Improving Shift Invariance in Convolutional Neural Networks through Translation Invariant Polyphase Sampling

Core Concepts

The core message of this paper is that maximum-sampling bias (MSB) in existing pooling operators is negatively correlated with shift invariance in convolutional neural networks (CNNs), and the authors propose a novel learnable pooling operator called Translation Invariant Polyphase Sampling (TIPS) along with two regularization techniques to reduce MSB and improve shift invariance.

Abstract

The paper starts by discussing the importance of shift invariance in visual recognition models and how existing pooling operators in CNNs, such as max pooling and average pooling, can break shift invariance. The authors introduce the concept of maximum-sampling bias (MSB), which quantifies the bias of a pooling operator to select and propagate the maximum value of the signal.

Through a large-scale correlation analysis, the authors show that MSB is negatively correlated with shift invariance across multiple CNN architectures, datasets, and pooling methods. Based on this insight, they propose a novel pooling operator called Translation Invariant Polyphase Sampling (TIPS) that discourages MSB and improves shift invariance.

TIPS learns to sample polyphase decompositions of the input feature maps using a learnable mixing function. To further improve shift invariance, the authors introduce two regularization techniques: LFM to discourage known failure modes of shift invariance, and Lundo to learn to undo standard shift transformations.

The authors evaluate TIPS on multiple image classification and semantic segmentation benchmarks, and show that it consistently outperforms previous shift-invariant pooling operators in terms of accuracy, shift consistency, and shift fidelity, while also exhibiting greater robustness to adversarial attacks and natural corruptions.

Stats

Shifting an image by a few pixels horizontally and/or vertically should not affect the category predicted by an image classifier.
Conventional pooling operators in CNNs, such as max pooling and average pooling, break shift invariance by violating the Nyquist sampling theorem and aliasing high-frequency signals.
The authors define maximum-sampling bias (MSB) as the fraction of window locations for which the maximum signal value is sampled during pooling.
The authors observe a strong negative correlation between MSB and shift invariance across multiple CNN architectures, datasets, and pooling methods.

Quotes

"Shifting an image by a few pixels horizontally and/or vertically should not affect the category predicted by an image classifier such as a convolutional neural network (CNN)."
"Recent studies have also found shift invariant visual recognition models to be more robust on out-of-distribution testing and adversarial attacks, therefore improving shift invariance in CNNs is consequential."
"We observe a strong negative correlation between MSB and shift invariance, i.e. models with higher MSB are the least shift invariant."

Key Insights Distilled From

Improving Shift Invariance in Convolutional Neural Networks with Translation Invariant Polyphase Sampling

by Sourajit Sah... at arxiv.org 04-12-2024

https://arxiv.org/pdf/2404.07410.pdf

Deeper Inquiries

How can the insights from this work be extended to other types of visual transformations beyond shift, such as rotation, scaling, or affine transformations

The insights from this work on improving shift invariance in CNNs can be extended to other types of visual transformations such as rotation, scaling, or affine transformations by considering the underlying principles that contribute to shift invariance. For example, techniques like Translation Invariant Polyphase Sampling (TIPS) focus on reducing biases towards maximum signal values in pooling operations, which can be generalized to other transformations by adapting the pooling mechanisms to prioritize important features regardless of the transformation applied.
For rotation transformations, the pooling mechanisms can be designed to be rotation-invariant by considering the orientation of features and their importance in the pooling process. Scaling transformations can be addressed by incorporating scale-invariant pooling techniques that prioritize features based on their scale-invariance properties. Affine transformations can be tackled by developing pooling strategies that are affine-invariant, ensuring that features are consistently captured regardless of affine distortions.
By understanding the core principles of shift invariance and adapting them to different types of visual transformations, it is possible to enhance the robustness and generalization capabilities of neural networks across a variety of transformation scenarios.

What are the potential trade-offs between improving shift invariance and other desirable properties of CNNs, such as computational efficiency or representational capacity

Improving shift invariance in CNNs may involve trade-offs with other desirable properties of neural networks, such as computational efficiency or representational capacity.

Computational Efficiency: Techniques like Translation Invariant Polyphase Sampling (TIPS) may introduce additional computational overhead due to the learnable pooling mechanisms and regularization terms. While TIPS aims to improve shift invariance, this could potentially increase the computational cost of training and inference, impacting the overall efficiency of the network.

Representational Capacity: Enhancing shift invariance through methods like TIPS may require sacrificing some degree of representational capacity. By focusing on specific features that are more invariant to shifts, there could be a trade-off in the network's ability to capture fine-grained details or complex patterns that are sensitive to shifts. This trade-off between shift invariance and representational capacity needs to be carefully balanced based on the specific requirements of the task at hand.

Generalization: Improving shift invariance may lead to better generalization to unseen data and robustness to perturbations. However, this focus on shift invariance could potentially limit the network's ability to adapt to variations in other types of transformations or introduce biases that affect performance on certain types of data distributions.

Overall, the trade-offs between improving shift invariance and other properties of CNNs should be carefully considered based on the specific goals of the model and the requirements of the task.

Could the principles of TIPS be applied to other types of neural network architectures beyond CNNs, such as transformers or graph neural networks

The principles of Translation Invariant Polyphase Sampling (TIPS) can be applied to other types of neural network architectures beyond CNNs, such as transformers or graph neural networks, by adapting the pooling mechanisms to suit the specific characteristics of these architectures.

Transformers: In transformer architectures, where self-attention mechanisms are used for capturing relationships between different input tokens, the principles of TIPS can be integrated by modifying the attention mechanisms to be more invariant to shifts in the input tokens. This could involve designing attention mechanisms that prioritize features based on their translation-invariant properties, similar to how TIPS prioritizes features in pooling operations.

Graph Neural Networks (GNNs): For graph neural networks, which operate on graph-structured data, the concepts of TIPS can be applied by developing pooling strategies that are invariant to node permutations or graph transformations. By incorporating translation-invariant pooling mechanisms in GNNs, the networks can better capture important graph features regardless of the spatial arrangement of nodes.

By adapting the principles of TIPS to different neural network architectures, it is possible to enhance the robustness and generalization capabilities of these models across various types of data and transformations.