LoKiFormer: Locality-aware Attention with Decoupled Knowledge Memory for Efficient Large Language Model Pretraining

LLMs encode both general capabilities and domain-specific knowledge in a single set of parameters. We ask whether this capacity can be reorganized: keeping broadly useful computation in a shared backbone, while moving specialized knowledge into external memory modules. We propose \emph{knowledge offloading} (KOFF), a framework for decomposing a pretrained LLM into a sparse shared backbone and domain-specific memories. Starting from a frozen base model, we jointly learn a structured pruning mask and lightweight recovery modules, implemented as LoRA adapters and learned key-value caches. Across Llama and Qwen models from 3B to 8B, we find that non-trivial capacity can be moved out of the shared backbone without a large loss in model ability. At around 12% global sparsity, KOFF preserves much of the unpruned model's performance, while pruning the same frozen model without memories degrades sharply. Ablations show that LoRA and learned KV memories are complementary, and specialization analyses suggest that the learned decomposition is meaningful: language-specific neurons are preferentially removed while language-general neurons largely remain in the backbone. These results suggest that knowledge can be reallocated between a shared core and swappable external memories.

Continuous knowledge updating for pre-trained large language models (LLMs) is increasingly necessary yet remains challenging. Although inference-time methods like In-Context Learning (ICL) and Retrieval-Augmented Generation (RAG) are popular, they face constraints in context budgets, costs, and retrieval fragmentation. Departing from these context-dependent paradigms, this work investigates a parametric approach using Low-Rank Adaptation (LoRA) as a modular knowledge memory. Although few recent works examine this concept, the fundamental mechanics governing its capacity and composability remain largely unexplored. We bridge this gap through the first systematic empirical study mapping the design space of LoRA-based memory, ranging from characterizing storage capacity and optimizing internalization to scaling multi-module systems and evaluating long-context reasoning. Rather than proposing a single architecture, we provide practical guidance on the operational boundaries of LoRA memory. Overall, our findings position LoRA as the complementary axis of memory alongside RAG and ICL, offering distinct advantages.

Large Language Models (LLMs) have become the central paradigm in artificial intelligence, yet the core computational primitive of attention has remained structurally unchanged. Local Linear Attention (LLA) is an attention mechanism derived from nonparametric statistics in the test-time regression framework. In contrast to prior research on efficient attention variants, LLA upgrades the local constant estimate in softmax attention to a local linear estimate, yielding provably superior bias-variance tradeoffs for associative memory. However, LLA has not been scaled in LLM pretraining due to computational and numerical stability concerns. We introduce Parallax, a parameterized Local Linear Attention that is scalable for LLMs. Parallax eliminates the numerical solver in LLA and learns an extra query-like projector that probes the KV covariance. We place Parallax within a family of attention mechanisms connected by the bandwidth, the probe construction and the affine structure. We propose a hardware-aware algorithm that increases the arithmetic intensity over FlashAttention, shifting attention into a more compute bound regime. Our prototype decode kernel matches or outperforms FlashAttention 2/3 across diverse batch sizes and context lengths. We pretrain Parallax at 0.6B and 1.7B scales and find consistent perplexity improvements throughout pretraining with gains that transfer to downstream benchmarks. The advantage persists under both parameter-matched and compute-matched controls, demonstrating a Pareto improvement. We perform careful pretraining ablations and identify a novel phenomenon whereby Muon unlocks the capacity of Parallax. To our knowledge, this is the first empirical demonstration of strong architecture-optimizer codesign for attention mechanisms in the architecture research literature.