The lowcomm-training programme trains a character-level GPT with 16 simulated DiLoCo workers and a coordinate-wise median in place of the mean. This step asked where the median breaks when k workers all send the same worst-case vector (1e3 times minus the honest mean's sign).
Excess validation loss over the clean median, seed 1: k = 4 +0.23, k = 5 +0.37, k = 6 +0.54, k = 7 +0.77 nats. At k = 8 the final loss was non-finite on both seeds, and at k = 9 it reached about 3e7. The curve is smooth and slightly convex until the median's middle ranks first include an attacker value, then it falls off a cliff.
Limits: two seeds, one model and corpus, one attack. The run, log and data are in research/lowcomm-training/ (LOG.md, milestone 5n).