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128-473: Kuaishou Technology ( Chinese : 快手 ; lit. 'quick hand') is a Chinese publicly traded partly state-owned holding company based in Haidian District , Beijing , that was founded in 2011 by Hua Su (宿华) and Cheng Yixiao (程一笑). The company is known for developing a mobile app for sharing users' short videos , a social network , and video special effects editor. As of 2019, it has

256-469: A nucleus that has a vowel (which can be a monophthong , diphthong , or even a triphthong in certain varieties), preceded by an onset (a single consonant , or consonant + glide ; a zero onset is also possible), and followed (optionally) by a coda consonant; a syllable also carries a tone . There are some instances where a vowel is not used as a nucleus. An example of this is in Cantonese, where

384-560: A software engineer . The company is headquartered in Haidian District , Beijing . Kuaishou's predecessor "GIF Kuaishou" was founded in March 2011. GIF Kuaishou was a mobile app with which users could make and share GIF pictures. In November 2012, Kuaishou became a short video community and a platform with which users could record and share videos. By 2013, the app had reached 100 million daily users. By 2019, it had exceeded 200   million active daily users. In March 2017, Kuaishou closed

512-457: A subject–verb–object word order , and like many other languages of East Asia, makes frequent use of the topic–comment construction to form sentences. Chinese also has an extensive system of classifiers and measure words , another trait shared with neighboring languages such as Japanese and Korean. Other notable grammatical features common to all the spoken varieties of Chinese include the use of serial verb construction , pronoun dropping , and

640-510: A Chinese character is the morpheme, as characters represent the smallest grammatical units with individual meanings in the Chinese language. Estimates of the total number of Chinese words and lexicalized phrases vary greatly. The Hanyu Da Zidian , a compendium of Chinese characters, includes 54,678 head entries for characters, including oracle bone versions. The Zhonghua Zihai (1994) contains 85,568 head entries for character definitions and

768-599: A Shanghai resident may speak both Standard Chinese and Shanghainese ; if they grew up elsewhere, they are also likely fluent in the dialect of their home region. In addition to Standard Chinese, a majority of Taiwanese people also speak Taiwanese Hokkien (also called 台語 ; 'Taiwanese' ), Hakka , or an Austronesian language . A speaker in Taiwan may mix pronunciations and vocabulary from Standard Chinese and other languages of Taiwan in everyday speech. In part due to traditional cultural ties with Guangdong , Cantonese

896-473: A US$ 350 million investment round that was led by Tencent . In January 2018, Forbes estimated the company's valuation to be US$ 18 billion. In April 2018, Kuaishou's app was briefly banned from Chinese app stores after China Central Television (CCTV) reported on the platform popularizing videos of teenage mothers. In 2019, the company announced a partnership with the People's Daily , an official newspaper of

1024-462: A central variety (i.e. prestige variety, such as Standard Mandarin), as the issue requires some careful handling when mutual intelligibility is inconsistent with language identity. The Chinese government's official Chinese designation for the major branches of Chinese is 方言 ; fāngyán ; 'regional speech', whereas the more closely related varieties within these are called 地点方言 ; 地點方言 ; dìdiǎn fāngyán ; 'local speech'. Because of

1152-1030: A certain probability distribution γ {\displaystyle \gamma } over [ 0 , ∞ ) {\displaystyle [0,\infty )} , then the score-matching loss function is defined as the expected Fisher divergence: L ( θ ) = E t ∼ γ , x t ∼ ρ t [ ‖ f θ ( x t , t ) ‖ 2 + 2 ∇ ⋅ f θ ( x t , t ) ] {\displaystyle L(\theta )=E_{t\sim \gamma ,x_{t}\sim \rho _{t}}[\|f_{\theta }(x_{t},t)\|^{2}+2\nabla \cdot f_{\theta }(x_{t},t)]} After training, f θ ( x t , t ) ≈ ∇ ln ⁡ ρ t {\displaystyle f_{\theta }(x_{t},t)\approx \nabla \ln \rho _{t}} , so we can perform

1280-1246: A change of variables, L s i m p l e , t = E x 0 , x t ∼ q [ ‖ ϵ θ ( x t , t ) − x t − α ¯ t x 0 σ t ‖ 2 ] = E x t ∼ q , x 0 ∼ q ( ⋅ | x t ) [ ‖ ϵ θ ( x t , t ) − x t − α ¯ t x 0 σ t ‖ 2 ] {\displaystyle L_{simple,t}=E_{x_{0},x_{t}\sim q}\left[\left\|\epsilon _{\theta }(x_{t},t)-{\frac {x_{t}-{\sqrt {{\bar {\alpha }}_{t}}}x_{0}}{\sigma _{t}}}\right\|^{2}\right]=E_{x_{t}\sim q,x_{0}\sim q(\cdot |x_{t})}\left[\left\|\epsilon _{\theta }(x_{t},t)-{\frac {x_{t}-{\sqrt {{\bar {\alpha }}_{t}}}x_{0}}{\sigma _{t}}}\right\|^{2}\right]} and

1408-615: A compromise between the pronunciations of different regions. The royal courts of the Ming and early Qing dynasties operated using a koiné language known as Guanhua , based on the Nanjing dialect of Mandarin. Standard Chinese is an official language of both the People's Republic of China and the Republic of China (Taiwan), one of the four official languages of Singapore , and one of

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1536-714: A corresponding increase in the number of homophones . As an example, the small Langenscheidt Pocket Chinese Dictionary lists six words that are commonly pronounced as shí in Standard Chinese: In modern spoken Mandarin, however, tremendous ambiguity would result if all of these words could be used as-is. The 20th century Yuen Ren Chao poem Lion-Eating Poet in the Stone Den exploits this, consisting of 92 characters all pronounced shi . As such, most of these words have been replaced in speech, if not in writing, with less ambiguous disyllabic compounds. Only

1664-700: A debut on the Hong Kong Stock Exchange, with its shares soaring by 194% at the opening. However, the company soon faced significant challenges due to stringent regulatory restrictions on Chinese internet companies, leading to a nearly 80% decline in its share price from its peak post-IPO. By December 2021, Kuaishou announced a major reorganization, including the layoff of 30% of its staff, primarily targeting mid-level employees earning an annual salary of $ 157,000 or more. This restructuring aimed to cut costs and mitigate financial losses. In October 2022, state-owned Beijing Radio and Television Station took

1792-400: A denoising network can be used as for score-based diffusion. In DDPM, the sequence of numbers 0 = σ 0 < σ 1 < ⋯ < σ T < 1 {\displaystyle 0=\sigma _{0}<\sigma _{1}<\cdots <\sigma _{T}<1} is called a (discrete time) noise schedule . In general, consider

1920-636: A density q {\displaystyle q} , we wish to learn a score function approximation f θ ≈ ∇ ln ⁡ q {\displaystyle f_{\theta }\approx \nabla \ln q} . This is score matching . Typically, score matching is formalized as minimizing Fisher divergence function E q [ ‖ f θ ( x ) − ∇ ln ⁡ q ( x ) ‖ 2 ] {\displaystyle E_{q}[\|f_{\theta }(x)-\nabla \ln q(x)\|^{2}]} . By expanding

2048-846: A long enough diffusion process, we end up with some x T {\displaystyle x_{T}} that is very close to N ( 0 , I ) {\displaystyle N(0,I)} , with all traces of the original x 0 ∼ q {\displaystyle x_{0}\sim q} gone. For example, since x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} we can sample x t | x 0 {\displaystyle x_{t}|x_{0}} directly "in one step", instead of going through all

2176-698: A loss function, also known as the Hyvärinen scoring rule , that can be minimized by stochastic gradient descent. Suppose we need to model the distribution of images, and we want x 0 ∼ N ( 0 , I ) {\displaystyle x_{0}\sim N(0,I)} , a white-noise image. Now, most white-noise images do not look like real images, so q ( x 0 ) ≈ 0 {\displaystyle q(x_{0})\approx 0} for large swaths of x 0 ∼ N ( 0 , I ) {\displaystyle x_{0}\sim N(0,I)} . This presents

