On-device research index

arXiv research

A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.

169,051 papers · 148 categories

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48 results for “linear separators”

Bandit Multiclass Linear Classification for the Group Linear Separable Casecs.LG

Improved mistake bound for group linear separable cases in online multiclass linear classification.

problem Improving mistake bounds for online multiclass linear classification under group linear separable conditions.

method Refined group weak linear separability condition and rational kernel approach.

result Achieved a mistake bound of

K\cdot 2^{ ilde{O}(\sqrt{1/γ}\log L)})

under group weak linear separable condition.

Online Multiclass Classification Group Linear Separability Rational Kernel Mistake Bound

2019-12-21abs ↗pdf ↗

Bandit Multiclass Linear Classification: Efficient Algorithms for the Separable Casecs.LG

Efficient algorithms for online multiclass linear classification with bandit feedback under linear separability conditions.

problem Efficient online multiclass linear classification with bandit feedback for separable data.

method Design of efficient algorithms based on kernel Perceptron for strong and weak linear separability conditions.

result Near-optimal mistake bounds of $O\left( K/γ^2 ight)$ for strong separability and

\min (2^{\widetilde{O}(K \log^2 (1/γ))}, 2^{\widetilde{O}(\sqrt{1/γ} \log K)})

for weak separability.

online learning multiclass classification bandit feedback linear separability kernel Perceptron

2019-02-06abs ↗pdf ↗

Shallow Neural Network can Perfectly Classify an Object following Separable Probability Distributioncs.LG

Shallow neural nets classify objects perfectly if their distribution is linearly separable.

problem Designing efficient neural networks for classification.

method Constructed shallow sigmoid-type neural networks.

result Achieves 100% accuracy for datasets following a linear separability condition.

neural networks classification sigmoid function separable probability distribution linear separability

2019-04-19abs ↗pdf ↗

On Linear Separation Capacity of Self-Supervised Representation Learningstat.ML

This paper investigates how data augmentation improves linear separation of manifold data.

problem Understanding how data augmentation enhances linear separation of manifold data.

method Investigates the conditions under which self-supervised representations can linearly separate multi-manifold data.

result Self-supervised learning can linearly separate manifolds with a smaller distance than unsupervised learning.

data augmentation self-supervised learning linear separation multi-manifold representation learning

2023-10-29abs ↗pdf ↗

Provably robust blind source separation of linear-quadratic near-separable mixtureseess.SP

New algorithms improve blind source separation for linear-quadratic mixtures.

problem Blind source separation of linear-quadratic mixtures under separability assumptions.

method Proposed two algorithms: SNPALQ and BF. SNPALQ generalizes SNPA for LQ model, BF post-processes SNPALQ.

result Proven robustness and computational tractability of SNPALQ in separating sources even with noise.

blind source separation linear-quadratic model separability successive nonnegative projection product terms

2020-11-24abs ↗pdf ↗

Non-linear ICA based on Cramer-Wold metriccs.LG

CW-ICA improves on ANICA for non-linear source separation.

problem Non-linear source separation challenges with many applications.

method CW-ICA extends ANICA by using a simpler, closed-form optimization target.

result CW-ICA achieves comparable results to ANICA without adversarial training.

ICA non-linear source separation Cramer-Wold metric

2019-03-01abs ↗pdf ↗

One-Class Semi-Supervised Learning: Detecting Linearly Separable Class by its Meanstat.ML

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an…

2017-05-02abs ↗pdf ↗

The Implicit Bias of Adam on Separable Datastat.ML

Adam optimizes linear classifiers with separable data.

problem Understanding Adam's implicit bias in linear logistic regression.

method Study of Adam's behavior on linearly separable data.

result Adam converges to a linear classifier with maximum

\ell_\infty

-margin.

