Fidelity Isn't Accuracy: When Linearly Decodable Functions Fail to Match the Ground Truth

• URL: http://arxiv.org/abs/2506.12176v3
• Date: Thu, 21 Aug 2025 22:13:17 GMT
• Title: Fidelity Isn't Accuracy: When Linearly Decodable Functions Fail to Match the Ground Truth
• Authors: Jackson Eshbaugh,
• Abstract summary: A linearity score $lambda(f)$ measures how well a regression network's output can be mimicked by a linear model.<n>This framework is evaluated on both synthetic and real-world datasets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Neural networks excel as function approximators, but their complexity often obscures the types of functions they learn, making it difficult to explain their behavior. To address this, the linearity score $\lambda(f)$ is introduced, a simple and interpretable diagnostic that quantifies how well a regression network's output can be mimicked by a linear model. Defined as the $R^2$ value between the network's predictions and those of a trained linear surrogate, $\lambda(f)$ measures linear decodability: the extent to which the network's behavior aligns with a structurally simple model. This framework is evaluated on both synthetic and real-world datasets, using dataset-specific networks and surrogates. High $\lambda(f)$ scores reliably indicate alignment with the network's outputs; however, they do not guarantee accuracy with respect to the ground truth. These results highlight the risk of using surrogate fidelity as a proxy for model understanding, especially in high-stakes regression tasks.

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