Individual neurons in neural networks often represent a mixture of unrelated features. This phenomenon, called polysemanticity, can make interpreting neural networks more difficult and so we aim to understand its causes. We propose doing so through the lens of feature \emph{capacity}, which is the fractional dimension each feature consumes in the embedding space. We show that in a toy model the optimal capacity allocation tends to monosemantically represent the most important features, polysemantically represent less important features (in proportion to their impact on the loss), and entirely ignore the least important features. Polysemanticity is more prevalent when the inputs have higher kurtosis or sparsity and more prevalent in some architectures than others. Given an optimal allocation of capacity, we go on to study the geometry of the embedding space. We find a block-semi-orthogonal structure, with differing block sizes in different models, highlighting the impact of model architecture on the interpretability of its neurons.

Current language models are considered to have sub-human capabilities at natural language tasks like question-answering or writing code. However, language models are not trained to perform well at these tasks, they are trained to accurately predict the next token given previous tokes in tokenized text. It is not clear whether language models are better or worse than humans at next token prediction. To try to answer this question, we performed two distinct experiments to directly compare humans and language models on this front: one measuring top-1 accuracy and the other measuring perplexity. In both experiments, we find humans to be consistently \emph{worse} than even relatively small language models like GPT3-Ada at next-token prediction.

Many real world learning tasks involve complex or hard-to-specify objectives, and using an easier-to-specify proxy can lead to poor performance or misaligned behavior. One solution is to have humans provide a training signal by demonstrating or judging performance, but this approach fails if the task is too complicated for a human to directly evaluate. We propose Iterated Amplification, an alternative training strategy which progressively builds up a training signal for difficult problems by combining solutions to easier subproblems. Iterated Amplification is closely related to Expert Iteration (Anthony et al., 2017; Silver et al., 2017b), except that it uses no external reward function. We present results in algorithmic environments, showing that Iterated Amplification can efficiently learn complex behaviors.