Michael Brenndoerfer | Data & AI, Private Equity, Technology

Michael Brenndoerfer

ALBERT › Iterative Refinement

Michael BrenndoerferUpdated July 19, 20253 min read

Language AI HandbookAll chapters

Part 24 of 67BERT and Variants

Chapter 174ALBERT › Iterative Refinement

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Cross-layer sharing creates an interesting computational pattern. Instead of passing through 12 different transformations, the input passes through the same transformation 12 times. Each iteration refines the representation, similar to how iterative algorithms converge toward a solution.

In[22]:

Code

def track_layer_representations(model, input_ids):
    """Track how representations evolve through repeated layer applications."""

    batch_size, seq_len = input_ids.shape
    positions = torch.arange(seq_len, device=input_ids.device).unsqueeze(0)

    # Get initial embeddings
    x = model.token_embedding(input_ids)
    x = x + model.position_embedding(positions)
    x = model.embedding_projection(x)
    x = model.embedding_norm(x)

    # Track representations at each iteration
    representations = [x.detach().clone()]

    for i in range(model.num_layers):
        x = model.shared_layer(x)
        representations.append(x.detach().clone())

    return representations

In[23]:

Code

# Create a small model for visualization
torch.manual_seed(42)
small_albert = ALBERTEncoder(
    vocab_size=1000,
    embedding_dim=32,
    hidden_dim=64,
    num_heads=4,
    intermediate_dim=128,
    num_layers=6,
)

# Random input
input_ids = torch.randint(0, 1000, (1, 10))
representations = track_layer_representations(small_albert, input_ids)

Out[24]:

Console

Representation Change Between Iterations:
  Iteration 0 → 1: 7.2268
  Iteration 1 → 2: 6.6079
  Iteration 2 → 3: 6.1655
  Iteration 3 → 4: 5.7893
  Iteration 4 → 5: 5.3263
  Iteration 5 → 6: 5.0161

The representation changes decrease across iterations, indicating that repeated applications of the same layer produce diminishing modifications. This convergence-like behavior suggests the model is iteratively refining toward a stable representation rather than making dramatic changes at each step.

We can visualize how similar representations are across iterations using cosine similarity. If shared layers truly perform iterative refinement, we should see adjacent iterations being more similar than distant ones:

Out[25]:

Visualization

Seven-by-seven cosine-similarity heatmap for the embedding state and six shared-layer iterations, with a bright green diagonal and lower similarity farther from the diagonal. — Cosine similarity between representations in one shared-layer example. The bright green diagonal marks self-similarity, adjacent iterations remain similar, and early-to-late pairs have lower similarity. The pattern illustrates gradual change under repeated application of one layer.

Out[26]:

Visualization

Line plot showing representation change magnitude decreasing across iterations. — L2 change between successive representations in one six-iteration shared-layer example. The change decreases at every step in this run, illustrating convergence-like refinement without claiming that every trained ALBERT follows the same trajectory.

This iterative behavior has theoretical connections to fixed-point computation and recurrent neural networks. The shared layer learns a single step of refinement, and multiple applications accumulate into a complete transformation.