In artificial intelligence, an embedding is a learned representation for discrete or categorical data, such as words, images, or user IDs. It maps these high-dimensional, often sparse inputs into a dense, continuous-valued vector in a lower-dimensional space. The key characteristic of this vector space is that it captures semantic relationships; items with similar meanings or functions are positioned closer to one another. This numerical representation is more efficient and meaningful for machine learning models to process compared to raw, high-dimensional data like one-hot encoded vectors.

1. University Courseware (Stanford): Jurafsky

D.

& Martin

J. H. (2023). Speech and Language Processing (3rd ed. draft). In Chapter 6

"Vector Semantics and Embeddings

" the text defines embeddings as "a short

dense vector for each word

" contrasting them with sparse

high-dimensional vectors. The chapter focuses on how these vectors represent meaning in a geometric space. (See Chapter 6

Section 6.3).

2. Official Vendor Documentation (TensorFlow): Google. (n.d.). Embeddings. TensorFlow Core. Retrieved from tensorflow.org. The official documentation states

"An embedding is a mapping from discrete objects

such as words

to vectors of real numbers... The embedding is a lookup table that maps from integer indices (which stand for specific words) to dense vectors (their embeddings)." (See the "Introduction" section).

3. Academic Publication: Mikolov

T.

Chen

K.

Corrado

G.

& Dean

J. (2013). Efficient Estimation of Word Representations in Vector Space. arXiv:1301.3781. The foundational Word2Vec paper introduces the concept of learning "high-quality distributed vector representations that capture a large number of precise syntactic and semantic word relationships." This describes the core purpose of embeddings. (See Abstract and Section 1: Introduction).

4. University Courseware (MIT): MIT 6.S191: Introduction to Deep Learning. (2021). Lecture 4: Sequence Modeling. The lecture describes embeddings as a way to "learn a low-dimensional

dense representation of words" to overcome the sparsity and lack of relationship information in one-hot vectors. (Available on YouTube and course website

discussion typically occurs in the first 15-20 minutes of the NLP/Sequence lecture).