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Central pattern generators (CPGs) are self-organizing biological neural circuits [1] [2] that produce rhythmic outputs in the absence of rhythmic input. [3] [4] [5] They are the source of the tightly-coupled patterns of neural activity that drive rhythmic and stereotyped motor behaviors like walking, swimming, breathing, or chewing.
An example where convolutions of generating functions are useful allows us to solve for a specific closed-form function representing the ordinary generating function for the Catalan numbers, C n. In particular, this sequence has the combinatorial interpretation as being the number of ways to insert parentheses into the product x 0 · x 1 ·⋯ ...
In probability theory and statistics, the moment-generating function of a real-valued random variable is an alternative specification of its probability distribution.Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions.
The generation effect is typically achieved in cognitive psychology experiments by asking participants to generate words from word fragments. [2] This effect has also been demonstrated using a variety of other materials, such as when generating a word after being presented with its antonym, [3] synonym, [1] picture, [4] arithmetic problems, [2] [5] or keyword in a paragraph. [6]
In statistics and in empirical sciences, a data generating process is a process in the real world that "generates" the data one is interested in. [1] This process encompasses the underlying mechanisms, factors, and randomness that contribute to the production of observed data.
Other generating functions of random variables include the moment-generating function, the characteristic function and the cumulant generating function. The probability generating function is also equivalent to the factorial moment generating function , which as E [ z X ] {\displaystyle \operatorname {E} \left[z^{X}\right]} can also be ...
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For example, GPT-3, and its precursor GPT-2, [11] are auto-regressive neural language models that contain billions of parameters, BigGAN [12] and VQ-VAE [13] which are used for image generation that can have hundreds of millions of parameters, and Jukebox is a very large generative model for musical audio that contains billions of parameters. [14]