Optimal Euclidean structure minimizes energy in weighted toroidal graphs.
problem Finding the optimal Euclidean structure for weighted toroidal graphs.
method Minimizing Dirichlet energy over all possible Euclidean structures and realizations within a fixed homotopy class.
result The optimal Euclidean structure induces a weighted Delaunay decomposition.
In the present paper, we study deformations of polar weighted homogeneous polynomials which are also polar weighted homogeneous polynomials. We describe a round handle decomposition of the Milnor fibration of a deformation of a polar weighted homogeneous polynomial concretely and give the number of round handles by the…
We study in detail Hodge-Helmholtz decompositions in non-smooth exterior domains filled with inhomogeneous and anisotropic media. We show decompositions of alternating differential forms belonging to weighted Sobolev spaces into irrotational and solenoidal forms. These decompositions are essential tools, for example, i…
CDFD analyzes circularity and directionality in weighted directed networks.
problem Analyzing circularity and directionality in weighted directed networks.
method CDFD framework separates flow into circular and acyclic components.
result CDFD yields a normalized circularity index capturing flow in cycles and directionality.
Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.
problem Finding optimal discrete harmonic maps between hyperbolic surfaces.
method Minimizing Dirichlet energy over all possible hyperbolic structures and realizations within a fixed homotopy class.
result At the optimal hyperbolic structure, the discrete harmonic map and edge weights are induced from a weighted Delaunay decomposition.
Tensor decomposition methods are popular tools for learning latent variables given only lower-order moments of the data. However, the standard assumption is that we have sufficient data to estimate these moments to high accuracy. In this work, we consider the case in which certain dimensions of the data are not always …
We consider a decomposition method for compressive streaming data in the context of online compressive Robust Principle Component Analysis (RPCA). The proposed decomposition solves an n-ℓ1 cluster-weighted minimization to decompose a sequence of frames (or vectors), into sparse and low-rank components, from com…
The paper provides precise estimates for isoperimetric inequalities on weighted manifolds.
problem Quantitative isoperimetric inequalities on weighted Riemannian manifolds.
method Analyzes L1, Lp, and W2 estimates for the push-forward of measures. result Close approximation of the guiding function's push-forward to Gaussian measure.
The study examines Fisher information matrices and neural tangent kernels for simple ReLU networks with random weights.
problem Understanding the relationship between Fisher information matrices and neural tangent kernels for 2-layer ReLU networks.
method Analyzes Fisher information matrices and neural tangent kernels for 2-layer ReLU networks with random hidden weights, focusing on spectral decomposition and eigenfunctions.
result Obtained an approximation formula for functions represented by 2-layer neural networks.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
problem Handling large-scale tensor data with missing entries and outliers.
method Auto-weighted steepest descent method for missing entries and outliers identification, FGMC and RStS strategies.
result Outperforms existing TR decomposition methods in the presence of outliers and runs faster than robust tensor completion algorithms.
Study evaluates thresholds for removing noise from DNN weights using random matrix theory.
problem Removing noise from deep neural network weights for better approximation.
method Model weights as signal + noise, use random matrix theory to estimate thresholds, evaluate using cosine similarity.
result Proposed threshold estimation method improves approximation quality.
MSD removes dequantization bottleneck in LLM inference by approximating high-precision activations.
problem Dequantization bottleneck in LLM inference on modern AI accelerators.
method MSD decomposes high-precision activations into multiple low-precision components for direct multiplication with quantized weights.
result MSD avoids INT8-to-BF16 weight conversion, reducing dequantization cycles and HBM traffic.
We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
problem Efficiency and stability in deep learning models with weight matrix compression.
method Spectral Tensor Train Parameterization (STTP) of weight matrices.
result Improved compression and training stability in neural networks.
We establish connections between the problem of learning a two-layer neural network and tensor decomposition. We consider a model with feature vectors x∈Rd, r hidden units with weights {wi}1≤i≤r and output y∈R, i.e., $y=\sum_{i=1}^r σ( \boldsymbol w_i…
The paper analyzes how re-weighting helps in reducing variance in high-dimensional kernel methods under covariate shifts.
problem The challenge of high-dimensional kernel methods under covariate shifts and the role of re-weighting.
method Derives asymptotic expansion of high-dimensional kernels under covariate shifts, analyzes bias-variance decomposition, and characterizes the regularized kernel.
result Re-weighting helps in decreasing variance and can be seen as a data-dependent regularization.
