BPPSA: Scaling Back-propagation by Parallel Scan Algorithm
Bibliographic record
Abstract
In an era when the performance of a single compute device plateaus, software must be designed to scale on massively parallel systems for better runtime performance. However, in the context of training deep learning models, the popular back-propagation (BP) algorithm imposes a strong sequential dependency in the process of gradient computation. Under model parallelism, BP takes $Θ(n)$ steps to complete which hinders its scalability on parallel systems ($n$ represents the number of compute devices into which a model is partitioned). In this work, in order to improve the scalability of BP, we reformulate BP into a scan operation which is a primitive that performs an in-order aggregation on a sequence of values and returns the partial result at each step. We can then scale such reformulation of BP on parallel systems by our modified version of the Blelloch scan algorithm which theoretically takes $Θ(\log n)$ steps. We evaluate our approach on a vanilla Recurrent Neural Network (RNN) training with synthetic datasets and a RNN with Gated Recurrent Units (GRU) training with the IRMAS dataset, and demonstrate up to $2.75\times$ speedup on the overall training time and $108\times$ speedup on the backward pass. We also demonstrate that the retraining of pruned networks can be a practical use case of our method.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.002 | 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 | 0.003 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 0.004 |
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".