Datasets:

pathcosmos
/

korean-pretrain-math

text stringlengths 187 100k	h int64 -9,223,350,399,993,883,000 9,223,362,999B
Bayes and his Theorem My earlier post on Bayesian probability seems to have generated quite a lot of readers, so this lunchtime I thought I’d add a little bit of background. The previous discussion started from the result $P(B\|AC) = K^{-1}P(B\|C)P(A\|BC) = K^{-1} P(AB\|C)$ where $K=P(A\|C).$ Although this is called Ba...	6,938,091,883,879,350,000
Physical Quantity Analogous to Inductance 1. May 12, 2013 tapan_ydv Hi, I understand that some physical quantities in electromagnetism are analogous to physical quantities in heat transfer. For instance, electric field is analogous to temperature gradient. I want to know which physical quantity in heat transfer is...	41,068,961,062,669,100
# MicroEJ Test Suite Engine¶ ## Introduction¶ The MicroEJ Test Suite Engine is a generic tool made for validating any development project using automatic testing. This section details advanced configuration for users who wish to integrate custom test suites in their build flow. The MicroEJ Test Suite Engine allows ...	8,555,282,766,386,044,000
T-Test In R On Microarray Data 3 1 Entering edit mode 10.4 years ago Diana ▴ 900 Hello everyone, I'm trying to do a simple t-test on my microarray sample in R. My sample looks like this: gene_id gene sample_1 value_1 sample_2 value_2 XLOC_000001 LOC425783 Renal 20.8152...	8,446,342,001,928,797,000
#jsDisabledContent { display:none; } My Account \| Register \| Help # Sampling distribution Article Id: WHEBN<phone> Reproduction Date: Title: Sampling distribution Author: World Heritage Encyclopedia Language: English Subject: Collection: Statistical Theory Publisher: World Heritage Encyclopedia Publication Date: ...	9,152,948,592,201,887,000
By Kimserey Lam with # Conemu A Better Command Prompt For Windows Jul 22nd, 2017 - written by Kimserey with . When developing multiple Web api under multiple Visual Studio solutions, it can become very tedious to maintain, run and debug. Opening multiple instances of Visual Studio is very costly in term of memory an...	3,996,342,206,087,263,000
# Math Help - partial derivative notation question 1. ## partial derivative notation question what does the notation at the bottom mean? the second derivative wrt z over the partial of y times the partial of x. Is that right? and what does that mean procedurally? 2. ## Re: partial derivative notation question It me...	1,363,723,818,554,399,200
# Compute the Frequency Response of a Multistage Decimator Figure 1a shows the block diagram of a decimation-by-8 filter, consisting of a low-pass finite impulse response (FIR) filter followed by downsampling by 8 [1]. A more efficient version is shown in Figure 1b, which uses three cascaded decimate-by-two filters. ...	4,939,402,991,831,209,000
# Why are vacancy rate and unemployment rate negatively correlated? Why is this the case? Since Vacancy rate is defined as following, let $A,Q,U$ denote number of vacancies in the economy, labor force, unemployed respectively. $$\frac{A}{A+Q-U}$$ Here we can see that if unemployed increase vacancy rate would go up...	-8,986,490,158,531,197,000
Issue No. 08 - August (2008 vol. 19) ISSN: 1045-9219 pp: 1099-1110 ABSTRACT Peer-to-peer (P2P) networks often demand scalability, low communication latency among nodes, and low system-wide overhead. For scalability, a node maintains partial states of a P2P network and connects to a few nodes. For fast communication, a ...	-3,661,826,999,987,699,700
## Category Archives: Pre-RMO ### Rules for Inequalities If a, b and c are real numbers, then 1. $a < b \Longrightarrow a + c< b + c$ 2. $a < b \Longrightarrow a - c < b - c$ 3. $a < b \hspace{0.1in} and \hspace{0.1in}c > 0 \Longrightarrow ac < bc$ 4. $a < b \hspace{0.1in} and \hspace{0.1in}c < 0 \Longrightarrow bc ...	-6,048,312,157,531,424,000
# Probability of getting 2 Aces, 2 Kings and 1 Queen in a five card poker hand (Part II) So I reworked my formula in method 1 after getting help with my original question - Probability of getting 2 Aces, 2 Kings and 1 Queen in a five card poker hand. But I am still getting results that differ...although they are much ...	