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Bibliographic Details
Main Authors:	Demir, Samet, Dogan, Zafer
Format:	Preprint
Published:	2025
Subjects:	Machine Learning
Online Access:	https://arxiv.org/abs/2503.00856
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Learning Beyond the Gaussian Data: Learning Dynamics of Neural Networks on an Expressive and Cumulant-Controllable Data Model
by: Ure, Onat, et al.
Published: (2026)

Asymptotic Study of In-context Learning with Random Transformers through Equivalent Models
by: Demir, Samet, et al.
Published: (2025)

Optimal Attention Temperature Improves the Robustness of In-Context Learning under Distribution Shift in High Dimensions
by: Demir, Samet, et al.
Published: (2025)

Input-Label Correlation Governs a Linear-to-Nonlinear Transition in Random Features under Spiked Covariance
by: Demir, Samet, et al.
Published: (2024)

Implicitly Normalized Online PCA: A Regularized Algorithm with Exact High-Dimensional Dynamics
by: Demir, Samet, et al.
Published: (2025)

Learning Rate Should Scale Inversely with High-Order Data Moments in High-Dimensional Online Independent Component Analysis
by: Gultekin, M. Oguzhan, et al.
Published: (2025)

Benefits of Online Tilted Empirical Risk Minimization: A Case Study of Outlier Detection and Robust Regression
by: Yildirim, Yigit E., et al.
Published: (2025)

Learnability and Competition in High-Dimensional Multi-Component ICA
by: Genc, Eser Ilke, et al.
Published: (2026)

Exploring the Precise Dynamics of Single-Layer GAN Models: Leveraging Multi-Feature Discriminators for High-Dimensional Subspace Learning
by: Bond, Andrew, et al.
Published: (2024)

A Theory of Non-Linear Feature Learning with One Gradient Step in Two-Layer Neural Networks
by: Moniri, Behrad, et al.
Published: (2023)

Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent
by: Moniri, Behrad, et al.
Published: (2026)

How Two-Layer Neural Networks Learn, One (Giant) Step at a Time
by: Dandi, Yatin, et al.
Published: (2023)

Convergence Analysis of Two-Layer Neural Networks under Gaussian Input Masking
by: Kolomvaki, Afroditi, et al.
Published: (2026)

Latent Chain-of-Thought Improves Structured-Data Transformers
by: Dudley, Carson, et al.
Published: (2026)

How Does Gradient Descent Learn Features -- A Local Analysis for Regularized Two-Layer Neural Networks
by: Zhou, Mo, et al.
Published: (2024)

Step by Step: Adaptive Gradient Descent for Training L-Lipschitz Neural Networks
by: Sung, Kyle, et al.
Published: (2025)

One-Pass Sparsified Gaussian Mixtures
by: Kightley, Eric, et al.
Published: (2019)

Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks
by: Jin, Bangti, et al.
Published: (2025)

Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks
by: Xu, Xianliang, et al.
Published: (2024)

Balancing Learning Rates Across Layers: Exact Two-Step Dynamics and Optimal Scaling in Linear Neural Networks
by: Pang, Tianyu, et al.
Published: (2026)

A Gap Between the Gaussian RKHS and Neural Networks: An Infinite-Center Asymptotic Analysis
by: Kumar, Akash, et al.
Published: (2025)

Provable Unlearning with Gradient Ascent on Two-Layer ReLU Neural Networks
by: Melamed, Odelia, et al.
Published: (2025)

Diffusion Model Conditioning on Gaussian Mixture Model and Negative Gaussian Mixture Gradient
by: Lu, Weiguo, et al.
Published: (2024)

uGMM-NN: Univariate Gaussian Mixture Model Neural Network
by: Ali, Zakeria Sharif
Published: (2025)

Generalization Guarantees of Gradient Descent for Multi-Layer Neural Networks
by: Wang, Puyu, et al.
Published: (2023)

Stochastic Gradient Descent for Two-layer Neural Networks
by: Cao, Dinghao, et al.
Published: (2024)

A Unified Framework for Data-Free One-Step Sampling via Wasserstein Gradient Flows
by: Wang, Chenguang, et al.
Published: (2026)

Asymptotic Smoothing of the Lipschitz Loss Landscape in Overparameterized One-Hidden-Layer ReLU Networks
by: Baturin, Saveliy
Published: (2026)

Global Convergence of Gradient EM for Over-Parameterized Gaussian Mixtures
by: Zhou, Mo, et al.
Published: (2025)

Effective Capacitance Modeling Using Graph Neural Networks
by: Dogan, Eren, et al.
Published: (2025)

Analyzing Neural Scaling Laws in Two-Layer Networks with Power-Law Data Spectra
by: Worschech, Roman, et al.
Published: (2024)

Rethinking Benign Overfitting in Two-Layer Neural Networks
by: Xu, Ruichen, et al.
Published: (2025)

Analytic Convolutional Layer: A Step to Analytic Neural Network
by: Cui, Jingmao, et al.
Published: (2024)

On the Hardness of Learning One Hidden Layer Neural Networks
by: Li, Shuchen, et al.
Published: (2024)

A Lightweight and Gradient-Stable Neural Layer
by: Yu, Yueyao, et al.
Published: (2021)

Absence of Closed-Form Descriptions for Gradient Flow in Two-Layer Narrow Networks
by: Park, Yeachan
Published: (2024)

One-Step Graph-Structured Neural Flows for Irregular Multivariate Time Series Classification
by: Gao, Mengzhou, et al.
Published: (2026)

Structured Diffusion Models with Mixture of Gaussians as Prior Distribution
by: Jia, Nanshan, et al.
Published: (2024)

Graph Neural Network Generalization with Gaussian Mixture Model Based Augmentation
by: Abbahaddou, Yassine, et al.
Published: (2024)

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

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