AFM Tutorial: Attentional Factorization Machine

AFM Tutorial: Attentional Factorization Machine#

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#

AFM adds attention mechanism to FM to learn the importance of different feature interactions automatically.

Paper: Xiao et al. 2017 - Attentional Factorization Machines

How AFM Works#

Architecture#

FM + Attention:

  1. Feature Embeddings: v_i for each feature

  2. Element-wise Products: v_i ⊙ v_j for all pairs

  3. Attention Network: Learn weights for each interaction

  4. Weighted Sum: Combine interactions by importance

Key Innovation: Not all feature interactions equally important

Architecture:

Features → Embed → [Pairwise Products] → Attention → Sum → Linear → Pred

Mathematical Foundation#

Attention-Based Pooling:

α_ij = h^T ReLU(W(v_i ⊙ v_j) + b)
a_ij = exp(α_ij) / Σ exp(α_kl)

AFM Formula:

ŷ = w_0 + Σ w_i·x_i + p^T Σ_{i,j} a_ij(v_i ⊙ v_j)x_i x_j

where:

  • ⊙ is element-wise product

  • a_ij is attention weight for (i,j) interaction

  • p is projection vector

vs FM:

FM:  Σ <v_i, v_j>  # equal weight
AFM: Σ a_ij(v_i ⊙ v_j)  # learned weight

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.AFM_base import AFM_base as AFM
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 = AFM(
    name="AFM_Model",
    embedding_dim=10,
    attention_dim=64,
    dropout=0.6,
    reg=1e-6,
    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/afm_model')

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

Key Takeaways#

When to Use AFM#

✅ Perfect For:

  • Sparse feature interactions

  • CTR prediction

  • When interactions vary in importance

  • Interpretable recommendations

  • Feature engineering insights

❌ Not For:

  • Need very deep interactions (use DeepFM)

  • Sequential patterns (use RNN)

  • Dense feature spaces

  • Very large scale (slower than FM)

Best Practices#

  1. Embedding Dim: 8-16 (smaller than FM)

  2. Attention Dim: 32-64

  3. Dropout: 0.5-0.7 on attention layer

  4. Regularization: L2 = 1e-6 to 1e-4

  5. Learning Rate: 0.001-0.01

  6. Batch Normalization: After attention

  7. Activation: ReLU in attention network

  8. Visualization: Analyze learned attention weights

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#

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