The efficient application of automatic differentiation for computing gradients in financial applications
Bibliographic record
Abstract
Automatic differentiation (AD) is a practical field of computational mathematics that is of growing interest across many industries, including finance. The use of reverse-mode AD is particularly interesting, since it allows for the computation of gradients in the same time required to evaluate the objective function itself. However, it requires excessive memory. This memory requirement can make reverse-mode AD infeasible in some cases (depending on the function complexity and available RAM) and slower than expected in others, due to the use of secondary memory and nonlocalized memory references. However, it turns out that many complex (expensive) functions in finance exhibit a natural substitution structure. In this paper, we illustrate this structure in computational finance as it arises in calibration and inverse problems, and determine Greeks in a Monte Carlo setting. In these cases, the required memory is a small fraction of that required by reverse-mode AD, but the computing time complexity is the same. In fact, our results indicate a significant realized speedup compared with straight reverse-mode AD.
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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 | 0.001 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 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".