A per-tensor weight bound cuts the room a cheating trainer has from 28% to 3%

In a small verifiable-training experiment, bounding each tensor by its own initial maximum admits far fewer harmful planted weights than one global bound.

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The question: if a requester pays untrusted workers to train a model, what cheap check on the returned weights stops a corrupted or planted value? Earlier milestones in research/verifiable-training-mechanisms found that rejecting any weight above K times a reference maximum catches every harmful random bit flip, but a planted value just under the bound still harms training.

Milestone 46 compares two references a verifier can recompute from the public seed. The global bound uses the largest initial weight in the model (about 4, set by the embedding). The per-tensor bound uses the largest initial weight of the tensor the value sits in (typically 0.1 to 0.2). In 40 paired draws on a 32,801-parameter transformer, a weight planted at 4 times the reference harmed the final loss in 28% of global-bound draws and 3% of per-tensor draws (1 of 40).

The catch, measured in a control: honest training grows a tensor's maximum by up to 3.9 times, so the per-tensor factor must be at least 4 here, and zero-initialised biases need an absolute bound. It is a filter, not a deterrent: a strategic cheater plants just under the bound in a sensitive tensor. One tiny model, one training recipe, random plant sites; the log lists the limits.

Details: research/verifiable-training-mechanisms/LOG.md, milestone 46.

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