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Record W2906945318 · doi:10.48550/arxiv.1810.10813

Inverse Problems in Topological Persistence

2018· preprint· en· W2906945318 on OpenAlex
Steve Oudot, Elchanan Solomon

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

VenuearXiv (Cornell University) · 2018
Typepreprint
Languageen
FieldComputer Science
TopicTopological and Geometric Data Analysis
Canadian institutionsToronto Metropolitan University
Fundersnot available
KeywordsPersistence (discontinuity)InverseTopological data analysisTopology (electrical circuits)MathematicsGeologyGeometryCombinatoricsAlgorithm

Abstract

fetched live from OpenAlex

In this survey, we review the literature on inverse problems in topological\npersistence theory. The first half of the survey is concerned with the question\nof surjectivity, i.e. the existence of right inverses, and the second half\nfocuses on injectivity, i.e. left inverses. Throughout, we highlight the tools\nand theorems that underlie these advances, and direct the reader's attention to\nopen problems, both theoretical and applied.\n

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 categoriesMeta-epidemiology (narrow)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: none
GenreCandidate signal: Empirical · Consensus signal: Empirical
Teacher disagreement score0.441
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
Bibliometrics0.0010.002
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0030.004
Research integrity0.0000.001
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 head0.144
GPT teacher head0.196
Teacher spread0.052 · 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