I mean I have little doubt that there are trade secrets that these companies have. Specific algorithms and models. And yeah, industry labs are often ahead here.
But I read your claim as saying that there are broad methods and approaches that they hide. And that's, while possible, more peculiar. Most of the tech industry labs don't keep their theoretical research secret. Practically anything that could be published is.
As for 3, the way you described the "rediscovery" made it sound like those Labs were a number of steps ahead, so I hope you pardon my misunderstanding.
At the highest level there are broad approaches which are kept secret in the financial industry, but the reason that's peculiar is because their efficacy is inherently antagonistic to publicity. Tech firms (mostly) don't lose utility of their trade secrets if they're exposed, they just lose first mover advantages on those techniques. But if everyone is aware of your techniques in finance, your techniques cease to have an edge.
Like I said in the original comment: this isn't (to my knowledge at least) pure mathematics that's being kept secret. But there are absolutely families of techniques and algorithms whose applications to finance are nontrivial, non-incremental and very well guarded.
I guess my only followup would be are these "techniques" more akin (in broadness) to ResNet, or to Dropout? (to use an area that I believe we're both familiar with)
In other words, techniques that are broadly applicable to the field, or techniques that maybe spawn a family of related techniques, but appear to be useful only in a specific subdomain.
But I read your claim as saying that there are broad methods and approaches that they hide. And that's, while possible, more peculiar. Most of the tech industry labs don't keep their theoretical research secret. Practically anything that could be published is.
As for 3, the way you described the "rediscovery" made it sound like those Labs were a number of steps ahead, so I hope you pardon my misunderstanding.