An Introduction to Complex Random Tensors
Bibliographic record
Abstract
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine Learning, and Control Systems, the concepts of linear algebra combined with random variables have been indispensable tools. With the evolution of these subjects to multi-domain communication systems, multi-way signal processing, high dimensional data analysis, and multi-linear systems theory, there is a need to bring in multi-linear algebra equipped with the notion of random tensors. Also, since several such application areas deal with complex-valued entities, it is imperative to study this subject from a complex random tensor perspective, which is the focus of this paper. Using tools from multi-linear algebra, we characterize statistical properties of complex random tensors, both proper and improper, study various correlation structures, and fundamentals of tensor valued random processes. Furthermore, the asymptotic distribution of various tensor eigenvalue and singular value definitions is also considered, which is subsequently used for the study of spiked real tensor models that consider the recovery of low rank tensor signals perturbed by noise. This paper aims to provide an overview of the state of the art in random tensor theory of both complex and real valued tensors, for the purpose of enabling its application in engineering and applied science.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot 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.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
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".