New adaptive strategy for active learning with smooth boundaries.
problem Adaptive active learning in multivariate classification with unknown distributional parameters.
method Combining insights from recent works, reduction to univariate-adaptive strategies.
result Near-optimal rates achieved without prior knowledge of distributional parameters.
Hidden cost: Smoothing shrinks decision boundaries, affecting class-wise accuracy.
problem The fragility of machine learning models and the need for robustness verification.
method Randomized smoothing approach to achieve statistical robustness.
result Smoothed classifiers' decision boundaries shrink, leading to class-wise accuracy disparity.
New findings discourage use of boundary constraints in RL model parameter estimation.
problem Inference of RL model parameters using optimization methods is hindered by boundary constraints.
method Investigated interior point and deterministic direct search algorithms for optimization under smooth vs. boundary constraints.
result Boundary constraints lead to substantial truncation effects, discouraging their use.
SBAMDT uses adaptive soft splits to model complex decision boundaries.
problem Limited ability of standard decision trees to capture complex decision boundaries.
method Probabilistic additive decision tree model with adaptive soft multivariate splits.
result Demonstrated improved predictive performance on synthetic and real datasets.
The paper explores the geometry and topology of DNN decision boundaries.
problem Understanding the geometric and topological properties of DNN decision boundaries.
method Differential geometry and the Gauss-Bonnet-Chern theorem.
result Computed the Euler characteristics of compact decision boundaries.
Researchers compute exact decision boundaries of neural networks.
problem Finding exact decision boundaries of trained neural networks is intractable.
method Developed mathematical tools to investigate decision boundaries of trained deep models.
result Some simplifying assumptions about decision boundaries are unreliable.
Paper proposes a new method for knowledge distillation using adversarial samples to improve classifier performance.
problem Improving the generalization performance of a classifier by transferring information related to its decision boundary.
method The paper introduces a method that uses adversarial samples to train a student classifier, focusing on samples supporting the decision boundary.
result The proposed method significantly improves knowledge distillation and achieves state-of-the-art performance.
This work connects the Hessian to the decision boundary complexity in neural networks.
problem Understanding the decision boundary complexity in high-dimensional input space.
method Characterizing the decision boundary using the Hessian top eigenvectors and analyzing the number of outliers.
result The number of outliers in the Hessian spectrum is proportional to the complexity of the decision boundary.
DeepDIG generates samples near decision boundaries of deep neural networks for better understanding.
problem Limited knowledge of how deep neural networks make decisions.
method Adversarial example generation to create samples near decision boundaries.
result Characterized decision boundaries of various deep neural network models.
Study decision boundaries using heat diffusion and probabilistic techniques.
problem Understanding the geometry of decision boundaries in machine learning.
method Using Brownian motion and probabilistic techniques to analyze decision boundaries.
result Decision boundaries exhibit persistent 'wiggly and fuzzy' regions, even under adversarial attacks.
This work uses tropical geometry to understand neural network decision boundaries.
problem Characterizing neural network decision boundaries with piecewise linear activations.
method Tropical geometry applied to a simple neural network model.
result Decision boundaries are a subset of a tropical hypersurface related to a polytope formed by zonotopes.
We analyze decision boundaries using topological data analysis.
problem Quantifying deep neural network complexity for model selection.
method We use labeled Čech complex, plain labeled Vietoris-Rips complex, and locally scaled labeled Vietoris-Rips complex to infer persistent homology of decision boundaries.
result We provide theoretical conditions and analysis for recovering the homology of a decision boundary from samples.
Decision trees and shallow neural networks have different geometric complexities, impacting their interpretability and accuracy.
problem The geometric simplicity of decision boundaries in decision trees conflicts with the approximation capabilities of shallow neural networks.
method Analysis of the Radon total variation (RTV) seminorm to compare geometric complexity of decision regions and neural network approximations.
result Smooth barrier scores can approximate decision regions with finite RTV, but their performance depends on the tube-mass condition near the decision boundary.
Notes on linear classifiers and outliers, improving decision boundaries.
problem Negative impact of outliers on linear classifier decision boundaries.
method Use of least-squares cost function, scaling to reduce outlier significance.
result Improved decision boundaries through scaling outliers.
New method measures generalizability of deep neural networks based on decision boundary complexity.
problem Lack of generalization methods for deep neural networks.
method Created Decision Boundary Complexity (DBC) score to measure DNN complexity.
result Simpler decision boundaries lead to better generalizability, supporting Occam's Razor.
