The TSVD (Truncated Singular Value Decomposition) framework which efficiently maintains orthonormality through QR decomposition and caching is presented, and a spectral energy heuristic is introduced to select the rank of the resulting low-rank weight matrices.
Abstract
LLM pretraining is extremely costly; therefore, parameter-efficient LLM architectures have recently emerged as a compelling research direction. One such promising approach is to represent the parameters as orthonormal low-rank weight matrices. However, maintaining orthonormality during training is computationally expensive, making it impractical. This paper presents the TSVD (Truncated Singular Value Decomposition) framework which efficiently maintains orthonormality through QR decomposition and caching. Furthermore, a spectral energy heuristic is introduced to select the rank of the resulting low-rank weight matrices. Empirical evaluations across model sizes show that TSVD matches or outperforms full-parameter baselines at a fraction of the compute cost. TSVD thus provides a scalable, computationally efficient foundation for LLM pretraining.
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