The Stochastic Delta Rule: Faster and More Accurate Deep Learning Through Adaptive Weight Noise
Bibliographic record
Abstract
Abstract Multilayer neural networks have led to remarkable performance on many kinds of benchmark tasks in text, speech, and image processing. Nonlinear parameter estimation in hierarchical models is known to be subject to overfitting and misspecification. One approach to these estimation and related problems (e.g., saddle points, colinearity, feature discovery) is called Dropout. The Dropout algorithm removes hidden units according to a binomial random variable with probability p prior to each update, creating random “shocks” to the network that are averaged over updates (thus creating weight sharing). In this letter, we reestablish an older parameter search method and show that Dropout is a special case of this more general model, stochastic delta rule (SDR), published originally in 1990. Unlike Dropout, SDR redefines each weight in the network as a random variable with mean μwij and standard deviation σwij. Each weight random variable is sampled on each forward activation, consequently creating an exponential number of potential networks with shared weights (accumulated in the mean values). Both parameters are updated according to prediction error, thus resulting in weight noise injections that reflect a local history of prediction error and local model averaging. SDR therefore implements a more sensitive local gradient-dependent simulated annealing per weight converging in the limit to a Bayes optimal network. We run tests on standard benchmarks (CIFAR and ImageNet) using a modified version of DenseNet and show that SDR outperforms standard Dropout in top-5 validation error by approximately 13% with DenseNet-BC 121 on ImageNet and find various validation error improvements in smaller networks. We also show that SDR reaches the same accuracy that Dropout attains in 100 epochs in as few as 40 epochs, as well as improvements in training error by as much as 80%.
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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 | 0.008 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 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".