2304-432: A method to learn a model that can sample from a highly complex probability distribution. They used techniques from non-equilibrium thermodynamics , especially diffusion . Consider, for example, how one might model the distribution of all naturally-occurring photos. Each image is a point in the space of all images, and the distribution of naturally-occurring photos is a "cloud" in space, which, by repeatedly adding noise to

2432-576: A millennium. The Four Commanderies of Han were established in northern Korea in the 1st century BCE but disintegrated in the following centuries. Chinese Buddhism spread over East Asia between the 2nd and 5th centuries CE, and with it the study of scriptures and literature in Literary Chinese. Later, strong central governments modeled on Chinese institutions were established in Korea, Japan, and Vietnam, with Literary Chinese serving as

2560-609: A minority ownership stake in Kuaishou. In April 2024, a Financial Times article citing current and former Kuaishou employees stated that the company has been running an ageist redundancy programme known internally as "Limestone", culling workers in their mid-30s. In June 2024, Kuaishou released its diffusion transformer text-to-video model , Kling, which they claimed could generate two minutes of video at 30 frames per second and in 1080p resolution. The model has been compared to that of OpenAI 's Sora text-to-video model. It

2688-511: A noise prediction network is trained, it can be used for generating data points in the original distribution in a loop as follows: Score-based generative model is another formulation of diffusion modelling. They are also called noise conditional score network (NCSN) or score-matching with Langevin dynamics (SMLD). Consider the problem of image generation. Let x {\displaystyle x} represent an image, and let q ( x ) {\displaystyle q(x)} be

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2816-437: A particle: d x t = ∇ x t ln ⁡ q ( x t ) d t + d W t {\displaystyle dx_{t}=\nabla _{x_{t}}\ln q(x_{t})dt+dW_{t}} To deal with this problem, we perform annealing . If q {\displaystyle q} is too different from a white-noise distribution, then progressively add noise until it

2944-724: A potential energy function U ( x ) = − ln ⁡ q ( x ) {\displaystyle U(x)=-\ln q(x)} , and a lot of particles in the potential well, then the distribution at thermodynamic equilibrium is the Boltzmann distribution q U ( x ) ∝ e − U ( x ) / k B T = q ( x ) 1 / k B T {\displaystyle q_{U}(x)\propto e^{-U(x)/k_{B}T}=q(x)^{1/k_{B}T}} . At temperature k B T = 1 {\displaystyle k_{B}T=1} ,

3072-415: A problem for learning the score function, because if there are no samples around a certain point, then we can't learn the score function at that point. If we do not know the score function ∇ x t ln ⁡ q ( x t ) {\displaystyle \nabla _{x_{t}}\ln q(x_{t})} at that point, then we cannot impose the time-evolution equation on

3200-425: A score-based network can be used for denoising diffusion. Conversely, the continuous limit x t − 1 = x t − d t , β t = β ( t ) d t , z t d t = d W t {\displaystyle x_{t-1}=x_{t-dt},\beta _{t}=\beta (t)dt,z_{t}{\sqrt {dt}}=dW_{t}} of

3328-542: A secure reconstruction of Proto-Sino-Tibetan, the higher-level structure of the family remains unclear. A top-level branching into Chinese and Tibeto-Burman languages is often assumed, but has not been convincingly demonstrated. The first written records appeared over 3,000 years ago during the Shang dynasty . As the language evolved over this period, the various local varieties became mutually unintelligible. In reaction, central governments have repeatedly sought to promulgate

3456-572: A sequence of noises σ t := σ ( λ t ) {\displaystyle \sigma _{t}:=\sigma (\lambda _{t})} , which then derives the other quantities β t = 1 − 1 − σ t 2 1 − σ t − 1 2 {\displaystyle \beta _{t}=1-{\frac {1-\sigma _{t}^{2}}{1-\sigma _{t-1}^{2}}}} . In order to use arbitrary noise schedules, instead of training

3584-508: A similar way to the use of Latin and Ancient Greek roots in European languages. Many new compounds, or new meanings for old phrases, were created in the late 19th and early 20th centuries to name Western concepts and artifacts. These coinages, written in shared Chinese characters, have then been borrowed freely between languages. They have even been accepted into Chinese, a language usually resistant to loanwords, because their foreign origin

3712-678: A single language. However, their lack of mutual intelligibility means they are sometimes considered to be separate languages in a family . Investigation of the historical relationships among the varieties of Chinese is ongoing. Currently, most classifications posit 7 to 13 main regional groups based on phonetic developments from Middle Chinese , of which the most spoken by far is Mandarin with 66%, or around 800 million speakers, followed by Min (75 million, e.g. Southern Min ), Wu (74 million, e.g. Shanghainese ), and Yue (68 million, e.g. Cantonese ). These branches are unintelligible to each other, and many of their subgroups are unintelligible with

3840-537: A strictly increasing monotonic function σ {\displaystyle \sigma } of type R → ( 0 , 1 ) {\displaystyle \mathbb {R} \to (0,1)} , such as the sigmoid function . In that case, a noise schedule is a sequence of real numbers λ 1 < λ 2 < ⋯ < λ T {\displaystyle \lambda _{1}<\lambda _{2}<\cdots <\lambda _{T}} . It then defines

3968-508: A sum of pure randomness (like a Brownian walker ) and gradient descent down the potential well. The randomness is necessary: if the particles were to undergo only gradient descent, then they will all fall to the origin, collapsing the distribution. The 2020 paper proposed the Denoising Diffusion Probabilistic Model (DDPM), which improves upon the previous method by variational inference . To present

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4096-631: A unified standard. The earliest examples of Old Chinese are divinatory inscriptions on oracle bones dated to c.  1250 BCE , during the Late Shang . The next attested stage came from inscriptions on bronze artifacts dating to the Western Zhou period (1046–771 BCE), the Classic of Poetry and portions of the Book of Documents and I Ching . Scholars have attempted to reconstruct

4224-575: A variety of Yue from a small coastal area around Taishan, Guangdong . In parts of South China, the dialect of a major city may be only marginally intelligible to its neighbors. For example, Wuzhou and Taishan are located approximately 260 km (160 mi) and 190 km (120 mi) away from Guangzhou respectively, but the Yue variety spoken in Wuzhou is more similar to the Guangzhou dialect than

4352-473: A worldwide user base of over 200   million, leading the “Most Downloaded” lists of the Google Play and Apple App Store in eight countries, such as Brazil. In Pakistan and Indonesia, this app is known as Snack Video . It is often referred to as " Kwai " in overseas markets. Its main competitor is Douyin , which is known as TikTok outside China. Kuaishou's overseas team is led by the former CEO of

4480-602: Is Taishanese. Wuzhou is located directly upstream from Guangzhou on the Pearl River , whereas Taishan is to Guangzhou's southwest, with the two cities separated by several river valleys. In parts of Fujian , the speech of some neighbouring counties or villages is mutually unintelligible. Local varieties of Chinese are conventionally classified into seven dialect groups, largely based on the different evolution of Middle Chinese voiced initials: Proportions of first-language speakers The classification of Li Rong , which

4608-463: Is a Wiener process (multidimensional Brownian motion). Now, the equation is exactly a special case of the overdamped Langevin equation d x t = − D k B T ( ∇ x U ) d t + 2 D d W t {\displaystyle dx_{t}=-{\frac {D}{k_{B}T}}(\nabla _{x}U)dt+{\sqrt {2D}}dW_{t}} where D {\displaystyle D}

4736-806: Is a gaussian with mean zero and variance one. To find the second one, we complete the rotational matrix: [ z ″ z ‴ ] = [ α t − α ¯ t σ t β t σ t ? ? ] [ z z ′ ] {\displaystyle {\begin{bmatrix}z''\\z'''\end{bmatrix}}={\begin{bmatrix}{\frac {\sqrt {\alpha _{t}-{\bar {\alpha }}_{t}}}{\sigma _{t}}}&{\frac {\sqrt {\beta _{t}}}{\sigma _{t}}}\\?&?\end{bmatrix}}{\begin{bmatrix}z\\z'\end{bmatrix}}} Since rotational matrices are all of

