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Bibliographic Details
Main Authors:	Braun, Guillaume, Bao, Han, Huang, Wei, Imaizumi, Masaaki
Format:	Preprint
Published:	2026
Subjects:	Machine Learning
Online Access:	https://arxiv.org/abs/2601.22652
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Neuron Block Dynamics for XOR Classification with Zero-Margin
by: Braun, Guillaume, et al.
Published: (2026)

Fast Escape, Slow Convergence: Learning Dynamics of Phase Retrieval under Power-Law Data
by: Braun, Guillaume, et al.
Published: (2025)

Dichotomy of Feature Learning and Unlearning: Fast-Slow Analysis on Neural Networks with Stochastic Gradient Descent
by: Imai, Shota, et al.
Published: (2026)

High-Dimensional Limit of Stochastic Gradient Flow via Dynamical Mean-Field Theory
by: Nishiyama, Sota, et al.
Published: (2026)

Effect of Weight Quantization on Learning Models by Typical Case Analysis
by: Kashiwamura, Shuhei, et al.
Published: (2024)

Precise gradient descent training dynamics for finite-width multi-layer neural networks
by: Han, Qiyang, et al.
Published: (2025)

Robust Gradient Descent for Phase Retrieval
by: Buna, Alex, et al.
Published: (2024)

Iteration and Stochastic First-order Oracle Complexities of Stochastic Gradient Descent using Constant and Decaying Learning Rates
by: Imaizumi, Kento, et al.
Published: (2024)

Spectrum-Adaptive Generalization Bounds for Trained Deep Transformers
by: Sakai, Mana, et al.
Published: (2026)

High-dimensional Contextual Bandit Problem without Sparsity
by: Komiyama, Junpei, et al.
Published: (2023)

Extended Wasserstein-GAN Approach to Causal Distribution Learning: Density-Free Estimation and Minimax Optimality
by: Tamano, Shu, et al.
Published: (2026)

Approximation of Permutation Invariant Polynomials by Transformers: Efficient Construction in Column-Size
by: Takeshita, Naoki, et al.
Published: (2025)

Benign Overfitting in Time Series Linear Models with Over-Parameterization
by: Nakakita, Shogo, et al.
Published: (2022)

Precise Dynamics of Diagonal Linear Networks: A Unifying Analysis by Dynamical Mean-Field Theory
by: Nishiyama, Sota, et al.
Published: (2025)

Finite-Sample Inference for Sparsely Permuted Linear Regression
by: Ota, Hirofumi, et al.
Published: (2026)

Bayesian Analysis for Over-parameterized Linear Model via Effective Spectra
by: Wakayama, Tomoya, et al.
Published: (2023)

Minimax Rates of Estimation for Optimal Transport Map between Infinite-Dimensional Spaces
by: Ponnoprat, Donlapark, et al.
Published: (2025)

Automatic Domain Adaptation by Transformers in In-Context Learning
by: Hataya, Ryuichiro, et al.
Published: (2024)

Zero Generalization Error Theorem for Random Interpolators via Algebraic Geometry
by: Yoshida, Naoki, et al.
Published: (2025)

Infinite-Width Limit of a Single Attention Layer: Analysis via Tensor Programs
by: Sakai, Mana, et al.
Published: (2025)

Effect of Random Learning Rate: Theoretical Analysis of SGD Dynamics in Non-Convex Optimization via Stationary Distribution
by: Yoshida, Naoki, et al.
Published: (2024)

Optimal Dynamic Regret by Transformers for Non-Stationary Reinforcement Learning
by: Chen, Baiyuan, et al.
Published: (2025)

High-dimensional Nonparametric Contextual Bandit Problem
by: Iwazaki, Shogo, et al.
Published: (2025)

Minimax Optimal Estimation of Transport-Growth Pairs in Unbalanced Optimal Transport
by: Ponnoprat, Donlapark, et al.
Published: (2026)

Anti Mode-Collapse in Mean-Field Transformer via Auxiliary Variables
by: Imaizumi, Masaaki, et al.
Published: (2026)

Any-stepsize Gradient Descent for Separable Data under Fenchel-Young Losses
by: Bao, Han, et al.
Published: (2025)

Parameter-free Clipped Gradient Descent Meets Polyak
by: Takezawa, Yuki, et al.
Published: (2024)

On the Optimization and Generalization of Two-layer Transformers with Sign Gradient Descent
by: Li, Bingrui, et al.
Published: (2024)

Federated Learning with Relative Fairness
by: Nakakita, Shogo, et al.
Published: (2024)

Demystifying MaskGIT Sampler and Beyond: Adaptive Order Selection in Masked Diffusion
by: Hayakawa, Satoshi, et al.
Published: (2025)

Stochastic Gradient Descent in the Saddle-to-Saddle Regime of Deep Linear Networks
by: Corlouer, Guillaume, et al.
Published: (2026)

Gradient Descent as a Shrinkage Operator for Spectral Bias
by: Lucey, Simon
Published: (2025)

Distillation of Discrete Diffusion through Dimensional Correlations
by: Hayakawa, Satoshi, et al.
Published: (2024)

Federated Unlearning with Gradient Descent and Conflict Mitigation
by: Pan, Zibin, et al.
Published: (2024)

How Does Label Noise Gradient Descent Improve Generalization in the Low SNR Regime?
by: Huang, Wei, et al.
Published: (2025)

Harmonized Gradient Descent for Class Imbalanced Data Stream Online Learning
by: Zhou, Han, et al.
Published: (2025)

Learning High-Dimensional Parity Functions with Product Networks using Gradient Descent
by: Larue, Guillaume, et al.
Published: (2026)

Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers
by: Isobe, Noboru, et al.
Published: (2026)

Occam Gradient Descent
by: Kausik, B. N.
Published: (2024)

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// 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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