HyLo: A Hybrid Low-Rank Natural Gradient Descent Method
Bibliographic record
Abstract
This work presents a Hybrid Low-Rank Natural Gradient Descent method, called HyLo, that accelerates the training time of deep neural networks. Natural gradient descent (NGD) requires computing the inverse of the Fisher information matrix (FIM), which is typically expensive at largescale. Kronecker factorization methods such as KFAC attempt to improve NGD's running time by approximating the FIM with Kronecker factors. However, the size of Kronecker factors increases quadratically as the model size grows. Instead, in HyLo, we use the Sherman-Morrison-Woodbury variant of NGD (SNGD) and propose a reformulation of SNGD to resolve its scalability issues. HyLo uses a computationally-efficient low-rank factorization to achieve superior timing for Fisher inverses. We evaluate HyLo on large models including ResNet-50, U-Net, and ResNet-32 on up to 64 GPUs. HyLo converges 1.4×-2.1× faster than the state-of-the-art distributed implementation of KFAC and reduces the computation and communication time up to 350 × and 10.7× on ResNet-50.
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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".