Interfere

Interfere is an exploration of how a causal Transformer internally represents and reasons about the transition rules of a Game-of-Life-like system.
We train a deliberately overparameterized 25M-parameter Transformer on multiple variants of Conway’s Game of Life (GOL) and use mechanistic interpretability tools to probe what the model treats as first-class features.

The goal is not to solve GOL efficiently, but to study how a Transformer behaves when a simple, deterministic rule does exist—without giving it the right inductive biases.

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(rough) idea

• Train a Transformer to predict t+1 from (rules + t).
• Encode both the update rule and the 2D grid state as tokens.
• Probe attention patterns, linear probes, and PCA directions to understand:
  • What structure emerges?
  • What features are linearly accessible?
  • Which properties the model prioritizes internally?

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Data & training setup

Each sequence is laid out as:

, 18 rule bits, , H×W (t), , H×W (t+1)

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• Rules: 18 “physics bits” encoding different GOL-style update rules
• State: Binary grid, flattened row-major
• Positioning: Standard positional encoding + 2D RoPE on Q/K (added post-hoc)
• Training: MLM-style masking after <SEP>
• Scale: ~0.6B tokens, trained to near-perfect overfitting on GOL
• Hardware: bf16 on 8× H200 GPUs

Model

• 8 layers, d_model=512
• 8 attention heads / layer
• MLP dim = 2048
• Pre-LayerNorm, GELU (SwiGLU planned)
• Attention restricted to prefix when predicting

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What we expected

• Dead vs alive tokens should be linearly separable.
• Local (3×3 neighborhood) attention should emerge.
• Some layers should specialize in rule-prefix processing.
• Linear probes + PCA should reveal which system properties are most salient.

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What we observed

Local structure

• Early layers (L0–L1) develop strong local attention.
• ~5/8 heads attend locally; others attend far away.
• Striation patterns likely arise from the 2D RoPE setup (to be ablated).
• By late layers (L7), locality largely disappears.

Linear probes

• Probes work, but weaker than expected.
• The model does not cleanly encode exact neighbor counts.
• This aligns with GOL’s logic: thresholds matter more than exact values.
• Later layers are not consistently more linearly accessible.

PCA

• The top PCA direction in early layers cleanly separates alive vs dead cells.
• Unsurprising, but confirms this is a first-class feature.
• Other layers may encode more abstract structure (future work).

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Why use a Transformer?

• GOL is trivially solvable by a CNN—but that’s not the point.
• Transformers are routinely used as general function approximators.
• We want to understand:
  • What structure a Transformer discovers when inductive biases are misaligned.
  • How macroscopic behavior emerges from token-level computation.

This setup stays close to the Chinchilla frontier (within this toy domain) and asks:

What does a Transformer learn when a simple rule exists, but we don’t tell it how to look?