Measuring Neural Network Complexity via Effective Degrees of Freedom

Fuente: arXiv

Saved in:

Bibliographic Details
Main Authors:	Zhou, Jia, Landsittel, Douglas
Format:	Preprint
Published:	2026
Subjects:	Methodology Machine Learning 62M45
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

Efficient Neural Network Approaches for Conditional Optimal Transport with Applications in Bayesian Inference
by: Wang, Zheyu Oliver, et al.
Published: (2023)

Deep Neural Networks for Doubly Robust Estimation with Nonprobability Survey Samples
by: Dai, Yufang, et al.
Published: (2026)

Designing Time-Series Models With Hypernetworks & Adversarial Portfolios
by: Staněk, Filip
Published: (2024)

Drift Estimation for Diffusion Processes Using Neural Networks Based on Discretely Observed Independent Paths
by: Zhao, Yuzhen, et al.
Published: (2025)

Using Artificial Neural Networks to Predict Claim Duration in a Work Injury Compensation Environment
by: Almudevar, Anthony
Published: (2026)

Adaptive Retrieval helps Reasoning in LLMs -- but mostly if it's not used
by: Shakya, Srijan, et al.
Published: (2026)

A Point Process Model for Optimizing Repeated Personalized Action Delivery to Users
by: Merkov, Alexander, et al.
Published: (2025)

Critical Points of Random Neural Networks
by: Di Lillo, Simmaco
Published: (2025)

Custom Loss Functions in Fuel Moisture Modeling
by: Hirschi, Jonathon
Published: (2025)

GT-PCA: Effective and Interpretable Dimensionality Reduction with General Transform-Invariant Principal Component Analysis
by: Heinrichs, Florian
Published: (2024)

Revisiting semi-supervised training objectives for differentiable particle filters
by: Li, Jiaxi, et al.
Published: (2024)

Random Vector Functional Link Networks for Function Approximation on Manifolds
by: Needell, Deanna, et al.
Published: (2020)

Fractal and Regular Geometry of Deep Neural Networks
by: Di Lillo, Simmaco, et al.
Published: (2025)

The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence
by: Liu, Kejun
Published: (2026)

Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models
by: Mösching, Alexandre, et al.
Published: (2023)

Localized Sparse Principal Component Analysis of Multivariate Time Series in Frequency Domain
by: Namdari, Jamshid, et al.
Published: (2024)

Sharp Bounds on the Approximation Rates, Metric Entropy, and $n$-widths of Shallow Neural Networks
by: Siegel, Jonathan W., et al.
Published: (2021)

Log-Gaussian Gamma Processes for Training Bayesian Neural Networks in Raman and CARS Spectroscopies
by: Härkönen, Teemu, et al.
Published: (2023)

Towards an Algebraic Framework For Approximating Functions Using Neural Network Polynomials
by: Rafi, Shakil, et al.
Published: (2024)

Decentralized Inference for Spatial Data Using Low-Rank Models
by: Shi, Jianwei, et al.
Published: (2025)

Minimaxity and Admissibility of Bayesian Neural Networks
by: Coulson, Daniel Andrew, et al.
Published: (2026)

Generalization error bounds for two-layer neural networks with Lipschitz loss function
by: Nguwi, Jiang Yu, et al.
Published: (2026)

A Complete Symmetry Classification of Shallow ReLU Networks
by: Ramakrishnan, Pranavkrishnan
Published: (2026)

Statistical Inference with Stochastic Gradient Methods under $ϕ$-mixing Data
by: Liu, Ruiqi, et al.
Published: (2023)

Spatio-Temporal Jump Model for Urban Thermal Comfort Monitoring
by: Cortese, Federico P., et al.
Published: (2024)

Approximation Rates for Shallow ReLU$^k$ Neural Networks on Sobolev Spaces via the Radon Transform
by: Mao, Tong, et al.
Published: (2024)

Counterfactual Forecasting for Panel Data
by: Deb, Navonil, et al.
Published: (2025)

Efficient Time-Series Approximation with Linear Recurrent Neural Networks: Architecture Learning and Predictive Power
by: Stolzenburg, Frieder, et al.
Published: (2018)

Using Time Structure to Estimate Causal Effects
by: Hochsprung, Tom, et al.
Published: (2025)

Concentration inequalities for high-dimensional linear processes with dependent innovations
by: Mendes, Eduardo Fonseca, et al.
Published: (2023)

ASNN: Learning to Suggest Neural Architectures from Performance Distributions
by: Hong, Jinwook
Published: (2025)

A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems
by: Yang, Tianlin, et al.
Published: (2026)

Partial Trace-Class Bayesian Neural Networks
by: Carter, Arran, et al.
Published: (2025)

From Theory to Application: A Practical Introduction to Neural Operators in Scientific Computing
by: Jha, Prashant K.
Published: (2025)

Optimal Approximation Rates for Deep ReLU Neural Networks on Sobolev and Besov Spaces
by: Siegel, Jonathan W.
Published: (2022)

A comparison between initialization strategies for the infinite hidden Markov model
by: Cortese, Federico P., et al.
Published: (2025)

Learning non-equilibrium diffusions with Schrödinger bridges: from exactly solvable to simulation-free
by: Zhang, Stephen Y., et al.
Published: (2025)

Mixture of segmentation for heterogeneous functional data
by: Brault, Vincent, et al.
Published: (2023)

A Plug-and-Play Method with Inpainting Network for Bayesian Uncertainty Quantification in Imaging
by: Wang, Xiaoyu, et al.
Published: (2023)

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'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"d5c7f7b00ed16a6acbd2047a6c635643"
ui	"standard"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790960257.8789 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "d5c7f7b00ed16a6acbd2047a6c635643" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"VUFIND_SESSION=d5c7f7b00ed16a6acbd2047a6c635643; ui=standard; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"35972"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2602_13442/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2602_13442/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790960257.8746
REQUEST_TIME	1790960257

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"d5c7f7b00ed16a6acbd2047a6c635643"
ui	"standard"
language	"en"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790960257.8789 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "d5c7f7b00ed16a6acbd2047a6c635643" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1433}
SessionHelper	Laminas\Stdlib\ArrayObject {#1759}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"VUFIND_SESSION=d5c7f7b00ed16a6acbd2047a6c635643; ui=standard; language=en"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.217.142"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"35972"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2602_13442/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2602_13442/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790960257.8746
REQUEST_TIME	1790960257

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Similar Items

Environment & details:

Environment & details: