This is a survey of the theory of complex projective (CP^1) structures on compact surfaces. After some preliminary discussion and definitions, we concentrate on three main topics: (1) Using the Schwarzian derivative to parameterize the moduli space (2) Thurston's parameterization of the moduli space using grafting (3) …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,657 papers · 148 categories
Trend · papers per month
48 results for “parameterized complexity”
The paper analyzes the complexity of untangling knots with a given number of moves.
problem Determining if a knot diagram can be untangled with a specified number of moves.
method Parameterized complexity analysis with respect to the defect, a measure of move efficiency.
result The problem belongs to W[P] when parameterized by defect, and is W[P]-hard by reduction.
Local PCA detects intrinsic parameterization of complex thermo-chemical state-spaces.
problem Detecting intrinsic parameterization of complex thermo-chemical state-spaces.
method Local PCA applied to local clusters of data.
result Local PCA finds meaningful parameterization linked to local stoichiometry, reaction progress, and soot formation processes.
Study on teaching complexity in graphs, proving hardness and tractability.
problem Computing the minimum number of examples per concept for teaching.
method Classical and parameterized complexity analysis, NP-hardness, upper and lower bounds, fixed-parameter tractability.
result Nearly complete understanding of teaching complexity in graphs.
Efficient conformal parameterization of multiply-connected surfaces using quasi-conformal theorycs.GR
Two novel algorithms for conformal parameterization of multiply-connected surfaces.
problem Parameterization of surfaces with holes.
method Developed efficient methods using quasi-conformal theory.
result Efficient conformal parameterization of multiply-connected surfaces.
New method tackles over-parameterized matrix sensing with FGD, improving statistical and computational complexity.
problem Solving low rank matrix sensing with over-specified factors when rank is unknown.
method Decomposing the factorized matrix into column spaces to capture extra ranks and analyze convergence.
result Convergence to a statistical error of after iterations.
A Novel Framework for Policy Mirror Descent with General Parameterization and Linear Convergencestat.ML
Novel framework for policy optimization with general parameterization and linear convergence.
problem Lack of theoretical guarantees for policy optimization with general parameterization schemes.
method Mirror descent approach for policy optimization with general parameterization.
result First result of linear convergence for policy-gradient-based method with general parameterization.
The paper proposes methods for volumetric parameterization of 3D solid manifolds.
problem Complex structure of solid manifolds makes conventional approaches ineffective.
method Incorporates models to preserve geometric structure, achieve density equalization, and balance distortions.
result Various 3D manifold parameterizations with different properties can be achieved.
Develops a method for conformal parameterization of point clouds without fixed boundaries.
problem Desirable distortion in fixed-boundary parameterizations of point clouds.
method Free-boundary conformal parameterization method involving approximation of point cloud Laplacian and boundary treatment.
result High-quality point cloud meshing achieved through the proposed method.
Credit risk stress tests can misrepresent default probabilities due to inconsistent parameterization.
problem Misleading default probability projections in credit risk stress tests.
method Analysis of credit risk stress testing models and their parameterization.
result Current portfolios tend to align with through-the-cycle portfolios, leading to spurious default rate projections.
Memorizing without overfitting: Bias, variance, and interpolation in over-parameterized modelsstat.ML
New insights into bias and variance in over-parameterized models.
problem Understanding bias and variance in over-parameterized models.
method Analytic expressions derived from statistical physics for two minimal models.
result Over-parameterized models can overfit even in noiseless conditions.
Geometric Occam's Razor shapes deep learning solutions.
problem Understanding the regularization in over-parameterized neural networks.
method Analyzing the geometric model complexity and Dirichlet energy in neural networks.
result Over-parameterized neural networks are implicitly regularized by geometric model complexity.
The true distribution parameterizations of commonly used image datasets are inaccessible. Rather than designing metrics for feature spaces with unknown characteristics, we propose to measure GAN performance by evaluating on explicitly parameterized, synthetic data distributions. As a case study, we examine the performa…
We consider reinforcement learning in parameterized Markov Decision Processes (MDPs), where the parameterization may induce correlation across transition probabilities or rewards. Consequently, observing a particular state transition might yield useful information about other, unobserved, parts of the MDP. We present a…
We classify the 6-dimensional Lie algebras that can be endowed with an abelian complex structure and parameterize, on each of these algebras, the space of such structures up to holomorphic isomorphism.
