Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memoryand compute-footprint can be reduced by compression. In this work, we focus on compression through tensorization and low-rank representations. Whereas classical approaches search for a low-rank approximation by minimizing an isotropic norm such as the Frobenius norm in weight-space, we use data-informed norms that measure the error in function space. Concretely, we minimize the change in the layer's output distribution, which can be expressed as (W fW)Σ1/2 F where Σ1/2 is the square root of the covariance matrix of the layer's input and W, fW are the original and compressed weights. We propose new alternating least square algorithms for the two most common tensor decompositions (Tucker-2 and CPD) that directly optimize the new norm. Unlike conventional compression pipelines, which almost always require post-compression fine-tuning, our data-informed approach often achieves competitive accuracy without any fine-tuning. We further show that the same covariance-based norm can be transferred from one dataset to another with only a minor accuracy drop, enabling compression even when the original training dataset is unavailable. Experiments on several CNN architectures (ResNet-18/50, and GoogLeNet) and datasets (ImageNet, FGVC-Aircraft, Cifar10, and Cifar100) confirm the advantages of the proposed method.

Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often required to alleviate prohibitive workloads on hardware. Despite the remarkable success of backpropagation, the algorithm itself is not capable of considering such constraints unless additional algorithms are applied simultaneously. To address this issue, we propose the constrained backpropagation (CBP) algorithm based on the pseudo-Lagrange multiplier method to obtain the optimal set of weights that satisfy a given set of constraints. The defining characteristic of the proposed CBP algorithm is the utilization of a Lagrangian function (loss function plus constraint function) as its objective function. We considered various types of constraints -- binary, ternary, one-bit shift, and two-bit shift weight constraints. As a post-training method, CBP applied to AlexNet, ResNet-18, ResNet-50, and GoogLeNet on ImageNet, which were pre-trained using the conventional backpropagation. For most cases, the proposed algorithm outperforms the state-of-the-art methods on ImageNet, e.g., 66.6\%, 74.4\%, and 64.0\% top-1 accuracy for ResNet-18, ResNet-50, and GoogLeNet with binary weights, respectively. This highlights CBP as a learning algorithm to address diverse constraints with the minimal performance loss by employing appropriate constraint functions.

Neural networks are widely used for image-related tasks but typically demand considerable computing power. Once a network has been trained, however, its memory- and compute-footprint can be reduced by compression. In this work, we focus on compression through tensorization and low-rank representations. Whereas classical approaches search for a low-rank approximation by minimizing an isotropic norm such as the Frobenius norm in weight-space, we use data-informed norms that measure the error in function space. Concretely, we minimize the change in the layer's output distribution, which can be expressed as $\lVert (W - \widetilde{W}) Σ^{1/2}\rVert_F$ where $Σ^{1/2}$ is the square root of the covariance matrix of the layer's input and $W$, $\widetilde{W}$ are the original and compressed weights. We propose new alternating least square algorithms for the two most common tensor decompositions (Tucker-2 and CPD) that directly optimize the new norm. Unlike conventional compression pipelines, which almost always require post-compression fine-tuning, our data-informed approach often achieves competitive accuracy without any fine-tuning. We further show that the same covariance-based norm can be transferred from one dataset to another with only a minor accuracy drop, enabling compression even when the original training dataset is unavailable. Experiments on several CNN architectures (ResNet-18/50, and GoogLeNet) and datasets (ImageNet, FGVC-Aircraft, Cifar10, and Cifar100) confirm the advantages of the proposed method.

We are very happy to hear that all reviewers found the paper interesting and well written. Below we provide point-by-point responses to selected comments. All reviewers commented on that it would have been interesting to see results on real-world datasets. "controlled way" results in a cleaner and more informative numerical evaluation. The distribution-free bounds are typically between 0.99 and 1, We will add these additional experimental results to the revised supplementary material.

Backward propagation of errors (backpropagation) is a method to minimize objective functions (e.g., loss functions) of deep neural networks by identifying optimal sets of weights and biases. Imposing constraints on weight precision is often required to alleviate prohibitive workloads on hardware. Despite the remarkable success of backpropagation, the algorithm itself is not capable of considering such constraints unless additional algorithms are applied simultaneously. To address this issue, we propose the constrained backpropagation (CBP) algorithm based on the pseudo-Lagrange multiplier method to obtain the optimal set of weights that satisfy a given set of constraints. The defining characteristic of the proposed CBP algorithm is the utilization of a Lagrangian function (loss function plus constraint function) as its objective function.

