Technical note: “Bit by bit”: a practical and general approach for evaluating model computational complexity vs. model performance
Bibliographic record
Abstract
One of the main objectives of the scientific enterprise is the development of well-performing yet parsimonious models for all natural phenomena and systems. In the 21st century, scientists usually represent their models, hypotheses, and experimental observations using digital computers. Measuring performance and parsimony of computer models is therefore a key theoretical and practical challenge for 21st century science. “Performance” here refers to a model's ability to reduce predictive uncertainty about an object of interest. “Parsimony” (or complexity) comprises two aspects: descriptive complexity – the size of the model itself which can be measured by the disk space it occupies – and computational complexity – the model's effort to provide output. Descriptive complexity is related to inference quality and generality; computational complexity is often a practical and economic concern for limited computing resources. In this context, this paper has two distinct but related goals. The first is to propose a practical method of measuring computational complexity by utility software “Strace”, which counts the total number of memory visits while running a model on a computer. The second goal is to propose the “bit by bit” method, which combines measuring computational complexity by “Strace” and measuring model performance by information loss relative to observations, both in bit. For demonstration, we apply the “bit by bit” method to watershed models representing a wide diversity of modelling strategies (artificial neural network, auto-regressive, process-based, and others). We demonstrate that computational complexity as measured by “Strace” is sensitive to all aspects of a model, such as the size of the model itself, the input data it reads, its numerical scheme, and time stepping. We further demonstrate that for each model, the bit counts for computational complexity exceed those for performance by several orders of magnitude and that the differences among the models for both computational complexity and performance can be explained by their setup and are in accordance with expectations. We conclude that measuring computational complexity by “Strace” is practical, and it is also general in the sense that it can be applied to any model that can be run on a digital computer. We further conclude that the “bit by bit” approach is general in the sense that it measures two key aspects of a model in the single unit of bit. We suggest that it can be enhanced by additionally measuring a model's descriptive complexity – also in bit.
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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 | 0.024 | 0.181 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.007 |
| Science and technology studies | 0.002 | 0.008 |
| Scholarly communication | 0.006 | 0.017 |
| Open science | 0.005 | 0.009 |
| Research integrity | 0.004 | 0.008 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".