This paper presents a method to compute the {\it quasi-conformal parameterization} (QCMC) for a multiply-connected 2D domain or surface. QCMC computes a quasi-conformal map from a multiply-connected domain onto a punctured disk associated with a given Beltrami differential. The Beltrami differential, which me…
This paper introduces a new bound to explain generalization in over-parameterized models.
problem Understanding why some over-parameterized models generalize well while others do not.
method PAC-Chernoff bounds and smoothness measures based on large deviation theory.
result Interpolators with smoother structures generalize better, according to the new theoretical framework.
Unified framework for learning quantum models from limited measurements.
problem Sample complexity and measurement shots in classical learning of quantum models.
method Unified learning framework considering probabilistic quantum measurements.
result Asymmetrical effects and interplay of sample size and measurement shots on learning performance.
Distribution Free Uncertainty for the Minimum Norm Solution of Over-parameterized Linear Regressioncs.LG
The paper explores how over-parameterized linear regression models generalize without violating learning theory principles.
problem Understanding how over-parameterized linear regression models generalize without violating learning theory principles.
method The paper uses the predictive normalized maximum likelihood (pNML) learner to investigate the minimum norm solution of over-parameterized linear regression models.
result The model generalizes well when the test sample lies in a subspace spanned by eigenvectors associated with large eigenvalues of the training data.
Gradient Descent with Projection learns low-degree polynomials efficiently.
problem Learning low-degree spherical polynomials with neural networks.
method Over-parameterized two-layer neural network with Gradient Descent with Projection.
result Achieves nearly minimax optimal sample complexity and risk bound.
The study provides a generalization bound for a family of implicit networks.
problem Theoretical understanding of implicit networks' generalization is limited.
method A generalization bound is derived for a family of implicit networks using a covering number argument for Rademacher complexity.
result A theoretical generalization bound is established for implicit networks.
A new method reduces complexity and uncertainty in neural networks.
problem Uncertainty quantification in complex neural networks.
method Condensed Stein Variational Gradient Descent (cSVGD) method.
result Condensed SVGD provides uncertainty quantification on parameters.
Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and prevents the network from overfitting. In this work, we introduce the gradient gap d…
Bézier-GAN optimizes airfoil design by reducing shape complexity.
problem High computational cost in aerodynamic shape optimization.
method Generative adversarial networks (GANs) to learn compact shape representations.
result Empirically accelerates optimization convergence by at least two times.
MO-PaDGAN improves multi-objective optimization by generating diverse and high-performing designs.
problem Challenges in parameterizing engineering designs for multi-objective optimization.
method MO-PaDGAN uses a generative adversarial network with a Determinantal Point Processes loss function to address these challenges.
result MO-PaDGAN generates designs with improved performance and coverage, even surpassing training data.
The paper axiomatizes strong emergence in parameterized field theories and proves existence theorems.
problem Formalizing and proving existence of strong emergence in parameterized field theories.
method Axiomatization and proof of existence theorems for strong emergence between Lagrangian field theories.
result Existence of strong emergence phenomena between parameterized Lagrangian field theories.
We introduce new definitions of universal and superuniversal computable codes, which are based on a code's ability to approximate Kolmogorov complexity within the prescribed margin for all individual sequences from a given set. Such sets of sequences may be singled out almost surely with respect to certain probability …
Bounds projective structure norms by bending lamination lengths.
problem Bounding the -norm of projective structures.
method Using the Thurston parameterization and Krasnov-Schlenker's -volume theory.
result Upper bounds on -norm of holomorphic quadratic differential by the length of bending lamination.
The paper introduces various canonical parameterizations for 2D-curved shapes.
problem Comparing unparameterized simple curves in the plane.
method Proposes diverse canonical parameterizations, including arc-length and curvature-based.
result Natural parameterizations correspond to physical movements and are geometric invariants.
The recently proposed option-critic architecture Bacon et al. provide a stochastic policy gradient approach to hierarchical reinforcement learning. Specifically, they provide a way to estimate the gradient of the expected discounted return with respect to parameters that define a finite number of temporally extended ac…
Bayesian Double Descentstat.ML
Bayesian interpretation explains double descent in deep learning models.
problem Understanding the risk function behavior of over-parameterized models.
method Bayesian model selection, Dickey-Savage ratio, ridge regression, global-local shrinkage.
result Double descent phenomenon explained through Bayesian interpretation.
