Review and compare model order reduction methods for process engineering.
problem Creating computationally efficient yet accurate models for real-time applications.
method Nonlinear model order reduction methods, including general-purpose and tailored approaches for chemical processes.
result Comparison of eight model order reduction methods applied to an air separation process model.
We give a simple explicit formula for turnover reduction when a large number of alphas are traded on the same execution platform and trades are crossed internally. We model turnover reduction via alpha correlations. Then, for a large number of alphas, turnover reduction is related to the largest eigenvalue and the corr…
A new construction of naturally reductive spaces is presented. This construction gives a large amount of new families of naturally reductive spaces. First the infinitesimal models of the new naturally reductive spaces are constructed. A concrete transitive group of isometries is given for the new spaces and also the na…
Adapts DR objectives for both sample and feature size reduction.
problem Simultaneously reduce sample and feature sizes.
method Semi-relaxed Gromov-Wasserstein optimal transport.
result OT plan delivers competitive hard clustering.
This paper proposes BRIEF, a backward reduction algorithm that explores compact CNN-model designs from the information flow perspective. This algorithm can remove substantial non-zero weighting parameters (redundant neural channels) of a network by considering its dynamic behavior, which traditional model-compaction te…
Efficiently transforms samples from various statistical models.
problem Approximately transforming samples from one statistical model to another without knowing the source model's parameters.
method Constructs computationally efficient procedures to reduce uniform, Erlang, and Laplace models to general target families.
result Establishes nonasymptotic reductions between canonical high-dimensional problems, such as mixtures of experts, phase retrieval, and signal denoising.
Paper compares Lagrangian reduction methods for rigid body systems.
problem Modeling and reduction of rigid body systems with rotors.
method Euler-Poincaré reduction by the whole group and reduction by stages.
result Equivalence of equations and conservation laws are tracked.
Optimizes variance reduction in Heston model using large and moderate deviations.
problem Improving variance reduction in stochastic volatility models.
method Large and moderate deviations theory applied to Heston model.
result Derives closed-form solutions for optimal change of measure.
MARS optimizes large model training by reducing variance, outperforming AdamW.
problem Training large models efficiently and scalably.
method Unified optimization framework MARS combining preconditioned gradient updates and variance reduction.
result MARS outperforms AdamW in training GPT-2 models.
A method constructs a stochastic surrogate from dimensionality reduction results for high-dimensional uncertainty quantification.
problem High-dimensional uncertainty quantification with physics-based models.
method Constructs a stochastic surrogate model from dimensionality reduction results.
result Preserves convenience of sequential dimensionality reduction and Gaussian process regression while overcoming limitations.
Enhances SDR via Hellinger correlation for better data dependency understanding.
problem Improving sufficient dimension reduction in single-index models.
method Developed a new method using Hellinger correlation for detecting the dimension reduction subspace.
result Significantly enhances and outperforms existing SDR methods through deeper data dependency understanding.
Efficiently reduces rank of non-negative matrices with quadratic time complexity.
problem Efficiently reducing the rank of non-negative matrices.
method Formulated rank reduction as a mean-field approximation using a log-linear model.
result Optimal solution for minimizing KL divergence can be computed in closed form.
Data balancing reduces variance in machine learning models.
problem Reduction of variance in machine learning models.
method Non-asymptotic statistical bound and eigenvalue decay of Markov operators.
result Data balancing across modalities and sources reduces variance.
New algorithm balances spatial data approximation and prediction accuracy.
problem Lack of methods considering spatial correlation and downstream modeling in dimension reduction.
method Formalizes approximation and modeling utility as metrics, proposes a balanced algorithm.
result Optimal trade-off between approximation accuracy and downstream modeling utility.
In statistical learning, high covariate dimensionality poses challenges for robust prediction and inference. To address this challenge, supervised dimension reduction is often performed, where dependence on the outcome is maximized for a selected covariate subspace with smaller dimensionality. Prevalent dimension reduc…
The BC(n) Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups o…
Reduces complexity of financial contagion dynamics on networks.
problem Complexity of financial contagion dynamics on networks.
method Dimensional reduction methods (degree-weighted and spectral reduction).
result Spectral reduction better handles heterogeneous networks.
