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Nice article (paper?). I was aware of JP crutchfield work on statistics for complexity theory for a while now but never thought of making a connection to deep

by gryn 2y ago

Nice article (paper?). I was aware of JP crutchfield work on statistics for complexity theory for a while now but never thought of making a connection to deep learning even though his framework is generic enough to apply to any predictor. The question though, which is mentioned as a next step. is how would you go around modeling the data generating process of the "the real world" or of the training datasets of current models even older ones like gpt2 ? I have a guess that meta-process state-space size is going to increase exponentially making this unusable. The good news is that computational mechanics is a treasure trove so there's room for a lot of papers to explore this subject applied to deep learning especially and I'm excited about the intersection with the work we've recently seen about mechanistic interpretability.

yorwba 2y ago
In this case, the curse of dimensionality is working in our favor, as the volume of an n-dimensional simplex also grows exponentially, so it is perfectly suited to hold the exponential state space of the mixed-state presentation. Updating from one mixed-state to another just involves updating for each pure state in the mixture and then mixing the resulting states together, so everything is neatly linear. One way to represent the training data would be to have one state per token position that emits the corresponding token and advances to the next position, or to a randomly sampled other document if there's no next position. That matches the way LLMs are actually trained, but of course typical transformers have a much smaller residual stream dimension than the number of training tokens, so it needs to conflate some states, and synchronizing with the training data is also not what we want models to do, otherwise we would be using infini-gram https://arxiv.org/abs/2401.17377 https://arxiv.org/abs/2401.17377 to regurgitate exact matches.

by gryn 2y ago

yorwba 2y ago

In this case, the curse of dimensionality is working in our favor, as the volume of an n-dimensional simplex also grows exponentially, so it is perfectly suited to hold the exponential state space of the mixed-state presentation. Updating from one mixed-state to another just involves updating for each pure state in the mixture and then mixing the resulting states together, so everything is neatly linear. One way to represent the training data would be to have one state per token position that emits the corresponding token and advances to the next position, or to a randomly sampled other document if there's no next position. That matches the way LLMs are actually trained, but of course typical transformers have a much smaller residual stream dimension than the number of training tokens, so it needs to conflate some states, and synchronizing with the training data is also not what we want models to do, otherwise we would be using infini-gram https://arxiv.org/abs/2401.17377 https://arxiv.org/abs/2401.17377 to regurgitate exact matches.