# Mechanistic Mode Connectivity

arXiv: https://arxiv.org/abs/2211.08422 · HTML: https://mlsanity.com/paper/2211.08422/

## Key facts

- Cited by 50 papers in the map (data through 14 Oct 2026).
- Builds on 107 of its 127 references that are in the map.
- First posted on arXiv 15 Nov 2022.

## Builds on (most cited first, 30 of 107)

- [Shortcut Learning in Deep Neural Networks](https://mlsanity.com/paper/2004.07780/) (2020)
- [Invariant Risk Minimization](https://mlsanity.com/paper/1907.02893/) (2019)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [Do ImageNet Classifiers Generalize to ImageNet?](https://mlsanity.com/paper/1902.10811/) (2019)
- [Rethinking the Role of Demonstrations: What Makes In-Context Learning Work?](https://mlsanity.com/paper/2202.12837/) (2022)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [Model soups: averaging weights of multiple fine-tuned models improves accuracy without increasing inference time](https://mlsanity.com/paper/2203.05482/) (2022)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Deep CORAL: Correlation Alignment for Deep Domain Adaptation](https://mlsanity.com/paper/1607.01719/) (2016)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Right for the Wrong Reasons: Diagnosing Syntactic Heuristics in Natural Language Inference](https://mlsanity.com/paper/1902.01007/) (2019)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [Out-of-Distribution Generalization via Risk Extrapolation (REx)](https://mlsanity.com/paper/2003.00688/) (2020)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [An Empirical Study of Example Forgetting during Deep Neural Network Learning](https://mlsanity.com/paper/1812.05159/) (2018)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Recognition in Terra Incognita](https://mlsanity.com/paper/1807.04975/) (2018)
- [The Implicit Bias of Gradient Descent on Separable Data](https://mlsanity.com/paper/1710.10345/) (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)
- [Gradient Descent Finds Global Minima of Deep Neural Networks](https://mlsanity.com/paper/1811.03804/) (2018)
- [Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks](https://mlsanity.com/paper/1901.08584/) (2019)
- [Variational Autoencoders and Nonlinear ICA: A Unifying Framework](https://mlsanity.com/paper/1907.04809/) (2019)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Last Layer Re-Training is Sufficient for Robustness to Spurious Correlations](https://mlsanity.com/paper/2204.02937/) (2022)

## Built on by (most cited first, 30 of 50)

- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [The Platonic Representation Hypothesis](https://mlsanity.com/paper/2405.07987/) (2024)
- [Assessing the Brittleness of Safety Alignment via Pruning and Low-Rank Modifications](https://mlsanity.com/paper/2402.05162/) (2024)
- [Latent Adversarial Training Improves Robustness to Persistent Harmful Behaviors in LLMs](https://mlsanity.com/paper/2407.15549/) (2024)
- [Eight Methods to Evaluate Robust Unlearning in LLMs](https://mlsanity.com/paper/2402.16835/) (2024)
- [The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networks](https://mlsanity.com/paper/2306.17844/) (2023)
- [Mechanistically analyzing the effects of fine-tuning on procedurally defined tasks](https://mlsanity.com/paper/2311.12786/) (2023)
- [Deep Model Fusion: A Survey](https://mlsanity.com/paper/2309.15698/) (2023)
- [Defending Against Unforeseen Failure Modes with Latent Adversarial Training](https://mlsanity.com/paper/2403.05030/) (2024)
- [ColD Fusion: Collaborative Descent for Distributed Multitask Finetuning](https://mlsanity.com/paper/2212.01378/) (2022)
- [Going Beyond Linear Mode Connectivity: The Layerwise Linear Feature Connectivity](https://mlsanity.com/paper/2307.08286/) (2023)
- [ICLR: In-Context Learning of Representations](https://mlsanity.com/paper/2501.00070/) (2024)
- [Merging by Matching Models in Task Parameter Subspaces](https://mlsanity.com/paper/2312.04339/) (2023)
- [Quantification of Uncertainty with Adversarial Models](https://mlsanity.com/paper/2307.03217/) (2023)
- [Proving Linear Mode Connectivity of Neural Networks via Optimal Transport](https://mlsanity.com/paper/2310.19103/) (2023)
- [Layer-wise Linear Mode Connectivity](https://mlsanity.com/paper/2307.06966/) (2023)
- [Compositional Capabilities of Autoregressive Transformers: A Study on Synthetic, Interpretable Tasks](https://mlsanity.com/paper/2311.12997/) (2023)
- [A Closer Look at Model Adaptation using Feature Distortion and Simplicity Bias](https://mlsanity.com/paper/2303.13500/) (2023)
- [C2M3: Cycle-Consistent Multi-Model Merging](https://mlsanity.com/paper/2405.17897/) (2024)
- [Beyond the Permutation Symmetry of Transformers: The Role of Rotation for Model Fusion](https://mlsanity.com/paper/2502.00264/) (2025)
- [In-Context Learning Dynamics with Random Binary Sequences](https://mlsanity.com/paper/2310.17639/) (2023)
- [Unveiling the Basin-Like Loss Landscape in Large Language Models](https://mlsanity.com/paper/2505.17646/) (2025)
- [From Dormant to Deleted: Tamper-Resistant Unlearning Through Weight-Space Regularization](https://mlsanity.com/paper/2505.22310/) (2025)
- [Project and Probe: Sample-Efficient Domain Adaptation by Interpolating Orthogonal Features](https://mlsanity.com/paper/2302.05441/) (2023)
- [Understanding Mode Connectivity via Parameter Space Symmetry](https://mlsanity.com/paper/2505.23681/) (2025)
- [Towards an Understanding of Stepwise Inference in Transformers: A Synthetic Graph Navigation Model](https://mlsanity.com/paper/2402.07757/) (2024)
- [The Butterfly Effect: Neural Network Training Trajectories Are Highly Sensitive to Initial Conditions](https://mlsanity.com/paper/2506.13234/) (2025)
- [Shared Parameter Subspaces and Cross-Task Linearity in Emergently Misaligned Behavior](https://mlsanity.com/paper/2511.02022/) (2025)
- [Improving Model Fusion by Training-time Neuron Alignment with Fixed Neuron Anchors](https://mlsanity.com/paper/2402.01342/) (2024)
- [Uncovering, Explaining, and Mitigating the Superficial Safety of Backdoor Defense](https://mlsanity.com/paper/2410.09838/) (2024)

## Abstract (arXiv)

We study neural network loss landscapes through the lens of mode connectivity, the observation that minimizers of neural networks retrieved via training on a dataset are connected via simple paths of low loss. Specifically, we ask the following question: are minimizers that rely on different mechanisms for making their predictions connected via simple paths of low loss? We provide a definition of mechanistic similarity as shared invariances to input transformations and demonstrate that lack of linear connectivity between two models implies they use dissimilar mechanisms for making their predictions. Relevant to practice, this result helps us demonstrate that naive fine-tuning on a downstream dataset can fail to alter a model's mechanisms, e.g., fine-tuning can fail to eliminate a model's reliance on spurious attributes. Our analysis also motivates a method for targeted alteration of a model's mechanisms, named connectivity-based fine-tuning (CBFT), which we analyze using several synthetic datasets for the task of reducing a model's reliance on spurious attributes.