-6,869,037,298,877,924,000
# Amplified risk of spatially compounding droughts during co-occurrences of modes of natural ocean variability ## Abstract Spatially compounding droughts over multiple regions pose amplifying pressures on the global food system, the reinsurance industry, and the global economy. Using observations and climate model si...	443,182,305,778,396,900
# Relation between independent increments and Markov property Independent increments and Markov property.do not imply each other. I was wondering • if being one makes a process closer to being the other? • if there are cases where one implies the other? Thanks and regards! - To see this, assume that $(X_n)_{n\ge0}...	2,492,027,009,281,825,000
What is the derivative of f(x)=(e^(2x))(ln(x))? Mar 3, 2017 $f ' \left(x\right) = {e}^{2 x} \left(2 \ln x + \frac{1}{x}\right)$ Explanation: The derivative of $\ln x$ is $\frac{1}{x}$ The derivative of ${e}^{g} \left(x\right)$is ${e}^{g} \left(x\right) \cdot g ' \left(x\right)$ The derivative of $h \left(x\right) \...	6,361,942,980,229,011,000
Mathspp Blog A blog dedicated to mathematics and programming! This blog has a really interesting assortment of articles on mathematics and programming. You can use the tags to your right to find topics that interest you, or you may want to have a look at You can also subscribe to the blog newsletter. 1187 str and r...	-2,012,949,818,495,950,000
Integers to soundnote for midi generation To generate a midi file given two lists of integers of equal length, one for the note pitch and one for the corresponding note duration (tempo), I'd like to use the built in Midi file generator, but am not sure how to proceed to map the integers to the soundnote "C#" etc, I wo...	-5,915,604,733,790,687,000
FIND THE ANSWERS # What is the domain range of y= -10/x. compare to the equation y = 1/x? ### Answer this question • What is the domain range of y= -10/x. compare to the equation y = 1/x? ## Answers Discusses the domain and range of a function, ... I'll just list the x-values for the domain and the y-values for th...	-6,519,569,026,763,918,000
An integer is a number that includes 0, positive numbers, and negative numbers. It can never be a fraction, decimal, or percent. Integers are mainly used in our day-to-day lives in mathematical terms. Get to know the definition, operations, and use of integers in the below-mentioned sections. Also, get the example ques...	3,652,826,158,759,155,700
## MATH1111 Quizzes Local Linearity and the Differential Quiz Web resources available Questions This quiz tests the work covered in lecture on local linearity and the differential and corresponds to Section 14.3 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al.). There is a ...	4,287,761,196,437,853,700
## FR0568 #41 Forum for the GRE subject test in mathematics. thmsrhn Posts: 17 Joined: Fri Mar 26, 2010 7:18 am ### FR0568 #41 Hey can any solve this for me? I know how to solve the line intergral, but what are the upper and lower limits? origin415 Posts: 61 Joined: Fri Oct 23, 2009 11:42 pm ### Re: FR0568 #41 W...	8,473,803,684,625,468,000
Consider the following multilayer perceptron network. (The transfer function of the hidden layer... Consider the following multilayer perceptron network. (The transfer function of the hidden layer is The initial weights and biases are: Perform one iteration of the standard steepest descent backpropagation (use matri...	-6,172,726,156,314,540,000
# tfg.geometry.transformation.axis_angle.from_euler_with_small_angles_approximation Converts small Euler angles to an axis-angle representation. Under the small angle assumption, $$\sin(x)$$ and $$\cos(x)$$ can be approximated by their second order Taylor expansions, where $$\sin(x) \approx x$$ and $$\cos(x) \...	-196,062,539,821,492,380
# Algebra Puzzle – Challenge 50 This is another math puzzle and brain teaser that is interactive, challenging, and entertaining for those who love Math challenges! ## Challenge: If 11 workers can build 11 cars in 11 days, then how many days would it take 7 workers to build 7 cars? A- 7 B- 9 C- 11 D- 14 E- 18 #...	3,765,056,360,005,691,000
Want to ask us a question? Click here Browse Questions Ad 0 votes # A charge of $8 \;mC$ is located at the origin. Calculate the work done in taking a small charge of $−2 \times 10^{−9} C$ from a point $P (0, 0, 3 cm)$ to a point $Q (0, 4 cm, 0),$ via a point $R (0, 6 cm, 9 cm).$ Can you answer this question? ## 1 A...	569,646,711,178,021,760