A new kernel improves tensor classification accuracy and reduces computation time.
problem Challenges in classifying high-dimensional tensor data.
method Proposes a weighted subspace exponential kernel based on Tucker decomposition.
result The new kernel outperforms existing methods in accuracy and computational efficiency.
Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…
Updated polynomial for virtual tangles, compatible with decompositions.
problem Generalizing polynomial for virtual tangles.
method Updated multi-variable affine index polynomial, introduced Turaev moves.
result Polynomial compatible with tangle decompositions and crossing weight recovery.
In this paper we study the problem of learning the weights of a deep convolutional neural network. We consider a network where convolutions are carried out over non-overlapping patches with a single kernel in each layer. We develop an algorithm for simultaneously learning all the kernels from the training data. Our app…
LoRAs enable efficient adaptation of large models; this paper explores processing LoRA weights with machine learning.
problem Efficient processing of low-rank weight decompositions in large finetuned models.
method Developed symmetry-aware invariant and equivariant LoL models to process LoRA weights.
result LoL models can predict CLIP scores, finetuning data attributes, and accuracy on downstream tasks.
Researchers determined the second homology group of a specific symplectic derivation Lie algebra.
problem Determining the entire homology group of a specific symplectic derivation Lie algebra.
method Used classical representation theory of Sp(2g; Q) and weight decomposition.
result Determined H_2(\mathfrak{c}_g^{+})
The monitoring and management of numerous and diverse time series data at Alibaba Group calls for an effective and scalable time series anomaly detection service. In this paper, we propose RobustTAD, a Robust Time series Anomaly Detection framework by integrating robust seasonal-trend decomposition and convolutional ne…
Simplified analysis of SGD for linear regression with weight averaging.
problem Understanding SGD optimization in linear regression models.
method Simplified analysis using linear algebra tools, bypassing complex operator manipulations.
result Recovery of bias and variance bounds for SGD in linear regression.
Develops exact and invariant study-based decompositions for network meta-analysis.
problem Lack of exact contribution decompositions in network meta-analysis.
method Contrast-space projection formulation of NMA, study-based definition of direct and indirect evidence.
result Exact covariance-aware decompositions of NMA estimator into direct and indirect contributions.
Paper identifies key function spaces for ReLU networks based on Fisher information.
problem Understanding the structure of Fisher information matrices in ReLU networks.
method Spectral decomposition of Fisher information matrices, focusing on the first three eigenspaces.
result The first three eigenspaces account for 97.7% of the trace of the Fisher information matrix, corresponding to spherical harmonic functions of order ≤2.
Wide neural networks learn features under μP, identifying weights and decomposing support.
problem Feature learning in wide neural networks under μP. method Proving mean-field limit, characterizing identifiability, sparse-dictionary decomposition, and feature-learning-error decomposition.
result The triple (w∗,Dorb∗,S∗) identifies the natural learning cell of the architecture-data pair (σ,ρ). Counting HCMU sphere components using weighted trees.
problem Counting components of moduli space of HCMU spheres.
method Using weighted plane trees to characterize HCMU spheres with a single integral conical angle, and an explicit counting formula is derived.
result An explicit counting formula for the components of the moduli space of HCMU spheres.
New criteria for ideal circle patterns on surfaces.
problem Determining when a surface supports ideal circle patterns.
method Introducing a character L(D,Φ) and using combinatorial Ricci flows. result Simpler and more easily verifiable criteria for ideal circle patterns.
A new tensor ring mixture model improves density estimation efficiency.
problem Efficient probability density estimation in statistical machine learning.
method Tensor ring decomposition with mixture model for adaptive weights.
result Enhanced expressive capability and flexibility in density estimation.
Random braids that are formed by multiplying randomly chosen permutation braids are studied by analyzing their behavior under Garside's weighted decomposition and cycling. Using this analysis, we propose a polynomial-time algorithm to the conjugacy problem that is successful for random braids in overwhelming probabilit…
CW-EDMD improves prediction accuracy by learning local Koopman models for different state-space regions.
problem Inefficient global Koopman operator approximation for distinct local dynamics.
method Cluster-Weighted EDMD (CW-EDMD) learns a soft phase-space partition and per-cluster EDMD operators using EM objective.
result CW-EDMD significantly reduces prediction errors across various systems and configurations.
