We show that there are strong relationships between approaches to optm
ization and learning based on statistical physics or mixtures of exper
ts. In particular, the EM algorithm can be interpreted as converging e
ither to a local maximum of the mixtures model or to a saddle point so
lution to the statistical physics system. An advantage of the statisti
cal physics approach is that it naturally gives rise to a heuristic co
ntinuation method, deterministic annealing, for finding good solutions
.