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korean-pretrain-math

한국어 · English · 简体中文 · 繁體中文 · 日本語 · Français · Deutsch · Español · Português (Brasil) · हिन्दी · العربية · עברית · Русский

한국어

개요

이 저장소는 아래에 표시한 한 소스의 정제·분리 자료를 제공합니다. 동일 소스의 전체 파일은 통합 corpus의 해당 폴더에서도 받을 수 있습니다. 데이터의 고정 버전과 문서의 갱신 버전은 구분합니다.

문서 번역 언어는 학습 데이터에 그 언어가 포함된다는 뜻이 아닙니다. 주 자연언어는 한국어·영어이며 웹·수학·코드에 다른 언어가 섞일 수 있습니다.

구성과 규모


소스	owm
문서 수	5,448,920
train 문서	5,394,603
eval 문서	54,317
텍스트 bytes	13,950,498,334


tokens	9,738,184,520
eval tokens	98,186,477
revision	v1.0.0
upstream	open-web-math/open-web-math
upstream license	odc-by-1.0
provenance_status	`shard_provenance_available_document_urls_not_restored`

처리와 분리

웹은 공백 정리, 길이·반복·언어 휴리스틱, 일부 개인정보 패턴 마스킹을 거칩니다. 초기 샤드 내부 hash와 최종 웹 NFC SHA256의 기준은 다릅니다. 코드 정제는 대소문자·들여쓰기·원문 Unicode를 보존하고 경로·라이선스 표기·생성 코드·일부 비밀정보 패턴을 검사합니다. 동일 본문·웹 NFC 동등 본문·코드 저장소의 연결 그룹을 train/eval로 분리합니다.

사용법

아래 명령은 저장소 루트에서 실행합니다. 새 출력/다운로드 디렉터리를 사용하고 다운로드 전에 범위·용량·고정 revision을 확인하세요. 합성 CPU 예제는 외부 데이터를 받지 않습니다. 실제 데이터는 별도 배포에서 필요한 파일만 선택하고 CHECKSUMS.json 또는 소스별 manifest의 크기·SHA256을 검증하세요.

python -m pip install "pyarrow>=19,<20" "huggingface_hub>=0.34,<1" "tokenizers>=0.21,<0.23" "transformers==4.55.2" "requests>=2,<3"

from huggingface_hub import snapshot_download
root = snapshot_download('pathcosmos/korean-pretrain-math', repo_type="dataset",
    revision='v1.0.0', allow_patterns=['text/*.parquet', 'source.json', 'manifest.json', 'release.json', 'LICENSE-SCOPE.md'],
    local_dir='korean-pretrain-math', token=False)

from pathlib import Path
import subprocess, sys
from huggingface_hub import snapshot_download
reader = snapshot_download("pathcosmos/korean-pretrain-corpus", repo_type="dataset", revision="v1.1.0",
    allow_patterns=["examples/*"], local_dir="corpus-reader", token=False)
subprocess.run([sys.executable, str(Path(reader) / "examples/stream_documents.py"),
    "--repo", "pathcosmos/korean-pretrain-corpus", "--revision", "v1.1.0", "--source", "owm",
    "--split", "train", "--limit", "10"], check=True)

examples/stream_documents.py · manifest.json

모델과 학습

모델은 RMSNorm·RoPE·GQA·SwiGLU를 사용하는 순수 PyTorch Dense decoder입니다. 실제 3B 경로는 FSDP2·8GPU·eager이며 문맥4096, micro batch4, global batch2,097,152 tokens, peak LR3e-4, 목표57,000step입니다. 예제의 CPU micro 모델과 실제 분산 학습 경로는 다릅니다. 체크포인트 재개에는 모델·optimizer·RNG·입력/설정 계약 검증이 필요합니다.

최적화·벤치마크

worker·thread·batch·SQLite 캐시·RAM·로컬/NFS와 eager/compile·정밀도·GPU 메모리를 비교했습니다. 총시간·처리량·peak 메모리·내용/수치 동등성을 함께 확인하고 채택·기각 이유를 기록합니다. 47개 캠페인·99개 결과 JSON을 제공하며 빠르더라도 수치 조건에 실패한 후보를 권장하지 않습니다. 짧은 표본의 최적값을 전체 최적값으로 주장하지 않습니다.

검증

GH 소스 공개판의 독립 CPU 검사는284통과/9건너뜀, 새 GitHub CPU 환경은258통과/35건너뜀입니다. 건너뜀은 원래 운영 기록 또는 별도 파일시스템이 필요한 검사입니다. 합성 quickstart는120문서·train100/eval20·vocab272·108,864parameter 모델로 저장/재개 후 model과optimizer 일치를 확인합니다. 데이터 배포의 내용 해시·분할/reader 검사와 전체3B 독립 재현은 구분합니다.

release.json · source.json

출처와 라이선스

프로젝트 원본 코드는 MIT, 원본 설명문은 CC BY4.0입니다. 이는 원문 데이터의 권리를 대신하지 않습니다. 소스별 라이선스·귀속·고지·알려진 미확정 항목은 source.json, LICENSE-SCOPE.md와 출처 문서를 확인하세요. 모든 원문에 대한 무조건적 상업 재배포 허가를 주장하지 않습니다.

open-web-math/open-web-math · source.json · LICENSE-SCOPE.md

한계

전역 유사중복 제거·개인정보/secret 완전 제거·공식 평가 오염 없음·최종 모델 품질을 보장하지 않습니다. 공개 시점의 본학습은 진행 중이며 SFT·모델 export·공식 언어능력 benchmark 완료를 뜻하지 않습니다. 과거 실험11개 코드 참조/고유9hash는 원본 snapshot을 회수하지 못했습니다. 일부 운영 도구는 별도 원래 실행 manifest가 필요합니다.

