Implementing Convolutional Neural Networks Using Hartley Stochastic Computing With Adaptive Rate Feature Map Compression
Bibliographic record
Abstract
Energy consumption and the latency of convolutional neural networks (CNNs) are two important factors that limit their applications specifically for embedded devices. Fourier-based frequency domain (FD) convolution is a promising low-cost alternative to conventional implementations in the spatial domain (SD) for CNNs. FD convolution performs its operation with point-wise multiplications. However, in CNNs, the overhead for the Fourier-based FD-convolution surpasses its computational saving for small filter sizes. In this work, we propose to implement convolutional layers in the FD using the Hartley transform (HT) instead of the Fourier transformation. We show that the HT can reduce the convolution delay and energy consumption even for small filters. With the HT of parameters, we replace convolution with point-wise multiplications. HT lets us compress input feature maps, in convolutional layers, before convolving them with filters. In this regard, we introduce two compression techniques: fixed-rate and adaptive-rate. In the fixed-rate compression, we select frequency domain input feature map (IFMap) coefficients with a constant pattern over all convolutional layers. However, for the adaptive-rate IFMap compression, the network, itself, learns to keep or discard coefficients, during training. Also, to optimize the hardware implementation of our methods (fixed- and adaptive-rate compressions), we utilize stochastic computing (SC) to perform the point-wise multiplications in the FD. In this regard, we re-formalize the HT to better match with SC. We show that, compared to conventional Fourier-based convolution, Hartley SC-based convolution can achieve$1.33\times$speedup, and energy is reduced by 23% on a Virtex 7 FPGA when we implement AlexNet over CIFAR-10 based on the fixed-rate compression. Also, we show that if we utilize the adaptive-rate compression, we receive 16% and 15% latency improvement and energy consumption reduction, respectively, compared to the fixed-rate 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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".