Convex-Concave Programming: An Effective Alternative for Optimizing Shallow Neural Networks
Bibliographic record
Abstract
In this study, we address the challenges of non-convex optimization in neural networks (NNs) by formulating the training of multilayer perceptron (MLP) NNs as a difference of convex functions (DC) problem. Utilizing the basic convex–concave algorithm to solve our DC problems, we introduce two alternative optimization techniques,DC-GDandDC-OPT, for determining MLP parameters. By leveraging the non-uniqueness property of the convex components in DC functions, we generate strongly convex components for the DC NN cost function. This strong convexity enables our proposed algorithms,DC-GDandDC-OPT, to achieve aniteration complexityof$O\left(\log \left(\frac{1}{\varepsilon }\right)\right)$, surpassing that of other solvers, such as stochastic gradient descent (SGD), which has aniteration complexityof$O\left(\frac{1}{\varepsilon }\right)$. This improvement raises the convergence rate from sublinear (SGD) to linear (ours) while maintaining comparabletotal computational costs. Furthermore, conventional NN optimizers likeSGD,RMSprop, andAdamare highly sensitive to the learning rate, adding computational overhead for practitioners in selecting an appropriate learning rate. In contrast, ourDC-OPTalgorithm is hyperparameter-free (i.e., it requires no learning rate), and ourDC-GDalgorithm is less sensitive to the learning rate, offering comparable accuracy to other solvers. Additionally, we extend our approach to a convolutional NN architecture, demonstrating its applicability to modern NNs. We evaluate the performance of our proposed algorithms by comparing them to conventional optimizers such asSGD,RMSprop, andAdamacross various test cases. The results suggest that our approach is a viable alternative for optimizing shallow MLP NNs.
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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) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 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".