# PLDR-LLM: Large Language Model from Power Law Decoder Representations

arXiv: https://arxiv.org/abs/2410.16703 · HTML: https://mlsanity.com/paper/2410.16703/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 45 references that are in the map.
- First posted on arXiv 22 Oct 2024.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [SentencePiece: A simple and language independent subword tokenizer and detokenizer for Neural Text Processing](https://mlsanity.com/paper/1808.06226/) (2018)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Aligning AI With Shared Human Values](https://mlsanity.com/paper/2008.02275/) (2020)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Subword Regularization: Improving Neural Network Translation Models with Multiple Subword Candidates](https://mlsanity.com/paper/1804.10959/) (2018)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [MobileLLM: Optimizing Sub-billion Parameter Language Models for On-Device Use Cases](https://mlsanity.com/paper/2402.14905/) (2024)
- [Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks](https://mlsanity.com/paper/1907.04595/) (2019)

## Built on by (most cited first, 4 of 4)

- [PLDR-LLMs Learn A Generalizable Tensor Operator That Can Replace Its Own Deep Neural Net At Inference](https://mlsanity.com/paper/2502.13502/) (2025)
- [PLDR-LLMs Reason At Self-Organized Criticality](https://mlsanity.com/paper/2603.23539/) (2026)
- [Power law graph attention: exact generalization of scaled dot-product attention, empirical collapse at inference](https://mlsanity.com/paper/2608.10288/) (2026)
- [Training and Inference Dynamics of PLDR-LLMs: Row-Map Collapse, Renormalization, and Predictive Reduction](https://mlsanity.com/paper/2609.34130/) (2026)

## Abstract (arXiv)

We present the Large Language Model from Power Law Decoder Representations (PLDR-LLM), a language model that leverages non-linear and linear transformations through Power Law Graph Attention mechanism to generate well-defined deductive and inductive outputs. We pretrain the PLDR-LLMs of varying layer sizes with a small batch size of 32 and ~8B tokens from the RefinedWeb dataset, and show that they achieve competitive performance in zero-shot and few-shot settings compared to scaled dot-product LLMs of similar model size reported in the literature. We show that deductive outputs of PLDR-LLMs can be used to compare model characteristics or improve the performance by introducing the Directed Acyclic Graph (DAG) loss as a metric and regularizer. Our results indicate that the initial maximum learning rate and warm-up steps have a lasting impact on deductive outputs throughout the pretraining. We provide a detailed description of PLDR-LLM architecture, its implementation and the pretraining procedure.