Are there any theoretical limits on the information that can be encoded in an embedding of a given size?

In a vector, the number of dimensions depends on the length of your vector — “n”. So if an embedding has 150 numbers or n=150, the vector has 150 dimensions. An embedding refers to the reduction of high-dimensional data, such as unstructured text, to a representation with fewer dimensions, such as a vector. Nov 9, 2023 ... Each vertical band in this plot represents a value in one of the embedding space's 1536 dimensions. Mathematically, an embedding space, or ... Aug 18, 2020 ... An embedding of the topological space X into Euclidean space Rn is just a map ϕ:X→Rn such that ϕ:X→ϕ(X) is a homeomorphism. Sep 6, 2023 ... The authors of word2vec are somewhat vague, recommending somewhere between 100 and 1000 dimensions. Other authors pick numbers like 100 or 300. Aug 13, 2024 ... Bi-Encoders produce a vector representation for a given sentence or document chunk; which is usually a single vector of a fixed dimension. Note ... Dec 9, 2023 ... ... size or length. Common vector dimensionalities include 384 ... A single dimension in a vector embedding does not mean anything, as ... Embed an image in a note. To embed an image: ![[Engelbart.jpg]]. Engelbart.jpg > outline. You can change the image dimensions, by adding |640x480 to the link ... Embedding capsules, gelatin, easy molds, BEEM® capsules, tissue processing, critical point dryer from Electron Microscopy Sciences. output_dimensionality. Optional: int. Used to specify output embedding size. If set, output embeddings will be truncated to the size specified.