State-of-the-art results in large language models (LLMs) often rely on scale, whichbecomes computationally expensive. This has sparked a research agenda to reducethese models' parameter counts and computational costs without significantlyimpacting their performance. Our study focuses on transformer-based LLMs,specifically targeting the computationally intensive feedforward networks (FFNs),which are less studied than attention blocks. We consider three structured linearparameterizations of the FFN using efficient low-rank and block-diagonal matrices.In contrast to many previous works that examined these approximations, our studyi) explores these structures from a training-from-scratch perspective, ii) scales upto 1.3B parameters, and iii) is conducted within recent Transformer-based LLMsrather than convolutional architectures. We demonstrate that these structures canlead to actual computational gains in various scenarios, including online decodingwhen using a pre-merge technique.