English

Overview

This repository provides the cleaned, split material for the single source identified below. The same source files are also available in its directory within the unified corpus. Pinned data versions and documentation revisions are distinct.

Translation languages do not imply training-data coverage in those languages. The principal natural languages are Korean and English; web, math and code may contain other languages.

Contents and scale


Source	owm
Documents	5,448,920
Train documents	5,394,603
Evaluation documents	54,317
Text bytes	13,950,498,334


tokens	9,738,184,520
eval tokens	98,186,477
revision	v1.0.0
upstream	open-web-math/open-web-math
upstream license	odc-by-1.0
provenance_status	`shard_provenance_available_document_urls_not_restored`

Processing and splits

Web processing applies whitespace cleanup, length/repetition/language heuristics and selected PII-pattern masking. Initial within-shard hashes differ from final web NFC SHA256. Code filtering preserves case, indentation and original Unicode while checking paths, license labels, generated code and selected secret patterns. Connected groups of identical bodies, NFC-equivalent web bodies and code repositories are assigned to train/eval.

Usage

Run commands below from the repository root. Use new output/download directories and check scope, size and pinned revision first. The synthetic CPU example downloads no external data. Select only the needed files from the separate data releases and verify sizes/SHA256 against CHECKSUMS.json or the source manifests.

python -m pip install "pyarrow>=19,<20" "huggingface_hub>=0.34,<1" "tokenizers>=0.21,<0.23" "transformers==4.55.2" "requests>=2,<3"

from huggingface_hub import snapshot_download
root = snapshot_download('pathcosmos/korean-pretrain-math', repo_type="dataset",
    revision='v1.0.0', allow_patterns=['text/*.parquet', 'source.json', 'manifest.json', 'release.json', 'LICENSE-SCOPE.md'],
    local_dir='korean-pretrain-math', token=False)

from pathlib import Path
import subprocess, sys
from huggingface_hub import snapshot_download
reader = snapshot_download("pathcosmos/korean-pretrain-corpus", repo_type="dataset", revision="v1.1.0",
    allow_patterns=["examples/*"], local_dir="corpus-reader", token=False)
subprocess.run([sys.executable, str(Path(reader) / "examples/stream_documents.py"),
    "--repo", "pathcosmos/korean-pretrain-corpus", "--revision", "v1.1.0", "--source", "owm",
    "--split", "train", "--limit", "10"], check=True)

examples/stream_documents.py · manifest.json

Model and training

The model is a plain PyTorch dense decoder with RMSNorm, RoPE, GQA and SwiGLU. The actual3B path uses FSDP2,8GPUs and eager execution: context4096, micro batch4, global batch2,097,152tokens, peak LR3e-4 and target57,000steps. The CPU micro demonstration differs from distributed training. Exact resume requires model, optimizer, RNG and input/configuration contracts.

Optimization and benchmarks

Experiments compare workers, threads, batches, SQLite caches, RAM, local/NFS storage, eager/compile execution, precision and GPU memory. Total time, throughput, peak memory and content/numerical equivalence accompany adoption or rejection decisions.47 campaigns and99 result JSON files are included. Speed alone does not justify a numerically failing candidate, and a small sample does not establish a full-scale optimum.

Validation

The GH source release passed284 independent CPU tests with9 skips; fresh GitHub CPU CI passed258 with35 skips. Skips require original-run records or a second filesystem. The synthetic quickstart uses120documents, train100/eval20, vocab272 and a108,864parameter model, verifying exact model/optimizer resume. Dataset content-hash, split and reader checks are separate from full independent3B reproduction.

release.json · source.json

Sources and licensing

Original project code is MIT and original prose is CC BY4.0. These grants do not replace original-content rights. Consult source.json, LICENSE-SCOPE.md and provenance documents for source-specific conditions, attribution, notices and known unresolved items. Unrestricted commercial redistribution of every original text is not asserted.

open-web-math/open-web-math · source.json · LICENSE-SCOPE.md

Limitations

Global near-duplicate removal, complete PII/secret removal, contamination-free official evaluation and final model quality are not guaranteed. Main training was ongoing at the publication snapshot; SFT, model export and official language benchmarks are not completed features.11 historical code references/9unique hashes lack a recovered snapshot. Some operational tools require original-run manifests.