Normal forms and moduli stacks for flat connections on complex manifolds.
problem Understanding singular flat connections on complex manifolds.
method Introducing homogeneous Lie groupoids and studying their representation theory to prove normal form theorems and moduli space structures.
result Moduli spaces of singular flat connections admit the structure of algebraic quotient stacks.
Develops HCQRF for estimating heterogeneous treatment effects with censored data.
problem Estimating heterogeneous treatment effects on censored responses with high-dimensional variables.
method Hybrid Censored Quantile Regression Forest (HCQRF) combining random forests and censored quantile regression.
result Demonstrates the effectiveness and stability of HCQRF through simulation studies and real-world application.
Unified local and global explanations through functional decomposition of low dimensional structures.
problem Tackles the challenge of extracting meaningful local and global explanations from machine learning models.
method Proposes a new identification constraint to decompose the global representation into main and interaction components of arbitrary order.
result Unified local and global explanations by connecting partial dependence plots and interventional SHAP values.
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
We prove the quasimodularity of generating functions for counting torus covers, with and without Siegel-Veech weight. Our proof is based on analyzing decompositions of flat surfaces into horizontal cylinders. The quasimodularity arise as contour integral of quasi-elliptic functions. It provides an alternative proof of …
Proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
problem Existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
method Construct an isotopic map instead of edge-flipping algorithm, generalizing Dyer et al's method.
result Strict proof of existence and uniqueness of weighted Voronoi-Delaunay on polyhedral surfaces.
KEDformer improves long-term time series forecasting with seasonal-trend decomposition.
problem Accurate long-term predictions in energy, finance, and meteorology.
method Knowledge extraction-driven framework integrating seasonal-trend decomposition.
result KEDformer enhances model's ability to capture short-term and long-term patterns.
A new method for computing image curvature efficiently and accurately.
problem Low performance, low accuracy, and requirement of second order differentiability in conventional computation schemes.
method Proposes a novel discrete computation scheme for weighted Gaussian curvature.
result More accurate, computationally more efficient, and does not require second order differentiability.
Optimizes mixture models without parametrizing distributions using tensor decomposition.
problem Estimating conditionally-independent mixture models in high dimensions.
method Alternating least squares optimization scheme for tensor decomposition.
result Competitive performance and applicability to various models and applications.
The paper analyzes prediction error in nonstationary settings using weighted risk minimization.
problem Prediction under distribution drift and nonstationary conditions.
method General decomposition of excess risk into learning and drift terms, proving oracle inequalities under mixing conditions.
result Oracle inequalities for the learning error, providing bounds that hold uniformly over arbitrary weight classes.
Optimizes neural network training by dynamically updating Tucker decomposition ranks.
problem Redundant parameters in neural network architectures.
method Geometry-aware training of factorized layers in tensor Tucker format.
result Optimal locally approximating the original dynamics without initial rank knowledge.
Paper studies matching of samples from two distributions with a Gibbs probability weight.
problem Matching two independent i.i.d. samples from two distributions with a weighted cost.
method Uses chaos decomposition of polynomial functions of empirical distributions to derive asymptotics.
result Convergence of resulting random joint distribution to Schrödinger problem solution as N→∞.
Unified framework HASSLE-free decomposes large model weights into sparse and low-rank components.
problem Efficiently compress large foundation models to reduce inference costs.
method Designs a unified framework for sparse plus low-rank matrix decomposition with a local layer-wise reconstruction error objective.
result HASSLE-free framework significantly outperforms state-of-the-art methods in compression and evaluation benchmarks.
A family of parsimonious Gaussian cluster-weighted models is presented. This family concerns a multivariate extension to cluster-weighted modelling that can account for correlations between multivariate responses. Parsimony is attained by constraining parts of an eigen-decomposition imposed on the component covariance …
Klartag recently gave a beautiful alternative proof of the isoperimetric inequalities of Levy-Gromov, Bakry-Ledoux, Bayle and E. Milman on weighted Riemannian manifolds. Klartag's approach is based on a generalization of the localization method (so-called needle decompositions) in convex geometry, inspired also by opti…
We give a general description of the construction of weighted spherically symmetric metrics on vector bundle manifolds, i.e. the total space of a vector bundle E→M, over a Riemannian manifold M, when E is endowed with a metric connection. The tangent bundle of E admits a canonical decomposition and t…
Unified formula for arbitrary liquidity operations in weighted AMMs
problem Decentralized resource allocation in intelligent transportation systems
method Weighted invariant adapted from Balancer-type AMMs
result Unified formula for four resource allocation operations