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Main Author:	Wan, Jun
Format:	Preprint
Published:	2025
Subjects:	Artificial Intelligence
Online Access:	https://arxiv.org/abs/2501.06802
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author	Wan, Jun
author_facet	Wan, Jun
contents	In 2020, OpenAI proposed the first type of Scaling Laws, describing the relationships between model loss and the scale of parameters, data, and training computation. In 2024, OpenAI proposed the second type of Scaling Laws, describing the relationship between model inference performance and inference computation. In this paper, we analyze LLMs training and inference processes from the perspective of lossless compression using conditional Kolmogorov complexity, and unify these two types of Scaling Laws. We find that both types of Scaling Laws improve approximation of conditional Kolmogorov complexity by increasing execution steps of Turing machine. The first type of Scaling Laws increases execution steps by increasing number of model parameters. The second type of Scaling Laws increases execution steps by increasing the number of intermediate tokens.
format	Preprint
id	arxiv_https___arxiv_org_abs_2501_06802
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Unifying Two Types of Scaling Laws from the Perspective of Conditional Kolmogorov Complexity Wan, Jun Artificial Intelligence In 2020, OpenAI proposed the first type of Scaling Laws, describing the relationships between model loss and the scale of parameters, data, and training computation. In 2024, OpenAI proposed the second type of Scaling Laws, describing the relationship between model inference performance and inference computation. In this paper, we analyze LLMs training and inference processes from the perspective of lossless compression using conditional Kolmogorov complexity, and unify these two types of Scaling Laws. We find that both types of Scaling Laws improve approximation of conditional Kolmogorov complexity by increasing execution steps of Turing machine. The first type of Scaling Laws increases execution steps by increasing number of model parameters. The second type of Scaling Laws increases execution steps by increasing the number of intermediate tokens.
title	Unifying Two Types of Scaling Laws from the Perspective of Conditional Kolmogorov Complexity
topic	Artificial Intelligence
url	https://arxiv.org/abs/2501.06802

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// 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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