---
license: gpl-3.0
language:
- en
tags:
- captcha
- vision
- adversarial
library_name: pytorch
---

# 4-captcha solvers

Checkpoints for four-digit captcha recognition on the [pymlex/4-captcha](https://huggingface.co/datasets/pymlex/4-captcha) dataset. Two architectures are released: CompactCaptchaNet and CaptchaViT, each with a clean-trained and FGSM fine-tuned variant.

Source code, test predictions, and the full training pipeline: [github.com/pymlex/4-captcha](https://github.com/pymlex/4-captcha)

## Overview

Input is a grayscale $320 \times 80$ image with a four-digit string. Each model outputs logits $Z \in \mathbb{R}^{4 \times 10}$. The training objective is

$$L = \sum_{p=1}^{4} CE(Z_{:,p,:}, y_p)$$

FGSM perturbations follow

$$x_{adv} = clip(x + \varepsilon \cdot sign(\nabla_x L), 0, 1)$$

with $\varepsilon \in \{0.015, 0.03\}$.

| Split | Images |
|-------|--------|
| Clean train | 100,000 |
| Clean val | 5,000 |
| Clean test | 5,000 |
| Adv train per model | 20,000 |
| Adv val per model | 1,000 |
| Adv test per model | 1,000 |

## Architectures

**CompactCaptchaNet** — four stride-2 conv blocks, reshape to $(1280, 20)$, `Conv1d` temporal mixing, adaptive pool to four positions, linear heads. About 1.4M parameters.

**CaptchaViT** — patch size $16 \times 16$, embed dim 256, depth 6, eight heads, learned position queries over patch tokens. About 4.8M parameters.

Clean training runs for 20 epochs. Adversarial fine-tuning runs for 20 epochs on a 120k mixed clean and adversarial set. Checkpoints are stored under `checkpoints/{vit,cnn}/{clean,finetune}/`.

## Training curves

### ViT clean

![ViT clean training loss](plots/vit_clean_loss.png)

The summed cross-entropy $L$ should fall steadily over 20 epochs. A persistent gap between train loss and `val_clean_loss` points to overfitting on font and noise patterns. If loss remains near $4 \ln 10$, the model has not separated digit classes.

![ViT clean validation metrics](plots/vit_clean_val_metrics.png)

Validation exact match tracks the fraction of val images with a correct four-digit string. Per-position accuracy can exceed exact match because a single wrong digit zeros the sequence metric.

### ViT fine-tune

![ViT fine-tune training loss](plots/vit_finetune_loss.png)

Fine-tuning on the 120k mixed set should keep `val_clean_loss` near the clean checkpoint level while `val_adv_loss` drops relative to the clean-only model. Divergence between train and both val curves signals imbalance between clean and adversarial batches.

![ViT fine-tune validation metrics](plots/vit_finetune_val_metrics.png)

`val_adv_exact_match` measures robustness on FGSM images generated by the ViT clean checkpoint. A successful fine-tune raises adversarial exact match without collapsing clean exact match.

### CNN clean

![CNN clean training loss](plots/cnn_clean_loss.png)

The CNN typically converges faster than the ViT because inductive locality matches fixed digit slots. Compare final train and val loss to the ViT run at the same epoch count.

![CNN clean validation metrics](plots/cnn_clean_val_metrics.png)

CNN clean exact match on val is the reference for whether convolutional inductive bias helps on this rendering pipeline.

### CNN fine-tune

![CNN fine-tune training loss](plots/cnn_finetune_loss.png)

The same mixed-set objective as ViT fine-tune. CNN parameters are fewer, so watch for faster overfitting on adversarial noise.

![CNN fine-tune validation metrics](plots/cnn_finetune_val_metrics.png)

Compare `val_adv_exact_match` against the ViT fine-tune curve to see which architecture retains digit identity under FGSM.

## Test comparison

![Test model comparison](plots/test_model_comparison.png)

The chart groups four test metrics across ViT, ViT-FT, CNN, and CNN-FT.

**Clean EM** — accuracy on 5,000 held-out clean test images.

**Adv EM** — accuracy on 1,000 FGSM test images for the matching model family.

**Robustness gap** — clean EM minus adv EM for the same checkpoint. Lower gap means smaller clean-to-adv degradation.

**Attack success rate** — fraction of clean-correct predictions that become wrong under FGSM. Fine-tuning should reduce this bar while keeping clean EM high.

## Confusion matrices

![ViT clean adv test](plots/confusion/vit_clean_adv_test_confusion.png)

![CNN clean adv test](plots/confusion/cnn_clean_adv_test_confusion.png)

Each heatmap aggregates predictions over all four digit positions into a single $10 \times 10$ count matrix for FGSM test images from the clean checkpoint. Off-diagonal mass shows which digit pairs the attack exploits before fine-tuning.

## Dataset

[pymlex/4-captcha](https://huggingface.co/datasets/pymlex/4-captcha)

## Citation

```bibtex
@misc{zyukov2026_4captcha,
  author       = {Alex Zyukov},
  title        = {4-captcha: Synthetic Captcha Recognition and Adversarial Fine-tuning},
  year         = {2026},
  howpublished = {\url{https://github.com/pymlex/4-captcha}}
}
```

```bibtex
@article{dosovitskiy2020vit,
  title   = {An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale},
  author  = {Dosovitskiy, Alexey and Beyer, Lucas and Kolesnikov, Alexander and others},
  journal = {arXiv preprint arXiv:2010.11929},
  year    = {2020}
}
```

```bibtex
@article{goodfellow2014explaining,
  title   = {Explaining and Harnessing Adversarial Examples},
  author  = {Goodfellow, Ian J and Shlens, Jonathon and Szegedy, Christian},
  journal = {arXiv preprint arXiv:1412.6572},
  year    = {2014}
}
```

The models are under GPL-3.0 license.