Title: PLA: The Optimal Path from Softmax Attention to Linear Models via KV Cache Compression
Primary area: foundation or frontier models, including LLMs
Keywords: Linear Models, Fine-tune transformer to RNN, Linear attention, KV Cache Compression

Abstract: Transformers, despite their remarkable sequence modeling capabilities, are fundamentally constrained by the quadratic complexity of Softmax attention and the unbounded growth of the key–value (KV) cache. Replacing Softmax attention with linear variants has emerged as a promising direction, yet existing approaches lack a systematic functional comparison with Softmax attention, clear error analysis, and a theoretically guided roadmap for improvement. 
In this work, we approach the problem from the perspective of KV cache compression and present a theoretically grounded pathway from Softmax attention to linear models.
Our analysis reveals five critical components: redundancy elimination, tokenizer-level quantization and positional information separation, positional information compression, inter-layer similarity, and multi-state decomposition. For each, we provide succinct theoretical justification, derive error bounds, and demonstrate equivalence to existing mechanisms. Building on this pathway, we introduce PLA, a linearized attention model that inherits pretrained weights and achieves state-of-the-art performance. Notably, PLA surpasses strong baselines such as MVA and GSA on multiple benchmarks while requiring only 80\% of the fine-tuning resources. Our findings provide both theoretical clarity and practical guidance for advancing linear attention, highlighting a principled route towards efficient and scalable alternatives to Softmax attention.