Sound and Modular Activity Analysis for Automatic Differentiation in MLIR
Bibliographic record
Abstract
Computing derivatives is paramount for multiple domains ranging from training neural networks to precise climate simulations. While derivatives can be generated by AD (Automatic Differentiation) tools, they often require aggressive optimization to avoid compromising program performance. One of the central optimizations consists of identifying inactive operations that do not contribute to the partial derivatives of interest. Multiple tools provide activity analyses for a variety of input languages, though often with only informal correctness guarantees. This paper formally defines activity analysis for AD as an abstract interpretation, proves its soundness, and implements it within the MLIR compiler infrastructure. To account for MLIR’s genericity, a subset of MLIR’s internal representation amenable to AD is formalized for the first time. Furthermore, the paper proposes a sound intraprocedural approximation of the whole-program activity analysis via function summaries along with a mechanism to automatically derive these summaries from function definitions. The implementation is evaluated on a differentiation-specific benchmark suite. It achieves a 1.24X geometric mean speedup on CPU and a 1.7X geometric mean speedup on GPU in the runtime of generated programs, when compared to a baseline that does not use activity analysis. The evaluation also demonstrates that the intraprocedural analysis with function summaries proves inactive 100% of instructions proven inactive by the whole-program analysis.
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| 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".