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Record W2339224764 · doi:10.1145/1113439.1113452

Algebraic generalization

2005· article· en· W2339224764 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueACM SIGSAM Bulletin · 2005
Typearticle
Languageen
FieldComputer Science
TopicMachine Learning and Algorithms
Canadian institutionsWestern University
Fundersnot available
KeywordsGeneralizationUnificationAlgebraic numberAlgebraic expressionComputer scienceAlgebra over a fieldExpression (computer science)MathematicsPure mathematicsProgramming language

Abstract

fetched live from OpenAlex

We explore the notion of generalization in the setting of symbolic mathematical computing. By "generalization" we mean the process of taking a number of instances of mathematical expressions and producing new expressions that may be specialized to all the instances. We identify a number of ways in which generalization may be useful in the setting of computer algebra. We formalize this generalization as an antiunification problem.The process of antiunification is the dual of unification. It takes two expressions E 1 , E 2 ∈ E (Σ, V ) and produces E 3 ∈ E (Σ, V ) such that there exist substitutions σ 1 and σ 2 such that σ 1 ( E 3 ) = E 1 and σ 2 ( E 3 ) = E 2 . We call the pair of substitutions an antiunifier and the resulting expression a generalization of the expressions. An antiunifier always exists, but is not necessarily unique. There is, however, a unique most specific antiunifier that places the most restrictions on the variables. This gives the most specific generalization , which is unique up to renaming of variables.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesInsufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Not applicable · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.688
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0010.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.002

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.009
GPT teacher head0.237
Teacher spread0.228 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it