PNN Tutorial: Product-based Neural Network

PNN Tutorial: Product-based Neural Network#

Sandbox Model — Experimental

This model is part of the CoreRec Sandbox — an experimental collection of algorithms for research and exploration. Sandbox models are not production-tested and may have incomplete implementations. For production-ready models, see the Production Models.

Introduction#

PNN uses a product layer to capture interactive patterns between inter-field categories before feeding into fully connected layers.

Paper: Qu et al. 2016 - Product-based Neural Networks for User Response Prediction

How PNN Works#

Architecture#

Product Layer:

  1. Embedding Layer: Feature embeddings

  2. Product Layer:

    • Linear part (z): Concatenation

    • Quadratic part (p): Inner or Outer products of embeddings

  3. Hidden Layers: MLP on top of product layer

Key Innovation: Explicitly modeling feature interactions via products (IPNN/OPNN)

Architecture:

Embeddings -> [Linear z, Product p] -> MLP -> Prediction

Mathematical Foundation#

Inner Product (IPNN):

p_ij = <v_i, v_j>

Outer Product (OPNN):

p_ij = v_i v_j^T

Prediction:

l_1 = ReLU(W_z z + W_p p + b_1)
ŷ = σ(W_out l_n + b_out)

Reference Implementation#

Implementation Note

The code examples below are reference implementations for learning purposes. This is a sandbox model and has not been production-tested. Verify behavior thoroughly before using in production.

Step 1: Import and Load Data#

from corerec.sandbox.collaborative_full.nn_base.PNN_base import PNN_base as PNN
from cr_learn import ml_1m
from sklearn.model_selection import train_test_split
import numpy as np

# Load dataset with CORRECT API
data = ml_1m.load()  # Returns dict with 'ratings', 'users', 'movies'
ratings_df = data['ratings']  # DataFrame with user_id, movie_id, rating, timestamp

print(f"Loaded {len(ratings_df)} ratings")

# Split data
train_df, test_df = train_test_split(ratings_df, test_size=0.2, random_state=42)

# Extract arrays for model
train_users = train_df['user_id'].values
train_items = train_df['movie_id'].values
train_ratings = train_df['rating'].values

test_users = test_df['user_id'].values
test_items = test_df['movie_id'].values
test_ratings = test_df['rating'].values

Step 2: Initialize Model#

model = PNN(
    name="PNN_Model",
    embedding_dim=64,
    use_inner_product=True,
    epochs=20,
    batch_size=256,
    learning_rate=0.001,
    verbose=True
)

print(f"Initialized {model.name}")

Step 3: Train#

model.fit(
    user_ids=train_users,
    item_ids=train_items,
    ratings=train_ratings
)

print("Training complete!")

Step 4: Predict#

# Single prediction
score = model.predict(user_id=1, item_id=100)
print(f"Predicted score: {score:.3f}")

# Batch predictions
test_predictions = model.batch_predict(list(zip(test_users[:100], test_items[:100])))

Step 5: Recommend#

# Get top-10 recommendations for user
user_id = 1
recommendations = model.recommend(
    user_id=user_id,
    top_k=10
)

print(f"Top-10 recommendations for User {user_id}:")
for rank, item_id in enumerate(recommendations, 1):
    print(f"  {rank}. Item {item_id}")

Step 6: Evaluate#

from sklearn.metrics import mean_squared_error
import numpy as np

# Predict all test ratings
test_pred = [model.predict(u, i) for u, i in zip(test_users, test_items)]
rmse = np.sqrt(mean_squared_error(test_ratings, test_pred))
print(f"Test RMSE: {rmse:.4f}")

Step 7: Save & Load#

# Save model
model.save('artifacts/pnn_model')

# Load model
loaded = PNN.load('artifacts/pnn_model')
test_score = loaded.predict(1, 100)
print(f"Loaded model prediction: {test_score:.3f}")

Key Takeaways#

When to Use PNN#

✅ Perfect For:

  • CTR prediction

  • Multi-field categorical data

  • When interactions are crucial

  • Ad click prediction

❌ Not For:

  • High-dimensional sparse data without fields

  • Sequence modeling

Best Practices#

  1. Inner vs Outer: IPNN usually faster and sufficient

  2. Kernel Trick: Use factorization to speed up product layer

  3. Hidden Units: [256, 128, 64]

  4. Regularization: L2 or Dropout needed

Scaling & Production Considerations#

If you plan to move this sandbox model toward production use, consider:

  • Data Volume: Test with realistic dataset sizes; sandbox implementations may not be optimized for large-scale data.

  • Distributed Training: For datasets exceeding single-machine memory, consider wrapping the model in distributed training frameworks (e.g., PyTorch DDP, Horovod).

  • Hyperparameter Tuning: Use systematic search (Optuna, Ray Tune) rather than manual tuning. The defaults in sandbox models are not tuned for any specific domain.

  • Serving Latency: Profile inference time. Some architectures (e.g., attention-based) may need quantization or ONNX export for low-latency serving.

  • Monitoring: Implement A/B testing and online metrics (CTR, engagement, diversity) before replacing an existing system.

  • Validation: Write comprehensive unit tests and integration tests before deploying. Sandbox models do not have CI coverage.

Further Reading#

  • Paper: Qu et al. 2016 - Product-based Neural Networks for User Response Prediction

  • GitHub Repository

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