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Natural Language Generation (NLG) is the natural language processing task of generating natural language from a machine representation system such as a knowledge base or a logical form. — Wikipedia

Is NLG about building meaningful sentences, reports, etc.? Can NLG build valid dictionary words as well? For example, without consulting/reading from an English (or any language) dictionary, can an algorithm generate such words?

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Outside of context of NLG (thus not a direct answer to your whole question, but an answer to your question's title): Generating words from a character-level model has been done using RNNs exposed to large corpora of text, such as Wikipedia content, and trained to predict text character-by-character.

Used to generate content, the model is normally fed a few starting characters and asked to predict the next one. A choice is made from its most-likely predictions and fed back to it to continue the sequence.

Here is a blog showing some examples trained on some Shakespear and Wikipedia.

Such a network can and does generate nonsense words, although they are often fitting and might read like e.g. a noun or verb as you could expect depending on context. The sentence structure and grammar can come out sort of right, but the semantic content is usually complete gibberish.

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You are looking for Recurrent Neural Networks for character-level language models.

Have a look at this. https://github.com/karpathy/char-rnn

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