Deep Neural Networks (DNNs) are often over-parameterized for their tasks and can be compressed quite drastically by removing weights, a process called pruning. We investigate the impact of different pruning techniques on the classification performance and interpretability of GoogLeNet. We systematically apply unstructured and structured pruning, as well as connection sparsity (pruning of input weights) methods to the network and analyze the outcomes regarding the network's performance on the validation set of ImageNet. We also compare different retraining strategies, such as iterative pruning and one-shot pruning. We find that with sufficient retraining epochs, the performance of the networks can approximate the performance of the default GoogLeNet - and even surpass it in some cases. To assess interpretability, we employ the Mechanistic Interpretability Score (MIS) developed by Zimmermann et al. . Our experiments reveal that there is no significant relationship between interpretability and pruning rate when using MIS as a measure. Additionally, we observe that networks with extremely low accuracy can still achieve high MIS scores, suggesting that the MIS may not always align with intuitive notions of interpretability, such as understanding the basis of correct decisions.

In this paper, we propose a predictive quantifier to estimate the retraining cost of a trained model in distribution shifts. The proposed Aggregated Representation Measure (ARM) quantifies the change in the model's representation from the old to new data distribution. It provides, before actually retraining the model, a single concise index of resources - epochs, energy, and carbon emissions - required for the retraining. This enables reuse of a model with a much lower cost than training a new model from scratch. The experimental results indicate that ARM reasonably predicts retraining costs for varying noise intensities and enables comparisons among multiple model architectures to determine the most cost-effective and sustainable option.

Reading and interpreting chest X-ray images is one of the most radiologist's routines. However, it still can be challenging, even for the most experienced ones. Therefore, we proposed a multi-model deep learning-based automated chest X-ray report generator system designed to assist radiologists in their work. The basic idea of the proposed system is by utilizing multi binary-classification models for detecting multi abnormalities, with each model responsible for detecting one abnormality, in a single image. In this study, we limited the radiology abnormalities detection to only cardiomegaly, lung effusion, and consolidation. The system generates a radiology report by performing the following three steps: image pre-processing, utilizing deep learning models to detect abnormalities, and producing a report. The aim of the image pre-processing step is to standardize the input by scaling it to 128x128 pixels and slicing it into three segments, which covers the upper, lower, and middle parts of the lung. After pre-processing, each corresponding model classifies the image, resulting in a 0 (zero) for no abnormality detected and a 1 (one) for the presence of an abnormality. The prediction outputs of each model are then concatenated to form a 'result code'. The 'result code' is used to construct a report by selecting the appropriate pre-determined sentence for each detected abnormality in the report generation step. The proposed system is expected to reduce the workload of radiologists and increase the accuracy of chest X-ray diagnosis.

Gradient sparsification is a communication optimisation technique for scaling and accelerating distributed deep neural network (DNN) training. It reduces the increasing communication traffic for gradient aggregation. However, existing sparsifiers have poor scalability because of the high computational cost of gradient selection and/or increase in communication traffic. In particular, an increase in communication traffic is caused by gradient build-up and inappropriate threshold for gradient selection. To address these challenges, we propose a novel gradient sparsification method called MiCRO. In MiCRO, the gradient vector is partitioned, and each partition is assigned to the corresponding worker. Each worker then selects gradients from its partition, and the aggregated gradients are free from gradient build-up. Moreover, MiCRO estimates the accurate threshold to maintain the communication traffic as per user requirement by minimising the compression ratio error. MiCRO enables near-zero cost gradient sparsification by solving existing problems that hinder the scalability and acceleration of distributed DNN training. In our extensive experiments, MiCRO outperformed state-of-the-art sparsifiers with an outstanding convergence rate.

Deep neural networks (DNN) have achieved remarkable success in various fields, including computer vision and natural language processing. However, training an effective DNN model still poses challenges. This paper aims to propose a method to optimize the training effectiveness of DNN, with the goal of improving model performance. Firstly, based on the observation that the DNN parameters change in certain laws during training process, the potential of parameter prediction for improving model training efficiency and performance is discovered. Secondly, considering the magnitude of DNN model parameters, hardware limitations and characteristics of Stochastic Gradient Descent (SGD) for noise tolerance, a Parameter Linear Prediction (PLP) method is exploit to perform DNN parameter prediction. Finally, validations are carried out on some representative backbones. Experiment results show that compare to the normal training ways, under the same training conditions and epochs, by employing proposed PLP method, the optimal model is able to obtain average about 1% accuracy improvement and 0.01 top-1/top-5 error reduction for Vgg16, Resnet18 and GoogLeNet based on CIFAR-100 dataset, which shown the effectiveness of the proposed method on different DNN structures, and validated its capacity in enhancing DNN training efficiency and performance.