Squashing Activation Eval

---
name: squashing-activation-eval
description: Evaluates a novel 'Squashing' activation function against standard alternatives (ReLU, Sigmoid, Tanh) on synthetic 2D classification tasks and the Fashion-MNIST image classification benchmark. It measures how well continuously differentiable logical approximations perform compared to conventional non-linearities in terms of convergence speed and final classification accuracy. Use when the user wants to benchmark on Fashion-MNIST, Synthetic 2D Classification, or asks about evaluating this task. Reports test accuracy.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2010.08760
  bibtex_key: zeltner2020squashing
  confidence: high
---

# squashing-activation-eval

> Squashing activation functions in benchmark tests: towards eXplainable Artificial Intelligence using continuous-valued logic — Zeltner et al. (2020) (arXiv:2010.08760, 2020)

## What this evaluates

Evaluates a novel 'Squashing' activation function against standard alternatives (ReLU, Sigmoid, Tanh) on synthetic 2D classification tasks and the Fashion-MNIST image classification benchmark. It measures how well continuously differentiable logical approximations perform compared to conventional non-linearities in terms of convergence speed and final classification accuracy.

## Datasets

- **Fashion-MNIST** — total 70000; splits: train (60000), test (10000)
- **Synthetic 2D Classification** — total 500; splits: train (-1), test (-1)

## Metrics

- `test accuracy` **(primary)** — range: percent
  - Percentage of correctly classified instances in the held-out test set.
- `cross-entropy loss` — range: [0, ∞)
  - Negative log-likelihood averaged over the batch, used as the optimization objective.
- `train accuracy` — range: percent
  - Percentage of correctly classified instances in the training set.

## Input / output format

**Input**: 2D spatial coordinates (x, y) for synthetic tasks; 28×28 grayscale pixel arrays for Fashion-MNIST.

**Output**: Binary class label (0 or 1) for synthetic tasks; 10-class categorical label (0–9) for Fashion-MNIST.

## Scoring recipe

```python
def compute_accuracy(predictions, gold_labels):
    correct = sum(1 for p, g in zip(predictions, gold_labels) if p == g)
    return correct / len(gold_labels)

def compute_cross_entropy(predictions, gold_labels):
    # predictions: softmax probabilities, gold_labels: one-hot encoded
    return -sum(g[i] * log(predictions[i]) for i in range(len(gold_labels))) / len(gold_labels)
```

## Common pitfalls

- The Squashing function with a learnable β parameter requires more initial epochs to converge, which can skew early training comparisons if fixed epoch counts are used.
- The synthetic datasets lack a specified train/test split ratio in the text, making exact replication of the reported train/test accuracy difficult without the original data generation script.
- Static β and dynamic β configurations for the Squashing function are evaluated as separate runs but share identical baseline hyperparameters, potentially obscuring the true computational overhead of the learnable parameter.

## Evidence (verbatim from paper)

> The dataset is composed of two balanced classes, each containing 250 points. ... FASHION-MNIST, a dataset consisting of 60000 training images and 10000 test images. ... As a cost function cross-entropy function is applied ... train accuracy | test accuracy

## Citation

```bibtex
@misc{zeltner2020squashing,
  title={Squashing activation functions in benchmark tests: towards eXplainable Artificial Intelligence using continuous-valued logic},
  author={Zeltner et al. (2020)},
  year={2020},
  note={arXiv:2010.08760}
}
```

- arXiv: 2010.08760