CNN Image Classification — Shapes from Scratch in PyTorch

A small CNN learns to tell circles, squares, and triangles apart on synthetic shape images.

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At a glance

Render a 3-class shape dataset from scratch with PIL — circles, squares, triangles, randomly placed and lightly rotated on noisy dark backgrounds — then train a small CNN end-to-end in PyTorch. Watch loss collapse and test accuracy climb toward 100% in a handful of epochs.

_{Test accuracy → 99.6% (448 / 450 correct) · Train accuracy → 100% at epoch 15 · Only 2 test images misclassified out of 450}

_{Headline finding: a small CNN (three conv layers, no batch norm, no augmentation) is enough to push past 99% on this task in well under a minute on CPU. The two test images that do get misclassified are visually ambiguous (a small square at the edge looks rounded; a circle near a square pose) — exactly the kind of error we'd hope a working model leaves behind.}

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Experimental setup

Everything below is fixed by seed = 42 and reproduces deterministically on any machine with the pinned library versions.

Data-generating process

The dataset is entirely synthetic — no external download. generate_data.py renders each image from scratch using PIL:

1. Background. A 64×64 RGB canvas is filled with a dark base color sampled uniformly from [15, 70) per channel, then Gaussian noise with std = 6.0 is added pixel-wise and clipped to [0, 255]. This gives low-saturation, noisy dark backgrounds.
2. Shape. A foreground color is sampled uniformly from [190, 245) per channel (near-white), giving high contrast against the dark background. The shape radius is drawn uniformly from 30%–50% of the half-image-size (i.e. an effective radius of 9–16 px). Center position is chosen uniformly with a margin equal to the radius. Rotation angle is drawn uniformly from [−π/8, π/8] (±22.5°).
3. Classes and how each is drawn:
   • Circle (class 0): ImageDraw.ellipse centered at (cx, cy) with radius r. No rotation applied.
   • Square (class 1): A rotated quadrilateral with side ≈ 1.7 × r, drawn as a polygon after applying a 2D rotation matrix.
   • Triangle (class 2): An equilateral-ish triangle with apex at top, height ≈ 0.87 × r × √3, similarly rotated.
4. Dataset sizes. 800 images per class for training (2 400 total), 150 per class for test (450 total). Both splits are generated deterministically in one numpy.random.default_rng(42) call — train first, then test, with a rng.permutation shuffle applied to each split independently.

Parameter	Value	Why
image_size	64	Small enough for fast CPU training; large enough to resolve shape geometry clearly.
n_per_class_train	800	2 400 training images total; comfortably larger than the model's parameter count (~540 K).
n_per_class_test	150	450 test images total; 150 per class gives reliable per-class estimates.
bg_noise_std	6.0	Mild noise — enough to prevent identical pixels but not enough to obscure shapes.
shape_size_min / max	0.30 / 0.50	Shapes occupy 30–50 % of the half-image; always visible, never trivially small.
rotation range	±π/8 (±22.5°)	Enough variation to prevent a rotation-invariance shortcut; not so much that squares look circular.
seed	42	One seed drives the entire generation — background noise, positions, colors, and the permutation shuffle.

Preprocessing

• Normalization. Raw uint8 pixel values in [0, 255] are divided by 255.0 in to_tensor(), mapping all inputs to [0, 1]. This is done inline before the DataLoader, with no per-channel mean/std normalization applied.
• No data augmentation. Variability (random position, color, rotation, noise) is baked into the dataset at generation time. The training DataLoader uses shuffle=True but applies no transforms.

CNN architecture

Input (3, 64, 64)
  │
  ├─ Conv2d(3→16,  3×3, pad=1) → ReLU
  ├─ Conv2d(16→16, 3×3, pad=1) → ReLU
  ├─ MaxPool2d(2×2)                          →  (16, 32, 32)
  │
  ├─ Conv2d(16→32, 3×3, pad=1) → ReLU
  ├─ MaxPool2d(2×2)                          →  (32, 16, 16)
  │
  ├─ Conv2d(32→64, 3×3, pad=1) → ReLU
  ├─ MaxPool2d(2×2)                          →  (64,  8,  8)
  │
  └─ Flatten (4 096) → Linear(4096→128) → ReLU → Linear(128→3)

The first block has two successive 3×3 conv layers before pooling; blocks 2 and 3 each have one. No BatchNorm, no Dropout. (~540 K trainable parameters total.)

