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Tag: neural

  • Random Features for Operator-Valued Kernels: Bridging Kernel Methods and Neural Operators

    Random Features for Operator-Valued Kernels: Bridging Kernel Methods and Neural Operators arXiv:2603.00971v1 Announce Type: new Abstract: In this work, we investigate the generalization properties of random feature methods. Our analysis extends prior results for Tikhonov regularization to a broad class of spectral regularization techniques and further generalizes the setting to operator-valued kernels. This unified framework…

  • Algebraic Robustness Verification of Neural Networks

    Algebraic Robustness Verification of Neural Networks arXiv:2602.06105v1 Announce Type: new Abstract: We formulate formal robustness verification of neural networks as an algebraic optimization problem. We leverage the Euclidean Distance (ED) degree, which is the generic number of complex critical points of the distance minimization problem to a classifier’s decision boundary, as an architecture-dependent measure of…

  • How Convolutional Neural Networks Learn Musical Similarity

    How Convolutional Neural Networks Learn Musical Similarity Learning audio embeddings with contrastive learning and deploying them in a real music recommendation app The post How Convolutional Neural Networks Learn Musical Similarity appeared first on Towards Data Science. Luke Stuckey Go to original source

  • How to Build a Neural Machine Translation System for a Low-Resource Language

    How to Build a Neural Machine Translation System for a Low-Resource Language An introduction to neural machine translation The post How to Build a Neural Machine Translation System for a Low-Resource Language appeared first on Towards Data Science. Kaixuan Chen Go to original source

  • Teaching a Neural Network the Mandelbrot Set

    Teaching a Neural Network the Mandelbrot Set And why Fourier features change everything The post Teaching a Neural Network the Mandelbrot Set appeared first on Towards Data Science. Carlos Redondo Go to original source

  • Aligned explanations in neural networks

    Aligned explanations in neural networks arXiv:2601.04378v1 Announce Type: cross Abstract: Feature attribution is the dominant paradigm for explaining deep neural networks. However, most existing methods only loosely reflect the model’s prediction-making process, thereby merely white-painting the black box. We argue that explanatory alignment is a key aspect of trustworthiness in prediction tasks: explanations must be…

  • Neural Networks on Symmetric Spaces of Noncompact Type

    Neural Networks on Symmetric Spaces of Noncompact Type arXiv:2601.01097v1 Announce Type: new Abstract: Recent works have demonstrated promising performances of neural networks on hyperbolic spaces and symmetric positive definite (SPD) manifolds. These spaces belong to a family of Riemannian manifolds referred to as symmetric spaces of noncompact type. In this paper, we propose a novel…

  • The Machine Learning “Advent Calendar” Day 17: Neural Network Regressor in Excel

    The Machine Learning “Advent Calendar” Day 17: Neural Network Regressor in Excel Neural networks often feel like black boxes. In this article, we build a neural network regressor from scratch using only Excel formulas. By making every step explicit, from forward propagation to backpropagation, we show how a neural network learns to approximate non-linear functions…

  • WTNN: Weibull-Tailored Neural Networks for survival analysis

    WTNN: Weibull-Tailored Neural Networks for survival analysis arXiv:2512.09163v1 Announce Type: new Abstract: The Weibull distribution is a commonly adopted choice for modeling the survival of systems subject to maintenance over time. When only proxy indicators and censored observations are available, it becomes necessary to express the distribution’s parameters as functions of time-dependent covariates. Deep neural…

  • Neural Networks Are Blurry, Symbolic Systems Are Fragmented. Sparse Autoencoders Help Us Combine Them.

