Using bordered Floer theory, we construct an invariant for -orbifolds with singular set a knot that generalizes the hat flavor of Heegaard Floer homology for closed -manifolds . We show that for a large class of -orbifolds,…
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48 results for “ORB features”
Following Riley's work, for each 2-bridge link of slope $r\in\QQ$ and an integer or a half-integer greater than 1, we introduce the {\it Heckoid orbifold $\orbs(r;n)$} and the {\it Heckoid group $\Hecke(r;n)=π_1(\orbs(r;n))$ of index for }. When is an integer, $\orbs(r;n)$ is called an {\it eve…
Method predicts rarity of image features to support research integrity investigations.
problem Difficulty in determining if image reuse is by chance or intentional.
method Statistical estimation of ORB features' chance occurrence across PubMed Open Access Subset dataset.
result The method produces decreasingly smaller p-values for more complex imagery, supporting null hypothesis.
This paper aims to generalize Artin's ideas to establish an one-to-one correspondence between the orbit braid group and a quotient of a group formed by some particular homeomorphisms of a punctured plane. First, we find a faithful representation of $B^{orb}_n(\mathbb{C},\mathbb{Z}_p…
Constructs a family to handle unstable fibers on complex surfaces.
problem Handling unstable fibers on complex surfaces.
method Uses Teichmüller theory to construct a degenerating family over the moduli space.
result Any fibered complex surface with unstable fibers can be pulled back from the constructed family.
We determine several necessary and sufficient conditions for a closed almost-complex orbifold with cyclic local groups to admit a nonvanishing vector field. These conditions are stated separately in terms of the orbifold Euler-Satake characteristics of and its sectors, the Euler characteristics of the underlyin…
We study the Yamabe invariants of cylindrical manifolds and compact orbifolds with a finite number of singularities, by means of conformal geometry and the Atiyah-Patodi-Singer -index theory. For an -orbifold with singularities (where each group $Γ_j<O…
The paper defines a preorder on links and explores its implications for symmetric unions.
problem Understanding the relationships between links and their symmetric unions.
method Defining a preorder relation and proving properties of links and their orbifold groups.
result If a link is a Montesinos link with rational tangles, then is either a Montesinos link with at most rational tangles or a certain connected sum.
Wide neural networks learn features under P, identifying weights and decomposing support.
problem Feature learning in wide neural networks under P.
method Proving mean-field limit, characterizing identifiability, sparse-dictionary decomposition, and feature-learning-error decomposition.
result The triple identifies the natural learning cell of the architecture-data pair .
We give a formula of the connected component decomposition of the Alexander quandle: , where . We show that the connected component is isomorphic to with an expli…
An algorithm for determining the list of smallest volume right-angled hyperbolic polyhedra in dimension 3 is described. This algorithm has been implemented on computer using the program Orb to compute volumes, and the first 825 polyhedra in the list have been determined.
This paper presents a new exact sequence for orbifold braid groups and mapping class groups.
problem Understanding the relationship between orbifold braid groups and mapping class groups.
method Developed an exact sequence and used presentations of orbifold mapping class groups to determine the kernel.
result The kernel of the orbifold braid group is non-trivial and provides a new presentation.
A theory of orbit braidsmath.AT
This paper upbuilds the theoretical framework of orbit braids in by making use of the orbit configuration space , which enriches the theory of ordinary braids, where is a connected topological manifold of dimension at least 2 with an effective action of a finite group and the action of …
Defines fundamental racks for braid spaces of complex reflection groups.
problem Understanding fundamental racks for braid spaces of complex reflection groups.
method Defines an augmented rack associated to the orbifold fundamental group.
result Yields representations of the orbifold fundamental group on the cohomology of the rack space.
Orbifold uniformization of complex algebraic variety via polystable parabolic Higgs bundle
problem Uniformizing complex algebraic varieties using parabolic Higgs bundles
method Constructing a faithful monodromy representation and a period map
result Identifying orbifold toroidal compactification with canonical orbifold toroidal compactification
By applying the positivity theorem of direct images and a pluricanonical version of the structure theorem on the cohomology jumping loci à la Green-Lazarsfeld-Simpson, we show that the klt Kähler version of the Iitaka conjecture (Ueno, 1975) for (surjective morphism between compact Kähler manifolds…
SLAM-net learns to navigate visually in challenging indoor environments.
problem Challenges in SLAM for visual robot navigation, especially in noisy conditions.
method Differentiable SLAM Network (SLAM-net) that encodes a particle filter SLAM algorithm in a differentiable graph and learns components through backpropagation.
result Significantly outperforms ORB-SLAM in noisy conditions and improves the Habitat Challenge 2020 PointNav task.
