Is the "Valley of Confused Abstractions" real?

Sorry for not noticing this earlier. I'm not very active on LessWrong/AF. In case it's still helpful, a couple of thoughts...

Firstly, I think people shouldn't take this graph too seriously! I made it for a talk in ~2017, I think and even then it was intended as a vague intuition, not something I was confident in. I do occasionally gesture at it as a possible intuition, but it's just a vague idea which may or may not be true.

I do think there's some kind of empirical trend where models in some cases become harder to understand and then easier. For example:

• An MNIST model without a hidden layer (ie. a softmax generalized linear regression model) is easy to understand.
• An MNIST model with a single hidden layer is very hard to understand.
• Large convolutional MNIST/CIFAR models are perhaps slightly easier (you sometimes get nice convolutional filters).
• AlexNet is noticeably more interpretable. You start to see quite a few human interpretable neurons.
• InceptionV1 seems noticeably more interpretable still.

These are all qualitative observations / not rigorous / not systematic.

So what is going on? I think there are several hypotheses:

• Confused abstractions / Modeling Limitations - Weak models can't express the true abstractions, so they use a mixture of bad heuristics that are hard to reason about and much more complicated than the right thing. This is the original idea behind this curve.
• Overfitting - Perhaps it has less to do with the models and more to do with the data. See this paper where overfitting seems to make features less interpretable. So ImageNet models may be more interpretable because the dataset is harder and there's less extreme overfitting. 
• Superposition - It may be that apparent interpretability is actually all a result of superposition. For some reason, the later models have less superposition. For example, there are cases where larger models (with more neurons) may store less features in superposition.
• Overfitting - Superposition Interaction - There's reason to believe that overfitting may heavily exploit superposition (overfit features detect very specific cases and so are very sparse, which is ideal for superposition). Thus, models which are overfit may be difficult to interpret, not because overfit features are intrinsically uninterpretable but because they cause superposition.
• Other Interaction Effects - It may be that there are other interactions between the above arguments. For example, perhaps modeling limitations cause the model to represent weird heuristics, which then more heavily exploit superpositition. 
• Idiosyncrasies of Vision - It may be that the observations which motivated this curve are idiosyncratic to vision models, or maybe just the models I was studying.

I suspect it's a mix of quite a few of these.

In the case of language models, I think superposition is really the driving force and is quite different from the vision case (language model features seem to typically be much sparser than vision model ones).

I'm interested in hearing other people's takes on this question! I also found that a tiny modular addition model was very clean and interpretable. My personal guess is that discrete input data lends itself to clean, logical algorithms more so than than continuous input data, and that image models need to devote a lot of parameters to processing the inputs into meaningful features at all, in a way that leads to the confusion. OTOH, maybe I'm just overfitting.

I thought the peak of simple models would be something like a sparse Bag of Words model, and then all models that have been considered so far just go deeper and deeper into the valley of confused abstractions, and that we are not yet at the point where we can escape. But I might be wrong.

New (somewhat relevant) paper: 

Scale Alone Does not Improve Mechanistic Interpretability in Vision Models

Abstract: In light of the recent widespread adoption of AI systems, understanding the internal information processing of neural networks has become increasingly critical. Most recently, machine vision has seen remarkable progress by scaling neural networks to unprecedented levels in dataset and model size. We here ask whether this extraordinary increase in scale also positively impacts the field of mechanistic interpretability. In other words, has our understanding of the inner workings of scaled neural networks improved as well? We here use a psychophysical paradigm to quantify mechanistic interpretability for a diverse suite of models and find no scaling effect for interpretability - neither for model nor dataset size. Specifically, none of the nine investigated state-of-the-art models are easier to interpret than the GoogLeNet model from almost a decade ago. Latest-generation vision models appear even less interpretable than older architectures, hinting at a regression rather than improvement, with modern models sacrificing interpretability for accuracy. These results highlight the need for models explicitly designed to be mechanistically interpretable and the need for more helpful interpretability methods to increase our understanding of networks at an atomic level. We release a dataset containing more than 120'000 human responses from our psychophysical evaluation of 767 units across nine models. This dataset is meant to facilitate research on automated instead of human-based interpretability evaluations that can ultimately be leveraged to directly optimize the mechanistic interpretability of models.

Conclusion: In this paper, we set out to answer the question: Does scale improve the mechanistic interpretability of vision models? By running extensive psychophysical experiments and comparing various models, we come to the conclusion that none of the investigated axes seem to positively affect model interpretability: Neither the size of the model, nor that of the dataset, nor model architecture or training scheme improve interpretability. This result highlights the importance of building more interpretable models: unless we explicitly optimize for this property, we do not get it for free by just increasing downstream task performance.

Could it be that Chris's diagram gets recovered if the vertical scale is "total interpretable capabilities"? Like maybe tiny transformers are more interpretable in that we can understand ~all of what they're doing, but they're not doing much, so maybe it's still the case that the amount of capability we can understand has a valley and then a peak at higher capability.

I encountered a similarish pattern a long time ago

https://www.lesswrong.com/posts/RQpNHSiWaXTvDxt6R/coherent-decisions-imply-consistent-utilities?commentId=9Fm2zrYT9aRSdzSde