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September 2026 Active

Set Difference in 108 Parameters

A one-layer, two-head transformer has learned to identify the symbol removed from a set. Its residual stream is only two-dimensional and the entire model has 108 learned parameters. Your goal is to explain the algorithm implemented by those parameters, end to end.

The task

Choose four distinct symbols to form X, remove one symbol z to obtain Y, and independently shuffle both sets. The model sees [BOS] shuffle(X) [SEP] shuffle(Y) [SEP] and must predict z at the final separator.

Vocabulary16 symbols, ap, plus BOS and one shared SEP
Set sizeExactly four distinct symbols
ArchitectureOne causal attention-only layer; no MLP, LayerNorm, or biases
Dimensionsd_model=2, two heads, d_head=1
PositionsLearned absolute position embeddings
Parameters108
Accuracy100% on all 1,048,320 valid prompts

What counts as a complete solution?

We are looking for a human-understandable computational account of how the model obtains its answer. A complete solution should connect the entire path from embeddings to attention to head outputs to the final readout.

Prioritize clarity and understanding over exhaustiveness. A short, well-explained account of what the model actually computes is worth more than a long collection of plots.

Get started

The starter notebook loads the pre-trained weights from HuggingFace and walks you through basic inference and attention visualization. Open it in Colab, save a copy to your own Drive, and start exploring.

Submit your solution

Submit a link to a clean Colab notebook that explains your findings. Include well-labeled figures, state claims plainly, and distinguish observations from causal evidence. Think of the notebook as a presentation of the algorithm you found, not a transcript of exploratory work.

Deadline: September 30, 2026 (anywhere on Earth)