The central problem of cryptology is to prevent inference about either the key or the plaintext, despite the requirement to be able to reconstruct the plaintext from the ciphertext+key. So ciphers have to almost perfectly mix information.

Machine learning is possible because in the absence of perfect mixing, inference is possible (given many input output pairs), even if the information is many decibels down below the noise. So the information about what parameters need changing is present in the output despite many subsequent layers of processing. This means that a lot of mixing can be tolerated, and it's needed because you don't know in advance what the data flow should look like in detail, so the NN has to provide as many options as possible.

I think the contrast is more interesting: exact discrete trajectories in cryptography versus approximate continuous function approximation in neural networks.

In cryptography, you usually want a state space so large that nobody can accidentally find, reconstruct, or predict the same path you took.

In neural networks, you want an immense initial search space because NNs need to model the real world, which is highly complex and contains patterns that appear unpredictably. One aspect I think is often overlooked is that NNs are mostly deletive: they start with a very broad representational space and become progressively more specific by discarding what the NN perceives as irrelevant distinctions.

I think this puts the article's point about complexity and mixing in a clearer light. The same class of procedures achieves almost opposite effects. In neural networks, you want mixing so the model can approximate many possible paths at once. In cryptography, you want mixing so the path taken is unpredictable and hard to trace. The key difference is that, for NNs, an approximate path can be good enough. In cryptography, an approximate path is as useless as a very distant one.

There's a lot of multiplication of numbers in parallel, so it makes sense to try to fit that to matrices.

Cryptography is built bottom-up, but likewise it makes sense to exploit data structures that already exist in silicon.

The condition for carcinization is usually described as a kind of “shared condition.” After reading this article, that is what I felt.

In other words, from the perspective of shared conditions, isn’t it possible that systems receive similar pressures when they need to mix information?

1. There is a state space. 2. Each part of the input affects many parts of the output. 3. A simple rule is not enough, so nonlinearity becomes necessary. 4. But the hardware cannot be allowed to stall, so the system evolves toward a structure where simple transformations are repeated many times.

Ultimately, even across different fields, the core question is how to decompose complexity into atomic units. The choice of those units tends to converge under the pressures imposed by the underlying substrate. This seems to be the central thesis of the article.

This feels similar to how humans solve nonlinear differential equations.

If so, perhaps the structure of human cognition itself works in a similar way: when facing nonlinearity, we break it into smaller structures and design around those smaller parts.

Because my academic background is limited, I find it difficult to express this properly in language. But I think this kind of pressure can also be applied to programming and software theory.

When I think about software engineering, it also often starts from the smallest element that does not change easily, and then builds larger systems by composing those elements. In OOP, that unit is the conceptual object. In FP, it is the function. In DOP, it is data.

FP is mathematical. DOP is aligned with the data that computers store and transmit. OOP is connected to our abstract model of the world. That may be why different people are good at different paradigms.

OOP compresses the world into objects and responsibilities. FP compresses the world into functions and composition. DOP compresses the world into data and transformable structures. Utlimately, it is a question of how we cut complexity, what we choose as the minimal unit of decomposition.

Then what should this idea be called? And if we apply this to AI coding, what would it imply?

I have thoughts, but because I did not study enough, I feel frustrated that I cannot express them more fully. I wish I had learned more.

I've finished the Cryptography I on Coursera already. Can't recommend it enough