What the author refers to is the ability to iterate and update the internal memory. A classic transformer based LLM can only produce the next token and never go back and update old tokens or delete them. The best thing it can do is produce thinking tokens to serialize the internal state of the final layer so that it can pass it back into the first layer.

Just like the transformer was an advancement over LSTMs by making it possible to have perfect recall (reading every input), the only way to improve over the transformer is to build a deep equilibrium version, where the DEQ transformer is capable of updating its own memory (writing every output).

Such a machine would be considered a linear bounded automaton (a turing machine without unlimited tape) and therefore even the human brain could not have an architectural edge over it in terms of intelligence. The human brain could only have an edge in terms of energy efficiency.