ZORB: A Derivative-Free Backpropagation Algorithm for Neural Networks
Bibliographic record
Abstract
Gradient descent and backpropagation have enabled neural networks to achieve remarkable results in many real-world applications. Despite ongoing success, training a neural network with gradient descent can be a slow and strenuous affair. We present a simple yet faster training algorithm called Zeroth-Order Relaxed Backpropagation (ZORB). Instead of calculating gradients, ZORB uses the pseudoinverse of targets to backpropagate information. ZORB is designed to reduce the time required to train deep neural networks without penalizing performance. To illustrate the speed up, we trained a feed-forward neural network with 11 layers on MNIST and observed that ZORB converged 300 times faster than Adam while achieving a comparable error rate, without any hyperparameter tuning. We also broaden the scope of ZORB to convolutional neural networks, and apply it to subsamples of the CIFAR-10 dataset. Experiments on standard classification and regression benchmarks demonstrate ZORB's advantage over traditional backpropagation with Gradient Descent.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.004 |
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".