Proposes a new category of bundles for Lagrangian reduction in field theory.
problem Lagrangian reduction in field theory.
method Introduces a category of bundles to perform Lagrangian reduction by stages in covariant Field Theory.
result Formulates the Noether theorem in this new theoretical framework.
This work examines consistency issues in Gaussian Mixture Model reduction algorithms.
problem Consistency issues in Gaussian Mixture Model reduction algorithms.
method Discussion of the importance of dissimilarity measure choice and consistency of GMR algorithms.
result Most existing GMR algorithms are not consistent with a unique measure, leading to suboptimal reduced GMs.
A new method for reducing model complexity using neural active manifolds.
problem Uncertainty quantification in computationally expensive models.
method Autoencoders and surrogate models to discover a neural active manifold.
result Neural active manifolds reduce model variance in multifidelity sampling.
Unified model for reducing dimensions and clustering high-dimensional data.
problem High-dimensional data clustering and dimensionality reduction.
method Hierarchical mixtures of Gaussians (HMoGs) with closed-form likelihood and inference.
result Efficiently models hundreds of latent dimensions, improving clustering performance.
A new framework learns clustering and dimensionality reduction together.
problem Challenges in clustering high-dimensional data.
method Gradient-based manifold optimization for joint learning.
result Better performance compared to existing clustering algorithms.
Reduces field theories using Poisson-Poincaré method.
problem Reduction of field theories using Poisson-Poincaré method.
method Poisson-Poincaré reduction for field theories.
result Reduction procedure for field theories.
We obtain universal models for several types of locally conformal symplectic manifolds via pullback or reduction. The relation with recent embedding results for locally conformal Kähler manifolds is discussed.
New optimizer MARS-M combines variance reduction with Muon for faster LLM training.
problem Training large-scale neural networks efficiently.
method Integrates MARS variance reduction with Muon optimizer.
result MARS-M converges to a first-order stationary point at a rate of ildeO(T−1/3). Develops a new method for nonlinear dimension reduction using random features.
problem Statistical challenges in generalizing Gaussian process-based latent variable models to non-Gaussian data.
method Random feature latent variable models (RFLVMs) that approximate nonlinear relationships with linear functions of random features.
result RFLVMs produce comparable results to state-of-the-art methods on various data types.
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be reduced resulting in compact representations of shape and spatial structure. Th…
Bayesian framework reduces high-dimensional GP modeling costs.
problem Challenges in fitting Gaussian processes to high-dimensional inputs.
method Hierarchical Bayesian model with orthonormal projection matrix, incorporating Deep Gaussian Processes.
result Improves predictive performance and uncertainty quantification.
A model order reduction framework reduces financial risk analysis models efficiently.
problem Simulating high-dimensional financial risk models.
method Adaptive greedy sampling based on POD and surrogate modeling.
result Reduced models provide significant speedup with excellent accuracy.
In this paper we propose the macroblock scaling (MBS) algorithm, which can be applied to various CNN architectures to reduce their model size. MBS adaptively reduces each CNN macroblock depending on its information redundancy measured by our proposed effective flops. Empirical studies conducted with ImageNet and CIFAR-…
This paper reviews and compares supervised linear dimension-reduction techniques.
problem Lack of information in the response during unsupervised PCA reduces predictive performance.
method Review and comparison of supervised linear dimension-reduction techniques.
result PLS and LSPCA consistently outperform other techniques in simulations.
The paper simplifies complex jump-diffusion markets to complete models.
problem Pricing and hedging derivatives in incomplete jump-diffusion markets.
method Filtration reduction to a complete market, then consistency to original market.
result A unique equivalent martingale measure is obtained for pricing.
This paper addresses overfitting in dimension reduction methods by calibrating hyperparameters considering noise.
problem Overfitting in dimension reduction methods, especially t-SNE and UMAP, when data contains noise.
method Present a framework to calibrate hyperparameters in the presence of noise for t-SNE and UMAP.
result Recommended hyperparameter values for t-SNE and UMAP are too small and overfit the noise.
WeldNet reduces complex dynamics to simpler, manageable segments.
problem Complex, high-dimensional time-dependent datasets from physical processes are costly to simulate.
method Windowed Encoders for Learning Dynamics, splitting time domain into windows for nonlinear dimension reduction and propagator training.
result WeldNet captures nonlinear latent structures and dynamics, outperforming existing methods.
