Paper tackles phase retrieval with outliers using median-based pruning.
problem Phase retrieval with sparse outliers.
method Median-truncated nonconvex approach using gradient descent.
result Proves robustness and efficiency in recovering signals from corrupted measurements.
Constructs compactifications for median spaces with compact intervals.
problem Compactifications for median spaces with compact intervals.
method Generalises Roller boundaries of mCAT(0) cube complexes. result Recover zero-completions of Bandelt and Meletiou for median algebras.
Proves Tits alternative for finite rank median spaces, restricting group actions.
problem Understanding group actions on median spaces.
method Extending Caprace-Sageev machinery and Hagen's theory to median spaces.
result Groups acting on finite rank median spaces are more restricted.
New median geometry for complex hyperbolic spaces.
problem Characterizing spaces close to median geometry.
method Analysis of quasification of median geometry.
result Complex hyperbolic spaces cannot be at finite Hausdorff distance from a median space.
New concept of coarse medians for higher rank symmetric spaces.
problem Understanding medians in higher rank symmetric spaces.
method Introducing coarse r-median spaces and proving their existence. result Existence of coarse higher medians on divisible and quasi-homogeneous convex domains.
Unique median structures found in hyperbolic spaces.
problem Uniqueness of median structures in hyperbolic spaces.
method Analyzing product of hyperbolic spaces and properties of relative hyperbolicity.
result Non-hyperbolic pants graphs can have unique median structures.
Study on median algebra structures on Euclidean spaces and manifolds with local CAT(0) cubulation.
problem Understanding median algebra structures on Euclidean spaces and manifolds.
method Showed local CAT(0) cubulation for median structures on ER homology manifolds.
result Median structures on ER homology manifolds have a local CAT(0) cubulation structure.
We introduce median shapes for sets of shapes and prove their existence and regularity.
problem Computing the median of sets of shapes represented as integral currents.
method Developed a theoretical framework and computational methods for median shapes.
result Existence and regularity of medians for sets of shapes with shared boundaries.
Convex cores found for group actions on median spaces.
problem Understanding group actions on median spaces without metric or topology.
method Introduced convex cores for actions on finite-rank median algebras.
result Actions on median spaces have nonempty convex cores.
Enhanced survival trees improve computational efficiency and inference.
problem Censored failure time data and variable selection bias.
method Improved splitting procedure, intersected validation, fused regularization, and bootstrap-based bias correction.
result Valid confidence intervals for median survival times.
This paper is a short summary of our recent work on the medians and means of probability measures in Riemannian manifolds. Firstly, the existence and uniqueness results of local medians are given. In order to compute medians in practical cases, we propose a subgradient algorithm and prove its convergence. After that, F…
Lookahead pruning extends single-layer optimization to multi-layer, outperforming magnitude-based pruning.
problem Pruning neural networks to reduce computational cost and memory usage.
method Developed a multi-layer optimization approach extending the single-layer optimization of magnitude-based pruning.
result Consistently outperforms magnitude-based pruning on various networks, especially in high sparsity.
A method for estimating the median of gradients in stochastic optimization.
problem Robust gradient estimation in stochastic optimization for various applications.
method Stochastic Proximal Point Method for median gradient estimation.
result The proposed method can converge even under heavy-tailed, state-dependent noise.
This paper introduces online algorithms to estimate robust geometric median in large data streams.
problem Detecting outliers in large data sets using robust statistical measures.
method Online stochastic Newton methods for estimating the geometric median.
result Rates of convergence for online estimation of the geometric median.
New method for clustering binary data using nearest neighbor median shift.
problem Clustering binary data effectively.
method BinNNMS based on nearest neighbor median shift.
result BinNNMS accurately discovers cluster locations in binary data.
Recent pruning methods at initialization fall short of random pruning's accuracy.
problem Improving neural network accuracy through pruning at initialization.
method Various pruning methods (SNIP, GraSP, SynFlow, magnitude pruning) are evaluated; per-layer pruning decisions are proposed.
result Randomly shuffling or sampling initial weights preserves or improves accuracy, suggesting challenges with pruning heuristics.
The study finds that maximizing median returns is the only viable strategy in portfolio selection.
problem Difficulties in studying optimal portfolio strategies due to discontinuity and time inconsistency in maximizing median and quantile returns.
method Used intra-personal equilibrium approach to analyze portfolio selection under median and quantile maximization.
result Median maximization is the only viable strategy, with no investment in risky assets for other quantiles.
