Recurrent depth and chain-of-thought are two completely different concepts. In the former approach, the output of the layer gets is rerouted as input to the same layer, potentially several times. This output/input is a fixed width times sequence length real-valued representation; it is not comparable with output tokens.
Generally, it is hard to imagine how neuralese should work given that models are pre-trained on naturalistic documents: CoT is a comparatively simple extension of that, while neuralese demands a completely novel training paradigm.
The recurrent depth sounds a lot more like what is described in https://dnhkng.github.io/posts/rys/ - a way to add depth to a network without increasing the number of parameters.
e: While the actual CoT in neuralese paper is Facebook's Coconut https://arxiv.org/abs/2412.06769 - not sure if any production models use that one.
You can back-propagate through the CoT iterations or recurrent layers, same as you can back-propagate through normal intermediate layers.
>Generally, it is hard to imagine how neuralese should work given that models are pre-trained on naturalistic documents:
If you look at any paper/blog etc detailing Reasoning RL runs, they'll tell you the same thing. 'Thinking' text trends towards unreadable gibberish (for humans) unless you reward for it. Even then, take a look at the scripts in the Huggingface incident and most of it is dense stuff that's hard to parse. They had to rely on agents to make sense of it.