This paper identifies knot projections with reductivity two.
problem Determining knot projections with a specific reductivity level.
method Examined four types of reductivity (Seifert type splice, non-Seifert type splice, recursively, simultaneously) and their combinations.
result Identified all knot projections with reductivity two for the four definitions.
RMFGP combines multi-fidelity models for efficient uncertainty quantification.
problem Efficiently infer quantities of interest with limited high-fidelity data.
method Rotated multi-fidelity Gaussian process with dimension reduction and Bayesian active learning.
result RMFGP model improves accuracy and efficiency in high-dimensional problems.
The un-reduction procedure introduced previously in the context of Mechanics is extended to covariant Field Theory. The new covariant un-reduction procedure is applied to the problem of shape matching of images which depend on more than one independent variable (for instance, time and an additional labelling parameter)…
Efficiently transforms Gaussian data to simulate various target distributions.
problem Generating observations from different target distributions given a single Gaussian observation.
method Designs computationally efficient procedures to approximate target distributions.
result Establishes reduction-based computational lower bounds for high-dimensional statistical models.
Modeling data as being sampled from a union of independent subspaces has been widely applied to a number of real world applications. However, dimensionality reduction approaches that theoretically preserve this independence assumption have not been well studied. Our key contribution is to show that 2K projection vect…
This paper classifies instantons with closed reductions and provides examples of non-closed reductions.
problem Understanding the geometry of toric Kähler instantons with and without closed reductions.
method Sharp geometric criteria and examples of instantons with different reduction types.
result Established geometric criteria for closed reductions and classified asymptotic geometries.
Paper interprets UMAP and t-SNE as probabilistic MAP inference.
problem Understanding and interpreting UMAP and t-SNE.
method Interprets UMAP and t-SNE as MAP inference methods corresponding to a probabilistic model of the graph Laplacian.
result Shows UMAP and t-SNE can be understood as probabilistic inference methods.
Paper reduces vocabulary losslessly for language model cooperation.
problem Language models struggle to cooperate with different tokenizations.
method Established a theoretical framework for lossless vocabulary reduction.
result Efficiently converts models with different tokenizations to cooperate with maximal common vocabulary.
We consider locally conformal Kaehler geometry as an equivariant (homothetic) Kaehler geometry: a locally conformal Kaehler manifold is, up to equivalence, a pair (K,Γ) where K is a Kaehler manifold and Γa discrete Lie group of biholomorphic homotheties acting freely and properly discontinuously. We define a new invari…
In this paper we describe Routhian reduction as a special case of standard symplectic reduction, also called Marsden-Weinstein reduction. We use this correspondence to present a generalization of Routhian reduction for quasi-invariant Lagrangians, i.e. Lagrangians that are invariant up to a total time derivative. We sh…
Two reduction schemes for symplectic manifolds are shown equivalent.
problem Reduction of Hamiltonian systems on exact symplectic manifolds.
method Modified Marsden-Meyer-Weinstein reduction theorem for exact symplectic manifolds and contact manifolds.
result Reduction schemes are equivalent for exact symplectic manifolds and energy hypersurfaces.
The study reveals how synaptic correlations promote dimension reduction in neural networks.
problem Understanding how synaptic correlations affect neural correlations and dimension reduction in deep neural networks.
method A simplified model of dimension reduction considering pairwise correlations among synapses, using mathematical self-consistency for both binary and continuous synapses.
result Weakly-correlated synapses encourage dimension reduction compared to orthogonal synapses, and they also slow down the decorrelation process.
Study extends Kobayashi's method to non-reductive subgroups for homogeneous spaces.
problem Existence of compact Clifford-Klein forms in homogeneous spaces.
method Extend Kobayashi's method to non-reductive subgroups and compare Cartan projections and non-compact dimensions.
result Examples of homogeneous spaces without compact Clifford-Klein forms.
The purpose of this paper is to generalize the regular Optimal Reduction Theorem to general proper Dirac actions, formulated both in terms of point and orbit reduction. A comparison to general standard singular Dirac reduction is given emphasizing the desingularization role played by optimal reduction.