The Dimensional Analysis of Data Flow Programs That Include Multidimensional and User-Defined Functions
Bibliographic record
Abstract
This paper is to design Dimensional Analysis (DA) algorithms for the multidimensional Lucid, the equational data flow language, which also includes user-defined functions. The significance is that the DA is indispensable for an efficient implementation of multidimensional Lucid and should aid the implementation of other data flow systems, such as Google’s TensorFlow. Data flow is a form of computation in which components of Multidimensional Data-sets (MDDs) travel on communication lines in a network of processing stations. Each processing station incrementally transforms its input MDDs to its output, another (possibly very different) MDD. MDDs are very common in Health Information Systems and data science in general. An important concept is that of a relevant dimension. A dimension is relevant if the coordinate of that dimension is required to extract a value. It is essential that in calculating with MDDs we avoid non-relevant dimensions, otherwise, we duplicate entries (say, in a cache) and waste time and space.For example, if X is the MDD of raw rain measurements, its dimensionality is {location, day, hour}, and that of Y is {location, day}. Note that the dimensionality is more than just the rank, which is simply the number of dimensions. Previously, there was extensive research on data-flow itself, which we summarize. Nevertheless, an exhaustive literature search uncovered no relevant previous DA work. Our methodology is that we proceeded incrementally, solving increasingly difficult instances of DA corresponding to increasingly sophisticated language features. However, in this paper, we solved the DA of multidimensional Data Flow (DF) programs. We also solved the difficult problem (which the GLU (Granular Lucid) team never solved) of determining the dimensionality of the DF programs that include user-defined functions, including recursively defined functions. We do this by adapting the PyLucid interpreter (to produce the DAM interpreter) to evaluate the entire program over the (finite) domain of dimensionalities. As a result, the experimentally validated algorithms in our paper can produce useful upper bounds for the dimensionalities of the variables in multidimensional PyLucid programs. That also includes those with user-defined functions.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.042 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.004 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.006 | 0.013 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.002 | 0.006 |
| Insufficient payload (model declined to judge) | 0.005 | 0.002 |
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.
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 source (direct Gemma or distilled Codex), 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".