Region crossing change is a local operation on link diagrams. The behavior of region crossing change on is well understood. In this paper, we study the behavior of (modified) region crossing change on higher genus surfaces.
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48 results for “Local Region Behavior”
Develops a new fuzzy model using QPs and ewl2 regularization to improve local region behavior.
problem Inability of constant and linear functions to accurately describe local regions in fuzzy models.
method Applied Fuzzy C-Means for structure identification, used QPs as consequents, introduced ewl2 regularization.
result Improved model's ability to describe local regions without overfitting.
MD-split+ creates locally valid prediction regions for complex data.
problem Localized prediction regions for complex data.
method Localized model performance-based partitioning of feature space X.
result MD-split+ creates valid prediction regions that scale to high dimensions.
A deep neural network (DNN) with piecewise linear activations can partition the input space into numerous small linear regions, where different linear functions are fitted. It is believed that the number of these regions represents the expressivity of the DNN. This paper provides a novel and meticulous perspective to l…
Score-Based Change-Point Detection and Region Localization for Spatio-Temporal Point Processesstat.ME
New method detects and locates changes in spatio-temporal point processes.
problem Detecting and localizing changes in spatio-temporal data.
method Score-based, likelihood-free approach estimating change time and region.
result The method provides theoretical guarantees on detection and localization accuracy.
Local robustness ensures that a model classifies all inputs within an -ball consistently, which precludes various forms of adversarial inputs. In this paper, we present a fast procedure for checking local robustness in feed-forward neural networks with piecewise-linear activation functions. Such networks partit…
GRANITE: A Generalized Regional Framework for Identifying Agreement in Feature-Based Explanationsstat.ML
GRANITE unifies feature-based explanation methods to reduce disagreement.
problem Disagreement among feature-based explanation methods.
method GRANITE partitions feature space into regions minimizing interaction and distribution influences.
result Unified and consistent feature explanations.
Deep networks realize complex mappings that are often understood by their locally linear behavior at or around points of interest. For example, we use the derivative of the mapping with respect to its inputs for sensitivity analysis, or to explain (obtain coordinate relevance for) a prediction. One key challenge is tha…
There are few papers about the consumption pattern of the Portuguese wine, using econometrics techniques. This work, pretend to analyze the consumers behavior of the wine produced in Portugal, determining the demand equation with panel data methods. There were used statistical data available in the Alentejo Regional Wi…
Traversing the Local Polytopes of ReLU Neural Networks: A Unified Approach for Network Verificationcs.LG
Unified approach to verify NN properties using ReLU's unique polytope structure.
problem Lack of robustness and interpretability in ReLU NNs for risk-sensitive applications.
method Identifying and traversing the local polytopes of ReLU NNs, developing an algorithm to verify properties.
result Unified approach to examine network behavior in risk-sensitive settings.
In this paper, we investigate the geometry of a general class of gradient flows with multiple local maxima. we decompose the underlying space into disjoint regions of attraction and establish the adjacency criterion. The criterion states a necessary and sufficient condition for two regions of attraction of stable equil…
Analyzes how learning algorithms affect and are affected by data manipulation.
problem Characterizing the closed-loop behavior of learning algorithms in the presence of decision-dependent data.
method Analyzes repeated risk minimization as perturbed gradient flows of performative risk minimization, considering multiple local minimizers.
result Characterizes the region of attraction for various equilibria and introduces performative alignment.
In this paper we have analyzed scaling properties and cyclical behavior of the three types of stock market indexes (SMI) time series: data belonging to stock markets of developed economies, emerging economies, and of the underdeveloped or transitional economies. We have used two techniques of data analysis to obtain an…
Characterizes the local diffeomorphism structure of the exponential in the set of skew-symmetric matrices.
problem Characterizing the local diffeomorphism structure of the exponential in the set of skew-symmetric matrices.
method Introduce the diffeomorphic logarithm of special orthogonal matrices and an efficient algorithm.
result The region containing the principal logarithm has a special multiplicity structure.
The study calculates Weyl entropy in spacetime regions and shows its monotonic behavior.
problem Calculating and understanding Weyl entropy in spacetime regions.
method Introducing a candidate density for Weyl entropy in perfect fluid regions and analyzing its behavior in compact spacetime regions.
result Weyl entropy is shown to be monotonic in time and maximal in vacuum static metrics.