    Neural Networks Are Blurry, Symbolic Systems Are Fragmented. Sparse Autoencoders Help Us Combine Them. Neural and symbolic models compress the world in fundamentally different ways, and Sparse Autoencoders (SAEs) offer a bridge to connect them. The post Neural Networks Are Blurry, Symbolic Systems Are Fragmented. Sparse Autoencoders Help Us Combine Them. appeared first on Towards…

  • Neural Networks Learn Generic Multi-Index Models Near Information-Theoretic Limit

    Neural Networks Learn Generic Multi-Index Models Near Information-Theoretic Limit arXiv:2511.15120v1 Announce Type: new Abstract: In deep learning, a central issue is to understand how neural networks efficiently learn high-dimensional features. To this end, we explore the gradient descent learning of a general Gaussian Multi-index model $f(boldsymbol{x})=g(boldsymbol{U}boldsymbol{x})$ with hidden subspace $boldsymbol{U}in mathbb{R}^{rtimes d}$, which is the…

  • Understanding Convolutional Neural Networks (CNNs) Through Excel

    Understanding Convolutional Neural Networks (CNNs) Through Excel Deep learning is often seen as a black box. We know that it learns from data, but we rarely stop to ask how it truly learns. What if we could open that box and watch each step happen right before our eyes? With Excel, we can do exactly…

  • Neural Local Wasserstein Regression

    Neural Local Wasserstein Regression arXiv:2511.10824v1 Announce Type: new Abstract: We study the estimation problem of distribution-on-distribution regression, where both predictors and responses are probability measures. Existing approaches typically rely on a global optimal transport map or tangent-space linearization, which can be restrictive in approximation capacity and distort geometry in multivariate underlying domains. In this paper,…

  • Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths

    Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths arXiv:2511.11161v1 Announce Type: new Abstract: This paper addresses the nonparametric estimation of the drift function over a compact domain for a time-homogeneous diffusion process, based on high-frequency discrete observations from $N$ independent trajectories. We propose a neural network-based estimator and derive…

  • I Measured Neural Network Training Every 5 Steps for 10,000 Iterations

    I Measured Neural Network Training Every 5 Steps for 10,000 Iterations Image by Pixabay.com The post I Measured Neural Network Training Every 5 Steps for 10,000 Iterations appeared first on Towards Data Science. Javier Marin Go to original source

  • Siegel Neural Networks

    Siegel Neural Networks arXiv:2511.09577v1 Announce Type: new Abstract: Riemannian symmetric spaces (RSS) such as hyperbolic spaces and symmetric positive definite (SPD) manifolds have become popular spaces for representation learning. In this paper, we propose a novel approach for building discriminative neural networks on Siegel spaces, a family of RSS that is largely unexplored in machine…

  • Accuracy estimation of neural networks by extreme value theory

    Accuracy estimation of neural networks by extreme value theory arXiv:2511.00490v1 Announce Type: new Abstract: Neural networks are able to approximate any continuous function on a compact set. However, it is not obvious how to quantify the error of the neural network, i.e., the remaining bias between the function and the neural network. Here, we propose…

  • Bayesian neural networks with interpretable priors from Mercer kernels

    Bayesian neural networks with interpretable priors from Mercer kernels arXiv:2510.23745v1 Announce Type: new Abstract: Quantifying the uncertainty in the output of a neural network is essential for deployment in scientific or engineering applications where decisions must be made under limited or noisy data. Bayesian neural networks (BNNs) provide a framework for this purpose by constructing…

  • Neural Networks for Censored Expectile Regression Based on Data Augmentation

    Neural Networks for Censored Expectile Regression Based on Data Augmentation arXiv:2510.20344v1 Announce Type: new Abstract: Expectile regression neural networks (ERNNs) are powerful tools for capturing heterogeneity and complex nonlinear structures in data. However, most existing research has primarily focused on fully observed data, with limited attention paid to scenarios involving censored observations. In this paper,…

  • Distributionally robust approximation property of neural networks

    Distributionally robust approximation property of neural networks arXiv:2510.09177v1 Announce Type: new Abstract: The universal approximation property uniformly with respect to weakly compact families of measures is established for several classes of neural networks. To that end, we prove that these neural networks are dense in Orlicz spaces, thereby extending classical universal approximation theorems even beyond…

  • CINDES: Classification induced neural density estimator and simulator

    CINDES: Classification induced neural density estimator and simulator arXiv:2510.00367v1 Announce Type: new Abstract: Neural network-based methods for (un)conditional density estimation have recently gained substantial attention, as various neural density estimators have outperformed classical approaches in real-data experiments. Despite these empirical successes, implementation can be challenging due to the need to ensure non-negativity and unit-mass constraints,…