Adam optimizer implicit bias linear logistic regression separable data maximum margin

2024-06-15abs ↗pdf ↗

Supervised learning of sheared distributions using linearized optimal transportmath.ST

The paper extends optimal transport for linear separability of sheared distributions in supervised learning.

problem Learning on the space of probability measures using shifts and scalings.

method Embedding probability measures into

L^2

spaces using optimal transport, then applying regular machine learning techniques.

result Sheared distributions can be linearly separated under certain conditions, with bounds on transformations.

supervised learning probability measures optimal transport shearing linear separability

2022-01-25abs ↗pdf ↗

Separability is not the best goal for machine learningcs.LG

Neural networks use their hidden layers to transform input data into linearly separable data clusters, with a linear or a perceptron type output layer making the final projection on the line perpendicular to the discriminating hyperplane. For complex data with multimodal distributions this transformation is difficult t…

2018-07-08abs ↗pdf ↗

A spectral-based analysis of the separation between two-layer neural networks and linear methodsstat.ML

Spectral analysis shows neural networks separate from linear methods in approximating functions.

problem Separating two-layer neural networks from linear methods in function approximation.

method Spectral-based approach using Kolmogorov width and kernel spectrum.

result Upper and lower bounds on separation, explicit hard functions identified.

spectral analysis two-layer neural networks linear methods function approximation Kolmogorov width

2021-08-10abs ↗pdf ↗

Linear Separation via Optimismcs.LG

A new algorithm finds a separating hyperplane with fewer updates.

problem Finding a separating hyperplane with minimal updates.

method Optimistic Perceptron algorithm.

result The Optimistic Perceptron finds a separating hyperplane with no more than $rac{1}{γ}$ updates.

binary classification linear separation optimism Perceptron machine learning

2020-11-17abs ↗pdf ↗

A PC Algorithm for Max-Linear Bayesian Networksstat.ML

New PCstar algorithm discovers causal structure of max-linear Bayesian networks.

problem Discovering causal structure in max-linear Bayesian networks due to non-faithfulness.

method PC algorithm modified with

C^\ast

-separation assumptions.

result PCstar algorithm can orient additional edges not possible with standard PC algorithm.

max-linear Bayesian networks PC algorithm Causal discovery faithfulness conditional independence

2025-08-19abs ↗pdf ↗

Linearly Separable Features in Shallow Nonlinear Networks: Width Scales Polynomially with Intrinsic Data Dimensioncs.LG

Shallow nonlinear networks can separate classes linearly with polynomially scaling width.

problem Understanding the linear separability of deep networks' features.

method Modeling inputs as a union of low-dimensional subspaces and using random weights and quadratic activations.

result Shallow nonlinear networks can achieve linear separation with polynomially scaling width.

deep learning nonlinear networks linear separability shallow networks intrinsic dimensionality

2025-01-04abs ↗pdf ↗

The Power of Localization for Efficiently Learning Linear Separators with Noisecs.LG

We introduce a new approach for designing computationally efficient learning algorithms that are tolerant to noise, and demonstrate its effectiveness by designing algorithms with improved noise tolerance guarantees for learning linear separators. We consider both the malicious noise model and the adversarial label nois…

2013-07-31abs ↗pdf ↗

StrADiff: A Structured Source-Wise Adaptive Diffusion Framework for Linear and Nonlinear Blind Source Separationstat.ML

StrADiff separates sources from mixtures without labels, using structured priors.

problem Blind source separation of linear and nonlinear mixtures without labeled data.

method Structured Source-Wise Adaptive Diffusion Framework with Gaussian process priors.

result StrADiff can recover latent source trajectories in an unsupervised manner, especially stable in linear mixtures.

source separation blind separation structured priors Gaussian process diffusion

2026-04-04abs ↗pdf ↗

Variational Inference in high-dimensional linear regressionmath.ST

Study high-dimensional Bayesian linear regression using variational inference.

problem High-dimensional Bayesian linear regression with product priors.

method Non-linear large deviations theory and variational inference.

result Unique optimizer in variational problem governs posterior distribution under separation condition.

Bayesian linear regression variational inference high-dimensional product priors non-linear large deviations

2021-04-25abs ↗pdf ↗

Large-Sample Properties of Non-Stationary Source Separation for Gaussian Signalsmath.ST

Develops large-sample theory for non-stationary source separation.

problem Lack of large-sample results for non-stationary source separation methods.

method Large-sample theory for NSS-JD method under specific assumptions.

result Consistency of unmixing estimator and its convergence to Gaussian distribution.

non-stationary source separation joint diagonalization Gaussian signals large-sample properties blind source separation

2022-09-21abs ↗pdf ↗

Adversarial Noises Are Linearly Separable for (Nearly) Random Neural Networkscs.LG