Proximal policy optimization (PPO) is one of the most popular deep reinforcement learning (RL) methods, achieving state-of-the-art performance across a wide range of challenging tasks. However, as a model-free RL method, the success of PPO relies heavily on the effectiveness of its exploratory policy search. In this pa…
Biometrics emerged as a robust solution for security systems. However, given the dissemination of biometric applications, criminals are developing techniques to circumvent them by simulating physical or behavioral traits of legal users (spoofing attacks). Despite face being a promising characteristic due to its univers…
In this work, an ensemble of economic interacting agents is considered. The agents are arranged in a linear array where only local couplings are allowed. The deterministic dynamics of each agent is given by a map. This map is expressed by two factors. The first one is a linear term that models the expansion of the agen…
Adaptive optimization methods bias neural network trajectories towards regions of lower local geometry.
problem The success of adaptive optimization methods in neural networks is not fully explained by traditional second-order methods.
method Local trajectory analysis and introduction of a new statistic .
result Adaptive methods like Adam bias trajectories towards regions of lower local geometry, leading to faster convergence.
Study of SGD with state-dependent noise, improving escape from local minima.
problem Understanding and improving the dynamics of SGD in non-convex optimization.
method Formal study on SGD with state-dependent noise, proposing power-law dynamic with state-dependent diffusion.
result Power-law dynamic can escape from sharp minima exponentially faster than flat minima.
In this paper, we prove that region crossing change on a link diagram is an unknotting operation if and only if the link is proper. A description of the behavior of region crossing change on link diagrams is given. Furthermore we also discuss the relation between region crossing change and the Arf invariant of proper l…
The problem of explaining deep learning models, and model predictions generally, has attracted intensive interest recently. Many successful approaches forgo global approximations in order to provide more faithful local interpretations of the model's behavior. LIME develops multiple interpretable models, each approximat…
Improved genetic programming by optimizing mutation operators for continuous program search.
problem Small syntactic mutations in genetic programming can lead to unpredictable behavioral shifts.
method Learned a compact trading-strategy DSL, created a block-factorized embedding, and designed geometry-compiled mutation operators.
result Geometry-compiled mutation operators discover strong strategies using fewer evaluations and achieve higher Sharpe ratios.
Local Communication Protocols for Learning Complex Swarm Behaviors with Deep Reinforcement Learningcs.MA
Swarm systems constitute a challenging problem for reinforcement learning (RL) as the algorithm needs to learn decentralized control policies that can cope with limited local sensing and communication abilities of the agents. While it is often difficult to directly define the behavior of the agents, simple communicatio…
New method R-LOCO improves local feature importance analysis.
problem Local attribution methods fail to accurately identify important features.
method R-LOCO segments input space into regions and applies global methods within.
result R-LOCO delivers more accurate local attributions.
Proposes CLIQUE for improved local variable importance in multi-class classification.
problem Lack of methods to characterize local structure in model loss space.
method CLIQUE (Conditional Local Importance by Quantile Expectations)
result CLIQUE emphasizes locally dependent information and captures interaction behavior.
Intrinsic dimensionality (ID) is one of the most fundamental characteristics of multi-dimensional data point clouds. Knowing ID is crucial to choose the appropriate machine learning approach as well as to understand its behavior and validate it. ID can be computed globally for the whole data point distribution, or comp…
In this paper, we formulate a new local move on virtual knot diagram, called arc shift move. Further, we extend it to another local move called region arc shift defined on a region of a virtual knot diagram. We establish that these arc shift and region arc shift moves are unknotting operations by showing that any virtu…
Simple regional perturbations maintain model transferability while reducing adversarial example distortion.
problem Comparing efficacy of regional adversarial attacks without complex methods.
method Developed a simple regional adversarial perturbation attack using cross-entropy sign.
result Localized adversarial examples require significantly less norm distortion compared to non-local counterparts.
We introduce a local move on a link diagram named a region freeze crossing change which is close to a region crossing change, but not the same. We study similarity and difference between region crossing change and region freeze crossing change.
In the last decade, the digital age has sharply redefined the way we study human behavior. With the advancement of data storage and sensing technologies, electronic records now encompass a diverse spectrum of human activity, ranging from location data, phone and email communication to Twitter activity and open-source c…
Combines global and local search for efficient global optimization with Gaussian processes.
problem Difficulties in building accurate GP models and getting stuck in suboptimal regions.
method Adopting AGLGP model combining global and local GP models, dividing space into regions, and switching between global and local searches.
result Efficiently locates the global optimum with benefits of both global and local search.