  • Neural Optimal Transport Meets Multivariate Conformal Prediction

    Neural Optimal Transport Meets Multivariate Conformal Prediction arXiv:2509.25444v1 Announce Type: new Abstract: We propose a framework for conditional vector quantile regression (CVQR) that combines neural optimal transport with amortized optimization, and apply it to multivariate conformal prediction. Classical quantile regression does not extend naturally to multivariate responses, while existing approaches often ignore the geometry of…

  • PyTorch Explained: From Automatic Differentiation to Training Custom Neural Networks

    PyTorch Explained: From Automatic Differentiation to Training Custom Neural Networks Deep learning is shaping our world as we speak. In fact, it has been slowly revolutionizing software since the early 2010s. In 2025, PyTorch is at the forefront of this revolution, emerging as one of the most important libraries to train neural networks. Whether you…

  • From Genes to Neural Networks: Understanding and Building NEAT (Neuro-Evolution of Augmenting Topologies) from Scratch

    From Genes to Neural Networks: Understanding and Building NEAT (Neuro-Evolution of Augmenting Topologies) from Scratch Practical Neuroevolution: Reproducing NEAT’s Innovations and Code Walkthrough The post From Genes to Neural Networks: Understanding and Building NEAT (Neuro-Evolution of Augmenting Topologies) from Scratch appeared first on Towards Data Science. Carlos Redondo Go to original source

  • Regime-Aware Conditional Neural Processes with Multi-Criteria Decision Support for Operational Electricity Price Forecasting

    Regime-Aware Conditional Neural Processes with Multi-Criteria Decision Support for Operational Electricity Price Forecasting arXiv:2508.00040v1 Announce Type: cross Abstract: This work integrates Bayesian regime detection with conditional neural processes for 24-hour electricity price prediction in the German market. Our methodology integrates regime detection using a disentangled sticky hierarchical Dirichlet process hidden Markov model (DS-HDP-HMM) applied to…

  • Simulating Posterior Bayesian Neural Networks with Dependent Weights

    Simulating Posterior Bayesian Neural Networks with Dependent Weights arXiv:2507.22095v1 Announce Type: new Abstract: In this paper we consider posterior Bayesian fully connected and feedforward deep neural networks with dependent weights. Particularly, if the likelihood is Gaussian, we identify the distribution of the wide width limit and provide an algorithm to sample from the network. In…

  • Graph neural networks for residential location choice: connection to classical logit models

    Graph neural networks for residential location choice: connection to classical logit models arXiv:2507.21334v1 Announce Type: new Abstract: Researchers have adopted deep learning for classical discrete choice analysis as it can capture complex feature relationships and achieve higher predictive performance. However, the existing deep learning approaches cannot explicitly capture the relationship among choice alternatives, which has…

  • Physics-Informed Neural Networks for Inverse PDE Problems

    Physics-Informed Neural Networks for Inverse PDE Problems Solving the Heat Equation using DeepXDE. The post Physics-Informed Neural Networks for Inverse PDE Problems appeared first on Towards Data Science. Marco Hening Tallarico Go to original source

  • Bag of Coins: A Statistical Probe into Neural Confidence Structures

    Bag of Coins: A Statistical Probe into Neural Confidence Structures arXiv:2507.19774v1 Announce Type: new Abstract: Modern neural networks, despite their high accuracy, often produce poorly calibrated confidence scores, limiting their reliability in high-stakes applications. Existing calibration methods typically post-process model outputs without interrogating the internal consistency of the predictions themselves. In this work, we introduce…

  • Predicting Parkinson’s Disease Progression Using Statistical and Neural Mixed Effects Models: A Comparative Study on Longitudinal Biomarkers

    Predicting Parkinson’s Disease Progression Using Statistical and Neural Mixed Effects Models: A Comparative Study on Longitudinal Biomarkers arXiv:2507.20058v1 Announce Type: new Abstract: Predicting Parkinson’s Disease (PD) progression is crucial, and voice biomarkers offer a non-invasive method for tracking symptom severity (UPDRS scores) through telemonitoring. Analyzing this longitudinal data is challenging due to within-subject correlations and…

