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Bibliographic Details
Main Authors:	Adam, Maxwell, Furman, Zach, Hoogland, Jesse
Format:	Preprint
Published:	2025
Subjects:	Machine Learning
Online Access:	https://arxiv.org/abs/2509.26537
Tags:	Add Tag No Tags, Be the first to tag this record!

Differentiation and Specialization of Attention Heads via the Refined Local Learning Coefficient
by: Wang, George, et al.
Published: (2024)

Influence Dynamics and Stagewise Data Attribution
by: Lee, Jin Hwa, et al.
Published: (2025)

From Global to Local: A Scalable Benchmark for Local Posterior Sampling
by: Hitchcock, Rohan, et al.
Published: (2025)

Structural Inference: Interpreting Small Language Models with Susceptibilities
by: Baker, Garrett, et al.
Published: (2025)

Estimating the Local Learning Coefficient at Scale
by: Furman, Zach, et al.
Published: (2024)

Loss Landscape Degeneracy and Stagewise Development in Transformers
by: Hoogland, Jesse, et al.
Published: (2024)

Compressibility Measures Complexity: Minimum Description Length Meets Singular Learning Theory
by: Urdshals, Einar, et al.
Published: (2025)

Dynamics of Transient Structure in In-Context Linear Regression Transformers
by: Carroll, Liam, et al.
Published: (2025)

The Local Learning Coefficient: A Singularity-Aware Complexity Measure
by: Lau, Edmund, et al.
Published: (2023)

Topological Interpretability for Deep-Learning
by: Spannaus, Adam, et al.
Published: (2023)

Fast, Accurate and Interpretable Graph Classification with Topological Kernels
by: Wesołowski, Adam, et al.
Published: (2025)

The GeometricKernels Package: Heat and Matérn Kernels for Geometric Learning on Manifolds, Meshes, and Graphs
by: Mostowsky, Peter, et al.
Published: (2024)

Interpretable Kernels
by: Groenen, Patrick J. F., et al.
Published: (2025)

Geometric Learning with Positively Decomposable Kernels
by: Da Costa, Nathael, et al.
Published: (2023)

On Mitigating the Utility-Loss in Differentially Private Learning: A new Perspective by a Geometrically Inspired Kernel Approach
by: Kumar, Mohit, et al.
Published: (2023)

Learning Interpretable Characteristic Kernels via Decision Forests
by: Panda, Sambit, et al.
Published: (2018)

Multitask learning with semiempirical orbital charges enables sample-efficient MLIPs
by: Neporozhnii, Ihor, et al.
Published: (2026)

Survival Kernets: Scalable and Interpretable Deep Kernel Survival Analysis with an Accuracy Guarantee
by: Chen, George H.
Published: (2022)

Deep Learning for Modeling and Dispatching Hybrid Wind Farm Power Generation
by: Lawrence, Zach, et al.
Published: (2025)

A Tutorial on Dimensionless Learning: Geometric Interpretation and the Effect of Noise
by: Gan, Zhengtao Jake, et al.
Published: (2025)

IIKL: Isometric Immersion Kernel Learning with Riemannian Manifold for Geometric Preservation
by: Chen, Zihao, et al.
Published: (2025)

Eliciting Latent Predictions from Transformers with the Tuned Lens
by: Belrose, Nora, et al.
Published: (2023)

Applying Deep Learning to Anomaly Detection of Russian Satellite Activity for Indications Prior to Military Activity
by: Kurtenbach, David, et al.
Published: (2025)

Towards Understanding Sensitive and Decisive Patterns in Explainable AI: A Case Study of Model Interpretation in Geometric Deep Learning
by: Zhu, Jiajun, et al.
Published: (2024)

Response to Promises and Pitfalls of Deep Kernel Learning
by: Wilson, Andrew Gordon, et al.
Published: (2025)

Deep Kernel Learning for Stratifying Glaucoma Trajectories
by: Rushing, Bruce, et al.
Published: (2026)

Recurrent Deep Kernel Learning of Dynamical Systems
by: Botteghi, Nicolò, et al.
Published: (2024)

Are Foundation Models Useful for Bankruptcy Prediction?
by: Kostrzewa, Marcin, et al.
Published: (2025)

Deep Kernel Aalen-Johansen Estimator: An Interpretable and Flexible Neural Net Framework for Competing Risks
by: Shen, Xiaobin, et al.
Published: (2025)

Functional Scaling Laws in Kernel Regression: Loss Dynamics and Learning Rate Schedules
by: Li, Binghui, et al.
Published: (2025)

You Are What You Eat -- AI Alignment Requires Understanding How Data Shapes Structure and Generalisation
by: Lehalleur, Simon Pepin, et al.
Published: (2025)

Differentiable Kernel Ridge Regression for Deep Learning Pipelines
by: Mercier, Jean-Marc, et al.
Published: (2026)

Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent
by: Kumar, Mohit, et al.
Published: (2024)

A Geometric Modeling of Occam's Razor in Deep Learning
by: Sun, Ke, et al.
Published: (2019)

Data-Driven Integration Kernels for Interpretable Nonlocal Operator Learning
by: Ferretti, Savannah L., et al.
Published: (2026)

Promises of Deep Kernel Learning for Control Synthesis
by: Reed, Robert, et al.
Published: (2023)

Rhomboid Tiling for Geometric Graph Deep Learning
by: Zhang, Yipeng, et al.
Published: (2025)

The Role of Fibration Symmetries in Geometric Deep Learning
by: Velarde, Osvaldo, et al.
Published: (2024)

Stochastic Kernel Regularisation Improves Generalisation in Deep Kernel Machines
by: Milsom, Edward, 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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