New parameterization of Teichmüller spaces for complex Lie groups.
problem Classifying special components of moduli spaces of Higgs bundles.
method Introducing magical -triples and using their decomposition data.
result Constructs previously unknown components of higher Teichmüller spaces.
Introduces a neural network-based method for efficient state and parameter estimation in complex systems.
problem Efficiently estimating state paths and parameters from noisy measurements in high-dimensional nonlinear systems.
method Bayesian Information Field Theory with neural network parameterization and optimization algorithms.
result Proposes a method to simplify and enrich state path parameterizations using neural networks, improving inference accuracy.
There are currently two parameterizations used to derive fixed kernels corresponding to infinite width neural networks, the NTK (Neural Tangent Kernel) parameterization and the naive standard parameterization. However, the extrapolation of both of these parameterizations to infinite width is problematic. The standard p…
Proposes a new approach to generate sparse models from deep networks.
problem Training small networks can get stuck in local optima; over-parameterized models are preferred.
method Differential inclusion paths to generate a family of models from simple to complex.
result Algorithm converges to a critical point of empirical risks from any initializations.
The literature about history matching is vast and despite the impressive number of methods proposed and the significant progresses reported in the last decade, conditioning reservoir models to dynamic data is still a challenging task. Ensemble-based methods are among the most successful and efficient techniques current…
It is well known that quantifying uncertainty in the action-value estimates is crucial for efficient exploration in reinforcement learning. Ensemble sampling offers a relatively computationally tractable way of doing this using randomized value functions. However, it still requires a huge amount of computational resour…
New method reduces DSI complexity using RAE and LSTM for better posterior predictions.
problem Reducing complexity in data-space inversion for subsurface flow simulations.
method Recurrent Autoencoder (RAE) for dimension reduction and LSTM for flow-rate time series representation.
result RAE-based parameterization outperforms existing DSI treatments in statistical agreement with reference results.
Training neural networks is hard in fixed dimensions.
problem Training two-layer neural networks is computationally hard in fixed dimensions.
method Parameterized complexity analysis considering dimension and number of neurons.
result Training two-layer neural networks is NP-hard for two dimensions.
Optimal Morse matchings reveal essential structures of cell complexes which lead to powerful tools to study discrete geometrical objects, in particular discrete 3-manifolds. However, such matchings are known to be NP-hard to compute on 3-manifolds, through a reduction to the erasability problem. Here, we refine the stu…
New insights into training ReLU networks, especially as data dimensionality increases.
problem Understanding computational complexity of training ReLU networks with varying data dimensions.
method Analyzed the parameterized complexity of two-layer ReLU networks with respect to various loss functions, focusing on the influence of data dimensionality.
result Running time lower bounds and optimal brute-force strategies for training ReLU networks, extending previous results to broader loss functions.
Study motion planning for points avoiding obstacles in a plane.
problem Avoiding collisions for multiple points in a plane with unknown obstacles.
method Algebraic and topological tools for motion planning.
result New topological complexity for planar motion planning.
New parameterization for -knots simplifies their study.
problem Parameterizing -knots in a novel way.
method From minimal-length representatives of arcs in the multipunctured plane.
result Introduced parameterization is essentially unique for satellite -knots.
The matrix rate of returnphysics.soc-ph
In this paper we give definitions of matrix rates of return which do not depend on the choice of basis describing baskets. We give their economic interpretation. The matrix rate of return describes baskets of arbitrary type and extends portfolio analysis to the complex variable domain. This allows us for simultaneous a…
hyperSBINN improves drug cardiosafety assessment by efficiently modeling cardiac action potentials.
problem Complexity and limited data in modeling cardiac effects of drugs.
method Combining meta-learning with SBINNs to solve parameterized cardiac action potential models.
result hyperSBINN outperforms traditional solvers in speed and accuracy for predicting APD90 values.
This paper studies neural networks with bounded norms to avoid the curse of dimensionality.
problem The curse of dimensionality in approximating functions by neural networks.
method Investigates over-parameterized two-layer neural networks with norm constraints in RKHS.
result Improved sample complexity and generalization bounds for neural networks with bounded norms.
We show that strongly contracting geodesics in Outer space project to parameterized quasigeodesics in the free factor complex. This result provides a converse to a theorem of Bestvina--Feighn, and is used to give conditions for when a subgroup of has a quasi-isometric orbit map into the free …
Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz '96 Modelphysics.ao-ph
Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant str…