embedding
Let an agent explain the notion of embedding, relay its meaning across mathematics and its extension to machine learning from reference sources, distinguish the senses the aliases name, and steer a question to the right sense.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What embedding means.
Definition
Definition.
Definition
Definition.
- What does embedding mean in mathematics, and how does it differ from a general function or a projection? definition
- Which sense is meant, mathematical or machine-learning? boundary
Senses
The senses.
Senses
Senses.
- What are topological, elementary and machine-learning embeddings? definition
- Which entry fits the intended sense? action
Math Mathematics.
Topology
Topological embedding.
Topology
Topology.
- What is a topological embedding? provenance
- Which references are standard? provenance
Logic
Elementary embedding.
Logic
Logic.
- What is an elementary embedding in logic? provenance
- Which sources are cited? provenance
ML Machine learning.
Latent
Latent space.
Latent
Latent.
- What is a machine-learning embedding into a latent space? provenance
- Is the analogy to the mathematical sense loose? boundary
Kinds
Embedding kinds.
Kinds
Kinds.
- What are word and graph embeddings? provenance
- Which entry fits the specific kind? action
Context Context.
Preservation
What is preserved.
Preservation
Preservation.
- What structure does an embedding preserve in each field? provenance
- Which sources are cited? provenance
Use
Use.
Use
Use.
- How are embeddings used in practice? action
- Is the sense correctly identified? boundary
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- latent space, elementary embedding, fastText, graph embedding, knowledge graph embedding, Local flatness, RDF2Vec, book embedding, linkless embedding, planar embedding
What it is Filled
In mathematics, an embedding is a map that places one structure inside another so that the copy faithfully preserves the original structure; the term applies across geometry, topology and algebra. The registry aliases name several senses, including topological embeddings, elementary embeddings in logic, and, by extension, machine-learning embeddings such as word or graph embeddings that map items into a latent space of vectors. The precise meaning depends on the field, so the sense should be identified before answering.
Why it exists Filled
Let an agent explain the notion of embedding, relay its meaning across mathematics and its extension to machine learning from reference sources, distinguish the senses the aliases name, and steer a question to the right sense.
Distinguishing features Filled
- Structure-preserving
- Field-dependent meaning
- Extended to machine learning
- Maps into a larger space
What robots and AI may and may not do Filled
Must not
- Mix senses of embedding from different fields in an argument.
- Call a map an embedding when it does not preserve the structure.
- Overstate what an embedding preserves.
- Present a disputed proof involving embeddings as settled.
Only with a human decision
- Publishing a mathematical claim in someone else's name.
May
- Explain what an embedding is in the field the user is working in.
- Check whether a given map is injective and structure-preserving.
- Distinguish the mathematical sense from machine-learning vector embeddings.
Moral aspects Filled
- Precise terms matter; confusing them can invalidate results.
- Credit for mathematical work should be accurate.
Who is affected
- Students
- Researchers
- Readers of mathematical work
Owners Filled
Steward
Nobody: a mathematical concept held in common.
Links to other meta-models Filled
parent
- Q11348 - registry parent class
related
- function - in registry terms
- projection
- machine learning
- representation
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.embedding
- Wikidata: Q980509 (https://www.wikidata.org/wiki/Q980509)
Direct properties not applicable Not applicable
- field: mathematics and its extensions note
- key property: preserves structure note
- registry parent: function note
Plane XCT: no invented physical properties.
Recognition optional Filled
- A structure-preserving placement into a larger space
- Topological embedding, elementary embedding, latent space, word and graph embeddings
- A general function need not preserve structure; a projection may lose information
- Not a visible object; a map or representation, sometimes pictured as points in a space.
Capabilities and actions required Filled
- explain the mathematical notion
- relay the machine-learning extension
- distinguish the senses
- steer to the right meaning
Hazards and failure modes required Filled
- Mixing the senses
- Assuming one field s meaning everywhere
- Overstating the analogy to latent spaces
Standards and interfaces required Filled
- Mathematical definitions per field
Context of use required Filled
- Placing one structure faithfully inside another.
- topological embedding
- elementary embedding
- word embedding
- graph embedding
Sources Filled
- Wikidata item Q980509: embedding - identity and sense of the item
- Wikipedia: Embedding - general description of the item
Open questions
- Should each sense be a separate entry?
- How should the machine-learning sense be scoped?
- How should the senses be signposted?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q980509/spec.json