In 1987 Bieri, Neumann and Strebel introduced a geometric invariant for discrete groups. In this article we compute and explicitly describe the BNS-invariant for the pure braid groups.
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48 results for “BNS invariants”
The study examines groups with a specific automorphism property using BNS-invariant.
problem When does a group have the finitely generated fixed subgroup property?
method Using BNS-invariant to analyze groups of the form .
result Provides partial answers and examples for groups with the property.
The BNS invariant is applied to Kähler groups in new proofs and results.
problem Understanding properties of Kähler groups through the BNS invariant.
method Applications of the Bieri-Neumann-Strebel invariant on Kähler groups.
result Amenable Kähler groups have an empty complement of the BNS invariant.
Study BNS invariants to prove algebraic fibrations of certain groups.
problem Proving algebraic fibrations of group extensions.
method Study of BNS invariants to analyze group extensions.
result Groups with specific BNS invariants algebraically fiber.
A Bar-Natan homotopy typemath.GT
Spatial refinement of Bar-Natan homology constructed.
problem Link invariants and their homotopy types.
method CW-spectrum construction and stable homotopy type.
result Stable homotopy type of constructed CW-spectrum is a link invariant.
Theoretical Insight into Batch Normalization: Data Dependant Auto-Tuning of Regularization Ratestat.ML
This paper explains how batch normalization auto-tunes the regularization parameter based on data statistics.
problem Batch normalization accelerates deep learning training but the exact relationship to regularization is unclear.
method Theoretical analysis and empirical validation of batch normalization's role in auto-tuning the regularization parameter.
result Batch normalization auto-tunes the regularization parameter based on data statistics.
We describe the BNS invariant of Kaehler groups. As an application we prove that if the fundamental group of a Kaehler manifold is solvable, it is virtually nilpotent.
Batch Normalization (BN) improves both convergence and generalization in training neural networks. This work understands these phenomena theoretically. We analyze BN by using a basic block of neural networks, consisting of a kernel layer, a BN layer, and a nonlinear activation function. This basic network helps us unde…
Proves cosmetic surgery conjecture for strongly invertible knots.
problem Cosmetic surgery conjecture for strongly invertible knots.
method Combines recent results with Khovanov multicurve invariants and Conway tangles.
result Proves equivariant version of the Cosmetic Surgery Conjecture.
BN helps learn fragile features, which can improve adversarial robustness.
problem The role of batch normalization in adversarial training and its impact on robustness.
method Investigated the expressiveness of BN in learning robust features compared to random features.
result Adversarially fine-tuning BN layers can result in non-trivial adversarial robustness.
We study the Newton polytopes of determinants of square matrices defined over rings of twisted Laurent polynomials. We prove that such Newton polytopes are single polytopes (rather than formal differences of two polytopes); this result can be seen as analogous to the fact that determinants of matrices over commutative …
Post-shifted BN prevents filter collapse in BN networks, improving model performance.
problem Filter collapse in BN networks reduces network capacity and harms model performance.
method Post-shifted BN (psBN) to prevent filter collapse by making BN parameters trainable again.
result psBN prevents filter collapse and increases model performance in various tasks.
New algorithm learns any part of a Bayesian network structure efficiently.
problem Learning specific parts of a Bayesian network structure is computationally inefficient.
method APS-L, a new algorithm that divides V-structures into collider and non-collider types and recursively finds them in Markov blankets.
result The APSL algorithm efficiently and accurately learns any part of a Bayesian network structure.
Suppose that multiple experts (or learning algorithms) provide us with alternative Bayesian network (BN) structures over a domain, and that we are interested in combining them into a single consensus BN structure. Specifically, we are interested in that the consensus BN structure only represents independences all the g…
We give a geometric interpretation of Bar-Natan's universal invariant for the class of tangles in the 3-ball with four ends: we associate with such 4-ended tangles multicurves , that is, collections of immersed curves with local systems in the 4-punctured sphere. These multicurves …
Paper improves BN structure learning from incomplete data.
problem Learning BN structure from incomplete data.
method Node-Average Likelihood (NAL) approach.
result NAL proves consistent and identifiable for conditional Gaussian BNs.
