The Effect of Intrinsic Dataset Properties on Generalization: Unraveling Learning Differences Between Natural and Medical Images (2401.08865v3)

Abstract: This paper investigates discrepancies in how neural networks learn from different imaging domains, which are commonly overlooked when adopting computer vision techniques from the domain of natural images to other specialized domains such as medical images. Recent works have found that the generalization error of a trained network typically increases with the intrinsic dimension ($d_{data}$) of its training set. Yet, the steepness of this relationship varies significantly between medical (radiological) and natural imaging domains, with no existing theoretical explanation. We address this gap in knowledge by establishing and empirically validating a generalization scaling law with respect to $d_{data}$, and propose that the substantial scaling discrepancy between the two considered domains may be at least partially attributed to the higher intrinsic ``label sharpness'' ($K_\mathcal{F}$) of medical imaging datasets, a metric which we propose. Next, we demonstrate an additional benefit of measuring the label sharpness of a training set: it is negatively correlated with the trained model's adversarial robustness, which notably leads to models for medical images having a substantially higher vulnerability to adversarial attack. Finally, we extend our $d_{data}$ formalism to the related metric of learned representation intrinsic dimension ($d_{repr}$), derive a generalization scaling law with respect to $d_{repr}$, and show that $d_{data}$ serves as an upper bound for $d_{repr}$. Our theoretical results are supported by thorough experiments with six models and eleven natural and medical imaging datasets over a range of training set sizes. Our findings offer insights into the influence of intrinsic dataset properties on generalization, representation learning, and robustness in deep neural networks. Code link: https://github.com/mazurowski-lab/intrinsic-properties

• The paper demonstrates that intrinsic dataset dimension and label sharpness critically affect generalization error in both natural and medical image domains.
• It introduces a novel metric for label sharpness, revealing that higher sharpness in medical images increases susceptibility to adversarial attacks.
• Experimental validation with six CNN models across eleven datasets supports theoretical extensions linking training set intrinsic dimensions to learned representations.

Overview

Understanding the learning characteristics of neural networks across different image domains is a crucial research avenue. In a paper, significant progress is made toward deciphering the unique ways neural networks generalize knowledge when trained on natural images versus medical images. The paper introduces the concept of dataset intrinsic dimension and label sharpness, offering both theoretical and empirical insights into why networks might exhibit different behavior between these two domains.

Intrinsic Dataset Properties and Neural Learning

The intrinsic dimension of a dataset encapsulates the minimum degrees of freedom required to represent the data without significant loss of information. Prior research indicated that higher intrinsic dimensions tend to increase generalization error. Interestingly, this increase in error is notably different between natural and medical imaging, where the latter presents a steeper error curve.

To explain this phenomenon, researchers focus on a property called label sharpness, a metric they propose to quantify how similar images with different labels can be within a dataset. They discovered that medical imaging datasets typically showcase a higher label sharpness than those of natural images, suggesting that subtle image variations often result in label changes.

Adversarial Robustness

Another key discovery of this paper is the relationship between label sharpness and adversarial vulnerability. It was observed that networks trained on datasets with higher label sharpness are more susceptible to adversarial attacks. This vulnerability emphasized the pressing need for robust neural network models, particularly in critical areas such as medical imaging, where adversarial attacks can have severe implications.

Theoretical Extensions

The paper doesn't just stop at empirical observations but also ventures into theoretical grounds. It extends its analysis to the intrinsic dimensions of the learned representations of these networks, theorizing that the intrinsic dimension of the training set acts as an upper bound to that of the model's learned representations. This relationship provides a theoretical underpinning to the similarity of generalization error trends observed across intrinsic dimensions, regardless of whether they are related to datasets or learned representations.

Experimental Validation

Six convolutional neural network models were meticulously tested across eleven datasets from both natural and medical image domains, revealing that neural network behavior is indeed significantly influenced by the intrinsic properties of the datasets. The use of several models and datasets contributes to the robustness of the paper, while the remarkable alignment of the results with the proposed theory underpins the validity of their findings.

Implications

This paper not only progresses theoretical understanding but also paves the way for practical applications. It could, for instance, assist in predicting the difficulty of various learning tasks or inform the development of strategies to counteract adversarial vulnerabilities. Additionally, understanding the linkage between dataset and representation intrinsic dimensions may influence the architectural design choices of future neural networks, especially in applications like medical imagery where precision is paramount.

The paper, with its profound insights and thorough validation process, signifies a leap forward in our understanding of deep learning, setting a precedent for future investigations into the intricate relationship between neural network behavior and the intrinsic properties of training datasets.