Neurons in auto-regressive language models like GPT-2 can be interpreted by analyzing their activation patterns. Recent studies have shown that techniques such as dictionary learning, a form of post-hoc sparse coding, enhance this neuron-level interpretability. In our research, we are driven by the goal to fundamentally improve neural network interpretability by embedding sparse coding directly within the model architecture, rather than applying it as an afterthought. In our study, we introduce a white-box transformer-like architecture named Coding RAte TransformEr (CRATE), explicitly engineered to capture sparse, low-dimensional structures within data distributions. Our comprehensive experiments showcase significant improvements (up to 103% relative improvement) in neuron-level interpretability across a variety of evaluation metrics. Detailed investigations confirm that this enhanced interpretability is steady across different layers irrespective of the model size, underlining CRATE's robust performance in enhancing neural network interpretability. Further analysis shows that CRATE's increased interpretability comes from its enhanced ability to consistently and distinctively activate on relevant tokens. These findings point towards a promising direction for creating white-box foundation models that excel in neuron-level interpretation.