Adversarial noises are linearly separable for random neural networks.

problem The challenge of adversarial examples in neural networks.

method Theoretical proof and empirical evidence for two-layer networks with random initialization and neural tangent kernel setup.

result Adversarial noises are linearly separable with corresponding labels.

adversarial examples random neural networks linear separability gradient methods two-layer networks

2022-06-09abs ↗pdf ↗

In-Context Learning of Linear Dynamical Systems with Transformers: Approximation Bounds and Depth-Separationcs.LG

Transformers can learn noisy linear systems with depth and IID data.

problem Learning noisy linear dynamical systems with transformers.

method Theoretical analysis of multi-layer and single-layer transformers with respect to

L^2

-testing loss.

result Single-layer transformers have a non-diminishing lower bound on approximation error, suggesting depth separation.

transformers linear dynamical systems approximation bounds depth-separation IID data

2025-02-12abs ↗pdf ↗

Classification by Separating Hypersurfaces: An Entropic Approachcs.LG

A new method separates data points using entropy minimization over a hypercube.

problem Classifying data points with linear or non-linear decision boundaries.

method Minimizing entropy over a hypercube to find separating parameters.

result Efficient and versatile for linear and non-linear separability.

classification entropy hypersurfaces optimization

2025-07-03abs ↗pdf ↗

Revisiting Non-separable Binary Classification and its Applications in Anomaly Detectioncs.LG

We show linear XOR classification is possible and propose equality separation for anomaly detection.

problem Linearly separating XOR data.

method Equality separation, adapting SVM objective for data within/outside margin.

result Equality separation can detect both seen and unseen anomalies.

binary classification anomaly detection XOR problem SVM closed decision regions

2023-12-03abs ↗pdf ↗

Graph Convolution for Semi-Supervised Classification: Improved Linear Separability and Out-of-Distribution Generalizationcs.LG

Graph convolution improves linear separability and generalizes to out-of-distribution data.

problem Improving linear separability in semi-supervised classification.

method Applying graph convolution to mixtures of Gaussians in a stochastic block model.

result Graph convolution extends the linear separability regime by a factor of

1/\sqrt{D}

graph convolution semi-supervised classification linear separability out-of-distribution generalization stochastic block model

2021-02-13abs ↗pdf ↗

Large-scale randomized-coordinate descent methods with non-separable linear constraintsmath.OC

We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization. Unlike most CD methods, we do not assume the constraints to be separable, but let them be coupled linearly. To our knowledge, ours is the first CD method that allows linear coupling constraints, without making th…

2014-09-09abs ↗pdf ↗

BELIEF in Dependence: Leveraging Atomic Linearity in Data Bits for Rethinking Generalized Linear Modelsmath.ST

BELIEF framework interprets GLMs using binary linear models.

problem Understanding and interpreting generalized linear models (GLMs) with binary outcomes.

method Developed a framework called binary expansion linear effect (BELIEF) to interpret GLMs through transparent linear models.

result BELIEF framework reveals perfect predictors in complete separation scenarios.

binary linear models generalized linear models complete separation interpretation binary outcomes

2022-10-19abs ↗pdf ↗

Sample Complexity of Adversarially Robust Linear Classification on Separated Datacs.LG

New findings on robust learning with well-separated data.

problem Learning robust classifiers with well-separated classes.

method Analyzing sample complexity for linear classifiers with robustness.

result For linear classifiers on well-separated data, robust loss is at least $Ω(rac{d}{n})$.

robust learning sample complexity well-separated data linear classifiers adversarial robustness

2020-12-19abs ↗pdf ↗

Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confoundersstat.ML

We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected…

2018-07-09abs ↗pdf ↗

Generalization of an Upper Bound on the Number of Nodes Needed to Achieve Linear Separabilitystat.ML

An important issue in neural network research is how to choose the number of nodes and layers such as to solve a classification problem. We provide new intuitions based on earlier results by An et al. (2015) by deriving an upper bound on the number of nodes in networks with two hidden layers such that linear separabili…

2018-02-10abs ↗pdf ↗

Kernel PCA for Out-of-Distribution Detectioncs.LG

KPCA improves OoD detection by separating InD and OoD data.

problem Insufficiency of PCA in detecting OoD data from InD data.

method Kernel PCA (KPCA) with task-specific kernels.

result KPCA achieves superior OoD detection performance.