The paper shows how neural networks with less decision boundary variability generalize better.
problem Improving neural network generalizability by reducing decision boundary variability.
method Introduces new measures (algorithm DB variability and (ε,η)-data DB variability) to quantify decision boundary variability and proves theoretical bounds on generalizability. result Neural networks with lower decision boundary variability have better generalizability, as shown by extensive experiments and theoretical bounds.
Measures neural network decision boundary volume to predict model performance.
problem Understanding the geometry of deep learning models for better performance.
method Local surface volumes to measure decision boundary, applying Weyl's tube formula.
result Smaller surface volume correlates with higher classification accuracy.
New method initializes sigmoidal MLPs for interpretable shapes.
problem Creating interpretable decision boundaries in neural networks.
method Introducing a geometry-aware initialization for sigmoidal multi-layer perceptrons (MLPs) using tropical geometry.
result Sigmoidal MLPs can have decision boundaries aligned with prescribed shapes at initialization.
Deep learning models generalize by extending decision boundaries outside the convex hull of training data.
problem Understanding how deep learning models generalize beyond their training data.
method Investigation of decision boundaries inside and outside the convex hull of training sets, using various neural network architectures and training regimes.
result Over-parameterization is necessary for deep learning models to extend decision boundaries outside the convex hull of their training data.
Study on inventory management under uncertainty using smooth ambiguity preference.
problem Managing inventory under Knightian uncertainty with smooth ambiguity preference.
method Demonstrates continuous-time smooth ambiguity as the infinitesimal limit of Kalman-Bucy filtering with recursive robust utility. Solves forward-backward stochastic differential equations with quadratic growth to determine cost function. Derives value function and optimal control policy using variational inequalities and viscosity solutions. Transforms problem into two-dimensional singular control.
result Ambiguity drives decision-makers to act earlier, reducing the continuation region.
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.
Study reveals how features influence deep network decision boundaries.
problem Understanding the role of features in neural network decision boundaries.
method Adopted adversarial robustness tools to measure changes in CNN decision boundaries.
result Neural networks exhibit high invariance to non-discriminative features and are sensitive to small perturbations of training samples.
Deep neural networks' decision boundaries move closer to natural images during training.
problem Limited understanding of deep neural networks' decision boundaries and regions.
method Examined the minimum distance of data points to the decision boundary over training.
result The decision boundary moves closer to natural images during training, even in late epochs.
Improves GATs by adding margin-based constraints to prevent over-fitting and over-smoothing.
problem Over-fitting and over-smoothing in GATs.
method Margin-based constraints on attention weights and graph structure.
result Significant improvements over previous GATs on various datasets.
The paper proposes a policy learning framework for interpretable personalization.
problem Effective personalization of goods and services to improve revenues and maintain competitive edge.
method Policy learning with linear decision boundaries using causal inference and Bayesian optimization.
result The learned policy improves net sales revenue by 88.2% and provides insights into important features.
Deep neural networks converge quickly for classification tasks.
problem Classifying data with smooth decision boundaries, probabilities, or margins.
method Hinge loss and cross-entropy for training; analysis of convergence rates.
result DNNs achieve fast convergence rates under various conditions.
New method visualizes decision boundaries of classification models.
problem Difficulty in understanding how classification models interpret data.
method Hybrid supervised-unsupervised technique for visualizing decision boundaries.
result Provides interpretable maps for qualitative and quantitative analysis.
The goal of this paper is to analyze the geometric properties of deep neural network classifiers in the input space. We specifically study the topology of classification regions created by deep networks, as well as their associated decision boundary. Through a systematic empirical investigation, we show that state-of-t…
HopSkipJumpAttack efficiently generates adversarial examples with fewer queries.
problem Developing efficient adversarial attacks on trained models.
method A family of algorithms based on a gradient direction estimate using binary decision boundary information.
result Significantly fewer model queries required compared to previous methods.
Study Ricci tensor on spaces with boundary, offering new curvature conditions.
problem Curvature conditions on smooth metric measure spaces with boundaries.
method Generalization of Bakry-Emery's Ricci tensor to spaces with boundaries.
result New approach to curvature-dimension conditions on spaces with boundaries.
Proposes a method to speed up model selection for classification.
problem Time-consuming model selection process and lack of dataset-specific insights.
method Relaxes decision boundaries of neural decision trees to find equivalent or better models.
result Reduces the scope of exploration needed for model selection.
Boundary of fiber convex domains is a cohomological sphere.
problem Understanding the boundary properties of fiber convex domains.
method Analyzing smooth fiber convex domains with smooth boundaries.
result The boundary is a cohomological sphere.
