Singular Value Decomposition on Kronecker Adaptation for Large Language Model

• URL: http://arxiv.org/abs/2506.15251v1
• Date: Wed, 18 Jun 2025 08:28:53 GMT
• Title: Singular Value Decomposition on Kronecker Adaptation for Large Language Model
• Authors: Yee Hin Chong, Peng Qu,
• Abstract summary: Large pre-trained Transformer models achieve state-of-the-art results across diverse language and reasoning tasks.<n>Full fine-tuning incurs substantial storage, memory, and computational overhead.<n>We propose SoKA, a novel PEFT strategy that combines Kronecker-product tensor factorization with SVD-driven initialization and dynamic rank selection.
• Score: 0.8747606955991707
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Large pre-trained Transformer models achieve state-of-the-art results across diverse language and reasoning tasks, but full fine-tuning incurs substantial storage, memory, and computational overhead. Parameter-efficient fine-tuning (PEFT) methods mitigate these costs by learning only a small subset of task-specific parameters, yet existing approaches either introduce inference-time latency (adapter modules), suffer from suboptimal convergence (randomly initialized low-rank updates), or rely on fixed rank choices that may not match task complexity (Kronecker-based decompositions). We propose SoKA (SVD on Kronecker Adaptation), a novel PEFT strategy that combines Kronecker-product tensor factorization with SVD-driven initialization and spectrum-aware dynamic rank selection. Our Kronecker-Product SVD (KPSVD) procedure extracts principal components of the full weight update into compact Kronecker factors, while an adaptive rank selection algorithm uses energy-threshold and elbow-point criteria to prune negligible components. Empirical evaluation on LLaMA2-7B across arithmetic reasoning (GSM8K), formal mathematics (MATH), and code generation (MBPP) demonstrates that SoKA requires only 0.99M trainable parameters, 25% fewer than LoRA/PiSSA, while matching or exceeding baseline performance. Moreover, SoKA exhibits faster convergence and more stable gradients, highlighting its robustness and efficiency for large-scale model adaptation.

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