  • The surprising strength of weak classifiers for validating neural posterior estimates

    The surprising strength of weak classifiers for validating neural posterior estimates arXiv:2507.17026v1 Announce Type: new Abstract: Neural Posterior Estimation (NPE) has emerged as a powerful approach for amortized Bayesian inference when the true posterior $p(theta mid y)$ is intractable or difficult to sample. But evaluating the accuracy of neural posterior estimates remains challenging, with existing…

  • Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators

    Accelerating Hamiltonian Monte Carlo for Bayesian Inference in Neural Networks and Neural Operators arXiv:2507.14652v1 Announce Type: new Abstract: Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s…

  • Asymptotic convexity of wide and shallow neural networks

    Asymptotic convexity of wide and shallow neural networks arXiv:2507.01044v1 Announce Type: new Abstract: For a simple model of shallow and wide neural networks, we show that the epigraph of its input-output map as a function of the network parameters approximates epigraph of a. convex function in a precise sense. This leads to a plausible explanation…

  • Thompson Sampling in Function Spaces via Neural Operators

    Thompson Sampling in Function Spaces via Neural Operators arXiv:2506.21894v1 Announce Type: new Abstract: We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator’s output. We assume that functional evaluations are inexpensive, while queries to the operator (such as running a high-fidelity…

  • Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon

    Stable Minima of ReLU Neural Networks Suffer from the Curse of Dimensionality: The Neural Shattering Phenomenon arXiv:2506.20779v1 Announce Type: new Abstract: We study the implicit bias of flatness / low (loss) curvature and its effects on generalization in two-layer overparameterized ReLU networks with multivariate inputs — a problem well motivated by the minima stability and…

  • Posterior Contraction for Sparse Neural Networks in Besov Spaces with Intrinsic Dimensionality

    Posterior Contraction for Sparse Neural Networks in Besov Spaces with Intrinsic Dimensionality arXiv:2506.19144v1 Announce Type: new Abstract: This work establishes that sparse Bayesian neural networks achieve optimal posterior contraction rates over anisotropic Besov spaces and their hierarchical compositions. These structures reflect the intrinsic dimensionality of the underlying function, thereby mitigating the curse of dimensionality. Our…

  • Multilevel neural simulation-based inference

    Multilevel neural simulation-based inference arXiv:2506.06087v1 Announce Type: new Abstract: Neural simulation-based inference (SBI) is a popular set of methods for Bayesian inference when models are only available in the form of a simulator. These methods are widely used in the sciences and engineering, where writing down a likelihood can be significantly more challenging than constructing…

  • Models of Heavy-Tailed Mechanistic Universality

    Models of Heavy-Tailed Mechanistic Universality arXiv:2506.03470v1 Announce Type: new Abstract: Recent theoretical and empirical successes in deep learning, including the celebrated neural scaling laws, are punctuated by the observation that many objects of interest tend to exhibit some form of heavy-tailed or power law behavior. In particular, the prevalence of heavy-tailed spectral densities in Jacobians,…

  • Nash: Neural Adaptive Shrinkage for Structured High-Dimensional Regression

    Nash: Neural Adaptive Shrinkage for Structured High-Dimensional Regression arXiv:2505.11143v1 Announce Type: new Abstract: Sparse linear regression is a fundamental tool in data analysis. However, traditional approaches often fall short when covariates exhibit structure or arise from heterogeneous sources. In biomedical applications, covariates may stem from distinct modalities or be structured according to an underlying graph.…

  • Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks

    Extended Fiducial Inference for Individual Treatment Effects via Deep Neural Networks arXiv:2505.01995v1 Announce Type: new Abstract: Individual treatment effect estimation has gained significant attention in recent data science literature. This work introduces the Double Neural Network (Double-NN) method to address this problem within the framework of extended fiducial inference (EFI). In the proposed method, deep…

