Double Back-Propagation and Differential Machine Learning
Bibliographic record
Abstract
We have introduced a novel (ζ, e)-Double Back-propagation Scheme (DBS) applicable to any parametric model with convergence properties in terms of Mean Square Error. The DBS indicates that with an optimal number ζ of DBS updates, and appropriate e learning rate vector for all the model parameters, the Mean Square Error of both training and testing data get to be decreasing, and converge to zero for the training data. The DBS recommends a local Stochastic Gradient Descent (SGD) per observation after the model parameters have been obtained after a first-step estimation with any chosen optimization framework. It has been applied to the Shallow Potts Neural Network Model developed in a previous research by (Alahassa & Murua (2020)), and the results are outstanding. Not the least, we prove mathematically that under an assumption that if there exists a differentiable function that associate covariables (predictors) and target variables (our outputs) as well as their respective local DBS associated parameters, for each observation, we can make the train error and the test error converge to zero simultaneously by applying a dist-NN-h-Taylor Series-PMI model. This last model dictates that we can always differentiate sufficiently the model parameters using a combination of Taylor Approximation Theorem with h ≥ 2 order with a Perfect Multivariate Interpolation (PMI) framework, and finally, an optimal distance (dist) for a suitable Train-Test covariables association. Our main conclusion is that overfitting, mainly with the convergent DBS optimizer is the beginning of a new type of learning method, as we can still generalize our parametric model with local neighborhood learning with multivariate interpolation and fine tuned empirical differentiation.
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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 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".