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End-to-end Feature Alignment: A Simple CNN with Intrinsic Class Attribution

Parniyan Farvardin, David Chapman

Abstract

We present Feature-Align CNN (FA-CNN), a prototype CNN architecture with intrinsic class attribution through end-to-end feature alignment. Our intuition is that the use of unordered operations such as Linear and Conv2D layers cause unnecessary shuffling and mixing of semantic concepts, thereby making raw feature maps difficult to understand. We introduce two new order preserving layers, the dampened skip connection, and the global average pooling classifier head. These layers force the model to maintain an end-to-end feature alignment from the raw input pixels all the way to final class logits. This end-to-end alignment enhances the interpretability of the model by allowing the raw feature maps to intrinsically exhibit class attribution. We prove theoretically that FA-CNN penultimate feature maps are identical to Grad-CAM saliency maps. Moreover, we prove that these feature maps slowly morph layer-by-layer over network depth, showing the evolution of features through network depth toward penultimate class activations. FA-CNN performs well on benchmark image classification datasets. Moreover, we compare the averaged FA-CNN raw feature maps against Grad-CAM and permutation methods in a percent pixels removed interpretability task. We conclude this work with a discussion and future, including limitations and extensions toward hybrid models.

End-to-end Feature Alignment: A Simple CNN with Intrinsic Class Attribution

Abstract

We present Feature-Align CNN (FA-CNN), a prototype CNN architecture with intrinsic class attribution through end-to-end feature alignment. Our intuition is that the use of unordered operations such as Linear and Conv2D layers cause unnecessary shuffling and mixing of semantic concepts, thereby making raw feature maps difficult to understand. We introduce two new order preserving layers, the dampened skip connection, and the global average pooling classifier head. These layers force the model to maintain an end-to-end feature alignment from the raw input pixels all the way to final class logits. This end-to-end alignment enhances the interpretability of the model by allowing the raw feature maps to intrinsically exhibit class attribution. We prove theoretically that FA-CNN penultimate feature maps are identical to Grad-CAM saliency maps. Moreover, we prove that these feature maps slowly morph layer-by-layer over network depth, showing the evolution of features through network depth toward penultimate class activations. FA-CNN performs well on benchmark image classification datasets. Moreover, we compare the averaged FA-CNN raw feature maps against Grad-CAM and permutation methods in a percent pixels removed interpretability task. We conclude this work with a discussion and future, including limitations and extensions toward hybrid models.

Paper Structure

This paper contains 12 sections, 3 theorems, 21 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Contributions
  3. Approach
  4. Dampened Skip Connection
  5. 3D Global Average Pooling Classifier
  6. Proof of Grad-CAM equivalence
  7. Proof of Bounded Increment through Depth
  8. Results
  9. Classification Accuracy
  10. Pixel-Removal Saliency Evaluation
  11. Qualitative Evaluation
  12. Discussion and Future Work

Key Result

Theorem 1

Grad-CAM saliency maps are obtained by simply averaging together the $R$ penultimate feature maps designated to class $c$ as follows.

Figures (5)

  • Figure 1: Comarison of averaged FA-CNN raw featuremaps (Left) versus Grad-CAM maps (Right). Perturbation methods RISE and K-OCC are also shown (Far right). Deepest layers are equivalent (correl 1.0), and middle layers show strong similarity. Aligned features also show gradual morphing layer-by-layer through depth.
  • Figure 2: Diagram showing a single order-preserving FA-CNN Layer using the dampened skip connection.
  • Figure 3: Diagram showing The 3D Global Average Pooling head to compute pre-logits from Penultimate Feature Maps.
  • Figure 4: Classification Accuracy with Percent Pixels Removed on Layer 24 (top) and Layer 18 (bottom) on ImangeNet-100 Dataset.
  • Figure 5: Comarison of averaged FA-CNN raw featuremaps (Left) versus Grad-CAM maps (Right) and Perturbation methods (Far right).

Theorems & Definitions (5)

  • Theorem 1
  • proof
  • Theorem 2
  • Lemma 3
  • proof