4864-709: Is a group of languages spoken natively by the ethnic Han Chinese majority and many minority ethnic groups in China , as well as by various communities of the Chinese diaspora . Approximately 1.35 billion people, or 17% of the global population, speak a variety of Chinese as their first language . Chinese languages form the Sinitic branch of the Sino-Tibetan language family. The spoken varieties of Chinese are usually considered by native speakers to be dialects of

4992-1151: Is a normalization constant and often omitted. In particular, we note that x 1 : T | x 0 {\displaystyle x_{1:T}|x_{0}} is a gaussian process , which affords us considerable freedom in reparameterization . For example, by standard manipulation with gaussian process, x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} x t − 1 | x t , x 0 ∼ N ( μ ~ t ( x t , x 0 ) , σ ~ t 2 I ) {\displaystyle x_{t-1}|x_{t},x_{0}\sim N({\tilde {\mu }}_{t}(x_{t},x_{0}),{\tilde {\sigma }}_{t}^{2}I)} In particular, notice that for large t {\displaystyle t} ,

5120-471: Is accessible to the public on Kuaishou's video editing app KwaiCut via signing up for a waitlist with a Chinese phone number. Compared to its main short video platform competitor Douyin , Kuaishou is more popular with older users who live outside China's Tier 1 cities . Its initial popularity came from videos of Chinese rural life. Kuaishou also relied more on e-commerce revenue than on advertising revenue compared to its main competitor. As of 30 June 2024,

5248-1217: Is another gaussian. We also know that these are independent. Thus we can perform a reparameterization: x t − 1 = α ¯ t − 1 x 0 + 1 − α ¯ t − 1 z {\displaystyle x_{t-1}={\sqrt {{\bar {\alpha }}_{t-1}}}x_{0}+{\sqrt {1-{\bar {\alpha }}_{t-1}}}z} x t = α t x t − 1 + 1 − α t z ′ {\displaystyle x_{t}={\sqrt {\alpha _{t}}}x_{t-1}+{\sqrt {1-\alpha _{t}}}z'} where z , z ′ {\textstyle z,z'} are IID gaussians. There are 5 variables x 0 , x t − 1 , x t , z , z ′ {\textstyle x_{0},x_{t-1},x_{t},z,z'} and two linear equations. The two sources of randomness are z , z ′ {\textstyle z,z'} , which can be reparameterized by rotation, since

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5376-490: Is called either 华语 ; 華語 ; Huáyǔ or 汉语 ; 漢語 ; Hànyǔ ). Standard Chinese is based on the Beijing dialect of Mandarin. The governments of both China and Taiwan intend for speakers of all Chinese speech varieties to use it as a common language of communication. Therefore, it is used in government agencies, in the media, and as a language of instruction in schools. Diglossia is common among Chinese speakers. For example,

5504-520: Is compared to its immediate neighbors — e.g. how much more likely is an image of cat compared to some small variants of it? Is it more likely if the image contains two whiskers, or three, or with some Gaussian noise added? Consequently, we are actually quite uninterested in q ( x ) {\displaystyle q(x)} itself, but rather, ∇ x ln ⁡ q ( x ) {\displaystyle \nabla _{x}\ln q(x)} . This has two major effects: Let

5632-1743: Is designed so that for any starting distribution of x 0 {\displaystyle x_{0}} , we have lim t x t | x 0 {\displaystyle \lim _{t}x_{t}|x_{0}} converging to N ( 0 , I ) {\displaystyle N(0,I)} . The entire diffusion process then satisfies q ( x 0 : T ) = q ( x 0 ) q ( x 1 | x 0 ) ⋯ q ( x T | x T − 1 ) = q ( x 0 ) N ( x 1 | α 1 x 0 , β 1 I ) ⋯ N ( x T | α T x T − 1 , β T I ) {\displaystyle q(x_{0:T})=q(x_{0})q(x_{1}|x_{0})\cdots q(x_{T}|x_{T-1})=q(x_{0})N(x_{1}|{\sqrt {\alpha _{1}}}x_{0},\beta _{1}I)\cdots N(x_{T}|{\sqrt {\alpha _{T}}}x_{T-1},\beta _{T}I)} or ln ⁡ q ( x 0 : T ) = ln ⁡ q ( x 0 ) − ∑ t = 1 T 1 2 β t ‖ x t − 1 − β t x t − 1 ‖ 2 + C {\displaystyle \ln q(x_{0:T})=\ln q(x_{0})-\sum _{t=1}^{T}{\frac {1}{2\beta _{t}}}\|x_{t}-{\sqrt {1-\beta _{t}}}x_{t-1}\|^{2}+C} where C {\displaystyle C}

5760-468: Is diffusion tensor, T {\displaystyle T} is temperature, and U {\displaystyle U} is potential energy field. If we substitute in D = 1 2 β ( t ) I , k B T = 1 , U = 1 2 ‖ x ‖ 2 {\displaystyle D={\frac {1}{2}}\beta (t)I,k_{B}T=1,U={\frac {1}{2}}\|x\|^{2}} , we recover

5888-1037: Is explained thus: DDPM and score-based generative models are equivalent. This means that a network trained using DDPM can be used as a NCSN, and vice versa. We know that x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} , so by Tweedie's formula , we have ∇ x t ln ⁡ q ( x t ) = 1 σ t 2 ( − x t + α ¯ t E q [ x 0 | x t ] ) {\displaystyle \nabla _{x_{t}}\ln q(x_{t})={\frac {1}{\sigma _{t}^{2}}}(-x_{t}+{\sqrt {{\bar {\alpha }}_{t}}}E_{q}[x_{0}|x_{t}])} As described previously,

6016-522: Is indistinguishable from one. That is, we perform a forward diffusion, then learn the score function, then use the score function to perform a backward diffusion. Consider again the forward diffusion process, but this time in continuous time: x t = 1 − β t x t − 1 + β t z t {\displaystyle x_{t}={\sqrt {1-\beta _{t}}}x_{t-1}+{\sqrt {\beta _{t}}}z_{t}} By taking

6144-459: Is just the Maxwell–Boltzmann distribution of particles in a potential well V ( x ) = 1 2 ‖ x ‖ 2 {\displaystyle V(x)={\frac {1}{2}}\|x\|^{2}} at temperature 1. The initial distribution, being very much out of equilibrium, would diffuse towards the equilibrium distribution, making biased random steps that are

6272-474: Is not in equilibrium, unlike the final distribution. The equilibrium distribution is the Gaussian distribution N ( 0 , I ) {\displaystyle N(0,I)} , with pdf ρ ( x ) ∝ e − 1 2 ‖ x ‖ 2 {\displaystyle \rho (x)\propto e^{-{\frac {1}{2}}\|x\|^{2}}} . This

6400-603: Is often described as a 'monosyllabic' language. However, this is only partially correct. It is largely accurate when describing Old and Middle Chinese; in Classical Chinese, around 90% of words consist of a single character that corresponds one-to-one with a morpheme , the smallest unit of meaning in a language. In modern varieties, it usually remains the case that morphemes are monosyllabic—in contrast, English has many multi-syllable morphemes, both bound and free , such as 'seven', 'elephant', 'para-' and '-able'. Some of

6528-445: Is only about an eighth as many as English. All varieties of spoken Chinese use tones to distinguish words. A few dialects of north China may have as few as three tones, while some dialects in south China have up to 6 or 12 tones, depending on how one counts. One exception from this is Shanghainese which has reduced the set of tones to a two-toned pitch accent system much like modern Japanese. A very common example used to illustrate

