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Record W4319653486 · doi:10.48550/arxiv.2302.03160

Stretching maps for tensors

2023· preprint· en· W4319653486 on OpenAlexfundno aff
Vyacheslav Futorny, Mikhail Neklyudov, Kaiming Zhao

Bibliographic record

VenuearXiv (Cornell University) · 2023
Typepreprint
Languageen
FieldMathematics
TopicTensor decomposition and applications
Canadian institutionsnot available
FundersConselho Nacional de Desenvolvimento Científico e TecnológicoNatural Sciences and Engineering Research Council of CanadaNational Natural Science Foundation of China
KeywordsTensor (intrinsic definition)Construct (python library)Symmetry (geometry)MathematicsAlgebraic numberOrder (exchange)Pure mathematicsAlgebra over a fieldInvariants of tensorsAlgebraic structureMathematical analysisComputer scienceGeometry

Abstract

fetched live from OpenAlex

We consider an algebra of even-order square tensors and introduce a stretching map which allows us to represent tensors as matrices. The stretching map could be understood as a generalized matricization. It conserves algebraic properties of the tensors. In the same time, we don't necessarily assume injectivity of the stretching map. Dropping the injectivity condition allows us to construct examples of stretching maps with additional symmetry properties. Furthermore, the noninjectivity leads to the averaging of the tensor and possibly could be used to compress the data.

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.

How this classification was reachedexpand

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 categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.154
Threshold uncertainty score1.000

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 science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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 head0.249
GPT teacher head0.266
Teacher spread0.017 · 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

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

Study designTheoretical or conceptual
Domainnot available
GenreEmpirical

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

Quick stats

Citations0
Published2023
Admission routes1
Has abstractyes

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