Unique map connects curve pairs to abelian varieties.
problem Uniqueness of the Prym map between curve pairs and abelian varieties.
method Holomorphic map construction, classification of homomorphisms, geometric group theory.
result Prym map is the unique nonconstant holomorphic map for and .
ELS framework improves safety alignment by dynamically steering LLMs towards helpful responses.
problem Over-Refusal in Aligned Large Language Models
method Fine-tuning free framework using an Energy-Based Model (EBM) to dynamically steer LLMs during inference.
result Extensive experiments show a significant reduction in false refusals (from 57.3% to 82.6%) while maintaining safety performance.
In this paper we enumerate and classify the ``simplest'' pairs (M,G) where M is a closed orientable 3-manifold and G is a trivalent graph embedded in M. To enumerate the pairs we use a variation of Matveev's definition of complexity for 3-manifolds, and we consider only (0,1,2)-irreducible pairs, namely pairs (M,G) suc…
The paper studies the topology and geometry of simple orbifolds, generalizing concepts from simple polytopes.
problem Understanding the topology and geometry of simple orbifolds.
method Generalizing concepts from simple polytopes to simple orbifolds, focusing on simple handlebodies.
result Characterization of orbifold-aspherical properties and the existence of rank-two free abelian subgroups in terms of combinatorics.
Identifies features most relevant to concept drift in data.
problem Identifying features most relevant to concept drift.
method Distinguishing between drift inducing and faithfully drifting features; deriving minimal subsets of features to characterize drift.
result Derives a detection algorithm for concept drift.
Paper predicts EEG features from acoustic features using RNN and GAN.
problem Predicting EEG features from acoustic features.
method Recurrent Neural Network (RNN) and Generative Adversarial Network (GAN).
result Lower RMSE and normalized RMSE values compared to generating acoustic features from EEG features.
Relative Feature Importancestat.ML
Introduces RFI for assessing feature importance relative to any subset of features.
problem Lack of nuanced feature importance computation.
method Generalizes PFI and CFI to assess relative feature importance.
result Derives general interpretation rules for RFI.
A single pre-trained agent guides feature selection using knockoffs.
problem Feature selection challenges in AI-readiness of data.
method Generates knockoff features and uses reinforcement learning.
result Optimal feature subset identified with reduced dependency on target variable.
Feature networks link ML features via graph structure for enhanced learning.
problem Enhancing feature expressiveness and learning efficiency in machine learning.
method Graph representation of feature vectors, leveraging Fourier and functional analysis.
result Feature networks enable novel, complex feature dependencies.
Approach for selecting features by discarding nuisance and correlated ones.
problem Large datasets with correlated and nuisance features.
method Laplacian score criterion, autoencoder architecture, concrete layer.
result Outperforms similar approaches in clustering performance.
New stability measures for similar features improve feature selection accuracy.
problem Existing stability measures fail to distinguish similar features in highly correlated datasets.
method Introduce new adjusted stability measures that consider feature similarities.
result One new stability measure considers highly similar features as interchangeable.
Counterexamples show HSIC feature selection misses critical features.
problem Feature selection using HSIC misses important features.
method Feature selection via HSIC maximization.
result HSIC feature selection can miss critical features.
Validity of Feature Importance in Low-Performing Machine Learning for Tabular Biomedical Datastat.ML
This paper shows feature importance remains valid even in low-performing models.
problem Feature importance validity in low-performing machine learning models for biomedical data.
method Experiments with synthetic and real biomedical datasets to compare feature rank stability under different data reductions.
result Feature importance can be maintained even at low performance levels if data size is adequate.
New algorithms select and rank features from MTS without feature extraction.
problem Feature extraction step for MTS classification.
method Directly computes similarity between time series and assesses cluster structure matching labels.
result Techniques match labels well without feature extraction.
