A Second Examination of Trigonometric Step Sizes and Their Impact on Warm Restart SGD for Non-Smooth and Non-Convex Functions
Bibliographic record
Abstract
This paper presents a second examination of trigonometric step sizes and their impact on Warm Restart Stochastic Gradient Descent (SGD), an essential optimization technique in deep learning. Building on prior work with cosine-based step sizes, this study introduces three novel trigonometric step sizes aimed at enhancing warm restart methods. These step sizes are formulated to address the challenges posed by non-smooth and non-convex objective functions, ensuring that the algorithm can converge effectively toward the global minimum. Through rigorous theoretical analysis, we demonstrate that the proposed approach achieves an O1T convergence rate for smooth non-convex functions and extend the analysis to non-smooth and non-convex scenarios. Experimental evaluations on FashionMNIST, CIFAR10, and CIFAR100 datasets reveal significant improvements in test accuracy, including a notable 2.14% increase on CIFAR100 compared to existing warm restart strategies. These results underscore the effectiveness of trigonometric step sizes in enhancing optimization performance for deep learning models.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".