determinant of the Laplacian within a conformal class of metrics with fixed area occurs at a metric of constant curvature and, for negative Euler characteristic, exhibited a flow from a given metric to a constant cu…
Study projective deformations of hyperbolic 3-orbifolds with turnover ends.
problem Deformations of hyperbolic 3-orbifolds with turnover ends in projective geometry.
method Projective deformations of hyperbolic 3-orbifolds with turnover ends, focusing on totally geodesic generalized cusps.
result Turnover funnels remain totally geodesic and the deformed projective 3-orbifold remains properly convex.
Gauge theory connects hyperbolic metrics to Virasoro orbits, revealing their geometric and topological properties.
problem Understanding the relationship between hyperbolic metrics and Virasoro orbits.
method Using SL(2,R) gauge theory on a cylinder, assigning flat SL(2,R) gauge fields to Virasoro orbits.
result Affirmative answer to the question that all Virasoro orbits arise as moduli spaces of hyperbolic metrics.
We propose a dynamical theory of market liquidity that predicts that the average supply/demand profile is V-shaped and {\it vanishes} around the current price. This result is generic, and only relies on mild assumptions about the order flow and on the fact that prices are (to a first approximation) diffusive. This natu…
Improved MUSE boosts performance and reduces error in Bayesian inference.
problem Hierarchical Bayesian inference problems
method Implicit differentiation applied to MUSE algorithm
result Significant speedup and improved accuracy compared to Hamiltonian Monte Carlo
The automorphisms of a two-generator free group acting on the space of orientation-preserving isometric actions of on hyperbolic 3-space defines a dynamical system. Those actions which preserve a hyperbolic plane but not an orientation on that plane is an invariant subsystem, which reduces to an action on R^3 by polyno…
In the first part of this work we explore the geometry of infinite type surfaces and the relationship between its convex core and space of ends. In particular, we show that a geodesically complete hyperbolic surface is made up of its convex core with funnels attached along the simple closed geodesic components and half…
Study improves cryptocurrency price prediction using unlabeled text data.
problem Predicting cryptocurrency returns from unlabelled text data.
method Introduced weak learning approach to finetune BERT on unlabeled text data.
result Finetuning pretrained NLP models with weak labels enhances forecast accuracy.
Unified framework connects physical laws and machine learning.
problem Combining physical laws and machine learning for scientific applications.
method Universal Differential Equations (UDEs) as a unifying framework.
result Wide variety of applications can be efficiently handled through UDE formalism.
The paper compares Dirichlet and Neumann eigenvalues on various curved surfaces.
problem Comparing eigenvalues on curved surfaces.
method Variational principle of the Hodge Laplacian on 1-forms.
result Strict inequalities between Dirichlet and Neumann eigenvalues on specific surfaces.
Delayed rejection HMC improves sampling efficiency for multiscale distributions.
problem Hamiltonian Monte Carlo struggles with wide-ranging distributions, especially in high-curvature areas.
method Introduces a delayed rejection variant of HMC, using geometrically smaller step sizes for retries.
result Up to five-fold performance gains in effective sample size per gradient evaluation.
Differential Cohomotopy theory predicts brane interactions via chord diagrams.
problem Quantization of brane charges and moduli spaces.
method Differential refinement of Cohomotopy theory, configuration spaces, chord diagrams.
result Higher observables on brane moduli spaces are given by weight systems on chord diagrams.
Maximizing product use is a central goal of many businesses, which makes retention and monetization two central analytics metrics in games. Player retention may refer to various duration variables quantifying product use: total playtime or session playtime are popular research targets, and active playtime is well-suite…
Improves classifier performance in multi-stage processes with adversarial autoencoders and multi-task learning.
problem Challenges in training classifiers due to varying sample sizes and information content across stages.
method Combines adversarial autoencoders, multi-task learning, and semi-supervised learning to address underfitting and overfitting.
result Our approach outperforms state-of-the-art methods across different domains.