Kernel PCA Out-of-Distribution Deep Neural Networks Principal Component Analysis Non-linear Mapping

2024-02-05abs ↗pdf ↗

slimTrain -- A Stochastic Approximation Method for Training Separable Deep Neural Networkscs.LG

slimTrain simplifies DNN training by separating features and adapting hyperparameters.

problem Challenges in training deep neural networks, including non-convexity, non-smoothness, and hyperparameter sensitivity.

method slimTrain exploits separability in DNN architectures to reduce hyperparameter sensitivity and improve convergence.

result slimTrain outperforms existing methods with recommended hyperparameters and reduces sensitivity to remaining hyperparameters.

deep neural networks stochastic optimization separability hyperparameter sensitivity linear models

2021-09-28abs ↗pdf ↗

Unsupervised Separation of Dynamics from Pixelscs.CV

Learn object dynamics from unlabeled images.

problem Unsupervised learning of multiple object dynamics from unlabeled video sequences.

method Probabilistic model generating noisy positions, followed by non-linear rendering. Efficient inference method for querying the model.

result Efficient inference of object dynamics from unlabeled images.

unsupervised learning object dynamics image sequences state-space models non-linear rendering

2019-07-20abs ↗pdf ↗

Active and passive learning of linear separators under log-concave distributionscs.LG

We provide new results concerning label efficient, polynomial time, passive and active learning of linear separators. We prove that active learning provides an exponential improvement over PAC (passive) learning of homogeneous linear separators under nearly log-concave distributions. Building on this, we provide a comp…

2012-11-06abs ↗pdf ↗

Robust Inference Methods for Latent Group Panel Models under Possible Group Non-Separationecon.EM

Paper develops robust methods for panel data with latent groups, improving inference under group separation violations.

problem Inference in latent group panel models under group separation violations.

method Selective conditional inference approach to derive conditional distribution of coefficients given estimated group structure.

result Valid inference under violations of group separation, superior to traditional asymptotic methods.

latent group models conditional inference panel data robust inference group separation violations

2025-11-23abs ↗pdf ↗

Semi-blind Source Separation via Sparse Representations and Online Dictionary Learningcs.SD

This work examines a semi-blind single-channel source separation problem. Our specific aim is to separate one source whose local structure is approximately known, from another a priori unspecified background source, given only a single linear combination of the two sources. We propose a separation technique based on lo…

2012-12-03abs ↗pdf ↗

Algorithms for slate bandits with non-separable reward functionsstat.ML

New algorithms reduce slate bandit regret for large slates, outperforming existing methods.

problem Non-separable reward functions in slate bandits with many slates.

method Design of algorithms with sub-linear regret.

result Sub-linear regret with respect to the time horizon for large number of slates.

slate bandits non-separable reward sub-linear regret large number of slates

2020-04-21abs ↗pdf ↗

Separation capacity of linear reservoirs with random connectivity matrixstat.ML

Reservoir computing's success depends on mapping different input time series to separable states.

problem Quantifying the ability of random linear reservoirs to map different input time series.

method Mathematical framework using spectral properties of the connectivity matrix.

result Separation capacity is fully characterized by the spectral properties of the connectivity matrix.

reservoir computing random matrices spectral properties separation capacity time series

2024-04-26abs ↗pdf ↗

Boosting Network Weight Separability via Feed-Backward Reconstructioncs.LG

Boosts neural network performance by improving weight separability.

problem Improving the separability of weight vectors in neural networks.

method Proposes a new evaluation metric and feed-backward reconstruction loss to encourage weight separability.

result Improves visual recognition performance across various tasks.

neural networks weight separability feed-backward reconstruction image classification face recognition

2019-10-20abs ↗pdf ↗

The Implicit Bias of AdaGrad on Separable Datastat.ML

AdaGrad on linear problems converges to SVM direction.

problem Understanding AdaGrad's implicit bias on linear classification.

method Characterizing AdaGrad's convergence direction as a quadratic optimization problem.

result AdaGrad converges to a direction similar to SVM's solution.