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6656-2062: Is some unknown gaussian noise. Now we see that estimating x 0 {\displaystyle x_{0}} is equivalent to estimating z {\displaystyle z} . Therefore, let the network output a noise vector ϵ θ ( x t , t ) {\displaystyle \epsilon _{\theta }(x_{t},t)} , and let it predict μ θ ( x t , t ) = μ ~ t ( x t , x t − σ t ϵ θ ( x t , t ) α ¯ t ) = x t − ϵ θ ( x t , t ) β t / σ t α t {\displaystyle \mu _{\theta }(x_{t},t)={\tilde {\mu }}_{t}\left(x_{t},{\frac {x_{t}-\sigma _{t}\epsilon _{\theta }(x_{t},t)}{\sqrt {{\bar {\alpha }}_{t}}}}\right)={\frac {x_{t}-\epsilon _{\theta }(x_{t},t)\beta _{t}/\sigma _{t}}{\sqrt {\alpha _{t}}}}} It remains to design Σ θ ( x t , t ) {\displaystyle \Sigma _{\theta }(x_{t},t)} . The DDPM paper suggested not learning it (since it resulted in "unstable training and poorer sample quality"), but fixing it at some value Σ θ ( x t , t ) = ζ t 2 I {\displaystyle \Sigma _{\theta }(x_{t},t)=\zeta _{t}^{2}I} , where either ζ t 2 = β t  or  σ ~ t 2 {\displaystyle \zeta _{t}^{2}=\beta _{t}{\text{ or }}{\tilde {\sigma }}_{t}^{2}} yielded similar performance. With this,

6784-668: Is specifically meant. However, when one of the above words forms part of a compound, the disambiguating syllable is generally dropped and the resulting word is still disyllabic. For example, 石 ; shí alone, and not 石头 ; 石頭 ; shítou , appears in compounds as meaning 'stone' such as 石膏 ; shígāo ; 'plaster', 石灰 ; shíhuī ; 'lime', 石窟 ; shíkū ; 'grotto', 石英 ; 'quartz', and 石油 ; shíyóu ; 'petroleum'. Although many single-syllable morphemes ( 字 ; zì ) can stand alone as individual words, they more often than not form multi-syllable compounds known as 词 ; 詞 ; cí , which more closely resembles

6912-611: Is the dimension of space, and Δ {\displaystyle \Delta } is the Laplace operator . If we have solved ρ t {\displaystyle \rho _{t}} for time t ∈ [ 0 , T ] {\displaystyle t\in [0,T]} , then we can exactly reverse the evolution of the cloud. Suppose we start with another cloud of particles with density ν 0 = ρ T {\displaystyle \nu _{0}=\rho _{T}} , and let

7040-489: Is the largest reference work based purely on character and its literary variants. The CC-CEDICT project (2010) contains 97,404 contemporary entries including idioms, technology terms, and names of political figures, businesses, and products. The 2009 version of the Webster's Digital Chinese Dictionary (WDCD), based on CC-CEDICT, contains over 84,000 entries. The most comprehensive pure linguistic Chinese-language dictionary,

7168-1516: Is to learn the parameters such that p θ ( x 0 ) {\displaystyle p_{\theta }(x_{0})} is as close to q ( x 0 ) {\displaystyle q(x_{0})} as possible. To do that, we use maximum likelihood estimation with variational inference. The ELBO inequality states that ln ⁡ p θ ( x 0 ) ≥ E x 1 : T ∼ q ( ⋅ | x 0 ) [ ln ⁡ p θ ( x 0 : T ) − ln ⁡ q ( x 1 : T | x 0 ) ] {\displaystyle \ln p_{\theta }(x_{0})\geq E_{x_{1:T}\sim q(\cdot |x_{0})}[\ln p_{\theta }(x_{0:T})-\ln q(x_{1:T}|x_{0})]} , and taking one more expectation, we get E x 0 ∼ q [ ln ⁡ p θ ( x 0 ) ] ≥ E x 0 : T ∼ q [ ln ⁡ p θ ( x 0 : T ) − ln ⁡ q ( x 1 : T | x 0 ) ] {\displaystyle E_{x_{0}\sim q}[\ln p_{\theta }(x_{0})]\geq E_{x_{0:T}\sim q}[\ln p_{\theta }(x_{0:T})-\ln q(x_{1:T}|x_{0})]} We see that maximizing

7296-545: Is to use a neural network parametrized by θ {\displaystyle \theta } . The network takes in two arguments x t , t {\displaystyle x_{t},t} , and outputs a vector μ θ ( x t , t ) {\displaystyle \mu _{\theta }(x_{t},t)} and a matrix Σ θ ( x t , t ) {\displaystyle \Sigma _{\theta }(x_{t},t)} , such that each step in

7424-769: Is trained to reverse the process of adding noise to an image. After training to convergence, it can be used for image generation by starting with an image composed of random noise, and applying the network iteratively to denoise the image. Diffusion-based image generators have seen widespread commercial interest, such as Stable Diffusion and DALL-E . These models typically combine diffusion models with other models, such as text-encoders and cross-attention modules to allow text-conditioned generation. Other than computer vision, diffusion models have also found applications in natural language processing such as text generation and summarization , sound generation, and reinforcement learning. Diffusion models were introduced in 2015 as

7552-429: Is typically called its " backbone ". The backbone may be of any kind, but they are typically U-nets or transformers . As of 2024 , diffusion models are mainly used for computer vision tasks, including image denoising , inpainting , super-resolution , image generation , and video generation. These typically involve training a neural network to sequentially denoise images blurred with Gaussian noise . The model

7680-501: Is used as an everyday language in Hong Kong and Macau . The designation of various Chinese branches remains controversial. Some linguists and most ordinary Chinese people consider all the spoken varieties as one single language, as speakers share a common national identity and a common written form. Others instead argue that it is inappropriate to refer to major branches of Chinese such as Mandarin, Wu, and so on as "dialects" because

7808-500: Is used in education, media, formal speech, and everyday life—though Mandarin is increasingly taught in schools due to the mainland's growing influence. Historically, the Chinese language has spread to its neighbors through a variety of means. Northern Vietnam was incorporated into the Han dynasty (202 BCE – 220 CE) in 111 BCE, marking the beginning of a period of Chinese control that ran almost continuously for

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7936-552: Is used in the Language Atlas of China (1987), distinguishes three further groups: Some varieties remain unclassified, including the Danzhou dialect on Hainan , Waxianghua spoken in western Hunan , and Shaozhou Tuhua spoken in northern Guangdong . Standard Chinese is the standard language of China (where it is called 普通话 ; pǔtōnghuà ) and Taiwan, and one of the four official languages of Singapore (where it

8064-428: Is very complex, with a large number of consonants and vowels, but they are probably not all distinguished in any single dialect. Most linguists now believe it represents a diasystem encompassing 6th-century northern and southern standards for reading the classics. The complex relationship between spoken and written Chinese is an example of diglossia : as spoken, Chinese varieties have evolved at different rates, while

8192-694: The β t → β ( t ) d t , d t z t → d W t {\displaystyle \beta _{t}\to \beta (t)dt,{\sqrt {dt}}z_{t}\to dW_{t}} limit, we obtain a continuous diffusion process, in the form of a stochastic differential equation : d x t = − 1 2 β ( t ) x t d t + β ( t ) d W t {\displaystyle dx_{t}=-{\frac {1}{2}}\beta (t)x_{t}dt+{\sqrt {\beta (t)}}dW_{t}} where W t {\displaystyle W_{t}}

8320-753: The Qieyun rime dictionary (601 CE), and a late period in the 10th century, reflected by rhyme tables such as the Yunjing constructed by ancient Chinese philologists as a guide to the Qieyun system. These works define phonological categories but with little hint of what sounds they represent. Linguists have identified these sounds by comparing the categories with pronunciations in modern varieties of Chinese , borrowed Chinese words in Japanese, Vietnamese, and Korean, and transcription evidence. The resulting system

