Early Verification of the Power Delivery Network in Integrated Circuits
Bibliographic record
Abstract
The verification of power grids in modern integrated circuits must start early in the design process when adjustments can be most easily incorporated. We adopt an existing early verification framework. The\nframework is vectorless, i.e., it does not require input test patterns and does not rely on simulating the power grid subject to these patterns. In this framework, circuit uncertainty is captured via a set of current constraints that capture what may be known or\nspecified from circuit behavior. Grid verification becomes a question of finding the worst-case grid behavior which, in turn, entails the solution of linear programs (LPs) whose size and number is proportional to the size of the grids. The thesis builds on this systematic framework for dealing with circuit uncertainty with the aim of improving efficiency and expanding the capabilities handled within.\nOne contribution introduces an efficient method based on a sparse approximate inverse technique to greatly reduce the size of the required linear programs while ensuring a user-specified over-estimation margin on the exact solution. The application of the\nmethod is exhibited under both R and RC grid models. Another contribution first extends grid verification under RC grid models to\nalso check for the worst-case branch currents. This would require as many LPs as there are branches. Then, it shows how to adapt the approximate inverse technique to speed up the branch current verification process. A third contribution proposes a novel approach to reduce the number of LPs in the voltage drop and branch current\nverification problems. This is achieved by examining dominance relations among node voltage drops and among branch currents. This\nallows us to replace a group of LPs by one conservative and tight LP. A fourth contribution proposes an efficient verification technique under RLC models. The proposed approach provides tight conservative\nbounds on the maximum and minimum worst-case voltage drops at every node on the grid.
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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 | 0.002 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".