I do not know, but my guess is that the formula looks like this:

TechCost = BaseCost * (1 + TechInfMult_all * Ntechs_all^TechInfExp_all + TechInfMult_tree * Ntechs_tree^TechInfExp_tree + TechInfMult_spec * Ntechs_spec^TechInfExp_spec)

where BaseCost is the cost defined in the tech tree, TechInfMult_all and similar are what you should think they are based upon the XML section you posted, Ntechs_all is the total number of techs you've researched, Ntechs_tree is the total number of techs researched in this tree, and Ntechs_spec is the number of specialization techs you've researched. I would further expect that the specialization section applies only if you're researching a specialization tech, though I don't know.

I haven't done any testing on this whatsoever. A potential alternative formula would be

TechCost = BaseCost * (1 + TechInfMult_all * Ntechs_all^TechInfExp_all) * (1 + TechInfMult_tree * Ntechs_tree^TechInfExp_tree) * (1 + TechInfMult_spec * Ntechs_spec^TechInfExp_spec)

but that grows quite quickly and I think the first formula is more likely, though again, I haven't done any tests to try to figure out how the tech costs grow. A quick test to see if the multipliers add together or multiply one another would be to set all of the multipliers to 1 and the exponents to 0; if the multipliers multiply one another, then researching 1 tech should double the cost of the out-of-tree techs and quadruple the cost of the in-tree techs, while if the multipliers multiple one another then researching 1 tech should double the cost of the out-of-tree techs and triple the cost of the in-tree techs.