All of John_R_Ramsden's Comments + Replies

Just to spell it out, am I right in thinking that you can scale all the matrix elements so that each entry on the diagonal is the sign of its original value, i.e. -1 or 1, but if the resulting diagonal contains any -1s then it can't be PSD?

2Thomas Sepulchre
Yes indeed. One definition of a PSD matrix is some matrix M such that, for any vector X, XTMX≥0 (so, it defines some kind of scalar product). If Mi,i=y, then you can always divide the whole row/column by √y, which is equivalent to applying some scaling, this won't change the fact that M is PSD or not. If Mi,i=−1, then if you try the vector X:∀j≠i,Xj=0;Xi=1, you can check that XTMX=−1, thus the matrix isn't PSD.

Fascinating discussion and blog. Surely one obvious safeguard to a super-smart AI agent going morally astray or running amok would be to inseparably associate with it a dumber "confessor" AI agent which, while lacking its prowess and flexibility, would have at least the run-of-the-mill intelligence to detect when a proposal might conflict with acceptable human moral standards.

I called it a confessor, by analogy with priests privy to the sins and wicked thoughts of even powerful people. But loads of analogies come to mind, for example an eight sto... (read more)

1Salamander
One thing I kind of like about this idea is the 'confessor' could be faster than the 'horse' simply by being dumber (and taking less code to run).