# Scaling Laws for Hypernetwork-Based Knowledge Injection in Large Language Models

arXiv: https://arxiv.org/abs/2607.19604 · HTML: https://mlsanity.com/paper/2607.19604/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 34 references that are in the map.
- First posted on arXiv 21 Jul 2026.

## Builds on (most cited first, 30 of 33)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [ERNIE: Enhanced Language Representation with Informative Entities](https://mlsanity.com/paper/1905.07129/) (2019)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Zero-Shot Relation Extraction via Reading Comprehension](https://mlsanity.com/paper/1706.04115/) (2017)
- [KEPLER: A Unified Model for Knowledge Embedding and Pre-trained Language Representation](https://mlsanity.com/paper/1911.06136/) (2019)
- [K-Adapter: Infusing Knowledge into Pre-Trained Models with Adapters](https://mlsanity.com/paper/2002.01808/) (2020)
- [K-BERT: Enabling Language Representation with Knowledge Graph](https://mlsanity.com/paper/1909.07606/) (2019)
- [FinGPT: Open-Source Financial Large Language Models](https://mlsanity.com/paper/2306.06031/) (2023)
- [Evaluating the Ripple Effects of Knowledge Editing in Language Models](https://mlsanity.com/paper/2307.12976/) (2023)
- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [Fine-Tuning or Retrieval? Comparing Knowledge Injection in LLMs](https://mlsanity.com/paper/2312.05934/) (2023)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [Domain Specialization as the Key to Make Large Language Models Disruptive: A Comprehensive Survey](https://mlsanity.com/paper/2305.18703/) (2023)
- [Revisiting Catastrophic Forgetting in Large Language Model Tuning](https://mlsanity.com/paper/2406.04836/) (2024)
- [Model Editing at Scale leads to Gradual and Catastrophic Forgetting](https://mlsanity.com/paper/2401.07453/) (2024)
- [Scaling Laws for Forgetting during Finetuning with Pretraining Data Injection](https://mlsanity.com/paper/2502.06042/) (2025)
- [WikiBigEdit: Understanding the Limits of Lifelong Knowledge Editing in LLMs](https://mlsanity.com/paper/2503.05683/) (2025)
- [Hyper-X: A Unified Hypernetwork for Multi-Task Multilingual Transfer](https://mlsanity.com/paper/2205.12148/) (2022)
- [UniEdit: A Unified Knowledge Editing Benchmark for Large Language Models](https://mlsanity.com/paper/2505.12345/) (2025)
- [Foundation Models Secretly Understand Neural Network Weights: Enhancing Hypernetwork Architectures with Foundation Models](https://mlsanity.com/paper/2503.00838/) (2025)
- [Question Answering on Patient Medical Records with Private Fine-Tuned LLMs](https://mlsanity.com/paper/2501.13687/) (2025)

## Built on by (most cited first, 2 of 2)

- [Infinite-Parameter LLMs: Generating and Adapting Weights from Live Data](https://mlsanity.com/paper/2609.18842/) (2026)
- [HyperZip: Efficient Data Compression through Personalized Diffusion LLMs with Hypernetworks](https://mlsanity.com/paper/2609.36357/) (2026)

## Abstract (arXiv)

Injecting factual knowledge into large language models (LLMs) reliably and at scale remains an open challenge. Hypernetworks provide a promising solution to large-scale knowledge injection. Although hypernetworks are typically applied for test-time adaptation, we explore their use in train-time knowledge injection, where, given a large corpus of facts, we train a hypernetwork to generate a fixed LoRA adapter that, when inserted into the target model, enable the model to answer questions about those facts. In this work, we investigate whether hypernetworks can be used to perform train-time knowledge injection and how this ability varies with scale. The scaling behavior of hypernetworks remains largely unstudied. Our design decouples the hypernetwork's injection capacity from the target model's general capability, enabling, for the first time, a rigorous study of scaling laws for hypernetwork architectures. We characterize how loss, reasoning accuracy, and out-of-distribution (OOD) generalization vary with hypernetwork depth, width, and target network size. We construct a large-scale dataset, called MegaWikiQA, containing tens of millions of multi-hop question-answer examples across 39 domains constructed from examples in Wikidata5M. Our results reveal: (i) hypernetwork-based injection exhibits broadly predictive power law scaling along all architecture axes; and (ii) hypernetworks are capable of reliable OOD generalization at increasing scales, suggesting that hypernetwork provides a promising alternative to other train-time adaptation methods such as LoRA finetuning and full fine-tuning, exhibiting steeper scaling exponents in all OOD evaluations. Together, these results establish hypernetworks as a principled and scalable substrate for train-time adaptation, and provide the first empirically grounded scaling laws to guide hypernetworks for factual reasoning in large language models.