8448-887: The Central Committee of the Chinese Communist Party , to help it experiment with the use of artificial intelligence in news. In June 2020, following the start of the 2020–2021 China–India skirmishes , the Government of India banned Kwai along with 58 other apps, citing "data and privacy issues". In January 2021, Kuaishou announced it was planning an initial public offering (IPO) to raise approximately US$ 5 billion. Kuaishou's stock completed its first day of trading at $ 300 Hong Kong dollars (HKD) (US$ 38.70), more than doubling its initial offer price, and causing its market value to rise to over $ 1 trillion HKD (US$ 159 billion). In February 2021, Kuaishou made

8576-533: The Korean , Japanese and Vietnamese languages, and today comprise over half of their vocabularies. This massive influx led to changes in the phonological structure of the languages, contributing to the development of moraic structure in Japanese and the disruption of vowel harmony in Korean. Borrowed Chinese morphemes have been used extensively in all these languages to coin compound words for new concepts, in

8704-710: The May Fourth Movement beginning in 1919. After the fall of the Northern Song dynasty and subsequent reign of the Jurchen Jin and Mongol Yuan dynasties in northern China, a common speech (now called Old Mandarin ) developed based on the dialects of the North China Plain around the capital. The 1324 Zhongyuan Yinyun was a dictionary that codified the rhyming conventions of new sanqu verse form in this language. Together with

8832-595: The National Language Unification Commission finally settled on the Beijing dialect in 1932. The People's Republic founded in 1949 retained this standard but renamed it 普通话 ; 普通話 ; pǔtōnghuà ; 'common speech'. The national language is now used in education, the media, and formal situations in both mainland China and Taiwan. In Hong Kong and Macau , Cantonese is the dominant spoken language due to cultural influence from Guangdong immigrants and colonial-era policies, and

8960-478: The oracle bone inscriptions created during the Shang dynasty c.  1250 BCE . The phonetic categories of Old Chinese can be reconstructed from the rhymes of ancient poetry. During the Northern and Southern period , Middle Chinese went through several sound changes and split into several varieties following prolonged geographic and political separation. The Qieyun , a rime dictionary , recorded

9088-596: The phonology of Old Chinese by comparing later varieties of Chinese with the rhyming practice of the Classic of Poetry and the phonetic elements found in the majority of Chinese characters. Although many of the finer details remain unclear, most scholars agree that Old Chinese differs from Middle Chinese in lacking retroflex and palatal obstruents but having initial consonant clusters of some sort, and in having voiceless nasals and liquids. Most recent reconstructions also describe an atonal language with consonant clusters at

9216-498: The score function be s ( x ) := ∇ x ln ⁡ q ( x ) {\displaystyle s(x):=\nabla _{x}\ln q(x)} ; then consider what we can do with s ( x ) {\displaystyle s(x)} . As it turns out, s ( x ) {\displaystyle s(x)} allows us to sample from q ( x ) {\displaystyle q(x)} using thermodynamics. Specifically, if we have

9344-904: The 12-volume Hanyu Da Cidian , records more than 23,000 head Chinese characters and gives over 370,000 definitions. The 1999 revised Cihai , a multi-volume encyclopedic dictionary reference work, gives 122,836 vocabulary entry definitions under 19,485 Chinese characters, including proper names, phrases, and common zoological, geographical, sociological, scientific, and technical terms. The 2016 edition of Xiandai Hanyu Cidian , an authoritative one-volume dictionary on modern standard Chinese language as used in mainland China, has 13,000 head characters and defines 70,000 words. Diffusion model There are various equivalent formalisms, including Markov chains , denoising diffusion probabilistic models, noise conditioned score networks, and stochastic differential equations. They are typically trained using variational inference . The model responsible for denoising

9472-736: The Boltzmann distribution is exactly q ( x ) {\displaystyle q(x)} . Therefore, to model q ( x ) {\displaystyle q(x)} , we may start with a particle sampled at any convenient distribution (such as the standard gaussian distribution), then simulate the motion of the particle forwards according to the Langevin equation d x t = − ∇ x t U ( x t ) d t + d W t {\displaystyle dx_{t}=-\nabla _{x_{t}}U(x_{t})dt+dW_{t}} and

9600-449: The Boltzmann distribution is, by Fokker-Planck equation, the unique thermodynamic equilibrium . So no matter what distribution x 0 {\displaystyle x_{0}} has, the distribution of x t {\displaystyle x_{t}} converges in distribution to q {\displaystyle q} as t → ∞ {\displaystyle t\to \infty } . Given

9728-912: The DDPM loss function is ∑ t L s i m p l e , t {\displaystyle \sum _{t}L_{simple,t}} with L s i m p l e , t = E x 0 ∼ q ; z ∼ N ( 0 , I ) [ ‖ ϵ θ ( x t , t ) − z ‖ 2 ] {\displaystyle L_{simple,t}=E_{x_{0}\sim q;z\sim N(0,I)}\left[\left\|\epsilon _{\theta }(x_{t},t)-z\right\|^{2}\right]} where x t = α ¯ t x 0 + σ t z {\displaystyle x_{t}={\sqrt {{\bar {\alpha }}_{t}}}x_{0}+\sigma _{t}z} . By

9856-1580: The Fokker-Planck equation, we find that ∂ t ρ T − t = ∂ t ν t {\displaystyle \partial _{t}\rho _{T-t}=\partial _{t}\nu _{t}} . Thus this cloud of points is the original cloud, evolving backwards. At the continuous limit, α ¯ t = ( 1 − β 1 ) ⋯ ( 1 − β t ) = e ∑ i ln ⁡ ( 1 − β i ) → e − ∫ 0 t β ( t ) d t {\displaystyle {\bar {\alpha }}_{t}=(1-\beta _{1})\cdots (1-\beta _{t})=e^{\sum _{i}\ln(1-\beta _{i})}\to e^{-\int _{0}^{t}\beta (t)dt}} and so x t | x 0 ∼ N ( e − 1 2 ∫ 0 t β ( t ) d t x 0 , ( 1 − e − ∫ 0 t β ( t ) d t ) I ) {\displaystyle x_{t}|x_{0}\sim N\left(e^{-{\frac {1}{2}}\int _{0}^{t}\beta (t)dt}x_{0},\left(1-e^{-\int _{0}^{t}\beta (t)dt}\right)I\right)} In particular, we see that we can directly sample from any point in

9984-798: The IID gaussian distribution is rotationally symmetric. By plugging in the equations, we can solve for the first reparameterization: x t = α ¯ t x 0 + α t − α ¯ t z + 1 − α t z ′ ⏟ = σ t z ″ {\displaystyle x_{t}={\sqrt {{\bar {\alpha }}_{t}}}x_{0}+\underbrace {{\sqrt {\alpha _{t}-{\bar {\alpha }}_{t}}}z+{\sqrt {1-\alpha _{t}}}z'} _{=\sigma _{t}z''}} where z ″ {\textstyle z''}

10112-565: The Latin-based Vietnamese alphabet . English words of Chinese origin include tea from Hokkien 茶 ( tê ), dim sum from Cantonese 點心 ( dim2 sam1 ), and kumquat from Cantonese 金橘 ( gam1 gwat1 ). The sinologist Jerry Norman has estimated that there are hundreds of mutually unintelligible varieties of Chinese. These varieties form a dialect continuum , in which differences in speech generally become more pronounced as distances increase, though

10240-423: The above equation. This explains why the phrase "Langevin dynamics" is sometimes used in diffusion models. Now the above equation is for the stochastic motion of a single particle. Suppose we have a cloud of particles distributed according to q {\displaystyle q} at time t = 0 {\displaystyle t=0} , then after a long time, the cloud of particles would settle into

10368-580: The application 99, and staff from Google, Facebook, Netflix, and TikTok were recruited to lead the company's international expansion. The China Internet Investment Fund , a state-owned enterprise controlled by the Cyberspace Administration of China , holds a golden share ownership stake in Kuaishou. Kuaishou is China's first short video platform that was developed in 2011 by engineer Hua Su and Cheng Yixiao. Prior to co-founding Kuaishou, Su Hua had worked for both Google and Baidu as