New graph properties inherited by Frechet mean and median.
problem Characterizing the average of graph-valued samples.
method Analysis of Frechet mean and median graphs.
result Edge density is hereditary in Frechet mean and median graphs.
The paper analyzes why the median heuristic works well in kernel methods.
problem Lack of theoretical understanding of the median heuristic's effectiveness.
method Convergence analysis and empirical investigations of kernel two-sample test.
result The median heuristic leads to asymptotic normality of bandwidth in kernel two-sample test.
ICE-Pruning accelerates deep neural network pruning by 9.61x.
problem Efficiently pruning deep neural networks while maintaining accuracy.
method Iterative pruning with automatic fine-tuning steps, freezing strategy, and custom learning rate scheduler.
result Significantly reduces pruning time by up to 9.61x.
Median sampling reduces the runtime of noisy evolutionary optimization problems.
problem Reduction of noise's negative effect in evolutionary optimization.
method Introducing median sampling into evolutionary algorithms and analyzing its performance.
result Median sampling reduces the expected runtime exponentially under onebit noise.
DSA efficiently allocates sparsity across layers for budgeted pruning.
problem Efficiently distributing resources (sparsity) across layers in pruning under resource constraints.
method DSA uses differentiable pruning to find continuous layer-wise pruning ratios via gradient-based optimization.
result DSA achieves superior performance and significantly reduces the time cost of pruning.
Study examines effects of pruning techniques on deep learning models.
problem Understanding the impact of pruning methods on deep learning model structure and dynamics.
method Investigated differences in connectivity and learning dynamics of pruned models using various iterative pruning techniques.
result Emergence of structure in pruned models through magnitude-based unstructured pruning and weight rewinding.
Tukey median performance analyzed under TV corruptions.
problem Performance analysis of Tukey median under TV corruptions.
method Analysis of Tukey median and projection algorithm under TV corruptions.
result Breakdown point reduced to 1/4 under TV corruptions, compared to 1/3 under Huber's model.
Pruning neural networks can improve test accuracy even with significant parameter reduction.
problem The tradeoff between generalization and stability in neural network pruning.
method Analysis of pruning behavior over training, focusing on instability and its relation to generalization.
result Pruning's benefit to generalization increases with its instability.
The consistency of Fréchet medians is proved for probability measures in proper metric spaces. In the context of Riemannian manifolds, assuming that the probability measure has more than a half mass lying in a convex ball and verifies some concentration conditions, the positions of its Fréchet medians are estimated. It…
This paper tackles ranking preferences through local consensus, improving prediction accuracy.
problem Predicting individual preferences over a set of items based on observed characteristics.
method Proposes ranking median regression, introducing local consensus/median for efficient learning.
result Developed efficient methods for ranking median regression, achieving fast learning rates.
Drop Pruning uses stochastic optimization to prune and recover weights, reducing model size and improving performance.
problem Complexity and inefficiency in pruning deep neural networks.
method Introduces stochastic optimization with 'drop away' and 'drop back' strategies to prune and recover weights.
result Achieves competitive compression performance and accuracy compared to state-of-the-art approaches.
New subspace prototype flag median improves clustering on noisy data.
problem Finding robust prototypes for datasets of images and videos.
method Proposes flag median and introduces FlagIRLS algorithm for its calculation.
result Flag median is robust to outliers and improves cluster purity.
In high dimensions, the mean and geometric median are nearly identical.
problem Understanding the relationship between mean and geometric median in high-dimensional spaces.
method Analytical derivation and simulation of the distance between mean and geometric median.
result The distance between mean and geometric median vanishes with dimensionality in high dimensions.
Improved median of means estimator with tighter bounds.
problem Improving the efficiency and reliability of median of means estimator.
method Modification of the median of means estimator with sub-Gaussian deviation bounds.
result Achieves nearly optimal constants under minimal assumptions.
Dynamic pruning during training reduces deep network complexity without significant accuracy loss.
problem High memory and computational requirements of deep networks during training and inference.
method Dynamic pruning of convolutional filters during training, using L1 normalization for optimization.
result L1 normalization-based pruning yields up to 50% reduction in filters with minimal accuracy loss.