In this paper, we empirically evaluate algorithms for learning four types of Bayesian network (BN) classifiers - Naive-Bayes, tree augmented Naive-Bayes, BN augmented Naive-Bayes and general BNs, where the latter two are learned using two variants of a conditional-independence (CI) based BN-learning algorithm. Experime…
Batch-normalization (BN) layers are thought to be an integrally important layer type in today's state-of-the-art deep convolutional neural networks for computer vision tasks such as classification and detection. However, BN layers introduce complexity and computational overheads that are highly undesirable for training…
In this paper, we establish some theoretical connections between Sum-Product Networks (SPNs) and Bayesian Networks (BNs). We prove that every SPN can be converted into a BN in linear time and space in terms of the network size. The key insight is to use Algebraic Decision Diagrams (ADDs) to compactly represent the loca…
Admissibility of Stein Shrinkage for Batch Normalization in the Presence of Adversarial Attacksstat.ML
Stein shrinkage improves BN robustness against adversarial attacks.
problem Improving BN robustness against adversarial attacks.
method Applying Stein shrinkage to BN mean and variance estimates.
result Stein shrinkage outperforms vanilla BN in adversarial settings.
This work analyzes Batch Normalization through convex optimization, providing insights and improved training methods.
problem Understanding and improving the effectiveness of Batch Normalization in deep neural networks.
method Introducing convex duality to model weight-decay regularized ReLU networks with BN, and designing an explicit regularization approach.
result Gradient Descent provides an algorithmic bias effect on BN networks, which can be explicitly encoded into the convex objective.
An Internal Covariate Shift Bounding Algorithm for Deep Neural Networks by Unitizing Layers' Outputscs.LG
This paper analyzes and improves the effectiveness of BN techniques in controlling Internal Covariate Shift.
problem The effectiveness of BN techniques in reducing Internal Covariate Shift (ICS) is limited, especially for high-dimensional outputs and noise.
method The paper introduces a measure for ICS using the Earth Mover (EM) distance, derives bounds for this measure, and proposes a unitization algorithm to further bound ICS.
result The unitization algorithm effectively bounds ICS, especially for low-dimensional outputs and small noise, and can be tuned to control ICS.
Alexander and Thurston norms, and the Bieri-Neumann-Strebel invariants for free-by-cyclic groupsmath.GR
We investigate Friedl-Lück's universal -torsion for descending HNN extensions of finitely generated free groups, and so in particular for -by- groups. This invariant induces a semi-norm on the first cohomology of the group which is an analogue of the Thurston norm for -manifold groups. We prove…
Batch normalization (BN) is a technique to normalize activations in intermediate layers of deep neural networks. Its tendency to improve accuracy and speed up training have established BN as a favorite technique in deep learning. Yet, despite its enormous success, there remains little consensus on the exact reason and …
Proposes BN layers for neural networks on complex domains, improving training stability and accuracy.
problem Training stability and accuracy issues in neural networks on complex domains.
method Developed Riemannian batch normalization (BN) layers with connections to existing layers.
result Demonstrated improved performance on radar clutter classification, node classification, and action recognition.
Classifier chain (CC) is a multi-label learning approach that constructs a sequence of binary classifiers according to a label order. Each classifier in the sequence is responsible for predicting the relevance of one label. When training the classifier for a label, proceeding labels will be taken as extended features. …
Batch normalization improves deep networks by aligning their decision boundaries with data.
problem Improving the performance and generalization of deep networks.
method Theoretical analysis of batch normalization as a function approximation technique for continuous piecewise affine splines.
result Batch normalization adapts the geometry of a deep network's partition to match the data, improving learning and generalization.
Batch Normalization (BN) is essential to effectively train state-of-the-art deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers during training using the statistics of each mini-batch. In this work, we study BN from the viewpoint of Fisher kernels. We show that assuming samples within a mini-ba…
Study improves BN TTA under distribution shift using higher-order asymptotics.
problem Improving BN TTA for changing data distributions.
method Integrates Edgeworth expansion and saddlepoint approximation with one-step M-estimation.
result Derives optimal weighting parameter for minimized mean-squared error.
Improved continual learning for neural networks with BN layers using K-FAC extension.
problem Continual learning challenges in neural networks with BN layers.
method Extended K-FAC method to account for inter-example relations, weight merging, and reparameterization for BN layers; proposed weight merging and reparameterization for BN layers; proposed method to select hyperparameters without source task data.
result Better performance in continual learning tasks with BN layers compared to baselines.
