Measuring Robustness of Machine Learning Models Using Harmonic Geometry

Core Concepts

Harmonic Robustness is a simple geometric technique to measure the robustness and explainability of any machine learning model, without requiring ground-truth labels or model internals.

Abstract

The paper introduces Harmonic Robustness, a method to test the robustness of any machine learning model. It is based on the concept of "harmonicity" - the degree to which the model function satisfies the harmonic mean-value property. This indicates the model's stability and explainability.
The key highlights are:

The method is model-agnostic and unsupervised, requiring only black-box access to the model.
It can reliably identify overfitting in models, as well as measure adversarial vulnerability across feature space.
Harmonic functions exhibit the mean-value property, where the value at any point is the average of the function over a surrounding ball. Deviations from this property, measured by the "anharmoniticity" metric γ, indicate instability and lack of explainability.
The computation of γ is linear in the number of data points and has good statistical convergence.
The method is demonstrated on simple models like decision trees and neural networks, as well as complex high-dimensional models like ResNet-50 and Vision Transformer.
For high-dimensional models, γ can be used to efficiently find adversarial examples and measure robustness across different classes.
The Harmonic Robustness metric provides a new way to assess model quality and stability, complementing existing metrics like accuracy and adversarial robustness.

Stats

The average logit drift after 25 adversarial steps is 0.88(2), while 25 times the average γ is 0.94.
For the ResNet-50 model, the average γ ranges from 0.020 to 0.082 across different animal classes.
For the Vision Transformer model, the average γ ranges from 0.027 to 0.082 across different animal classes.

Quotes

"Harmonic functions are natively explainable since, by the mean value property, the 'explanation' of any point is that it is the average of the points around it, which in turn are 'explained' by their neighboring points, etc., all the way up to the feature boundaries which have values fixed by some standard."
"The closer γ is to zero, the more explainable the model will be. Conversely, the more a model fails (1.2) at some point the more difficult it may be to explain, e.g., in the fraud domain if the average of several non-fraudulent events was predicted to be fraudulent."

Key Insights Distilled From

Harmonic Machine Learning Models are Robust

by Nicholas S. ... at arxiv.org 04-30-2024

https://arxiv.org/pdf/2404.18825.pdf

Deeper Inquiries

How can the Harmonic Robustness metric be extended to capture other desirable properties of machine learning models beyond stability and explainability, such as fairness and interpretability

The Harmonic Robustness metric can be extended to capture other desirable properties of machine learning models beyond stability and explainability by incorporating additional constraints and metrics into the evaluation process. For fairness, the metric could be adapted to measure the model's performance across different demographic groups or sensitive attributes, ensuring that predictions are equitable and unbiased. This could involve analyzing the distribution of predictions and outcomes to detect any disparities that may indicate unfair treatment.
Interpretability can also be addressed by incorporating measures of model transparency and comprehensibility into the evaluation framework. This could involve assessing the model's ability to provide explanations for its predictions, such as through feature importance analysis or generating human-readable explanations for complex decisions. By integrating these additional considerations into the Harmonic Robustness metric, a more comprehensive evaluation of the model's overall quality and reliability can be achieved.

What are the limitations of using the harmonic mean-value property as the underlying standard for model robustness, and are there alternative functional constraints that could be more appropriate in certain domains

While the harmonic mean-value property serves as a useful standard for measuring model robustness in terms of stability and explainability, it does have limitations that may restrict its applicability in certain domains. One limitation is that the harmonic property may not fully capture the complexities of real-world data and models, as it assumes a specific form of smoothness and interpolation that may not always hold true. In domains where the data is inherently non-harmonic or exhibits nonlinear relationships, the harmonic mean-value property may not provide an accurate measure of model robustness.
Alternative functional constraints that could be more appropriate in certain domains include measures of local linearity, curvature, or sparsity in the decision boundary. For example, in domains where decision boundaries are expected to be highly nonlinear or exhibit sharp transitions, metrics that capture the local curvature or abrupt changes in the decision surface may be more relevant for assessing model robustness. By incorporating these alternative constraints into the evaluation framework, a more nuanced and domain-specific assessment of model quality can be achieved.

Can the Harmonic Robustness metric be integrated into the model development lifecycle to guide architecture search, hyperparameter tuning, and other optimization processes, beyond just evaluating final model performance

The Harmonic Robustness metric can be integrated into the model development lifecycle to guide architecture search, hyperparameter tuning, and other optimization processes by providing a quantitative measure of model quality and stability at each stage of development. During architecture search, the metric can be used to compare different model architectures based on their harmonic robustness, helping to identify architectures that are more likely to generalize well and exhibit stable performance.
In hyperparameter tuning, the Harmonic Robustness metric can serve as an additional objective function to optimize for, alongside traditional performance metrics like accuracy or loss. By incorporating robustness as a key optimization criterion, developers can ensure that the final model not only performs well on the training data but also maintains stability and generalizability on unseen data.
Furthermore, the metric can be used to evaluate the impact of different optimization processes, such as data augmentation techniques or regularization methods, on the model's robustness. By monitoring changes in the Harmonic Robustness metric throughout the development lifecycle, developers can make informed decisions about which strategies are most effective in improving the overall quality and reliability of the model.