Understanding Transformer Architecture through Continuous Dynamics: A Partial Differential Equation Perspective

Fuente: arXiv

Salvato in:

Dettagli Bibliografici
Autori principali:	Zhang, Yukun, Zhou, Xueqing
Natura:	Preprint
Pubblicazione:	2024
Soggetti:	Machine Learning Artificial Intelligence Information Theory
Accesso online:	Acceder al recurso
Tags:	Aggiungi Tag Nessun Tag, puoi essere il primo ad aggiungerne!!

Documenti analoghi

Continuous-Time Attention: PDE-Guided Mechanisms for Long-Sequence Transformers
di: Zhang, Yukun, et al.
Pubblicazione: (2025)

Where to Add PDE Diffusion in Transformers
di: Zhang, Yukun, et al.
Pubblicazione: (2025)

Partial Information Decomposition for Data Interpretability and Feature Selection
di: Westphal, Charles, et al.
Pubblicazione: (2024)

Broadcast Channel Cooperative Gain: An Operational Interpretation of Partial Information Decomposition
di: Tian, Chao, et al.
Pubblicazione: (2025)

LLMs as Noisy Channels: A Shannon Perspective on Model Capacity and Scaling Laws
di: Ouyang, Xu, et al.
Pubblicazione: (2026)

Continual Learning-Aided Super-Resolution Scheme for Channel Reconstruction and Generalization in OFDM Systems
di: Chen, Jianqiao, et al.
Pubblicazione: (2025)

A Deep Latent Factor Graph Clustering with Fairness-Utility Trade-off Perspective
di: Ghodsi, Siamak, et al.
Pubblicazione: (2025)

Fairness Overfitting in Machine Learning: An Information-Theoretic Perspective
di: Laakom, Firas, et al.
Pubblicazione: (2025)

Accelerating Error Correction Code Transformers
di: Levy, Matan, et al.
Pubblicazione: (2024)

Uncertainty Quantification and Data Efficiency in AI: An Information-Theoretic Perspective
di: Simeone, Osvaldo, et al.
Pubblicazione: (2025)

Context Channel Capacity: An Information-Theoretic Framework for Understanding Catastrophic Forgetting
di: Cheng, Ran
Pubblicazione: (2026)

Compression via Pre-trained Transformers: A Study on Byte-Level Multimodal Data
di: Heurtel-Depeiges, David, et al.
Pubblicazione: (2024)

Understanding Action Effects through Instrumental Empowerment in Multi-Agent Reinforcement Learning
di: Selmonaj, Ardian, et al.
Pubblicazione: (2025)

Fixed-Budget Differentially Private Best Arm Identification
di: Chen, Zhirui, et al.
Pubblicazione: (2024)

Simple Convergence Proof of Adam From a Sign-like Descent Perspective
di: Peng, Hanyang, et al.
Pubblicazione: (2025)

Hybrid Mamba-Transformer Decoder for Error-Correcting Codes
di: Cohen, Shy-el, et al.
Pubblicazione: (2025)

Understanding LLM Behaviors via Compression: Data Generation, Knowledge Acquisition and Scaling Laws
di: Pan, Zhixuan, et al.
Pubblicazione: (2025)

Bottlenecked Transformers: Periodic KV Cache Consolidation for Generalised Reasoning
di: Oomerjee, Adnan, et al.
Pubblicazione: (2025)

Learning During Detection: Continual Learning for Neural OFDM Receivers via DMRS
di: Obeed, Mohanad, et al.
Pubblicazione: (2026)

In-Context Learning for MIMO Equalization Using Transformer-Based Sequence Models
di: Zecchin, Matteo, et al.
Pubblicazione: (2023)

Unraveling Text Generation in LLMs: A Stochastic Differential Equation Approach
di: Zhang, Yukun
Pubblicazione: (2024)

Generative Model-Aided Continual Learning for CSI Feedback in FDD mMIMO-OFDM Systems
di: Liu, Guijun, et al.
Pubblicazione: (2025)

Decision Making in Changing Environments: Robustness, Query-Based Learning, and Differential Privacy
di: Chen, Fan, et al.
Pubblicazione: (2025)

Fast Fourier Transform-Based Spectral and Temporal Gradient Filtering for Differential Privacy
di: Shin, Hyeju, et al.
Pubblicazione: (2025)

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

Dynamic Multi-Network Mining of Tensor Time Series
di: Obata, Kohei, et al.
Pubblicazione: (2024)

Knowledge Graph-Based Explainable and Generalized Zero-Shot Semantic Communications
di: Zhang, Zhaoyu, et al.
Pubblicazione: (2025)

Intent-Aware DRL-Based NOMA Uplink Dynamic Scheduler for IIoT
di: Mostafa, Salwa, et al.
Pubblicazione: (2024)

Dynamic Quality-Latency Aware Routing for LLM Inference in Wireless Edge-Device Networks
di: Bao, Rui, et al.
Pubblicazione: (2025)

A Wireless Foundation Model for Multi-Task Prediction
di: Sheng, Yucheng, et al.
Pubblicazione: (2025)

A General Error-Theoretical Analysis Framework for Constructing Compression Strategies
di: Zhang, Boyang, et al.
Pubblicazione: (2025)

Physically Parameterized Differentiable MUSIC for DoA Estimation with Uncalibrated Arrays
di: Chatelier, Baptiste, et al.
Pubblicazione: (2024)

A General Deep Learning Framework for Wireless Resource Allocation under Discrete Constraints
di: Wang, Yikun, et al.
Pubblicazione: (2026)

Capacity-Constrained Continual Learning
di: Wen, Zheng, et al.
Pubblicazione: (2025)

Integrated Sensing-Communication-Computation for Edge Artificial Intelligence
di: Wen, Dingzhu, et al.
Pubblicazione: (2023)

Optimality of Staircase Mechanisms for Vector Queries under Differential Privacy
di: Melbourne, James, et al.
Pubblicazione: (2026)

An Information Theoretic Perspective on Agentic System Design
di: He, Shizhe, et al.
Pubblicazione: (2025)

Estimating Mutual Information between Time Series and Temporal Event Sequences Across Diverse Analysis Tasks
di: Hu, Haoji, et al.
Pubblicazione: (2026)

MambaJSCC: Adaptive Deep Joint Source-Channel Coding with Generalized State Space Model
di: Wu, Tong, et al.
Pubblicazione: (2024)

On the Non-decoupling of Supervised Fine-tuning and Reinforcement Learning in Post-training
di: Niu, Xueyan, et al.
Pubblicazione: (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'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
VUFIND_SESSION	"8e9c674bfa6c224f50f0861b8975c5e8"
ui	"standard"
language	"it"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1790882315.7706 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "8e9c674bfa6c224f50f0861b8975c5e8" ]`]
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=8e9c674bfa6c224f50f0861b8975c5e8; ui=standard; language=it"
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	"47293"
REDIRECT_URL	""" /Record/\n arxiv_https___arxiv_org_abs_2408_09523/Similar """
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/%0Aarxiv_https___arxiv_org_abs_2408_09523/Similar"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1790882315.7652
REQUEST_TIME	1790882315

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler