TI-POOLING: Transformation-Invariant Pooling for Feature Learning in Convolutional Neural Networks

Abstract

In this paper we present a deep neural network topology that incorporates a simple to implement transformationinvariant pooling operator (TI-POOLING). This operator is able to efficiently handle prior knowledge on nuisance variations in the data, such as rotation or scale changes. Most current methods usually make use of dataset augmentation to address this issue, but this requires larger number of model parameters and more training data, and results in significantly increased training time and larger chance of under-or overfitting. The main reason for these drawbacks is that that the learned model needs to capture adequate features for all the possible transformations of the input. On the other hand, we formulate features in convolutional neural networks to be transformation-invariant. We achieve that using parallel siamese architectures for the considered transformation set and applying the TI-POOLING operator on their outputs before the fully-connected layers. We show that this topology internally finds the most optimal "canonical" instance of the input image for training and therefore limits the redundancy in learned features. This more efficient use of training data results in better performance on popular benchmark datasets with smaller number of parameters when comparing to standard convolutional neural networks with dataset augmentation and to other baselines.

Gabor Convolutional Networks

“…Despite the effectiveness of data augmentation, the main drawback is that learning all possible transformations usually requires a large number of network parameters, which significantly increases the training cost and the risk of overfitting. Most recently, TI-Pooling [18] alleviates the drawback by using parallel network architectures for the transformation set and applying the transformation invariant pooling operator on the outputs before the top layer. Nevertheless, with a builtin data augmentation, TI-Pooling requires significantly more training and testing computational cost than a standard CNN.…”

“…The learning weight decay is set as 0.00005, and the learning rate is reduced to half per 25 epochs. The state-of-the-art STN [19], TI-Pooling [18], ResNet [13] and ORNs [2] are exploited for comparison. Among them, STN is more robust to spatial transformation than the baseline CNNs, due to a spatial transform layer prior to the first convolution layer.…”

Understanding Image Representations by Measuring Their Equivariance and Equivalence

“…This can be as simple as averaging the features (Anselmi et al 2016), max-pooling (Laptev et al 2016;Cohen and Welling 2016) or simply by exploiting the group symmetry [such as ignoring the gradient 'sign' in Dalal and Triggs (2005) for vertical flip invariance].…”

Discrete Rotation Equivariance for Point Cloud Recognition

“…Data augmentation [6] is the most popular technique to mitigate the effects from rotations. Despite the simplicity, it often leads to larger amount of model parameters and is prone to under-or over-fitting [7]. Another drawback of data augmentation is its black-box nature, where it is completely unknown on how the network handles various transformation.…”