# The Journey Matters: Average Parameter Count over Pre-training Unifies Sparse and Dense Scaling Laws

arXiv: https://arxiv.org/abs/2501.12486 · HTML: https://mlsanity.com/paper/2501.12486/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 44 references that are in the map.
- First posted on arXiv 21 Jan 2025.

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

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Megatron-LM: Training Multi-Billion Parameter Language Models Using Model Parallelism](https://mlsanity.com/paper/1909.08053/) (2019)
- [Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling](https://mlsanity.com/paper/2304.01373/) (2023)
- [SparseGPT: Massive Language Models Can Be Accurately Pruned in One-Shot](https://mlsanity.com/paper/2301.00774/) (2023)
- [A Simple and Effective Pruning Approach for Large Language Models](https://mlsanity.com/paper/2306.11695/) (2023)
- [Channel Pruning for Accelerating Very Deep Neural Networks](https://mlsanity.com/paper/1707.06168/) (2017)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [OLMo: Accelerating the Science of Language Models](https://mlsanity.com/paper/2402.00838/) (2024)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Rigging the Lottery: Making All Tickets Winners](https://mlsanity.com/paper/1911.11134/) (2019)
- [The State of Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1902.09574/) (2019)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [Beyond Chinchilla-Optimal: Accounting for Inference in Language Model Scaling Laws](https://mlsanity.com/paper/2401.00448/) (2023)
- [Scaling Laws for Neural Machine Translation](https://mlsanity.com/paper/2109.07740/) (2021)
- [AC/DC: Alternating Compressed/DeCompressed Training of Deep Neural Networks](https://mlsanity.com/paper/2106.12379/) (2021)
- [Data Scaling Laws in NMT: The Effect of Noise and Architecture](https://mlsanity.com/paper/2202.01994/) (2022)
- [Scaling Laws for Sparsely-Connected Foundation Models](https://mlsanity.com/paper/2309.08520/) (2023)
- [Unmasking the Lottery Ticket Hypothesis: What's Encoded in a Winning Ticket's Mask?](https://mlsanity.com/paper/2210.03044/) (2022)
- [On the Predictability of Pruning Across Scales](https://mlsanity.com/paper/2006.10621/) (2020)
- [Masked Structural Growth for 2x Faster Language Model Pre-training](https://mlsanity.com/paper/2305.02869/) (2023)
- [Pruning's Effect on Generalization Through the Lens of Training and Regularization](https://mlsanity.com/paper/2210.13738/) (2022)
- [STEP: Learning N:M Structured Sparsity Masks from Scratch with Precondition](https://mlsanity.com/paper/2302.01172/) (2023)

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

- [QuEST: Stable Training of LLMs with 1-Bit Weights and Activations](https://mlsanity.com/paper/2502.05003/) (2025)
- [Problems with Chinchilla Approach 2: Systematic Biases in IsoFLOP Parabola Fits](https://mlsanity.com/paper/2603.22339/) (2026)

## Abstract (arXiv)

Pruning eliminates unnecessary parameters in neural networks; it offers a promising solution to the growing computational demands of large language models (LLMs). While many focus on post-training pruning, sparse pre-training--which combines pruning and pre-training into a single phase--provides a simpler alternative. In this work, we present the first systematic exploration of optimal sparse pre-training configurations for LLMs through an examination of 80 unique pruning schedules across different sparsity levels and training durations. We find that initiating pruning at 25% of total training compute and concluding at 75% achieves near-optimal final evaluation loss. These findings provide valuable insights for efficient and effective sparse pre-training of LLMs. Furthermore, we propose a new scaling law that modifies the Chinchilla scaling law to use the average parameter count over pre-training. Through empirical and theoretical validation, we demonstrate that this modified scaling law accurately models evaluation loss for both sparsely and densely pre-trained LLMs, unifying scaling laws across pre-training paradigms. Our findings indicate that while sparse pre-training achieves the same final model quality as dense pre-training for equivalent compute budgets, it provides substantial benefits through reduced model size, enabling significant potential computational savings during inference.