Mechanistic Mode Connectivity (2211.08422v3)

Abstract: 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.

• The paper introduces a novel definition of mechanistic similarity by linking neural network minimizers through shared invariances to input transformations.
• The study demonstrates that standard fine-tuning may not alter a model's internal mechanisms, emphasizing the need for advanced adjustment techniques.
• It proposes Connectivity-Based Fine-Tuning (CBFT) to exploit non-linear connectivity paths and reduce reliance on spurious attributes.

Mechanistic Mode Connectivity: An In-depth Analysis

In the presented work, titled "Mechanistic Mode Connectivity," the authors embark on a paper exploring the intricate relationships between neural network minimizers through the lens of mode connectivity. Mode connectivity refers to the observation that various loss minimizers of a neural network, obtained through training, are connected via simple paths in the parameter space that maintain low loss values. This research is concerned primarily with the question of whether or not these minimizers, which employ different mechanisms to make predictions, are still connected by such simple paths of low loss.

Key Findings and Contributions

1. Definition of Mechanistic Similarity: The authors introduce a novel definition of mechanistic similarity between neural networks, based on shared invariances to input transformations. This concept is crucial to understanding whether different networks trained on the same data rely on identical mechanisms or if their decision-making processes are fundamentally distinct. This is particularly relevant when considering the role of spurious correlations in predictive modeling.
2. Impact on Fine-tuning Practices: A significant practical implication of this research is its demonstration that naive fine-tuning processes may not effectively alter a model's internal mechanisms. Specifically, fine-tuning a model on a downstream dataset without addressing preexisting spurious attribute dependencies will not necessarily eliminate those dependencies. This suggests a need for more sophisticated model adjustment techniques, which the authors address with their connectivity-based fine-tuning method.
3. Connectivity-Based Fine-Tuning (CBFT): The researchers propose CBFT as a targeted approach to altering a model's mechanisms. This method leverages the insights gathered from studying the connectivity of mechanistically distinct models. The approach is analyzed extensively with synthetic datasets, particularly in reducing a model's reliance on spurious attributes by exploiting the nature of non-linear connectivity paths.
4. Empirical Evaluation and Theoretical Implications: The paper is reinforced by comprehensive empirical evaluations using synthetic datasets that embed manipulable cues. The authors find that while it is often challenging to establish linear mode connectivity between mechanistically dissimilar networks without permutation, these connections can be found with higher-order paths (e.g., quadratic paths). Furthermore, their theoretical and empirical analyses reveal that dissimilar mechanisms are reflected in the existence of barriers on linear paths, reaffirming the necessity of considering mechanistic properties when examining mode connectivity.

Implications and Future Prospects

The implications of this work are vast and multi-faceted, touching on theoretical, methodological, and practical aspects of machine learning. The insight that model mechanisms must be explicitly considered and adjusted highlights a gap in current transfer learning and fine-tuning techniques that the community must address, particularly in robust AI system design. Moreover, the novel connectivity-based fine-tuning strategy proposed by the authors could pave the way for more transparent and nuanced machine learning models, which are both efficient and robust in the face of distribution shifts and spurious correlations.

Future research directions could focus on expanding these concepts in more complex settings, such as real-world datasets with naturally occurring spurious correlations. Moreover, bridging these findings with mode connectivity implications for model ensembling, robust optimization, and lifelong learning offers promising avenues to leverage mechanistic insights for enhanced model generalization and reliability across domains.