I'm a cognitive neuroscientist. I'm not a specific expert on cognitive rehabilitation or training, though I've flirted with similar type of work. I work mainly in psychiatry.

Some of the things we have tried to do include brain stimulation to modulate cognition. Also I've at least read in the past about cognitive rehabilitation programs for different disorders. And I go to conferences where occasionally see posters on cognitive training and generalization

There is probably very little in the human brain that is as difficult to reliably affect as adult cognition. Our cognitive abilities are fairly set it seems by the time we are in our 20s. They can go down, and we can do things that maintain them. But it is very hard to increase those abilities. There may be certain transitory things, like going from a condition of sleeping very poorly to improving your sleep, which will have notable outcomes. But that's more the removal of something detrimental then adding something beneficial.

So I'm not surprised that the net result of a review paper is pretty much a null. Because the majority of things we have attempted to improve human cognition have not been very successful. Sometimes we can substantially train summon up on a few specific tasks, but then we find that extraordinary skill in one cognitive task doesn't generalize to non-trained tasks.

One of the downsides of a review, and I'll admit I didn't actually be the paper, is that they tend to jumble together several factors, and miss some of the nuance that can be happening. So it may be that some very specific cognitive abilities are somewhat enhanced either short-term or longer term by an increase in physical fitness. But a lot of studies that get done tend to be short, quick, and easy, or look at very broad strokes abilities. So maybe with further work we will identify some specific benefits, particularly in the cases of either very intense or longer term lifestyle type major changes.

And, none of this means exercise doesn't have other mental benefits. There's some decent evidence, at least last time I checked, of an antidepressant effect to physical activity. I had a colleague go off sick leave following chemotherapy treatment, because after everything was said and done they were exhausted and depressed. One of the things we talked about is the potential benefits if she can get back into running, because there is a mood boosting effect at least potentially.

So, information, cognition is very difficult to modify in adults. But there may be other mental benefits to physical activity as well. Get me have different benefits and different clinical populations.