Distributed Second-Order Optimization using Kronecker-Factored Approximations
Bibliographic record
Abstract
As more computational resources become available, machine learning researchers train ever larger neural networks on millions of data points using stochastic gradient descent (SGD). Although SGD scales well in terms of both the size of dataset and the number of parameters of the model, it has rapidly diminishing returns as parallel computing resources increase. Second-order optimization methods have an affinity for well-estimated gradients and large mini-batches, and can therefore benefit much more from parallel computation in principle. Unfortunately, they often employ severe approximations to the curvature matrix in order to scale to large models with millions of parameters, limiting their effectiveness in practice versus well-tuned SGD with momentum. The recently proposed K-FAC method(Martens and Grosse, 2015) uses a stronger and more sophisticated curvature approximation, and has been shown to make much more per-iteration progress than SGD, while only introducing a modest overhead. In this paper, we develop a version of K-FAC that distributes the computation of gradients and additional quantities required by K-FAC across multiple machines, thereby taking advantage of method’s superior scaling to large mini-batches and mitigating its additional overheads. We provide a Tensorflow implementation of our approach which is easy to use and can be applied to many existing codebases without modification. Additionally, we develop several algorithmic enhancements to K-FAC which can improve its computational performance for very large models. Finally, we show that our distributed K-FAC method speeds up training of various state-of-the-art ImageNet classification models by a factor of two compared to Batch Normalization(Ioffe and Szegedy, 2015).
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 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 | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
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".