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Main Authors:	Mousavi-Hosseini, Alireza, Erdogdu, Murat A.
Format:	Preprint
Published:	2026
Subjects:	Machine Learning Artificial Intelligence
Online Access:	https://arxiv.org/abs/2603.06957
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Learning Multi-Index Models with Neural Networks via Mean-Field Langevin Dynamics
by: Mousavi-Hosseini, Alireza, et al.
Published: (2024)

From Information to Generative Exponent: Learning Rate Induces Phase Transitions in SGD
by: Tsiolis, Konstantinos Christopher, et al.
Published: (2025)

When Do Transformers Outperform Feedforward and Recurrent Networks? A Statistical Perspective
by: Mousavi-Hosseini, Alireza, et al.
Published: (2025)

A Separation in Heavy-Tailed Sampling: Gaussian vs. Stable Oracles for Proximal Samplers
by: He, Ye, et al.
Published: (2024)

Distributional Training Data Attribution: What do Influence Functions Sample?
by: Mlodozeniec, Bruno, et al.
Published: (2025)

Training Large Language Models to Reason via EM Policy Gradient
by: Xu, Tianbing
Published: (2025)

Pruning is Optimal for Learning Sparse Features in High-Dimensions
by: Vural, Nuri Mert, et al.
Published: (2024)

Imbalanced Gradients in RL Post-Training of Multi-Task LLMs
by: Wu, Runzhe, et al.
Published: (2025)

DVPO: Distributional Value Modeling-based Policy Optimization for LLM Post-Training
by: Zhu, Dingwei, et al.
Published: (2025)

GVPO: Group Variance Policy Optimization for Large Language Model Post-Training
by: Zhang, Kaichen, et al.
Published: (2025)

Trust the Batch, On- or Off-Policy: Adaptive Policy Optimization for RL Post-Training
by: Fakoor, Rasool, et al.
Published: (2026)

BWLA: Breaking the Barrier of W1AX Post-Training Quantization for LLMs
by: Zhao, Zhixiong, et al.
Published: (2026)

Off-OAB: Off-Policy Policy Gradient Method with Optimal Action-Dependent Baseline
by: Meng, Wenjia, et al.
Published: (2024)

Gradient Extrapolation-Based Policy Optimization
by: Swapnil, Ismam Nur, et al.
Published: (2026)

Lightning OPD: Efficient Post-Training for Large Reasoning Models with Offline On-Policy Distillation
by: Wu, Yecheng, et al.
Published: (2026)

Policy-Gradient Training of Language Models for Ranking
by: Gao, Ge, et al.
Published: (2023)

On the Global Optimality of Policy Gradient Methods in General Utility Reinforcement Learning
by: Barakat, Anas, et al.
Published: (2024)

Optimal Control-Based Baseline for Guided Exploration in Policy Gradient Methods
by: Lyu, Xubo, et al.
Published: (2020)

Offline Model-Based Optimization via Policy-Guided Gradient Search
by: Chemingui, Yassine, et al.
Published: (2024)

Preference Goal Tuning: Post-Training as Latent Control for Frozen Policies
by: Zhao, Guangyu, et al.
Published: (2024)

Large Language Model Post-Training: A Unified View of Off-Policy and On-Policy Learning
by: Zhao, Shiwan, et al.
Published: (2026)

Performative Policy Gradient: Optimality in Performative Reinforcement Learning
by: Basu, Debabrota, et al.
Published: (2025)

Optimal Excess Risk Bounds for Empirical Risk Minimization on $p$-Norm Linear Regression
by: Hanchi, Ayoub El, et al.
Published: (2023)

Beyond GRPO and On-Policy Distillation: An Empirical Sparse-to-Dense Reward Principle for Language-Model Post-Training
by: Xu, Yuanda, et al.
Published: (2026)

DP-OPD: Differentially Private On-Policy Distillation for Language Models
by: Khadem, Fatemeh, et al.
Published: (2026)

Entropy-Gated Selective Policy Optimization:Token-Level Gradient Allocation for Hybrid Training of Large Language Models
by: Hu, Yuelin, et al.
Published: (2026)

Representation-Based Exploration for Language Models: From Test-Time to Post-Training
by: Tuyls, Jens, et al.
Published: (2025)

Certification for Differentially Private Prediction in Gradient-Based Training
by: Wicker, Matthew, et al.
Published: (2024)

Learning General Policies with Policy Gradient Methods
by: Ståhlberg, Simon, et al.
Published: (2025)

RiskPO: Risk-based Policy Optimization via Verifiable Reward for LLM Post-Training
by: Ren, Tao, et al.
Published: (2025)

Policy Gradient with Kernel Quadrature
by: Hayakawa, Satoshi, et al.
Published: (2023)

Policy Gradient with Tree Expansion
by: Dalal, Gal, et al.
Published: (2023)

Debate as Reward: A Multi-Agent Reward System for Scientific Ideation via RL Post-Training
by: Salimi, Moein, et al.
Published: (2026)

Dr. Post-Training: A Data Regularization Perspective on LLM Post-Training
by: Hu, Pingbang, et al.
Published: (2026)

Robust Finite-Memory Policy Gradients for Hidden-Model POMDPs
by: Galesloot, Maris F. L., et al.
Published: (2025)

Do Transformer World Models Give Better Policy Gradients?
by: Ma, Michel, et al.
Published: (2024)

$Q\sharp$: Provably Optimal Distributional RL for LLM Post-Training
by: Zhou, Jin Peng, et al.
Published: (2025)

Post-Training is About States, Not Tokens: A State Distribution View of SFT, RL, and On-Policy Distillation
by: Nie, Dong
Published: (2026)

Partial Policy Gradients for RL in LLMs
by: Mathur, Puneet, et al.
Published: (2026)

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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