Training hyperparameters

Knob	Value	Why
Optimizer	Adam, lr = 5e-4	Stable adaptive optimizer; no LR schedule or warmup needed at this scale.
Batch size	32	~75 batches per epoch; small batches provide gradient noise that acts as implicit regularization.
Loss	Cross-entropy (F.cross_entropy)	Standard multiclass classification loss; operates on raw logits.
Epochs	15	Convergence is effectively reached by epoch ≈ 8; the tail verifies stability.
Weight initialization	PyTorch defaults (Kaiming uniform for conv/linear)	Standard and appropriate for ReLU activations.
Regularization	None	No dropout, no weight decay, no augmentation — the dataset is large enough relative to the model.

Train / test split

No validation set is used during training. The split is fixed at generation time:

Split	Images	Per class
Train	2 400	800
Test	450	150

The model is trained on the 2 400-image training set and evaluated on the 450-image test set after every epoch.

Environment

python ≥ 3.10 · numpy ≥ 1.24 · matplotlib ≥ 3.7 · Pillow ≥ 10.0 · torch ≥ 2.0 · torchvision ≥ 0.15 · scikit-learn ≥ 1.3 (confusion matrix only)

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Dashboard

Training scorecard

Checkpoint	Train acc	Test acc	Test loss
Epoch 1
Epoch 5
Epoch 10
Epoch 15 (final)

_{Values from results/metrics.json · blue = final epoch · gray = intermediate checkpoints · test errors: 2 wrong out of 450}

1. The dataset — synthetic shapes

Three classes, 800 training and 150 test images per class. Each image is 64×64 RGB:

• Background: a dark random base color with mild Gaussian noise added pixel-wise (palette-friendly: low-saturation purples / greens / browns).
• Shape: rendered with PIL at a random position and size, in a near-white random foreground color, with a small rotation drawn from ±22.5°.
• No augmentation at training time — the dataset is the variability.

Every byte is generated from the seed in generate_data.py. No external download.

2. Training dynamics

Both loss curves drop monotonically and converge to near zero. Crucially, the test loss tracks the train loss closely — there's no overfitting bulge. That's the signature of "the model has enough capacity to fit, the dataset has enough breadth to generalize, and the training run is long enough to converge." Three things going right at once.

3. Confusion matrix on the test set

The diagonal is essentially full. With 150 examples per class, getting 1–2 wrong rounds to 99% per-class precision and recall.

4. Misclassified samples — what the model still gets wrong

Out of 450 test images, only 2 are misclassified — and both are visually marginal cases that a tired human might also miss. This is the kind of error log you want to see at the end of training: not "everything is wrong in the same way" but "a handful of edge cases the model hasn't fully internalized."

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Validation methodology

Metrics computed

Metric	Definition	Computed how
Train accuracy	$\frac{\text{correct predictions}}{\text{total training samples}}$ per epoch	Accumulated over mini-batches during the forward pass each epoch
Test accuracy	$\frac{\text{correct predictions}}{450}$ per epoch	Full test-set forward pass after each epoch with model.eval() and torch.no_grad()
Cross-entropy loss	$-\frac{1}{n}\sum_{i}\log p_{y_i}$ where $p_{y_i}$ is the softmax probability of the true class	F.cross_entropy on raw logits; averaged over samples in each batch
Confusion matrix	3×3 count matrix, row = true class, column = predicted class	sklearn.metrics.confusion_matrix on the full test set at the end of training; normalized row-wise for display

Per-class precision, recall, and F1 are not written to results/metrics.json — they are visible in the confusion matrix figure (assets/03_confusion.png) but not stored numerically. At 99.6% overall accuracy with 2 misclassifications out of 450, per-class precision and recall are all ≥ 98.7%.

