# Nexus: Same Pretraining Loss, Better Downstream Generalization via Common Minima

arXiv: https://arxiv.org/abs/2604.09258 · HTML: https://mlsanity.com/paper/2604.09258/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 96 references that are in the map.
- First posted on arXiv 10 Apr 2026.

## Builds on (most cited first, 30 of 72)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Federated Optimization in Heterogeneous Networks](https://mlsanity.com/paper/1812.06127/) (2018)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [FlashAttention-2: Faster Attention with Better Parallelism and Work Partitioning](https://mlsanity.com/paper/2307.08691/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [MiniCPM: Unveiling the Potential of Small Language Models with Scalable Training Strategies](https://mlsanity.com/paper/2404.06395/) (2024)
- [Learning to Reweight Examples for Robust Deep Learning](https://mlsanity.com/paper/1803.09050/) (2018)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (2017)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Local SGD Converges Fast and Communicates Little](https://mlsanity.com/paper/1805.09767/) (2018)

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

- [Hyperball May Not Be a Free Lunch](https://mlsanity.com/paper/2607.22444/) (2026)
- [TrajTok: Adaptive Spatial Tokenization for Trajectory Representation Learning](https://mlsanity.com/paper/2605.20134/) (2026)
- [DepthBench: Measuring How Residual Connections Enable More Computational Depth](https://mlsanity.com/paper/2609.32534/) (2026)
- [Generalization Dynamics of LM Pre-training](https://mlsanity.com/paper/2609.33150/) (2026)

## Abstract (arXiv)

The foundational capabilities of large language models are acquired during pretraining on internet-scale, highly heterogeneous data mixtures. In this work, we investigate an interesting geometric question regarding the converged state of pretraining: Does the model converge to a common minimizer across all data sources (e.g., creffig:cwaillustration:close), or merely a minimizer of the summed loss (e.g., creffig:cwaillustration:distant)? We hypothesize that the geometric "closeness" of task-specific minima is intrinsically linked to downstream generalization. We reveal that standard optimizers (e.g., AdamW) often converge to points where task-specific minima are distant from each other. To address this, we propose the Nexus optimizer, which encourages the closeness of these minima by maximizing gradient similarity during optimization. Experiments across models ranging from 130M to 3B parameters, various data mixtures and hyperparameter schedules, show that Nexus textitsignificantly boosts downstream performance, despite textitachieving the same pretraining loss (see creffig:demo:benchmark). Notably, on the 3B model, Nexus reduces the out-of-distribution loss by 0.012 and yields up to a 15.0% accuracy improvement on complex reasoning tasks (e.g., GSM8k). This finding challenges the reliance on pretraining loss as the sole proxy for model evaluation and demonstrates the importance of implicit biases in unlocking downstream generalization.