I agree this is an incredibly interesting paper. I am not a practitioner but I interpreted the gradient article differently. They didn’t directly find 64 nodes (activations) that represented the board state as I think you imply. They trained “64 independent two-layer MLP classifiers to classify each of the 64 tiles”. I interpret this to mean all activations are fed into a 2 layer MLP with the goal of predicting a single tile (white, black, empty). Then do that 64 times once for each tile (64 separately trained networks).
As much as I want to be enthusiastic about this, it’s not entirely clear to me that it is surprising that such a feat can be achieved. For example it may be possible to train a 2 layer MLP to predict the state of a tile directly from the inputs. It may be that the most influential activations are closer to the inputs then the outputs, implying that Othello-GPT itself doesn’t have a world model, instead showing that you can predict board colors from the transcript. Again, not a practitioner but once you are indirecting internal state through a 2 layer MLP it gets less obvious to me that the world model is really there. I think it would be more impressive if they were only taking “later” activations (further from the input), and using a linear classifier to ensure the world model isn’t in the tile predictor instead of Othello-GPT. I would appreciate it if somebody could illuminate or set my admittedly naive intuitions straight!
That said, I am reminded of another OpenAI paper [1] from way back in 2017 that blew my mind. Unsupervised “predict the next character” training on 82 million amazon reviews, then use the activations to train a linear classifier to predict sentiment. And it turns out they find a single neuron activation is responsible for the bulk of the sentiment!
As much as I want to be enthusiastic about this, it’s not entirely clear to me that it is surprising that such a feat can be achieved. For example it may be possible to train a 2 layer MLP to predict the state of a tile directly from the inputs. It may be that the most influential activations are closer to the inputs then the outputs, implying that Othello-GPT itself doesn’t have a world model, instead showing that you can predict board colors from the transcript. Again, not a practitioner but once you are indirecting internal state through a 2 layer MLP it gets less obvious to me that the world model is really there. I think it would be more impressive if they were only taking “later” activations (further from the input), and using a linear classifier to ensure the world model isn’t in the tile predictor instead of Othello-GPT. I would appreciate it if somebody could illuminate or set my admittedly naive intuitions straight!
That said, I am reminded of another OpenAI paper [1] from way back in 2017 that blew my mind. Unsupervised “predict the next character” training on 82 million amazon reviews, then use the activations to train a linear classifier to predict sentiment. And it turns out they find a single neuron activation is responsible for the bulk of the sentiment!
[1] https://openai.com/blog/unsupervised-sentiment-neuron/