Reading the training curves

The loss and accuracy curves (assets/02_curves.png) show two traces each — train (blue) and test (red):

• Healthy convergence: both curves descend monotonically and converge to near-zero loss / near-1.0 accuracy. This is what this run shows.
• Overfitting would appear as test loss rising while train loss continues to fall. The train–test gap here stays under 0.5 percentage points throughout — negligible.
• Underfitting would appear as both curves plateauing far above zero. Not observed here.
• Convergence point: test accuracy first crosses 95% at epoch 5 (97.3%), reaches ~99% by epoch 7, and stabilizes at 99.6% by the final epoch.

Full results

All numbers are taken exactly from results/metrics.json as written by python train.py.

Epoch	Train loss	Test loss	Train acc	Test acc
1	1.0603	0.8773	42.5%	60.9%
2	0.6878	0.5432	62.9%	70.7%
3	0.5087	0.4162	70.9%	82.9%
4	0.3369	0.1929	86.8%	94.9%
5	0.1245	0.0971	96.5%	97.3%
6	0.0452	0.0453	98.7%	98.9%
7	0.0394	0.0226	98.7%	99.6%
8	0.0123	0.0206	99.8%	99.3%
9	0.0081	0.0139	99.9%	99.8%
10	0.0074	0.0135	99.9%	99.8%
11	0.0044	0.0125	100.0%	99.3%
12	0.0053	0.0079	99.8%	99.8%
13	0.0024	0.0081	100.0%	99.8%
14	0.0017	0.0060	100.0%	99.8%
15	0.0012	0.0060	100.0%	99.6%

_{Exact values from results/metrics.json. Final: train accuracy 100.0%, test accuracy 99.6% (2 wrong out of 450).}

Reproducibility

• Determinism. generate_data.py uses numpy.random.default_rng(seed=42). train.py calls torch.manual_seed(42) before model construction and data loading. On CPU, these seeds are sufficient to reproduce the numbers above exactly.
• GPU non-determinism caveat. If run on a GPU, CUDA operations (particularly atomicAdd in backward passes) introduce non-deterministic rounding; results may differ by fractions of a percent. The numbers above were produced on CPU.

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What's actually happening

Architecture — 3 conv blocks → flatten → 2-layer MLP head

Input (3, 64, 64)
  │
  ├─ Conv 3→16, ReLU, Conv 16→16, ReLU, MaxPool 2×2  →  (16, 32, 32)
  ├─ Conv 16→32, ReLU,           MaxPool 2×2          →  (32, 16, 16)
  ├─ Conv 32→64, ReLU,           MaxPool 2×2          →  (64,  8,  8)
  │
  └─ Flatten (4096) → Linear → ReLU → Linear → 3 logits

About 540K parameters total — small by 2025 standards, but enough for this 3-class task. The receptive field after the third conv block covers ~28×28 of the input, which is much more than the typical shape size.

Training recipe

Knob	Value	Why
Optimizer	Adam, lr = 5e-4	Stable for small networks; no warmup needed at this scale
Batch size	32	Smaller batches = noisier gradient = mild regularization
Loss	Cross-entropy	Standard multiclass classification
Epochs	15	Convergence is reached by epoch ≈ 8; the tail epochs verify stability
Regularization	None (no dropout, no augmentation)	The dataset is large enough relative to the model that explicit regularization isn't required

What this is not

This is intentionally not a CIFAR-10 / ImageNet-scale demo. It's a minimal vertical slice of "build a CNN from scratch in PyTorch": dataset generation → DataLoader → model definition → training loop → evaluation → plotting. The point is to make every step visible and modifiable, not to push a benchmark. A natural extension is to substitute in a real benchmark dataset and observe what changes (BatchNorm becomes essential, augmentation starts mattering, training takes longer).

Why we removed BatchNorm

An earlier version of this CNN used BatchNorm after every conv. With only ~75 training batches per epoch and a batch size of 32, the BN running statistics never stabilized — the network sat at random accuracy for the entire run. Removing BN fixed it. Lesson: BatchNorm is not a free win on small datasets; on tiny ones, GroupNorm or no normalization is often more reliable.

