# LRM-1B: Towards Large Routing Model

arXiv: https://arxiv.org/abs/2507.03300 · HTML: https://mlsanity.com/paper/2507.03300/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 57 references that are in the map.
- First posted on arXiv 4 Jul 2025.

## Builds on (most cited first, 30 of 47)

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- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
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- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
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- [Scaling Language Models: Methods, Analysis & Insights from Training Gopher](https://mlsanity.com/paper/2112.11446/) (2021)
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- [Adafactor: Adaptive Learning Rates with Sublinear Memory Cost](https://mlsanity.com/paper/1804.04235/) (2018)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [POMO: Policy Optimization with Multiple Optima for Reinforcement Learning](https://mlsanity.com/paper/2010.16011/) (2020)
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- [The case for 4-bit precision: k-bit Inference Scaling Laws](https://mlsanity.com/paper/2212.09720/) (2022)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Stabilizing Transformer Training by Preventing Attention Entropy Collapse](https://mlsanity.com/paper/2303.06296/) (2023)
- [Physics of Language Models: Part 3.3, Knowledge Capacity Scaling Laws](https://mlsanity.com/paper/2404.05405/) (2024)
- [Neural Combinatorial Optimization with Heavy Decoder: Toward Large Scale Generalization](https://mlsanity.com/paper/2310.07985/) (2023)
- [Liger Kernel: Efficient Triton Kernels for LLM Training](https://mlsanity.com/paper/2410.10989/) (2024)
- [Hybrid Genetic Search for the CVRP: Open-Source Implementation and SWAP* Neighborhood](https://mlsanity.com/paper/2012.10384/) (2020)
- [Sym-NCO: Leveraging Symmetricity for Neural Combinatorial Optimization](https://mlsanity.com/paper/2205.13209/) (2022)
- [Multi-Decoder Attention Model with Embedding Glimpse for Solving Vehicle Routing Problems](https://mlsanity.com/paper/2012.10638/) (2020)
- [Scaling Laws for Precision](https://mlsanity.com/paper/2411.04330/) (2024)
- [Deep Policy Dynamic Programming for Vehicle Routing Problems](https://mlsanity.com/paper/2102.11756/) (2021)
- [Learning Collaborative Policies to Solve NP-hard Routing Problems](https://mlsanity.com/paper/2110.13987/) (2021)

## Abstract (arXiv)

Vehicle routing problems (VRPs) are central to combinatorial optimization with significant practical implications. Recent advancements in neural combinatorial optimization (NCO) have demonstrated promising results by leveraging neural networks to solve VRPs, yet the exploration of model scaling within this domain remains underexplored. Inspired by the success of model scaling in large language models (LLMs), this study introduces a Large Routing Model with 1 billion parameters (LRM-1B), designed to address diverse VRP scenarios. We present a comprehensive evaluation of LRM-1B across multiple problem variants, distributions, and sizes, establishing state-of-the-art results. Our findings reveal that LRM-1B not only adapts to different VRP challenges but also showcases superior performance, outperforming existing models. Additionally, we explore the scaling behavior of neural routing models from 1M to 1B parameters. Our analysis confirms power-law between multiple model factors and performance, offering critical insights into the optimal configurations for foundation neural routing solvers.