Parallel tracing of multiple trajectories in gradient descent algorithm with Cell Broadband Engine
Bibliographic record
Abstract
Explored here is the ability of Cell B.E. to efficiently reveal viable solutions of nonlinear function approximation with multilayer perceptron (MLP) employing gradient descent algorithm. The capacity of Cell BE to asynchronously trace several trajectories of implemented gradient descent algorithm from random set of starting points offers advantage of revealing statistical trends and classifying viable optimal approximations delivered by simulated function generator. Approximation conditions of surfaces of 2nd and 3rd order with saddle points, such as hyperbolic paraboloid z=x2-y2, and Monkey saddle z=x3-3xy2, are determined via implementation of gradient descent algorithm (its back propagation version) for 3 layers MPL. Demonstrated are conditions of generating function approximations with (1)highly irregular error distribution, (2)close to uniform error distribution as well as (3)enhanced approximation. In the last case the overall error is significantly smaller than that programmed in the algorithm to be attained via training patterns. Such enhanced solutions offer advantage of attaining highly accurate function representation within minimized resources of MLP (i.e. with minimized number of hidden neurons in the MLP).
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".