Stride 2 1-D, 2-D, and 3-D Winograd for Convolutional Neural Networks
Bibliographic record
Abstract
Convolutional neural networks (CNNs) have been widely adopted for computer vision applications. CNNs require many multiplications, making their use expensive in terms of both computational complexity and hardware. An effective method to mitigate the number of required multiplications is via the Winograd algorithm. Previous implementations of CNNs based on Winograd use the 2-D algorithm F(2 × 2,3 × 3), which reduces computational complexity by a factor of 2.25 over regular convolution. However, current Winograd implementations only apply when using a stride (shift displacement of a kernel over an input) of 1. In this article, we presented a novel method to apply the Winograd algorithm to a stride of 2. This method is valid for one, two, or three dimensions. We also introduced new Winograd versions compatible with a kernel of size 3, 5, and 7. The algorithms were successfully implemented on an NVIDIA K20c GPU. Compared to regular convolutions, the implementations for stride 2 are 1.44 times faster for a 3 × 3 kernel, 2.04× faster for a 5 × 5 kernel, 2.42× faster for a 7 × 7 kernel, and 1.73× faster for a 3 × 3 × 3 kernel. Additionally, a CNN accelerator using a novel processing element (PE) performs two 2-D Winograd stride 1, or one 2-D Winograd stride 2, and operations per clock cycle was implemented on an Intel Arria-10 field-programmable gate array (FPGA). We accelerated the original and our proposed modified VGG-16 architectures and achieved digital signal processor (DSP) efficiencies of 1.22 giga operations per second (GOPS)/DSPs and 1.33 GOPS/DSPs, respectively.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
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".