Based on: Total Stake Inference v2 (Notes)

Questions

Q: Does stake concentration affect accuracy of inference?

A: No

We created 100 distributions with increasing variance (greater variance = greater concentration) and ran simulations for 100 epochs for each one after beginning with an estimate 75% of the true stake. Taking the average of the last 10 epochs’ ratios between the epoch’s stake estimate and the true stake results in the following chart.

Result: As the ratios cluster close to 1 and show no clear trend, it’s safe to say that the inference is not affected by stake concentration.

Untitled.png

Simulation code

https://github.com/logos-co/nomos-pocs/blob/total-stake-infer-v2/cryptarchia/total-stake-inference-v2-concentration.ipynb

Q: How fast does the state inference adjust to sudden changes?

A: Within 5 epochs for shocks ≤ 50%

We set up the following stake distribution:

image.png

Then we ran simulations of convergence for 30 epochs from an initial stake estimate that was 5%, 10%, 25%, 50% greater and less than the true stake. The following are results for low stake estimates:

image.png

image.png

image.png

image.png

The following are results for high stake estimates:

image.png

image.png

image.png

image.png

We also plotted the normalised error in each epoch. For the low estimates:

image.png

image.png

image.png

image.png