Krishna C Puvvada, Faisal Ladhak, Santiago Akle Serano, Cheng-Ping Hsieh, Shantanu Acharya, Somshubra Majumdar, Fei Jia, Samuel Kriman, Simeng Sun, Dima Rekesh, Boris Ginsburg. Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing. 2025.

We propose a novel neural network architecture, the normalized Transformer (nGPT) with representation learning on the hypersphere. In nGPT, all vectors forming the embeddings, MLP, attention matrices and hidden states are unit norm normalized. The input stream of tokens travels on the surface of a hypersphere, with each layer contributing a displacement towards the target output predictions. These displacements are defined by the MLP and attention blocks, whose vector components also reside on the same hypersphere. Experiments show that nGPT learns much faster, reducing the number of training steps required to achieve the same accuracy by a factor of 4 to 20, depending on the sequence length.

Mingkai Deng, Jianyu Wang, Cheng-Ping Hsieh, Yihan Wang, Han Guo, Tianmin Shu, Meng Song, Eric Xing, Zhiting Hu. Proceedings of the 2022 Conference on Empirical Methods in Natural Language Processing. 2022.