# Manifold Metric: A Loss Landscape Approach for Predicting Model Performance

arXiv: https://arxiv.org/abs/2405.15895 · HTML: https://mlsanity.com/paper/2405.15895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 57 of its 67 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 30 of 57)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [HuggingFace's Transformers: State-of-the-art Natural Language Processing](https://mlsanity.com/paper/1910.03771/) (2019)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [GradNorm: Gradient Normalization for Adaptive Loss Balancing in Deep Multitask Networks](https://mlsanity.com/paper/1711.02257/) (2017)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Lifelong Learning with Dynamically Expandable Networks](https://mlsanity.com/paper/1708.01547/) (2017)
- [Linear Mode Connectivity and the Lottery Ticket Hypothesis](https://mlsanity.com/paper/1912.05671/) (2019)
- [Loss Surfaces, Mode Connectivity, and Fast Ensembling of DNNs](https://mlsanity.com/paper/1802.10026/) (2018)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [What is being transferred in transfer learning?](https://mlsanity.com/paper/2008.11687/) (2020)
- [Learn to Grow: A Continual Structure Learning Framework for Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1904.00310/) (2019)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [DyTox: Transformers for Continual Learning with DYnamic TOken eXpansion](https://mlsanity.com/paper/2111.11326/) (2021)
- [A Comprehensive Survey of Neural Architecture Search: Challenges and Solutions](https://mlsanity.com/paper/2006.02903/) (2020)
- [Net2Net: Accelerating Learning via Knowledge Transfer](https://mlsanity.com/paper/1511.05641/) (2015)
- [Neural Architecture Search without Training](https://mlsanity.com/paper/2006.04647/) (2020)
- [Loss landscapes and optimization in over-parameterized non-linear systems and neural networks](https://mlsanity.com/paper/2003.00307/) (2020)
- [Zero-Cost Proxies for Lightweight NAS](https://mlsanity.com/paper/2101.08134/) (2021)
- [Deep learning versus kernel learning: an empirical study of loss landscape geometry and the time evolution of the Neural Tangent Kernel](https://mlsanity.com/paper/2010.15110/) (2020)
- [BANANAS: Bayesian Optimization with Neural Architectures for Neural Architecture Search](https://mlsanity.com/paper/1910.11858/) (2019)
- [ZipIt! Merging Models from Different Tasks without Training](https://mlsanity.com/paper/2305.03053/) (2023)
- [Linear Mode Connectivity in Multitask and Continual Learning](https://mlsanity.com/paper/2010.04495/) (2020)

## Abstract (arXiv)

Determining the optimal model for a given task often requires training multiple models from scratch, which becomes impractical as dataset and model sizes grow. A more efficient alternative is to expand smaller pre-trained models, but this approach is underutilized due to a limited understanding of its impact on the training dynamics. Existing methods for quantifying this impact have notable limitations, including computation cost. To address this, we introduce a new perspective based on the loss landscape, which has been shown to contain a manifold of linearly connected minima. Specifically, we propose a metric that estimates the size of this manifold to study the impact of model expansion. Our experiments reveal a strong correlation between performance gains and our manifold metric, enabling more informed model comparison and offering a first step toward a geometry-driven approach for reliable model expansion. Notably, our metric outperforms other baselines, even when different types of expansion with equivalent number of parameters are applied to a model.