A new method reduces complexity of normalizing flows for MCMC preconditioning.
problem Improving sampling efficiency in MCMC algorithms for complex target distributions.
method Factorized preconditioning architecture combining a linear component and a conditional NF.
result Significantly better tail samples and higher effective sample sizes on various distributions.
Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iR…
Bayesian optimization has become a fundamental global optimization algorithm in many problems where sample efficiency is of paramount importance. Recently, there has been proposed a large number of new applications in fields such as robotics, machine learning, experimental design, simulation, etc. In this paper, we foc…
Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
problem Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
method Numerical simulations of static solutions to a particular class of problems in hyperelastic mechanics.
result Hyperelastic bodies in Riemannian manifolds can levitate due to curvature-induced forces.
Groups with Property (T) have fiber products with Property (T).
problem When does the fiber product of groups with Property (T) have Property (T)?
method Analyzing fiber products of groups with Property (T).
result Fiber products of groups with Property (T) also have Property (T).
We prove recognition theorems for codimension one manifold factors of dimension n≥4. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that X×R i…
The study shows that several properties are not profinite invariants.
problem Determining which properties are profinite invariants.
method Combining Rips constructions and iterated group-theoretic Dehn filling on hyperbolic virtually special groups.
result Several properties (stable commutator length, quasimorphisms, property NL, property FW∞, property FA, and non-abelian free subgroups) are not profinite invariants. We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …
The paper explores higher property T in lattices and its connections to geometric phenomena.
problem Understanding higher property T in lattices and related geometric phenomena.
method Operator-algebraic characterizations of higher property T and connections to lattice geometry.
result Unified framework for understanding higher property T and related geometric phenomena.
Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C. Then we i…
Groups of importance in group theory have flexible stability properties.
problem Stability and flexibility of groups in geometric and combinatorial group theory.
method Establishing Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for specific groups.
result Groups like 3-manifold groups, limit groups, and certain one-relator groups are very flexibly stable. This paper generalizes property (QT) to a broader class of groups.
problem Proving property (QT) for a wider range of groups.
method Using projection complex machinery and hierarchical hyperbolic groups.
result Established sufficient conditions for groups to have property (QT).
Proves a vanishing property for symplectic manifold cohomology.
problem Generalizing complex geometry results to symplectic geometry.
method Based on Tseng and Zhou's vanishing property under symplectic flatness.
result Establishes necessity of symplectic flatness for certain results.
Survey on foliations and diffeomorphism groups.
problem Relationship between algebraic and homotopical properties.
method Survey and analysis of existing literature.
result Explains the connection between diffeomorphism groups and foliations.
We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group G with a …
Study generalizes property elicitation to imprecise probabilities.
problem Minimizing risk over imprecise probability distributions.
method Maximin risk minimization over a set of imprecise probabilities.
result Conditions for elicitability of IP-properties.
Introduces bounded scale measure and generalizes property A.
problem Defining property A for large scale spaces with bounded geometry.
method Introduces bounded scale measure, shows its coarse invariance, and generalizes property A.
result Definition of property A for large scale spaces with bounded scale measure is a coarse invariant.
Study cohomological and metric properties of non-Kähler complex manifolds.
problem Understanding cohomological invariants and metrics of non-Kähler complex manifolds.
method Partial account of problems through cohomological and metric properties.
result Partial insights into cohomological and metric properties of non-Kähler manifolds.
Model predicts price polarity of real estate properties using website information.
problem Predicting price polarity of real estate properties.
method Uses doc2vec and xgboost to learn correlations between price and text descriptions of properties.
result Text descriptions provide slightly higher accuracy than features alone.
The paper explores the twisted Rokhlin property in mapping class groups of surfaces.
problem Classifying surfaces whose mapping class groups have the twisted Rokhlin property.
method Generalizing the Rokhlin property to the twisted version, the authors classify surfaces based on their mapping class groups' properties.
result The mapping class groups of connected orientable infinite-type surfaces without boundaries have the twisted Rokhlin property, while those of other surfaces do not.