Pipeline learns topological features for protein stability prediction.
problem Predicting protein stability using topological features.
method Data-driven method to learn topological features, comparing with expert features.
result Topological features achieve 92%-99% of SME-based models' performance.
In text classification, dictionaries can be used to define human-comprehensible features. We propose an improvement to dictionary features called smoothed dictionary features. These features recognize document contexts instead of n-grams. We describe a principled methodology to solicit dictionary features from a teache…
FeAT improves OOD generalization by learning richer features.
problem Improving feature learning for out-of-distribution (OOD) generalization.
method Feature Augmented Training (FeAT) iteratively augments and retains features from different subsets of training data.
result FeAT effectively learns richer features, boosting OOD performance.
The paper defines and analyzes feature complexity in DNNs, proposing metrics for feature disentanglement and evaluation.
problem Understanding and quantifying the complexity of features learned by deep neural networks.
method Proposes a definition and disentanglement of feature complexity orders, introduces metrics for reliability and over-fitting evaluation.
result Establishes a relationship between feature complexity and DNN performance, and proposes a generic mathematical tool for network compression and knowledge distillation.
Conventional mutual information (MI) based feature selection (FS) methods are unable to handle heterogeneous feature subset selection properly because of data format differences or estimation methods of MI between feature subset and class label. A way to solve this problem is feature transformation (FT). In this study,…
A new method for measuring conditional feature importance using generative models.
problem Challenges in evaluating feature importance given other feature values.
method Adversarial Random Forest (ARF) for generating on-manifold data points.
result cARFi method yields robust importance scores adaptable for various feature importance notions.
Existing feature selection methods fail to properly account for interactions between features when evaluating feature subsets. In this paper, we attempt to remedy this issue by using orthogonal variance decomposition to evaluate features. The orthogonality of the decomposition allows us to directly calculate the total …
CAN approximates explicit feature interactions for CTR prediction.
problem Learning explicit feature interactions from sparse features.
method Co-Action Network approximates explicit pairwise feature interactions without introducing too many additional parameters.
result CAN outperforms state-of-the-art CTR models and the cartesian product method.
Proposes a new feature selection method integrating feature relationships.
problem Feature selection in machine learning models.
method Integrates feature-feature and feature-target relationships via penalized mRMR.
result Correctly identifies inactive features, reducing false discoveries.
Online feature selection has been an active research area in recent years. We propose a novel diverse online feature selection method based on Determinantal Point Processes (DPP). Our model aims to provide diverse features which can be composed in either a supervised or unsupervised framework. The framework aims to pro…
New method disentangles feature importance scores in machine learning.
problem Misinterpretation of feature importance scores due to interactions and dependencies.
method Derive DIP (Disentangled Importance) decomposition of feature importance scores.
result DIP decomposition uniquely separates standalone contributions from interactions and dependencies.
Feature selection has been proven a powerful preprocessing step for high-dimensional data analysis. However, most state-of-the-art methods tend to overlook the structural correlation information between pairwise samples, which may encapsulate useful information for refining the performance of feature selection. Moreove…
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.
Orthogonal random features approximate a Bessel kernel, offering sharper bounds than random Fourier features.
problem Approximating Gaussian kernel efficiently for large datasets.
method Use of Haar orthogonal matrices to construct orthogonal random features and analyze their bias and variance.
result Orthogonal random features approximate a Bessel kernel, not the Gaussian kernel, with sharper bounds.
New methods for assessing and visualizing feature groups in machine learning models.
problem Lack of methods for interpreting feature groups in machine learning models.
method Permutation-based, refitting, and Shapley-based techniques for grouped feature importance. Introduced a sequential procedure for identifying stable feature combinations. Developed a combined features effect plot.
result Effective methods for assessing and visualizing the importance and effect of feature groups in machine learning models.
Learning with streaming data has attracted much attention during the past few years. Though most studies consider data stream with fixed features, in real practice the features may be evolvable. For example, features of data gathered by limited-lifespan sensors will change when these sensors are substituted by new ones…
Supporting evidence for adaptive feature program across diverse models.
problem Analyzing feature learning in neural networks.
method Over-parameterized sequence models and feature error measure (FEM).
result FEM is decreasing during training of adaptive feature models.