Grokking, Visualized

A small transformer learned to add numbers on a 113-hour clock. For thousands of steps it seemed only to have memorised; meanwhile it was building a general algorithm, and then, suddenly, it understood. This site shows — with the real network's weights, activations, gradients and outputs at every moment of training — what it learned and how it got there, explained step by step from scratch.

Learn step by step →Open the dashboard

Loss during training (log scale)

Training loss (blue) and test loss (red) at every 10th step; shaded bands are the three phases.

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How to read it · the math

\mathcal{L} = -\frac{1}{N}\sum_{(a,b)} \ln \softmax(\Logits(a,b))_{c^*}

Each curve is the average cross-entropy loss over its set of inputs. The vertical axis is a logarithmic scale, so each grid line is a factor of 10. Click anywhere to move the whole page to that step.

What to expect: Train loss falls during memorisation (until step 1,567 on the paper's run) while test loss rises, then, thousands of steps later, test loss collapses (grokking).

Learn step by step → · Source: [1] Fig. 2 · Computed by train.py / paper logs (code)

What you will find here

22 chapters that build everything from “what is a remainder?” to the paper's progress measures, defining every term and symbol before it is used, with worked examples and exact (short) quotes from the sources.
One big dashboard with every visualization linked together: drag through training and watch the network's embeddings turn into circles, its neurons into waves, and its memorisation melt away.
The real thing: the paper's own published training run [7], re-analysed with code that reproduces 26 of the 30 reported numbers and claims we checked, plus 22 networks we retrained ourselves: 16 of them (with and without weight decay) test the claims with preregistered statistics, the other 6 are descriptive controls.

Based on Nanda, Chan, Lieberum, Smith and Steinhardt, Progress measures for grokking via mechanistic interpretability (ICLR 2023) [1], the ARENA course chapter on grokking [3], and the videos by Neel Nanda with Jess Smith and Lawrence Chan, and by Welch Labs [8] [9] [10]. Built by Libor Burian. Code and data on GitHub.