Are you making the claim that the N bits of DNA involved in coding the brain can encode more than 2^N neural algorithms?

That's exactly what the article above explains. Did you read it?

Or do you think that the particular set of 2^N (assuming no redundancy, which is generous...) neural algorithms that N bits of DNA can encode are more likely to result in intelligence than a random sampling of algorithms of equivalent Kolmogorov complexity?

I am not sure I understand the question. Are you asking if I believe the brain is a large but mostly simply designed neural network? If that is the question, then no.

Or are you claiming that epigenetic factors are able to reliably transmit significantly more than N bits of mission-critical data across the generations

I am claiming that do get a human you must "host" the human genome in a pre-existing human. Sticking it in a mouse will not result in a human. What does that imply?

that epigenetic evolution is likely to thank for devising the human intelligence algorithm rather than evolution of DNA?

I don't see two kind of evolutions there. It's all just human evolution genome and all. After all, it's not like human dna is out there evolving in something else besides humans.

In humans the difference is muddled because the spec goes through such ridiculously complicated machinery to become the product

Yes!

but when it comes to designing algorithms, that complicated machinery might as well be a random shuffle for all it matters to the algorithm's proper functioning

What implies that? How do you go form yes a hugely complex compiler is necessary, to no we can just randomly shuffle the code and it'll be just as good?

How many bits does it take to describe the string "aaaaaaa"? Not many. How many bits to describe the human genome to a scientist? I'll just gzip it and email it and were done, awesome!

How many bits to describe a human brain or how to turn that genome into a human brain? Well lets see, its a complex self-modifying process, the human brain expands the number of sequence products exponentially and interestingly the mouse brain does not do this.

In mice the complexity difference between their brain and their genome is linear. In humans it is not.

In mice the Kolmogorov complexity of their brain is equal to the Kolmogorov complexity of their genome + some linear factor.

In humans it's the Kolmogorov complexity of our genome + a lot more.

How much is "a lot more"? No idea.

Is all of this inherited? Yes, partly through the genome, partly through the fact that that genome must be planted in a pre-existing human. Again, if you swap it out with a mice genome humans won't be giving birth to healthy mice and mice won't be producing humans.

You can move a simple sequence across species, like a glowing protein form jellyfish to rabbits for example. You can not move whole genomes in higher order life forms.

I think the disagreement between early and late singularity people often comes down to is the human brain mostly a large but simple mass of neurons or not.

I think computer scientist are often in the it's just a large neural network camp. Brain scientists are in the it's much more complicated than that camp. As a computer scientist and software engineer who's worked in biotech for many years, I agree with the brain scientists.