10496-660: The backward equation x t − 1 = x t α t − β t σ t α t ϵ θ ( x t , t ) + β t z t ; z t ∼ N ( 0 , I ) {\displaystyle x_{t-1}={\frac {x_{t}}{\sqrt {\alpha _{t}}}}-{\frac {\beta _{t}}{\sigma _{t}{\sqrt {\alpha _{t}}}}}\epsilon _{\theta }(x_{t},t)+{\sqrt {\beta _{t}}}z_{t};\quad z_{t}\sim N(0,I)} gives us precisely

10624-948: The backwards diffusion process by first sampling x T ∼ N ( 0 , I ) {\displaystyle x_{T}\sim N(0,I)} , then integrating the SDE from t = T {\displaystyle t=T} to t = 0 {\displaystyle t=0} : x t − d t = x t + 1 2 β ( t ) x t d t + β ( t ) f θ ( x t , t ) d t + β ( t ) d W t {\displaystyle x_{t-dt}=x_{t}+{\frac {1}{2}}\beta (t)x_{t}dt+\beta (t)f_{\theta }(x_{t},t)dt+{\sqrt {\beta (t)}}dW_{t}} This may be done by any SDE integration method, such as Euler–Maruyama method . The name "noise conditional score network"

10752-943: The continuous diffusion process without going through the intermediate steps, by first sampling x 0 ∼ q , z ∼ N ( 0 , I ) {\displaystyle x_{0}\sim q,z\sim N(0,I)} , then get x t = e − 1 2 ∫ 0 t β ( t ) d t x 0 + ( 1 − e − ∫ 0 t β ( t ) d t ) z {\displaystyle x_{t}=e^{-{\frac {1}{2}}\int _{0}^{t}\beta (t)dt}x_{0}+\left(1-e^{-\int _{0}^{t}\beta (t)dt}\right)z} . That is, we can quickly sample x t ∼ ρ t {\displaystyle x_{t}\sim \rho _{t}} for any t ≥ 0 {\displaystyle t\geq 0} . Now, define

10880-399: The different spoken dialects varies, but in general, there has been a tendency to a reduction in sounds from Middle Chinese. The Mandarin dialects in particular have experienced a dramatic decrease in sounds and so have far more polysyllabic words than most other spoken varieties. The total number of syllables in some varieties is therefore only about a thousand, including tonal variation, which

11008-484: The difficulties involved in determining the difference between language and dialect, other terms have been proposed. These include topolect , lect , vernacular , regional , and variety . Syllables in the Chinese languages have some unique characteristics. They are tightly related to the morphology and also to the characters of the writing system, and phonologically they are structured according to fixed rules. The structure of each syllable consists of

11136-576: The end of the syllable, developing into tone distinctions in Middle Chinese. Several derivational affixes have also been identified, but the language lacks inflection , and indicated grammatical relationships using word order and grammatical particles . Middle Chinese was the language used during Northern and Southern dynasties and the Sui , Tang , and Song dynasties (6th–10th centuries CE). It can be divided into an early period, reflected by

11264-413: The first one, 十 , normally appears in monosyllabic form in spoken Mandarin; the rest are normally used in the polysyllabic forms of respectively. In each, the homophone was disambiguated by the addition of another morpheme, typically either a near-synonym or some sort of generic word (e.g. 'head', 'thing'), the purpose of which is to indicate which of the possible meanings of the other, homophonic syllable

11392-1323: The form [ cos ⁡ θ sin ⁡ θ − sin ⁡ θ cos ⁡ θ ] {\textstyle {\begin{bmatrix}\cos \theta &\sin \theta \\-\sin \theta &\cos \theta \end{bmatrix}}} , we know the matrix must be [ z ″ z ‴ ] = [ α t − α ¯ t σ t β t σ t − β t σ t α t − α ¯ t σ t ] [ z z ′ ] {\displaystyle {\begin{bmatrix}z''\\z'''\end{bmatrix}}={\begin{bmatrix}{\frac {\sqrt {\alpha _{t}-{\bar {\alpha }}_{t}}}{\sigma _{t}}}&{\frac {\sqrt {\beta _{t}}}{\sigma _{t}}}\\-{\frac {\sqrt {\beta _{t}}}{\sigma _{t}}}&{\frac {\sqrt {\alpha _{t}-{\bar {\alpha }}_{t}}}{\sigma _{t}}}\end{bmatrix}}{\begin{bmatrix}z\\z'\end{bmatrix}}} and since

11520-491: The form of a word), to indicate a word's function within a sentence. In other words, Chinese has very few grammatical inflections —it possesses no tenses , no voices , no grammatical number , and only a few articles . They make heavy use of grammatical particles to indicate aspect and mood . In Mandarin, this involves the use of particles such as 了 ; le ; ' PFV ', 还 ; 還 ; hái ; 'still', and 已经 ; 已經 ; yǐjīng ; 'already'. Chinese has

11648-1153: The forward diffusion process can be approximately undone by x t − 1 ∼ N ( μ θ ( x t , t ) , Σ θ ( x t , t ) ) {\displaystyle x_{t-1}\sim N(\mu _{\theta }(x_{t},t),\Sigma _{\theta }(x_{t},t))} . This then gives us a backward diffusion process p θ {\displaystyle p_{\theta }} defined by p θ ( x T ) = N ( x T | 0 , I ) {\displaystyle p_{\theta }(x_{T})=N(x_{T}|0,I)} p θ ( x t − 1 | x t ) = N ( x t − 1 | μ θ ( x t , t ) , Σ θ ( x t , t ) ) {\displaystyle p_{\theta }(x_{t-1}|x_{t})=N(x_{t-1}|\mu _{\theta }(x_{t},t),\Sigma _{\theta }(x_{t},t))} The goal now

11776-897: The goal is to minimize the loss by stochastic gradient descent. The expression may be simplified to L ( θ ) = ∑ t = 1 T E x t − 1 , x t ∼ q [ − ln ⁡ p θ ( x t − 1 | x t ) ] + E x 0 ∼ q [ D K L ( q ( x T | x 0 ) ‖ p θ ( x T ) ) ] + C {\displaystyle L(\theta )=\sum _{t=1}^{T}E_{x_{t-1},x_{t}\sim q}[-\ln p_{\theta }(x_{t-1}|x_{t})]+E_{x_{0}\sim q}[D_{KL}(q(x_{T}|x_{0})\|p_{\theta }(x_{T}))]+C} where C {\displaystyle C} does not depend on

11904-767: The goal is to somehow reverse the process, so that we can start at the end and diffuse back to the beginning. By Fokker-Planck equation , the density of the cloud evolves according to ∂ t ln ⁡ ρ t = 1 2 β ( t ) ( n + ( x + ∇ ln ⁡ ρ t ) ⋅ ∇ ln ⁡ ρ t + Δ ln ⁡ ρ t ) {\displaystyle \partial _{t}\ln \rho _{t}={\frac {1}{2}}\beta (t)\left(n+(x+\nabla \ln \rho _{t})\cdot \nabla \ln \rho _{t}+\Delta \ln \rho _{t}\right)} where n {\displaystyle n}

12032-618: The government of the People's Republic of China, with Singapore officially adopting them in 1976. Traditional characters are used in Taiwan, Hong Kong, Macau, and among Chinese-speaking communities overseas . Linguists classify all varieties of Chinese as part of the Sino-Tibetan language family , together with Burmese , Tibetan and many other languages spoken in the Himalayas and the Southeast Asian Massif . Although

12160-405: The images, diffuses out to the rest of the image space, until the cloud becomes all but indistinguishable from a Gaussian distribution N ( 0 , I ) {\displaystyle N(0,I)} . A model that can approximately undo the diffusion can then be used to sample from the original distribution. This is studied in "non-equilibrium" thermodynamics, as the starting distribution