  • Learning the Simplest Neural ODE

    Learning the Simplest Neural ODE arXiv:2505.02019v1 Announce Type: new Abstract: Since the advent of the “Neural Ordinary Differential Equation (Neural ODE)” paper, learning ODEs with deep learning has been applied to system identification, time-series forecasting, and related areas. Exploiting the diffeomorphic nature of ODE solution maps, neural ODEs has also enabled their use in generative…

  • Balancing Interpretability and Flexibility in Modeling Diagnostic Trajectories with an Embedded Neural Hawkes Process Model

    Balancing Interpretability and Flexibility in Modeling Diagnostic Trajectories with an Embedded Neural Hawkes Process Model arXiv:2504.21795v1 Announce Type: new Abstract: The Hawkes process (HP) is commonly used to model event sequences with self-reinforcing dynamics, including electronic health records (EHRs). Traditional HPs capture self-reinforcement via parametric impact functions that can be inspected to understand how each…

  • Why Are Convolutional Neural Networks Great For Images?

    Why Are Convolutional Neural Networks Great For Images? The Universal Approximation Theorem states that a neural network with a single hidden layer and a nonlinear activation function can approximate any continuous function.  Practical issues aside, such that the number of neurons in this hidden layer would grow enormously large, we do not need other network architectures. A simple…

  • Sparse Gaussian Neural Processes

    Sparse Gaussian Neural Processes arXiv:2504.01650v1 Announce Type: new Abstract: Despite significant recent advances in probabilistic meta-learning, it is common for practitioners to avoid using deep learning models due to a comparative lack of interpretability. Instead, many practitioners simply use non-meta-models such as Gaussian processes with interpretable priors, and conduct the tedious procedure of training their…

  • Attractors in Neural Network Circuits: Beauty and Chaos

    Attractors in Neural Network Circuits: Beauty and Chaos The state space of the first two neuron activations over time follows an attractor. What is one thing in common between memories, oscillating chemical reactions and double pendulums? All these systems have a basin of attraction for possible states, like a magnet that draws the system towards certain…

  • Explainable Bayesian deep learning through input-skip Latent Binary Bayesian Neural Networks

    Explainable Bayesian deep learning through input-skip Latent Binary Bayesian Neural Networks arXiv:2503.10496v1 Announce Type: new Abstract: Modeling natural phenomena with artificial neural networks (ANNs) often provides highly accurate predictions. However, ANNs often suffer from over-parameterization, complicating interpretation and raising uncertainty issues. Bayesian neural networks (BNNs) address the latter by representing weights as probability distributions, allowing…

  • Exploring specialization and sensitivity of convolutional neural networks in the context of simultaneous image augmentations

    Exploring specialization and sensitivity of convolutional neural networks in the context of simultaneous image augmentations arXiv:2503.03283v1 Announce Type: new Abstract: Drawing parallels with the way biological networks are studied, we adapt the treatment–control paradigm to explainable artificial intelligence research and enrich it through multi-parametric input alterations. In this study, we propose a framework for investigating…

  • Post-Hoc Uncertainty Quantification in Pre-Trained Neural Networks via Activation-Level Gaussian Processes

    Post-Hoc Uncertainty Quantification in Pre-Trained Neural Networks via Activation-Level Gaussian Processes arXiv:2502.20966v1 Announce Type: new Abstract: Uncertainty quantification in neural networks through methods such as Dropout, Bayesian neural networks and Laplace approximations is either prone to underfitting or computationally demanding, rendering these approaches impractical for large-scale datasets. In this work, we address these shortcomings by…

  • Guiding Two-Layer Neural Network Lipschitzness via Gradient Descent Learning Rate Constraints

    Guiding Two-Layer Neural Network Lipschitzness via Gradient Descent Learning Rate Constraints arXiv:2502.03792v1 Announce Type: new Abstract: We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with Lipschitz activation functions, ensures…

  • Uncertainty Quantification with the Empirical Neural Tangent Kernel

    Uncertainty Quantification with the Empirical Neural Tangent Kernel arXiv:2502.02870v1 Announce Type: new Abstract: While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems. Several Bayesian uncertainty quantification (UQ) methods exist that are either cheap or reliable,…

