Brightlab
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Year 11 · 90 minutes
Does a calendar-shaped representation mean a model calculates directly on a calendar?
You will learn to: Compare direct cyclic arithmetic with encode → ordinary sum → remap, use Fourier probes, and evaluate transfer and causal controls.
Your mathematical model
Before opening the researchers’ model below, build a prediction you can test. A circle keeps the remainder after complete turns.
Start 0 · add 0
Start 3 · add 1
Start 8 · add 6
Blue solid = start. Pink dashed = added number. Thick green = sum. Each angle is 2π × remainder ÷ period. These three views repeat together every 10: they cannot distinguish 7 from 17.
The research question: August + 6 has ordinary sum 14, which maps to February. A final calendar circle alone cannot tell us whether an internal step used base-10 addition or direct mod-12 arithmetic. We need intermediate measurements and interventions.
Goodfire’s original research demonstration
Start with August + 6, then try 16 months after August. Follow the input and output representations on the period-2, period-5 and period-10 views. Which information survives a complete turn? Compare your mathematical prediction above with these recorded model activations.
The interactive below is hosted by Goodfire. If it does not fit your screen or your school blocks it, open the original in a full window ↗.
Source measurements and interface: Goodfire. Spark does not generate these recorded Llama results.
Goodfire’s original research demonstration
This experiment fixes the prompt at sixteen months after August. Change the available steering controls and compare the result with the baseline. This modifies internal features; it is stronger evidence than merely seeing a circle. It still does not establish every step of the model’s algorithm.
The interactive below is hosted by Goodfire. If it does not fit your screen or your school blocks it, open the original in a full window ↗.
Source measurements and interface: Goodfire. Spark does not generate these recorded Llama results.
Now investigate for yourself
The browser calculator is a transparent mathematical model. A small language model may not learn or reuse Llama’s mechanism. Poor transfer is a valid finding; a circular plot does not prove the mechanism.
Starting knowledge: Modular arithmetic, sine/cosine and train/test splits; basic Python is helpful for extensions.
Evidence to collect: Submit a cross-task experiment with model revision, split, layer, projection, held-out error and a limited causal claim.
Research basis: The paper’s Llama analysis finds ordinary addition shared across months, weekdays and hours, followed by remapping to the requested cycle. Calendar geometry alone would not establish that algorithm.
Goodfire research article ↗ · Full research paper ↗ · Setup and teaching guidance