Performance analysis of table-based approximations of the hyperbolic tangent activation function
Bibliographic record
Abstract
When designing an artificial neural network system in hardware, the implementation of the activation function is an important consideration. The hyperbolic tangent activation function is the most popular, and many approaches exist to approximate it, with varying trade-offs between area utilization and delay. Unfortunately, there is little data available reporting the minimum accuracy required of the activation function approximation in order to obtain good system-level performance; this is particularly the case for table-based approximation methods. In this paper, we demonstrate that table-based approximation methods are very well suited for implementing the tanh activation function, as well as its derivative in a variety of feed-forward artificial neural network topologies which employ the popular RPROP or Levenberg-Marquardt training algorithms. It is shown that when these training methods are used, an activation function possessing a relatively high maximum error can be used to obtain results comparable to floating point. This discovery suggests that these table-based methods can be employed with extreme efficiency in terms of area and speed, rendering them a promising option for any VLSI or FPGA artificial neural network hardware design.
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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 | 0.003 |
| 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 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".