  • Neural Networks – Intuitively and Exhaustively Explained

    Neural Networks – Intuitively and Exhaustively Explained An in-depth exploration of the most fundamental architecture in modern AI “The Thinking Part” by Daniel Warfield using MidJourney. All images by the author unless otherwise specified. Article originally made available on Intuitively and Exhaustively Explained. In this article we’ll form a thorough understanding of the neural network,…

  • Extension of Symmetrized Neural Network Operators with Fractional and Mixed Activation Functions

    Extension of Symmetrized Neural Network Operators with Fractional and Mixed Activation Functions arXiv:2501.10496v1 Announce Type: new Abstract: We propose a novel extension to symmetrized neural network operators by incorporating fractional and mixed activation functions. This study addresses the limitations of existing models in approximating higher-order smooth functions, particularly in complex and high-dimensional spaces. Our framework…

  • Globally Convergent Variational Inference

    Globally Convergent Variational Inference arXiv:2501.08201v1 Announce Type: new Abstract: In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound (ELBO), only convergence to a local optimum can be guaranteed. In this work,…

  • A Visual Understanding of Neural Networks

    A Visual Understanding of Neural Networks The math behind neural networks visually explained Continue reading on Towards Data Science » Reza Bagheri Go to original source

  • Deep Networks are Reproducing Kernel Chains

    Deep Networks are Reproducing Kernel Chains arXiv:2501.03697v1 Announce Type: cross Abstract: Identifying an appropriate function space for deep neural networks remains a key open question. While shallow neural networks are naturally associated with Reproducing Kernel Banach Spaces (RKBS), deep networks present unique challenges. In this work, we extend RKBS to chain RKBS (cRKBS), a new…

  • How Recurrent Neural Networks (RNNs) Are Revolutionizing Decision-Making Research

    How Recurrent Neural Networks (RNNs) Are Revolutionizing Decision-Making Research A deep dive into the world of computational modeling and its applications Continue reading on Towards Data Science » Kaushik Rajan Go to original source

  • Neural Networks Perform Sufficient Dimension Reduction

    Neural Networks Perform Sufficient Dimension Reduction arXiv:2412.19033v1 Announce Type: new Abstract: This paper investigates the connection between neural networks and sufficient dimension reduction (SDR), demonstrating that neural networks inherently perform SDR in regression tasks under appropriate rank regularizations. Specifically, the weights in the first layer span the central mean subspace. We establish the statistical consistency…

  • How Neural Networks Learn: A Probabilistic Viewpoint

    How Neural Networks Learn: A Probabilistic Viewpoint Understanding loss functions for training neural networks Machine learning is very hands-on, and everyone charts their own path. There isn’t a standard set of courses to follow, as was traditionally the case. There’s no ‘Machine Learning 101,’ so to speak. However, this sometimes leaves gaps in understanding. If you’re…

  • Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction

    Belted and Ensembled Neural Network for Linear and Nonlinear Sufficient Dimension Reduction arXiv:2412.08961v1 Announce Type: new Abstract: We introduce a unified, flexible, and easy-to-implement framework of sufficient dimension reduction that can accommodate both linear and nonlinear dimension reduction, and both the conditional distribution and the conditional mean as the targets of estimation. This unified framework…

  • Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs

    Nonparametric Filtering, Estimation and Classification using Neural Jump ODEs arXiv:2412.03271v1 Announce Type: new Abstract: Neural Jump ODEs model the conditional expectation between observations by neural ODEs and jump at arrival of new observations. They have demonstrated effectiveness for fully data-driven online forecasting in settings with irregular and partial observations, operating under weak regularity assumptions. This…

  • Visualizing Neural Network Internals

    Visualizing Neural Network Internals sentdex Go to original source

  • Training a neural netwok for data reduction and better generalization

    Training a neural netwok for data reduction and better generalization arXiv:2411.17180v1 Announce Type: new Abstract: The motivation for sparse learners is to compress the inputs (features) by selecting only the ones needed for good generalization. Linear models with LASSO-type regularization achieve this by setting the weights of irrelevant features to zero, effectively identifying and ignoring…