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Bibliographic Details
Main Author:	Yan, Hedong
Format:	Preprint
Published:	2025
Subjects:	Artificial Intelligence Machine Learning Statistics Theory
Online Access:	https://arxiv.org/abs/2503.21138
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O(d/T) Convergence Theory for Diffusion Probabilistic Models under Minimal Assumptions
by: Li, Gen, et al.
Published: (2024)

Can Generative Artificial Intelligence Survive Data Contamination? Theoretical Guarantees under Contaminated Recursive Training
by: Wang, Kevin, et al.
Published: (2026)

Counterfactual Generative Modeling with Variational Causal Inference
by: Wu, Yulun, et al.
Published: (2024)

Variational Causal Inference
by: Wu, Yulun, et al.
Published: (2022)

Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Models
by: Rajendran, Goutham, et al.
Published: (2024)

Guaranteed Recovery of Unambiguous Clusters
by: Mazooji, Kayvon, et al.
Published: (2025)

A Theory of the Mechanics of Information: Generalization Through Measurement of Uncertainty (Learning is Measuring)
by: Hazard, Christopher J., et al.
Published: (2025)

Foundations of Structural Causal Models with Latent Selection
by: Chen, Leihao, et al.
Published: (2024)

Diffusion Posterior Sampling is Computationally Intractable
by: Gupta, Shivam, et al.
Published: (2024)

Psychometric Tests for AI Agents and Their Moduli Space
by: Chojecki, Przemyslaw
Published: (2025)

Maximizing the Potential of Synthetic Data: Insights from Random Matrix Theory
by: Firdoussi, Aymane El, et al.
Published: (2024)

Scaling Laws in Linear Regression: Compute, Parameters, and Data
by: Lin, Licong, et al.
Published: (2024)

Path Regularization: A Near-Complete and Optimal Nonasymptotic Generalization Theory for Multilayer Neural Networks and Double Descent Phenomenon
by: Yu, Hao
Published: (2025)

Towards Efficient Online Exploration for Reinforcement Learning with Human Feedback
by: Li, Gen, et al.
Published: (2025)

Efficient Knowledge Distillation via Curriculum Extraction
by: Gupta, Shivam, et al.
Published: (2025)

Generalization Bounds: Perspectives from Information Theory and PAC-Bayes
by: Hellström, Fredrik, et al.
Published: (2023)

Improved Guarantees for Heterogeneous Treatment-Effect Estimation via Matrix Completion
by: Mehrotra, Anay, et al.
Published: (2026)

Is a Good Foundation Necessary for Efficient Reinforcement Learning? The Computational Role of the Base Model in Exploration
by: Foster, Dylan J., et al.
Published: (2025)

Adapting to Unknown Low-Dimensional Structures in Score-Based Diffusion Models
by: Li, Gen, et al.
Published: (2024)

RACER: Risk-Aware Calibrated Efficient Routing for Large Language Models
by: Hao, Sai, et al.
Published: (2026)

How Particle-System Random Batch Methods Enhance Graph Transformer: Memory Efficiency and Parallel Computing Strategy
by: Liu, Hanwen, et al.
Published: (2025)

Beyond Demand Estimation: Consumer Surplus Evaluation via Cumulative Propensity Weights
by: Bian, Zeyu, et al.
Published: (2026)

U-Nets as Belief Propagation: Efficient Classification, Denoising, and Diffusion in Generative Hierarchical Models
by: Mei, Song
Published: (2024)

A Score-Based Density Formula, with Applications in Diffusion Generative Models
by: Li, Gen, et al.
Published: (2024)

Performative Learning Theory
by: Rodemann, Julian, et al.
Published: (2026)

Evaluating LLMs When They Do Not Know the Answer: Statistical Evaluation of Mathematical Reasoning via Comparative Signals
by: Dong, Zihan, et al.
Published: (2026)

Foundations of Top-$k$ Decoding For Language Models
by: Noarov, Georgy, et al.
Published: (2025)

Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes
by: Lu, Miao, et al.
Published: (2022)

Don't Pass@k: A Bayesian Framework for Large Language Model Evaluation
by: Hariri, Mohsen, et al.
Published: (2025)

Statistical inference with belief functions: A survey
by: Cuzzolin, Fabio
Published: (2026)

A Quantitative Characterization of Forgetting in Post-Training
by: Balasubramanian, Krishnakumar, et al.
Published: (2026)

The Geometry of Benchmarks: A New Path Toward AGI
by: Chojecki, Przemyslaw
Published: (2025)

Deep Ensembles for Epistemic Uncertainty: A Frequentist Perspective
by: Jain, Anchit, et al.
Published: (2025)

A Fine-Grained Understanding of Uniform Convergence for Halfspaces
by: Kontorovich, Aryeh, et al.
Published: (2026)

A Diffusion Analysis of Policy Gradient for Stochastic Bandits
by: Lattimore, Tor
Published: (2026)

Enjoying Non-linearity in Multinomial Logistic Bandits: A Minimax-Optimal Algorithm
by: Boudart, Pierre, et al.
Published: (2025)

A note on the impossibility of conditional PAC-efficient reasoning in large language models
by: Zeng, Hao
Published: (2025)

A Statistical Analysis of Deep Federated Learning for Intrinsically Low-dimensional Data
by: Chakraborty, Saptarshi, et al.
Published: (2024)

Low-Dimensional Adaptation of Rectified Flow: A Diffusion and Stochastic Localization Perspective
by: Roy, Saptarshi, 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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