Sparse Autoencoders (SAEs) have shown promise in improving the interpretability of neural network activations, but can learn features that are not features of the input, limiting their effectiveness. We propose \textsc{Mutual Feature Regularization} \textbf{(MFR)}, a regularization technique for improving feature learning by encouraging SAEs trained in parallel to learn similar features. We motivate \textsc{MFR} by showing that features learned by multiple SAEs are more likely to correlate with features of the input. By training on synthetic data with known features of the input, we show that \textsc{MFR} can help SAEs learn those features, as we can directly compare the features learned by the SAE with the input features for the synthetic data. We then scale \textsc{MFR} to SAEs that are trained to denoise electroencephalography (EEG) data and SAEs that are trained to reconstruct GPT-2 Small activations. We show that \textsc{MFR} can improve the reconstruction loss of SAEs by up to 21.21\% on GPT-2 Small, and 6.67\% on EEG data. Our results suggest that the similarity between features learned by different SAEs can be leveraged to improve SAE training, thereby enhancing performance and the usefulness of SAEs for model interpretability.

Large language models (LLMs) fine-tuned by reinforcement learning from human feedback (RLHF) are becoming more widely deployed. We coin the term $\textit{Implicit Reward Model}$ (IRM) to refer to the changes that occur to an LLM during RLHF that result in high-reward generations. We interpret IRMs, and measure their divergence from the RLHF reward model used in the fine-tuning process that induced them. By fitting a linear function to an LLM's IRM, a reward model with the same type signature as the RLHF reward model is constructed, allowing for direct comparison. Additionally, we validate our construction of the IRM through cross-comparison with classifications of features generated by an LLM based on their relevance to the RLHF reward model. Better comprehending IRMs can help minimize discrepencies between LLM behavior and training objectives, which we believe to be an essential component of the $\textit{safety}$ and $\textit{alignment}$ of LLMs.

Self-supervised learning is the backbone of state of the art language modeling. It has been argued that training with predictive loss on a self-supervised dataset causes simulators: entities that internally represent possible configurations of real-world systems. Under this assumption, a mathematical model for simulators is built based in the Cartesian frames model of embedded agents, which is extended to multi-agent worlds through scaling a two-dimensional frame to arbitrary dimensions, where literature prior chooses to instead use operations on frames. This variant leveraging scaling dimensionality is named the Cartesian object, and is used to represent simulations (where individual simulacra are the agents and devices in that object). Around the Cartesian object, functions like token selection and simulation complexity are accounted for in formalizing the behavior of a simulator, and used to show (through the L\"obian obstacle) that a proof of alignment between simulacra by inspection of design is impossible in the simulator context. Following this, a scheme is proposed and termed Partial Simulation Extrapolation aimed at circumventing the L\"obian obstacle through the evaluation of low-complexity simulations.