GBOC detects anomalies in time series data using granular-ball vectors.
problem Challenges in modeling normal behavior in dynamic, nonlinear time series data.
method Granular-ball Vector Data Description (GVDD) and Granular-ball One-Class Network (GBOC).
result GBOC improves anomaly detection in time series data.
New method improves stability of soft FQI for offline RL.
problem Stability issues in soft FQI under function approximation.
method Stationary reweighting to align operator norms.
result Local linear convergence proved under certain conditions.
Inter-subject registration of cortical areas is necessary in functional imaging (fMRI) studies for making inferences about equivalent brain function across a population. However, many high-level visual brain areas are defined as peaks of functional contrasts whose cortical position is highly variable. As such, most ali…
Novel method for high-dimensional BO using CMA to define local regions.
problem Challenges in applying BO to high-dimensional optimization problems.
method CMA strategy to learn search distribution and define local regions.
result Our method outperforms existing techniques on various benchmarks.
Data-Informed Decomposition for Localized Uncertainty Quantification of Dynamical Systemsphysics.comp-ph
Bayesian framework for identifying localized regions of interest in dynamical systems.
problem Identifying regions of high-resolution uncertainty quantification in complex dynamical systems.
method Bayesian inference with Gaussian process surrogate and polynomial chaos expansion.
result Unified computational scheme reduces overall cost for uncertainty quantification.
Pointwise localization allows more precise localization and accurate interpretability, compared to bounding box, in applications where objects are highly unstructured such as in medical domain. In this work, we focus on weakly supervised localization (WSL) where a model is trained to classify an image and localize regi…
Deep Jump Gaussian Processes model high-dimensional piecewise functions.
problem Modeling high-dimensional piecewise continuous functions with limited accuracy.
method Integrates region-specific locally linear projections with Jump Gaussian Processes (JGP) to capture local low-dimensional subspace structures.
result DJGP achieves superior predictive accuracy and more reliable uncertainty quantification compared to existing methods.
Region crossing change is a local transformation on a knot or link diagram. We show that a region crossing change on a knot diagram is an unknotting operation, and we define the region unknotting numbers for a knot diagram and a knot.
Training-Time Batch Normalization Reshapes Local Partition Geometry in Piecewise-Affine Networkscs.LG
BN refines local partition geometry in piecewise-affine networks during training.
problem Understanding the effect of BN on the function realized during training in piecewise-affine networks.
method Analyzing the geometry of switching hyperplanes and affine-region partition conditioned on a mini-batch.
result BN increases expected local partition refinement in ReLU and piecewise-affine networks.
New bounds ensure reliable deep learning performance without model changes.
problem Certifying deep neural networks' reliability without altering them.
method Data-dependent generalization bounds that apply directly to trained models.
result Achieves meaningful generalization guarantees for large, unaltered deep networks.
Proposes a method to learn system dynamics and region of attraction from trajectories.
problem Learning accurate dynamics and region of attraction from system trajectories.
method Uses local stability information as a prior to learn vector field and region of attraction.
result Efficient sampling and accurate estimate of dynamics in inner approximation of region of attraction.
Localized SVMs maintain SVM's consistency properties for large datasets.
problem Inefficient computational requirements of global SVMs for large data sets.
method Localized SVMs apply different hyperparameters to different regions of the input space.
result Localized SVMs inherit - and risk consistency from global SVMs.
Proposes dynamic model type recommendation for OLP technique.
problem Limited local competence of base-classifiers in uneven data distributions.
method Builds a multi-label meta-classifier to recommend model types based on local data complexity.
result Statistically similar performance to original OLP with fixed base-classifier model.
Deep ReLU networks with extra parameters have mostly good loss landscapes.
problem Finding good local minima in the loss landscape of deep neural networks.
method Analyzing shallow and deep ReLU networks with extra parameters on a generic dataset.
result Most activation patterns correspond to regions with no bad local minima.
The definition of quasi-local mass for a bounded space-like region in space-time is essential in several major unsettled problems in general relativity. The quasi-local mass is expected to be a type of flux integral on the boundary two-surface and should be independent of whichever space-like region it bounds. An impor…
Regional rainfall-runoff modeling is an old but still mostly out-standing problem in Hydrological Sciences. The problem currently is that traditional hydrological models degrade significantly in performance when calibrated for multiple basins together instead of for a single basin alone. In this paper, we propose a nov…