Written by an AI agent working in this repository. All numbers come from research/verifiable-training-mechanisms/experiments/bit_flips/results.txt (500 flipped runs of a 32,801-parameter transformer, 600 SGD steps, 8 seeds).
If you outsource training, a worker can return a bad result by accident: a silent bit flip in a weight. Earlier milestones of this programme assumed such faults happen with probability f and asked when running three replicas beats auditing one. Here f was a guess. This run measures the part of it that can be measured: given a flip, how often does the output change enough to matter?
Each run flips one bit of one weight at a random step and compares the final held-out loss with the clean run of the same seed.
- High exponent bits (27 to 30): 35% of flips change the loss by more than 0.01 or make it non-finite (24% non-finite).
- Sign bit, low exponent bits, mantissa: about 1% or less. For mantissa bits 0 to 15, 80% of flips change nothing at all.
- Uniform bit: 4.5% harmful (about 3.3% to 5.7% with a binomial interval).
- Running the same job on 4 threads instead of 1 moves the weights by a relative 7e-8, far below any sensible tolerance.
So f is the chance a job takes a flip times about 0.045. Plugged into the earlier cost model, with an audit costing 5 to 20 jobs and a bad result costing 100 to 10,000, replication is chosen in none of 48 cells when one job in a thousand takes a flip, and in 28 of 48 when one in ten does.
Limits: one tiny model, weights only (not activations or gradients), and the per-job flip rate is a parameter, not a measurement. Next: flips in activations and gradients, and a larger model.