12288-562: The integral, and performing an integration by parts, E q [ ‖ f θ ( x ) − ∇ ln ⁡ q ( x ) ‖ 2 ] = E q [ ‖ f θ ‖ 2 + 2 ∇ 2 ⋅ f θ ] + C {\displaystyle E_{q}[\|f_{\theta }(x)-\nabla \ln q(x)\|^{2}]=E_{q}[\|f_{\theta }\|^{2}+2\nabla ^{2}\cdot f_{\theta }]+C} giving us

12416-435: The intermediate steps x 1 , x 2 , . . . , x t − 1 {\displaystyle x_{1},x_{2},...,x_{t-1}} . We know x t − 1 | x 0 {\textstyle x_{t-1}|x_{0}} is a gaussian, and x t | x t − 1 {\textstyle x_{t}|x_{t-1}}

12544-1657: The inverse of rotational matrix is its transpose, [ z z ′ ] = [ α t − α ¯ t σ t − β t σ t β t σ t α t − α ¯ t σ t ] [ z ″ z ‴ ] {\displaystyle {\begin{bmatrix}z\\z'\end{bmatrix}}={\begin{bmatrix}{\frac {\sqrt {\alpha _{t}-{\bar {\alpha }}_{t}}}{\sigma _{t}}}&-{\frac {\sqrt {\beta _{t}}}{\sigma _{t}}}\\{\frac {\sqrt {\beta _{t}}}{\sigma _{t}}}&{\frac {\sqrt {\alpha _{t}-{\bar {\alpha }}_{t}}}{\sigma _{t}}}\end{bmatrix}}{\begin{bmatrix}z''\\z'''\end{bmatrix}}} Plugging back, and simplifying, we have x t = α ¯ t x 0 + σ t z ″ {\displaystyle x_{t}={\sqrt {{\bar {\alpha }}_{t}}}x_{0}+\sigma _{t}z''} x t − 1 = μ ~ t ( x t , x 0 ) − σ ~ t z ‴ {\displaystyle x_{t-1}={\tilde {\mu }}_{t}(x_{t},x_{0})-{\tilde {\sigma }}_{t}z'''} The key idea of DDPM

12672-586: The language of administration and scholarship, a position it would retain until the late 19th century in Korea and (to a lesser extent) Japan, and the early 20th century in Vietnam. Scholars from different lands could communicate, albeit only in writing, using Literary Chinese. Although they used Chinese solely for written communication, each country had its own tradition of reading texts aloud using what are known as Sino-Xenic pronunciations . Chinese words with these pronunciations were also extensively imported into

12800-528: The late 19th century. Today Japanese is written with a composite script using both Chinese characters called kanji , and kana. Korean is written exclusively with hangul in North Korea, although knowledge of the supplementary Chinese characters called hanja is still required, and hanja are increasingly rarely used in South Korea. As a result of its historical colonization by France, Vietnamese now uses

12928-1261: The loss simplifies to L t = β t 2 2 α t σ t 2 ζ t 2 E x 0 ∼ q ; z ∼ N ( 0 , I ) [ ‖ ϵ θ ( x t , t ) − z ‖ 2 ] + C {\displaystyle L_{t}={\frac {\beta _{t}^{2}}{2\alpha _{t}\sigma _{t}^{2}\zeta _{t}^{2}}}E_{x_{0}\sim q;z\sim N(0,I)}\left[\left\|\epsilon _{\theta }(x_{t},t)-z\right\|^{2}\right]+C} which may be minimized by stochastic gradient descent. The paper noted empirically that an even simpler loss function L s i m p l e , t = E x 0 ∼ q ; z ∼ N ( 0 , I ) [ ‖ ϵ θ ( x t , t ) − z ‖ 2 ] {\displaystyle L_{simple,t}=E_{x_{0}\sim q;z\sim N(0,I)}\left[\left\|\epsilon _{\theta }(x_{t},t)-z\right\|^{2}\right]} resulted in better models. After

13056-810: The model, we need some notation. A forward diffusion process starts at some starting point x 0 ∼ q {\displaystyle x_{0}\sim q} , where q {\displaystyle q} is the probability distribution to be learned, then repeatedly adds noise to it by x t = 1 − β t x t − 1 + β t z t {\displaystyle x_{t}={\sqrt {1-\beta _{t}}}x_{t-1}+{\sqrt {\beta _{t}}}z_{t}} where z 1 , . . . , z T {\displaystyle z_{1},...,z_{T}} are IID samples from N ( 0 , I ) {\displaystyle N(0,I)} . This

13184-455: The more conservative modern varieties, usually found in the south, have largely monosyllabic words , especially with basic vocabulary. However, most nouns, adjectives, and verbs in modern Mandarin are disyllabic. A significant cause of this is phonetic erosion : sound changes over time have steadily reduced the number of possible syllables in the language's inventory. In modern Mandarin, there are only around 1,200 possible syllables, including

13312-456: The most followed account on the platform is Kuaishou Store with over 200 millions followers. The most followed individual account belongs to Chinese E-commerce businessman Xin Youzhi . Chinese language Chinese ( simplified Chinese : 汉语 ; traditional Chinese : 漢語 ; pinyin : Hànyǔ ; lit. ' Han language' or 中文 ; Zhōngwén ; 'Chinese writing')

13440-425: The mutual unintelligibility between them is too great. However, calling major Chinese branches "languages" would also be wrong under the same criterion, since a branch such as Wu, itself contains many mutually unintelligible varieties, and could not be properly called a single language. There are also viewpoints pointing out that linguists often ignore mutual intelligibility when varieties share intelligibility with

13568-583: The nasal sonorant consonants /m/ and /ŋ/ can stand alone as their own syllable. In Mandarin much more than in other spoken varieties, most syllables tend to be open syllables, meaning they have no coda (assuming that a final glide is not analyzed as a coda), but syllables that do have codas are restricted to nasals /m/ , /n/ , /ŋ/ , the retroflex approximant /ɻ/ , and voiceless stops /p/ , /t/ , /k/ , or /ʔ/ . Some varieties allow most of these codas, whereas others, such as Standard Chinese, are limited to only /n/ , /ŋ/ , and /ɻ/ . The number of sounds in

13696-762: The network does not have access to x 0 {\displaystyle x_{0}} , and so it has to estimate it instead. Now, since x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} , we may write x t = α ¯ t x 0 + σ t z {\displaystyle x_{t}={\sqrt {{\bar {\alpha }}_{t}}}x_{0}+\sigma _{t}z} , where z {\displaystyle z}

13824-538: The other varieties within the same branch (e.g. Southern Min). There are, however, transitional areas where varieties from different branches share enough features for some limited intelligibility, including New Xiang with Southwestern Mandarin , Xuanzhou Wu Chinese with Lower Yangtze Mandarin , Jin with Central Plains Mandarin and certain divergent dialects of Hakka with Gan . All varieties of Chinese are tonal at least to some degree, and are largely analytic . The earliest attested written Chinese consists of

13952-1921: The parameter, and thus can be ignored. Since p θ ( x T ) = N ( x T | 0 , I ) {\displaystyle p_{\theta }(x_{T})=N(x_{T}|0,I)} also does not depend on the parameter, the term E x 0 ∼ q [ D K L ( q ( x T | x 0 ) ‖ p θ ( x T ) ) ] {\displaystyle E_{x_{0}\sim q}[D_{KL}(q(x_{T}|x_{0})\|p_{\theta }(x_{T}))]} can also be ignored. This leaves just L ( θ ) = ∑ t = 1 T L t {\displaystyle L(\theta )=\sum _{t=1}^{T}L_{t}} with L t = E x t − 1 , x t ∼ q [ − ln ⁡ p θ ( x t − 1 | x t ) ] {\displaystyle L_{t}=E_{x_{t-1},x_{t}\sim q}[-\ln p_{\theta }(x_{t-1}|x_{t})]} to be minimized. Since x t − 1 | x t , x 0 ∼ N ( μ ~ t ( x t , x 0 ) , σ ~ t 2 I ) {\displaystyle x_{t-1}|x_{t},x_{0}\sim N({\tilde {\mu }}_{t}(x_{t},x_{0}),{\tilde {\sigma }}_{t}^{2}I)} , this suggests that we should use μ θ ( x t , t ) = μ ~ t ( x t , x 0 ) {\displaystyle \mu _{\theta }(x_{t},t)={\tilde {\mu }}_{t}(x_{t},x_{0})} ; however,