Paper proposes a new classifier for hyperbolic spaces using horospherical boundaries.
problem Optimization of large margin classifiers in hyperbolic spaces.
method Horospherical decision boundaries for geodesically convex optimization.
result Geodesically convex optimization leads to globally optimal solutions.
Enhances deep networks' robustness against adversarial attacks.
problem Vulnerability of deep neural networks to adversarial examples.
method Boundary Conditional GAN, generating boundary samples near decision boundary.
result Significant improvement in robustness against various adversarial attacks.
The paper proves estimates for solutions to nonlinear equations on manifolds with boundary.
problem Boundary estimates for fully nonlinear Yamabe equations on Riemannian manifolds.
method Deriving a priori second derivative estimates for subsolutions.
result Existence of smooth solutions with uniform estimates.
Boundary Dehn twists become trivial after abelianization.
problem Understanding the behavior of boundary Dehn twists in smooth mapping classes.
method Constructing diffeomorphisms and showing commutators represent boundary Dehn twists.
result Boundary Dehn twists become trivial after abelianization.
Convex polytope trees expand decision trees with interpretable boundaries.
problem High accuracy often requires many nodes in decision trees, reducing interpretability.
method CPT uses logical disjunction of weighted linear decision-makers, geometrically a convex polytope.
result CPT achieves high accuracy with fewer nodes compared to existing methods.
This paper addresses the importance of defining locality for accurate surrogate explanations.
problem Accurate approximation of local black-box decision boundaries for generating explanations.
method Proposes a novel approach to generate surrogate-based explanations centered on relevant places of the decision boundary, rather than on predictions.
result The proposed approach outperforms state-of-the-art methods and a straightforward improvement thereof on UCI datasets.
Decision tree learning heuristics fail even in smoothed analysis for complex targets.
problem Greedy decision tree learning heuristics fail for complex target functions in the smoothed analysis model.
method Construct counterexamples and analyze the behavior of heuristics in the smoothed setting and agnostic setting.
result Greedy decision tree learning heuristics can build trees of exponential depth before achieving high accuracy for certain complex target functions.
Decision trees are a popular technique in statistical data classification. They recursively partition the feature space into disjoint sub-regions until each sub-region becomes homogeneous with respect to a particular class. The basic Classification and Regression Tree (CART) algorithm partitions the feature space using…
Generalizes Poincaré-Hopf Theorem for piecewise smooth boundaries.
problem Conservation law for vector fields on surfaces with piecewise smooth boundaries.
method Generalization of the Poincaré-Hopf Theorem for real-analytic vector fields on surfaces with piecewise smooth boundaries.
result Conservation law for vector fields on surfaces with piecewise smooth boundaries.
Smooth solutions up to evolving free boundaries for degenerate equations.
problem Degenerate parabolic equations with evolving free boundaries.
method Smooth short-time existence using linear degenerate equations on a fixed domain.
result Smoothness up to the free boundary for the p-Laplacian evolution equation and α-Gauss curvature flow. Mixup reduces the sample complexity of finding optimal decision boundaries for more separable data.
problem Finding optimal decision boundaries in separable data distributions.
method Mixup technique applied to binary linear classification problems.
result Mixup significantly reduces the sample complexity for more separable data.
Capacity control, the bias/variance dilemma, and learning unknown functions from data, are all concerned with identifying effective and consistent fits of unknown geometric loci to random data points. A geometric locus is a curve or surface formed by points, all of which possess some uniform property. A geometric locus…
The paper examines the smoothness of hyperbolic metrics near boundaries.
problem Analyzing the regularity of asymptotically hyperbolic metrics near boundaries.
method Following Michael Anderson's method, the paper studies Cm,α conformally compact Riemannian metrics with Einstein equation. result The conformal compactifications of these metrics are Cm+2,α up to the boundary when Weyl curvature is in Cm,α and the boundary metric is in Cm+2,α. zoNNscan assesses uncertainty around neural network decision boundaries.
problem Uncertainty in decision boundaries of neural networks.
method zoNNscan uses confidence entropy and sampling in multidimensional space.
result zoNNscan detects higher uncertainty in adversarial and corner cases.
New algorithms learn in complex decision-making problems with smooth transitions.
problem Learning in complex decision-making problems with smooth transitions.
method UCB and PSRL philosophies applied to episodic Markov decision processes with kernel approximation.
result Low regret learning achieved in continuous state and action spaces.
We use flip points to explain and audit deep learning models, revealing decision boundaries and improving model performance.
problem Lack of interpretability in deep learning models hinders their use in important applications.
method Flip points are used to analyze decision boundaries of deep learning models with continuous output scores.
result Flip points reveal the least changes in input that would alter a model's classification, enabling better understanding and improvement of model behavior.