albert - a lite bert

# ALBERT - A Lite BERT

## Introduction & Motivation

ALBERT: lightweight BERT via parameter reduction. Factorized embeddings, cross-layer parameter sharing. Applications: mobile deployment, efficient inference.

Motivation: Reduce model size and computational cost.

Applications: Edge deployment, real-time inference, mobile NLP.

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## Core Concepts & Theory

### Factorized Embeddings

Separate word and hidden dimension sizes.

### Cross-Layer Parameter Sharing

Share weights across transformer layers.

### Sentence Ordering Prediction

Replace NSP with SOP task.

### Sparse Computation

Reduced FLOPs via architecture design.

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## Mathematical Formulation

Parameter Reduction:
$$ ext{params}_{ ext{ALBERT}} = V \cdot e + T(H^2 + 4H^2)$$

vs BERT:
$$ ext{params}_{ ext{BERT}} = V \cdot H + T(H^2 + 4H^2)$$

Factorization:
$$W = W_2 W_1 ext{ where } W_1 \in \mathbb{R}^{D imes e}, W_2 \in \mathbb{R}^{e imes D}$$

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## Advanced Theory & Extensions

### Knowledge Distillation

Compress via teacher.

### Multi-Head Attention Sharing

Share attention heads.

### Layer-Wise Adaptation

Fine-tune specific layers.

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## Computational Considerations

Embedding projection: O(V·e).

Shared transformer: O(T·H²).

Total: ~60% parameter reduction.

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## Practical Implementation Strategies

### Hyperparameter Factorization

Choose embedding vs hidden dimensions.

### Layer Sharing

Periodic vs full sharing.

### Mixed Precision

FP16 training for efficiency.

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## Benchmark Datasets & Evaluation

GLUE: Text understanding.

SQuAD: Reading comprehension.

RACE: Multiple choice QA.

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## Key Challenges & Limitations

### Task Performance Degradation

Slight accuracy loss for efficiency.

### Parameter Sharing Bottleneck

Shared parameters limit expressiveness.

### Training Instability

Harder to train than BERT.

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## Hyperparameter Tuning

Embedding dimension: 64-128.

Hidden dimension: 256-768.

Sharing pattern: Full or periodic.

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## Real-World Applications & Case Studies

Mobile Applications: On-device NLP.

Edge Devices: IoT deployment.

Fast Inference: Low-latency systems.

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## Integration with Other Methods

ALBERT + knowledge distillation; + quantization for further compression.

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## Summary & Key Takeaways

ALBERT achieves efficiency through parameter factorization and sharing.

Principles:
1. Factorization: Reduce embedding dimension.
2. Sharing: Reuse transformer layers.
3. SOP: Better pre-training task.
4. Efficiency: 70% fewer parameters than BERT.
5. Deployment: Mobile and edge ready.

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## Appendix: Practical Labs

### Lab 1: Factorized Embeddings

import numpy as np

def factorized_embedding(vocab_size, hidden_dim, embedding_dim):
 """Create factorized embedding: V*E + E*H instead of V*H"""
 # Word embedding to lower dimension
 word_embed = np.random.randn(vocab_size, embedding_dim) * 0.01
 
 # Lower dimension to hidden dimension
 project = np.random.randn(embedding_dim, hidden_dim) * 0.01
 
 params_factorized = vocab_size * embedding_dim + embedding_dim * hidden_dim
 params_standard = vocab_size * hidden_dim
 
 return params_factorized, params_standard

vocab = 30000
hidden = 768
embed = 128
fact_params, std_params = factorized_embedding(vocab, hidden, embed)
assert fact_params < std_params
print(f"✓ Factorized: {fact_params}, Standard: {std_params}")

### Lab 2: Cross-Layer Sharing

class SharedAlbertLayer:
 def __init__(self, hidden_dim):
 self.weights = np.random.randn(hidden_dim, hidden_dim) * 0.01
 
 def forward(self, x):
 return x @ self.weights

np.random.seed(42)
shared_layer = SharedAlbertLayer(768)
num_layers = 12

# Same weights reused
outputs = [shared_layer.forward(np.random.randn(256, 768)) for _ in range(num_layers)]
assert len(outputs) == num_layers
print("✓ Cross-layer sharing working")

### Lab 3: SOP Loss

import numpy as np

def sentence_order_prediction_loss(sent_a, sent_b, predictions):
 """SOP: predict if sentence pair is in correct order"""
 labels = np.array([1, 0]) # 1 for correct order, 0 for reversed
 loss = -np.mean(labels * np.log(predictions + 1e-8))
 return loss

np.random.seed(42)
sent_a = np.random.randn(768)
sent_b = np.random.randn(768)
preds = np.array([0.8, 0.2]) # Model prediction
loss = sentence_order_prediction_loss(sent_a, sent_b, preds)
assert loss > 0
print(f"✓ SOP loss: {loss:.4f}")

### Lab 4: Parameter Count Reduction

def compare_parameter_counts(vocab_size, hidden_dim, num_layers):
 """Compare BERT vs ALBERT parameter counts"""
 # BERT
 bert_embed = vocab_size * hidden_dim
 bert_layers = num_layers * (hidden_dim * hidden_dim * 2)
 bert_total = bert_embed + bert_layers
 
 # ALBERT (with factorization)
 embed_dim = 128
 albert_embed = vocab_size * embed_dim + embed_dim * hidden_dim
 albert_layers = 1 * (hidden_dim * hidden_dim * 2) # Shared
 albert_total = albert_embed + albert_layers
 
 reduction = 1 - (albert_total / bert_total)
 return reduction

reduction = compare_parameter_counts(30000, 768, 12)
assert reduction > 0.5
print(f"✓ Parameter reduction: {reduction:.1%}")

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