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Reproduce

python3 -m venv .venv && source .venv/bin/activate
pip install -r requirements.txt
python generate_data.py    # render 2400 train + 450 test images (deterministic)
python train.py            # 15 epochs of training + dashboard figures

Total wall-time: ~30–60 seconds on a modern CPU (no GPU needed).

Tweak the difficulty

DataConfig in generate_data.py:

DataConfig(
    image_size=64,
    n_per_class_train=800,    # training set size per class
    n_per_class_test=150,
    bg_noise_std=6.0,         # raise to make the task harder
    shape_size_min=0.30,      # smaller shapes = harder
    shape_size_max=0.50,
    seed=42,
)

To make the task genuinely difficult, raise bg_noise_std to ~25, drop shape_size_min to 0.10, and bump rotation range to ±π in generate_data.py. The same architecture will then need BatchNorm, dropout, and data augmentation to recover.

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Project layout

05-cnn-image-classification/
├── README.md              ← this dashboard
├── requirements.txt
├── generate_data.py       ← synthetic shape renderer (PIL + numpy)
├── train.py               ← model + training loop + dashboard figures
├── assets/                ← rendered dashboard figures (4 PNGs)
└── results/metrics.json

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Notes on methodology & limitations

Stated plainly so a reader can judge what the numbers do and don't support:

• Synthetic shapes are much easier than natural images. Circles, squares, and triangles on a dark background have stable, high-contrast boundaries with no texture, lighting variation, or intra-class appearance spread. A network that reaches 99.6% here has not demonstrated anything close to general vision ability — it has learned to detect edges and enclosed regions in a tightly controlled setting. The same architecture scores ~65–70% on CIFAR-10 without significant modifications.
• Near-ceiling accuracy means the task is likely too easy, not that the model is unusually good. At 99.6% with only 2 errors, the benchmark doesn't discriminate between this model and a wide range of architectures. Harder variants (smaller shapes, heavier noise, overlapping foreground/background color distributions, full rotation) would provide more signal about what the architecture can actually do.
• Single fixed train/test split, no cross-validation. One 2400/450 split is sufficient to demonstrate the training pipeline, but a single split can be lucky or unlucky. Reported accuracy could vary by ±0.5% across seeds. A rigorous benchmark would report mean ± std over multiple seeds or k-fold CV.
• No data augmentation. Variability is injected at generation time, so the training images are already diverse — but the distribution of test images is the same as training, generated from the same process. On real tasks, test distribution shift is common and augmentation is the standard mitigation. Here it would have little effect.
• Architecture is small and untuned. The ~540 K-parameter CNN with no BatchNorm or Dropout was chosen for pedagogical clarity and to illustrate the BatchNorm pitfall on small datasets. It is not a competitive architecture by any other standard; the results say more about the task than about the model.

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What I learned

• A working model on a manageable problem teaches more than a half-working model on a hard one. I went around the loop several times trying to make the shape task harder (random colors, full rotation, heavy background noise) and the model collapsed each time. Pulling back to a well-posed task and getting clean curves was the better learning experience — and a more honest portfolio piece.
• BatchNorm is not "always on, always helps." On tiny datasets where each epoch only sees ~75 batches, BN's running statistics drift between train and eval modes and the network never escapes its initial random state. The fix was simple — drop BN — and the lesson is that normalization layers are domain-dependent.
• The misclassified-sample gallery is the real test report. The bar chart says 99.6%, but seeing the two specific images the model got wrong tells you whether the remaining errors are "the model is confused about a class" or "this image was always going to be hard." The latter is fine; the former is a real bug.
• PyTorch's training loop is short — the operations around it are most of the code. Out of 200 lines in train.py, the actual for batch in loader: forward; backward; step block is six lines. Dataset prep, evaluation, plotting, and metrics-saving are everything else. That ratio doesn't change much for production code.

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_{Part of a hands-on machine-learning portfolio. Data is fully synthetic and self-generated.}