14080-729: The particles in the cloud evolve according to d y t = 1 2 β ( T − t ) y t d t + β ( T − t ) ∇ y t ln ⁡ ρ T − t ( y t ) ⏟ score function  d t + β ( T − t ) d W t {\displaystyle dy_{t}={\frac {1}{2}}\beta (T-t)y_{t}dt+\beta (T-t)\underbrace {\nabla _{y_{t}}\ln \rho _{T-t}\left(y_{t}\right)} _{\text{score function }}dt+{\sqrt {\beta (T-t)}}dW_{t}} then by plugging into

14208-405: The probability distribution over all possible images. If we have q ( x ) {\displaystyle q(x)} itself, then we can say for certain how likely a certain image is. However, this is intractable in general. Most often, we are uninterested in knowing the absolute probability of a certain image. Instead, we are usually only interested in knowing how likely a certain image

14336-589: The quantity on the right would give us a lower bound on the likelihood of observed data. This allows us to perform variational inference. Define the loss function L ( θ ) := − E x 0 : T ∼ q [ ln ⁡ p θ ( x 0 : T ) − ln ⁡ q ( x 1 : T | x 0 ) ] {\displaystyle L(\theta ):=-E_{x_{0:T}\sim q}[\ln p_{\theta }(x_{0:T})-\ln q(x_{1:T}|x_{0})]} and now

14464-404: The rate of change varies immensely. Generally, mountainous South China exhibits more linguistic diversity than the North China Plain . Until the late 20th century, Chinese emigrants to Southeast Asia and North America came from southeast coastal areas, where Min, Hakka, and Yue dialects were spoken. Specifically, most Chinese immigrants to North America until the mid-20th century spoke Taishanese ,

14592-552: The related subject dropping . Although the grammars of the spoken varieties share many traits, they do possess differences. The entire Chinese character corpus since antiquity comprises well over 50,000 characters, of which only roughly 10,000 are in use and only about 3,000 are frequently used in Chinese media and newspapers. However, Chinese characters should not be confused with Chinese words. Because most Chinese words are made up of two or more characters, there are many more Chinese words than characters. A more accurate equivalent for

14720-509: The relationship was first proposed in the early 19th century and is now broadly accepted, reconstruction of Sino-Tibetan is much less developed than that of families such as Indo-European or Austroasiatic . Difficulties have included the great diversity of the languages, the lack of inflection in many of them, and the effects of language contact. In addition, many of the smaller languages are spoken in mountainous areas that are difficult to reach and are often also sensitive border zones. Without

14848-517: The same equation as score-based diffusion: x t − d t = x t ( 1 + β ( t ) d t / 2 ) + β ( t ) ∇ x t ln ⁡ q ( x t ) d t + β ( t ) d W t {\displaystyle x_{t-dt}=x_{t}(1+\beta (t)dt/2)+\beta (t)\nabla _{x_{t}}\ln q(x_{t})dt+{\sqrt {\beta (t)}}dW_{t}} Thus,

14976-517: The six official languages of the United Nations . Standard Chinese is based on the Beijing dialect of Mandarin and was first officially adopted in the 1930s. The language is written primarily using a logography of Chinese characters , largely shared by readers who may otherwise speak mutually unintelligible varieties. Since the 1950s, the use of simplified characters has been promoted by

15104-561: The slightly later Menggu Ziyun , this dictionary describes a language with many of the features characteristic of modern Mandarin dialects. Up to the early 20th century, most Chinese people only spoke their local variety. Thus, as a practical measure, officials of the Ming and Qing dynasties carried out the administration of the empire using a common language based on Mandarin varieties , known as 官话 ; 官話 ; Guānhuà ; 'language of officials'. For most of this period, this language

15232-486: The stable distribution of N ( 0 , I ) {\displaystyle N(0,I)} . Let ρ t {\displaystyle \rho _{t}} be the density of the cloud of particles at time t {\displaystyle t} , then we have ρ 0 = q ; ρ T ≈ N ( 0 , I ) {\displaystyle \rho _{0}=q;\quad \rho _{T}\approx N(0,I)} and

15360-734: The term inside becomes a least squares regression, so if the network actually reaches the global minimum of loss, then we have ϵ θ ( x t , t ) = x t − α ¯ t E q [ x 0 | x t ] σ t = − σ t ∇ x t ln ⁡ q ( x t ) {\displaystyle \epsilon _{\theta }(x_{t},t)={\frac {x_{t}-{\sqrt {{\bar {\alpha }}_{t}}}E_{q}[x_{0}|x_{t}]}{\sigma _{t}}}=-\sigma _{t}\nabla _{x_{t}}\ln q(x_{t})} Thus,

15488-623: The tonal distinctions, compared with about 5,000 in Vietnamese (still a largely monosyllabic language), and over 8,000 in English. Most modern varieties tend to form new words through polysyllabic compounds . In some cases, monosyllabic words have become disyllabic formed from different characters without the use of compounding, as in 窟窿 ; kūlong from 孔 ; kǒng ; this is especially common in Jin varieties. This phonological collapse has led to

15616-547: The traditional Western notion of a word. A Chinese cí can consist of more than one character–morpheme, usually two, but there can be three or more. Examples of Chinese words of more than two syllables include 汉堡包 ; 漢堡包 ; hànbǎobāo ; 'hamburger', 守门员 ; 守門員 ; shǒuményuán ; 'goalkeeper', and 电子邮件 ; 電子郵件 ; diànzǐyóujiàn ; 'e-mail'. All varieties of modern Chinese are analytic languages : they depend on syntax (word order and sentence structure), rather than inflectional morphology (changes in

15744-512: The use of tones in Chinese is the application of the four tones of Standard Chinese, along with the neutral tone, to the syllable ma . The tones are exemplified by the following five Chinese words: In contrast, Standard Cantonese has six tones. Historically, finals that end in a stop consonant were considered to be " checked tones " and thus counted separately for a total of nine tones. However, they are considered to be duplicates in modern linguistics and are no longer counted as such: Chinese

15872-442: The variable x t | x 0 ∼ N ( α ¯ t x 0 , σ t 2 I ) {\displaystyle x_{t}|x_{0}\sim N\left({\sqrt {{\bar {\alpha }}_{t}}}x_{0},\sigma _{t}^{2}I\right)} converges to N ( 0 , I ) {\displaystyle N(0,I)} . That is, after

16000-452: The words in newspapers, and 60% of the words in science magazines. Vietnam, Korea, and Japan each developed writing systems for their own languages, initially based on Chinese characters , but later replaced with the hangul alphabet for Korean and supplemented with kana syllabaries for Japanese, while Vietnamese continued to be written with the complex chữ Nôm script. However, these were limited to popular literature until

16128-517: The written language used throughout China changed comparatively little, crystallizing into a prestige form known as Classical or Literary Chinese . Literature written distinctly in the Classical form began to emerge during the Spring and Autumn period . Its use in writing remained nearly universal until the late 19th century, culminating with the widespread adoption of written vernacular Chinese with

16256-453: Was a koiné based on dialects spoken in the Nanjing area, though not identical to any single dialect. By the middle of the 19th century, the Beijing dialect had become dominant and was essential for any business with the imperial court. In the 1930s, a standard national language ( 国语 ; 國語 ; Guóyǔ ), was adopted. After much dispute between proponents of northern and southern dialects and an abortive attempt at an artificial pronunciation,

16384-485: Was hidden by their written form. Often different compounds for the same concept were in circulation for some time before a winner emerged, and sometimes the final choice differed between countries. The proportion of vocabulary of Chinese origin thus tends to be greater in technical, abstract, or formal language. For example, in Japan, Sino-Japanese words account for about 35% of the words in entertainment magazines, over half

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