Instant Complexity Reduction in CNNs using Locality-Sensitive Hashing

To reduce the computational cost of convolutional neural networks (CNNs) for usage on resource-constrained devices, structured pruning approaches have shown promising results, drastically reducing floating-point operations (FLOPs) without substantial drops in accuracy. However, most recent methods require fine-tuning or specific training procedures to achieve a reasonable trade-off between retained accuracy and reduction in FLOPs. This introduces additional cost in the form of computational overhead and requires training data to be available. To this end, we propose HASTE (Hashing for Tractable Efficiency), a parameter-free and data-free module that acts as a plug-and-play replacement for any regular convolution module. It instantly reduces the network's test-time inference cost without requiring any training or fine-tuning. We are able to drastically compress latent feature maps without sacrificing much accuracy by using locality-sensitive hashing (LSH) to detect redundancies in the channel dimension. Similar channels are aggregated to reduce the input and filter depth simultaneously, allowing for cheaper convolutions. We demonstrate our approach on the popular vision benchmarks CIFAR-10 and ImageNet. In particular, we are able to instantly drop 46.72% of FLOPs while only losing 1.25% accuracy by just swapping the convolution modules in a ResNet34 on CIFAR-10 for our HASTE module.

Deep Neural Networks with Efficient Guaranteed Invariances

We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant convolutions are a popular approach to obtain equivariant representations. The desired corresponding invariance is then imposed using pooling operations. For rotations, it has been shown that using invariant integration instead of pooling further improves the sample complexity. In this contribution, we first expand invariant integration beyond rotations to flips and scale transformations. We then address the problem of incorporating multiple desired invariances into a single network. For this purpose, we propose a multi-stream architecture, where each stream is invariant to a different transformation such that the network can simultaneously benefit from multiple invariances. We demonstrate our approach with successful experiments on Scaled-MNIST, SVHN, CIFAR-10 and STL-10.

Dimensionality Reduced Training by Pruning and Freezing Parts of a Deep Neural Network, a Survey

State-of-the-art deep learning models have a parameter count that reaches into the billions. Training, storing and transferring such models is energy and time consuming, thus costly. A big part of these costs is caused by training the network. Model compression lowers storage and transfer costs, and can further make training more efficient by decreasing the number of computations in the forward and/or backward pass. Thus, compressing networks also at training time while maintaining a high performance is an important research topic. This work is a survey on methods which reduce the number of trained weights in deep learning models throughout the training. Most of the introduced methods set network parameters to zero which is called pruning. The presented pruning approaches are categorized into pruning at initialization, lottery tickets and dynamic sparse training. Moreover, we discuss methods that freeze parts of a network at its random initialization. By freezing weights, the number of trainable parameters is shrunken which reduces gradient computations and the dimensionality of the model's optimization space. In this survey we first propose dimensionality reduced training as an underlying mathematical model that covers pruning and freezing during training. Afterwards, we present and discuss different dimensionality reduced training methods.

Interspace Pruning: Using Adaptive Filter Representations to Improve Training of Sparse CNNs

Unstructured pruning is well suited to reduce the memory footprint of convolutional neural networks (CNNs), both at training and inference time. CNNs contain parameters arranged in $K \times K$ filters. Standard unstructured pruning (SP) reduces the memory footprint of CNNs by setting filter elements to zero, thereby specifying a fixed subspace that constrains the filter. Especially if pruning is applied before or during training, this induces a strong bias. To overcome this, we introduce interspace pruning (IP), a general tool to improve existing pruning methods. It uses filters represented in a dynamic interspace by linear combinations of an underlying adaptive filter basis (FB). For IP, FB coefficients are set to zero while un-pruned coefficients and FBs are trained jointly. In this work, we provide mathematical evidence for IP's superior performance and demonstrate that IP outperforms SP on all tested state-of-the-art unstructured pruning methods. Especially in challenging situations, like pruning for ImageNet or pruning to high sparsity, IP greatly exceeds SP with equal runtime and parameter costs. Finally, we show that advances of IP are due to improved trainability and superior generalization ability.

Improving the Sample-Complexity of Deep Classification Networks with Invariant Integration

Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. This makes them applicable to practically important use-cases where training data is scarce. Rather than being learned, this knowledge can be embedded by enforcing invariance to those transformations. Invariance can be imposed using group-equivariant convolutions followed by a pooling operation. For rotation-invariance, previous work investigated replacing the spatial pooling operation with invariant integration which explicitly constructs invariant representations. Invariant integration uses monomials which are selected using an iterative approach requiring expensive pre-training. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. Additionally, we replace monomials with different functions such as weighted sums, multi-layer perceptrons and self-attention, thereby streamlining the training of invariant-integration-based architectures. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets where rotation-invariant-integration-based Wide-ResNet architectures using monomials and weighted sums outperform the respective baselines in the limited sample regime. We achieve state-of-the-art results using full data on Rotated-MNIST and SVHN where rotation is a main source of intraclass variation. On STL-10 we outperform a standard and a rotation-equivariant convolutional neural network using pooling.

A Survey on Assessing the Generalization Envelope of Deep Neural Networks at Inference Time for Image Classification

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually nontransparent. A DNN delivers the correct output if the input is within the area enclosed by its generalization envelope. In this case, the information contained in the input sample is processed reasonably by the network. It is of large practical importance to assess at inference time if a DNN generalizes correctly. Currently, the approaches to achieve this goal are investigated in different problem set-ups rather independently from one another, leading to three main research and literature fields: predictive uncertainty, out-of-distribution detection and adversarial example detection. This survey connects the three fields within the larger framework of investigating the generalization performance of machine learning methods and in particular DNNs. We underline the common ground, point at the most promising approaches and give a structured overview of the methods that provide at inference time means to establish if the current input is within the generalization envelope of a DNN.

Boosting Deep Neural Networks with Geometrical Prior Knowledge: A Survey

While Deep Neural Networks (DNNs) achieve state-of-the-art results in many different problem settings, they are affected by some crucial weaknesses. On the one hand, DNNs depend on exploiting a vast amount of training data, whose labeling process is time-consuming and expensive. On the other hand, DNNs are often treated as black box systems, which complicates their evaluation and validation. Both problems can be mitigated by incorporating prior knowledge into the DNN. One promising field, inspired by the success of convolutional neural networks (CNNs) in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve. This promises an increased data-efficiency and filter responses that are interpretable more easily. In this survey, we try to give a concise overview about different approaches to incorporate geometrical prior knowledge into DNNs. Additionally, we try to connect those methods to the field of 3D object detection for autonomous driving, where we expect promising results applying those methods.

GraN: An Efficient Gradient-Norm Based Detector for Adversarial and Misclassified Examples

Deep neural networks (DNNs) are vulnerable to adversarial examples and other data perturbations. Especially in safety critical applications of DNNs, it is therefore crucial to detect misclassified samples. The current state-of-the-art detection methods require either significantly more runtime or more parameters than the original network itself. This paper therefore proposes GraN, a time- and parameter-efficient method that is easily adaptable to any DNN. GraN is based on the layer-wise norm of the DNN's gradient regarding the loss of the current input-output combination, which can be computed via backpropagation. GraN achieves state-of-the-art performance on numerous problem set-ups.

Invariant Integration in Deep Convolutional Feature Space

In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to construct a complete feature space invariant to finite transformation groups. We apply our proposed layer to explicitly insert invariance properties for vision-related classification tasks, demonstrate our approach for the case of rotation invariance and report state-of-the-art performance on the Rotated-MNIST dataset. Our method is especially beneficial when training with limited data.