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.
Batch normalization shifts models to rely more on non-robust features.
problem Understanding the impact of batch normalization on deep neural networks.
method Empirical analysis and a framework for disentangling robustness and usefulness.
result Batch normalization increases reliance on non-robust features, decreasing adversarial robustness.
Numerical analysis on locally risk-minimizing strategies for Barndorff-Nielsen and Shephard modelsq-fin.CP
Develops a numerical method for LRM strategies in BNS models with infinite active jumps.
problem Calculating locally risk-minimizing strategies for non-martingale BNS models with infinite active jumps.
method Modified Malliavin calculus expression and Monte Carlo method for non-martingale BNS models.
result Proposes a numerical method for LRM strategies in non-martingale BNS models with infinite active jumps.
Batch Normalization (BN) is capable of accelerating the training of deep models by centering and scaling activations within mini-batches. In this work, we propose Decorrelated Batch Normalization (DBN), which not just centers and scales activations but whitens them. We explore multiple whitening techniques, and find th…
A new BN method corrects size mismatch in WLF for imbalanced data.
problem Learning from imbalanced datasets in neural networks.
method Proposes weighted batch normalization (WBN) to correct size mismatch between BN and WLF.
result WBN corrects size mismatch and improves classification performance in imbalanced datasets.
Utilizing recently introduced concepts from statistics and quantitative risk management, we present a general variant of Batch Normalization (BN) that offers accelerated convergence of Neural Network training compared to conventional BN. In general, we show that mean and standard deviation are not always the most appro…
Paper compares hard and soft EM for BN learning from incomplete data.
problem Learning BNs from incomplete data using EM algorithms.
method Investigates the impact of imputation vs. belief propagation in hard and soft EM.
result A decision tree can guide practitioners in choosing the best EM algorithm.
Proposes a defense method against multiple adversarial video types.
problem Lack of multi-perturbation robustness in existing defense approaches.
method Adversarial training with multiple independent BN layers and a BN selection module.
result Demonstrates stronger multi-perturbation robustness against different adversarial video types.
Batch Normalization (BN) has become a cornerstone of deep learning across diverse architectures, appearing to help optimization as well as generalization. While the idea makes intuitive sense, theoretical analysis of its effectiveness has been lacking. Here theoretical support is provided for one of its conjectured pro…
In this study, we consider classification problems based on neural networks in data-imbalanced environment. Learning from an imbalanced data set is one of the most important and practical problems in the field of machine learning. A weighted loss function based on cost-sensitive approach is a well-known effective metho…
Paper proposes MABN to stabilize BN in small batch sizes.
problem Weakness of BN in small batch sizes limits its use in tasks with small batch sizes.
method Identifies and addresses two extra batch statistics in BN's backward propagation.
result MABN completely restores BN's performance in small batch sizes without additional nonlinear operations.
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the esti…
In this paper, we study the information-theoretic limits of learning the structure of Bayesian networks (BNs), on discrete as well as continuous random variables, from a finite number of samples. We show that the minimum number of samples required by any procedure to recover the correct structure grows as and $Ω…
Learning Markov blanket (MB) structures has proven useful in performing feature selection, learning Bayesian networks (BNs), and discovering causal relationships. We present a formula for efficiently determining the number of MB structures given a target variable and a set of other variables. As expected, the number of…
Investigates BNSR invariants of link and knot groups, proving specific properties.
problem Characterizing finiteness properties of normal subgroups in link and knot groups.
method Analyzes BNSR invariants of link and knot groups, proving specific properties.
result Proves specific conditions for finiteness properties of link and knot groups.
A commonly used stochastic model for derivative and commodity market analysis is the Barndorff-Nielsen and Shephard (BN-S) model. Though this model is very efficient and analytically tractable, it suffers from the absence of long range dependence and many other issues. For this paper, the analysis is restricted to crud…
We introduce the concept of G2(2)-structure on an orientable 3-manifold M using the setting of generalized geometry of type Bn, study their local deformation by making use of a Moser-type argument, and give a description of the cone of G2(2)-structures.
Generative adversarial networks (GANs) are highly effective unsupervised learning frameworks that can generate very sharp data, even for data such as images with complex, highly multimodal distributions. However GANs are known to be very hard to train, suffering from problems such as mode collapse and disturbing visual…