The study reveals flaws in pruning criteria and proposes a new assumption for better filter selection.
problem Flaws in existing pruning criteria for CNNs.
method Empirical experiments and Convolutional Weight Distribution Assumption.
result The Convolutional Weight Distribution Assumption improves filter selection in pruning.
Empirical median performs well in estimating location with varying scales.
problem Estimating location with varying scales in data.
method Analysis of empirical median as an estimator.
result Matching upper and lower bounds on estimation error.
Gibbs pruning optimizes neural networks by combining physics and regularization.
problem Large neural networks are impractical for many applications.
method Combines statistical physics and stochastic regularization to train and prune networks simultaneously.
result Gibbs pruning achieves state-of-the-art performance on ResNet-56.
New statistical mechanics analysis shows edge pruning outperforms node pruning in neural networks.
problem Theoretical understanding of neural network pruning effectiveness is lacking.
method Statistical mechanics analysis of a teacher-student framework.
result DPP node pruning method is superior to other methods, but edge pruning is better overall.
New estimator for symmetric kernel expectations, robust to missing data.
problem Efficient estimation of symmetric kernel expectations with missing data.
method Median-of-Incomplete-U-Statistics (MIU) estimator.
result Established finite-sample concentration rate for MIU.
New method prunes neural networks at initialization, improving performance.
problem Improving neural network compression at initialization.
method Formally characterizes initialization conditions for reliable pruning based on connection sensitivity.
result Improved neural network performance on image classification tasks.
Median-of-means sampling outperforms mean-of-means for large sample sizes in numerical integration.
problem Improving numerical integration accuracy in high dimensions.
method Median-of-means sampling compared to mean-of-means using RQMC methods.
result Median-of-means sampling is superior for large sample sizes, while mean-of-means is better for smaller sample sizes.
This paper introduces blind adversarial pruning to balance accuracy, efficiency, and robustness in neural networks.
problem Balancing accuracy, efficiency, and robustness in neural networks with limited resources.
method Adversarial pruning with a cutoff-scale strategy to dynamically adjust the strength of adversarial examples.
result Blind adversarial pruning improves the overall AER of pruned models compared to adversarial pruning.
Upper bound for Hausdorff distance between hyperbolic space and its medianization.
problem Calculating the Hausdorff distance between hyperbolic space and its medianization.
method Using de Sitter space to model finite-dimensional hyperbolic space and its medianization, calculating the Hausdorff distance.
result An upper bound for the Hausdorff distance between hyperbolic space and its medianization is calculated.
Paper proposes a novel method to improve matrix completion with median loss for large datasets.
problem Matrix completion with absolute deviation loss for large-scale data.
method Proposes a refinement step using pseudo data to improve inefficient estimators of median matrix completion.
result Turns inefficient estimators into a rate (near-)optimal matrix completion procedure.
Superrigidity theorem for actions on median spaces.
problem Actions of lattices on finite rank median spaces.
method Superrigidity and fixed point properties.
result Actions of irreducible lattices on finite rank median spaces have global fixed points.
A fast pruning algorithm for DNNs with GE guarantees.
problem Efficiently pruning DNNs without sacrificing accuracy.
method FeTa algorithm based on DC optimization, with GE analysis.
result FeTa is orders of magnitude faster and maintains GE.
Speeds up training and inference by pruning entire channels before training.
problem Training and inference speed in deep neural networks.
method Structured pruning applied before training, focusing on removing entire channels and hidden units.
result 2x speedup in training and 3x speedup in inference.
This paper analyzes privacy risks in neural network pruning and proposes a defense mechanism.
problem Privacy risks in neural network pruning due to membership inference attacks.
method Investigates the impact of pruning on prediction divergence and proposes a self-attention membership inference attack.
result Proposed defense mechanism mitigates privacy risks while maintaining sparsity and accuracy.
An efficient algorithm for k-median clustering in a sequential setting without substitutions.
problem Clustering a sequence of examples without being able to substitute centers later.
method An efficient algorithm with a multiplicative approximation factor of twice the offline algorithm's factor, and an optimal offline algorithm.
result The efficient algorithm achieves a good approximation of the optimal offline solution.
SPP prunes CNN weights probabilistically for faster inference.
problem Efficiently accelerate Convolutional Neural Networks (CNNs) without significant accuracy loss.
method Structured Probabilistic Pruning (SPP) with adjustable pruning probabilities.
result 4x speedup with minimal accuracy loss (0.3% for AlexNet, 0.8% for VGG-16).