AdaGrad SVM Linear Classification Implicit Bias Quadratic Optimization

2019-06-09abs ↗pdf ↗

Online Infinite-Dimensional Regression: Learning Linear Operatorsstat.ML

Online learning of linear operators between infinite-dimensional spaces is possible but with limitations.

problem Learning linear operators between infinite-dimensional Hilbert spaces in an online setting.

method Online learning approach for linear operators with bounded

p

-Schatten norm, proving impossibility for operator norm.

result Separation between online learnability and uniform convergence for bounded linear operators.

online learning infinite-dimensional spaces linear operators Schatten norm operator norm

2023-09-08abs ↗pdf ↗

A Coding-Theoretic Analysis of Hyperspherical Prototypical Learning Geometrycs.LG

Paper optimizes hyperspherical prototypes for better class separation.

problem Previous HPL approaches either lack principled optimisation or are limited to one latent dimension.

method Develops a principled optimisation procedure and uses linear block codes to create well-separated prototypes in various dimensions.

result Optimal prototype placement is characterized with achievable and converse bounds, showing near-optimality.

Hyperspherical Prototypical Learning Optimization Linear Block Codes Class Separation Prototype Placement

2024-07-10abs ↗pdf ↗

Informed Group-Sparse Representation for Singing Voice Separationeess.AS

Singing voice separation attempts to separate the vocal and instrumental parts of a music recording, which is a fundamental problem in music information retrieval. Recent work on singing voice separation has shown that the low-rank representation and informed separation approaches are both able to improve separation qu…

2018-01-09abs ↗pdf ↗

Grokking at the Edge of Linear Separabilitystat.ML

Grokking occurs in simple binary logistic classification near linear separability and noise.

problem Delayed generalization in binary logistic classification.

method Analytical and empirical insights into gradient descent dynamics near critical points.

result Logistic regression exhibits grokking when training data is nearly linearly separable from the origin with strong noise.

grokking gradient descent binary classification linear separability noise

2024-10-06abs ↗pdf ↗

Hierarchical Probabilistic Model for Blind Source Separation via Legendre Transformationstat.ML

A new method for blind source separation using hierarchical structure and KL divergence.

problem Blind source separation of complex interacting signals.

method Hierarchical log-linear model with KL divergence minimization.

result Superior performance compared to existing techniques on images and time series data.

blind source separation information geometry KL divergence hierarchical model complex interactions

2019-09-25abs ↗pdf ↗

On the achievability of blind source separation for high-dimensional nonlinear source mixturesstat.ML

For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world data that involve nonlinear source mixtures. This work theoretically validates that…

2018-08-02abs ↗pdf ↗

Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexityeess.SP

Algorithm finds frequencies, amplitudes, and phases of sinusoids in noisy data.

problem Finding frequencies, amplitudes, and phases of sinusoids in noisy data.

method Maximum likelihood approach to estimate tone parameters from contaminated observations. Successively estimates frequencies and jointly optimizes amplitudes and phases.

result Near-linear computational complexity (O(N)) for estimating

M

number of sinusoidal sources.

Blind source separation Sinusoids Maximum likelihood Frequency estimation Amplitude estimation

2022-03-27abs ↗pdf ↗

Calculation of Entailed Rank Constraints in Partially Non-Linear and Cyclic Modelscs.AI

The Trek Separation Theorem (Sullivant et al. 2010) states necessary and sufficient conditions for a linear directed acyclic graphical model to entail for all possible values of its linear coefficients that the rank of various sub-matrices of the covariance matrix is less than or equal to n, for any given n. In this pa…

2013-09-17abs ↗pdf ↗

A Projection Pursuit Forest Algorithm for Supervised Classificationstat.ML

This paper presents a new ensemble learning method for classification problems called projection pursuit random forest (PPF). PPF uses the PPtree algorithm introduced in Lee et al. (2013). In PPF, trees are constructed by splitting on linear combinations of randomly chosen variables. Projection pursuit is used to choos…

2018-07-19abs ↗pdf ↗

Learning Bijective Feature Maps for Linear ICAcs.LG

New model separates images into independent factors quickly and easily.

problem Separating high-dimensional data like images into independent latent factors.

method Combines bijective feature maps with linear ICA model on the Stiefel manifold.

result Models converge quickly and achieve better unsupervised latent factor discovery.

ICA bijective feature maps linear ICA Stiefel manifold image data

2020-02-18abs ↗pdf ↗