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1. Nonconvex Regularization for Network Slimming: Compressing CNNs Even More

   https://doi.org/https://doi.org/10.1007/978-3-030-64556-4_4  

   Bui, Kevin ; Park, Fredrick ; Zhang, Shuai ; Qi, Yingyong ; Xin, Jack ( December 2020 , International Symposium on Visual Computing, Lecture Notes in Computer Science)

   Bebis, G. (Ed.)

   In the last decade, convolutional neural networks (CNNs) have evolved to become the dominant models for various computer vision tasks, but they cannot be deployed in low-memory devices due to its high memory requirement and computational cost. One popular, straightforward approach to compressing CNNs is network slimming, which imposes an ℓ1 penalty on the channel-associated scaling factors in the batch normalization layers during training. In this way, channels with low scaling factors are identified to be insignificant and are pruned in the models. In this paper, we propose replacing the ℓ1 penalty with the ℓp and transformed ℓ1 (T ℓ1 ) penalties since these nonconvex penalties outperformed ℓ1 in yielding sparser satisfactory solutions in various compressed sensing problems. In our numerical experiments, we demonstrate network slimming with ℓp and T ℓ1 penalties on VGGNet and Densenet trained on CIFAR 10/100. The results demonstrate that the nonconvex penalties compress CNNs better than ℓ1 . In addition, T ℓ1 preserves the model accuracy after channel pruning, and ℓ1/2,3/4 yield compressed models with similar accuracies as ℓ1 after retraining. 

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2. Structured Sparsity of Convolutional Neural Networks via Nonconvex Sparse Group Regularization

   Kevin Bui, Fredrick Park ( January 2021 , Frontiers in applied mathematics and statistics)

   Convolutional neural networks (CNN) have been hugely successful recently with superior accuracy and performance in various imaging applications, such as classification, object detection, and segmentation. However, a highly accurate CNN model requires millions of parameters to be trained and utilized. Even to increase its performance slightly would require significantly more parameters due to adding more layers and/or increasing the number of filters per layer. Apparently, many of these weight parameters turn out to be redundant and extraneous, so the original, dense model can be replaced by its compressed version attained by imposing inter- and intra-group sparsity onto the layer weights during training. In this paper, we propose a nonconvex family of sparse group lasso that blends nonconvex regularization (e.g., transformed L1, L1 - L2, and L0) that induces sparsity onto the individual weights and L2,1 regularization onto the output channels of a layer. We apply variable splitting onto the proposed regularization to develop an algorithm that consists of two steps per iteration: gradient descent and thresholding. Numerical experiments are demonstrated on various CNN architectures showcasing the effectiveness of the nonconvex family of sparse group lasso in network sparsification and test accuracy on par with the current state of the art. 

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3. Tight Certification of Adversarially Trained Neural Networks via Nonconvex Low-Rank Semidefinite Relaxations

   Hong-Ming Chiu, Richard Y. ( July 2023 , Proceedings of Machine Learning Research)

   Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification that the model is truly robust against all future attacks. Unfortunately, when faced with adversarially trained models, all existing approaches have significant trouble making certifications that are strong enough to be practically useful. Linear programming (LP) techniques in particular face a “convex relaxation barrier” that prevent them from making high-quality certifications, even after refinement with mixed-integer linear programming (MILP) and branch-and-bound (BnB) techniques. In this paper, we propose a nonconvex certification technique, based on a low-rank restriction of a semidefinite programming (SDP) relaxation. The nonconvex relaxation makes strong certifications comparable to much more expensive SDP methods, while optimizing over dramatically fewer variables comparable to much weaker LP methods. Despite nonconvexity, we show how off-the-shelf local optimization algorithms can be used to achieve and to certify global optimality in polynomial time. Our experiments find that the nonconvex relaxation almost completely closes the gap towards exact certification of adversarially trained models. 

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4. Optimized FPGA-based Deep Learning Accelerator for Sparse CNN using High Bandwidth Memory

   https://doi.org/10.1109/FCCM51124.2021.00026  

   Jiang, Chao ; Ojika, David ; Patel, Bhavesh ; Lam, Herman ( May 2021 , IEEE Annual International Symposium on Field-Programmable Custom Computing Machines)

   null (Ed.)

   Large Convolutional Neural Networks (CNNs) are often pruned and compressed to reduce the amount of parameters and memory requirement. However, the resulting irregularity in the sparse data makes it difficult for FPGA accelerators that contains systolic arrays of Multiply-and-Accumulate (MAC) units, such as Intel’s FPGA-based Deep Learning Accelerator (DLA), to achieve their maximum potential. Moreover, FPGAs with low-bandwidth off-chip memory could not satisfy the memory bandwidth requirement for sparse matrix computation. In this paper, we present 1) a sparse matrix packing technique that condenses sparse inputs and filters before feeding them into the systolic array of MAC units in the Intel DLA, and 2) a customization of the Intel DLA which allows the FPGA to efficiently utilize a high bandwidth memory (HBM2) integrated in the same package. For end-to-end inference with randomly pruned ResNet-50/MobileNet CNN models, our experiments demonstrate 2.7x/3x performance improvement compared to an FPGA with DDR4, 2.2x/2.1x speedup against a server-class Intel SkyLake CPU, and comparable performance with 1.7x/2x power efficiency gain as compared to an NVidia V100 GPU. 

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5. DefT: Boosting Scalability of Deformable Convolution Operations on GPUs

   https://doi.org/10.1145/3582016.3582017  

   Hanson, Edward ; Horton, Mark ; Li, Hai ; Chen, Yiran ( March 2023 , The 28th ACM International Conference on Architectural Support for Programming Languages and Operating Systems, Volume 3 (ASPLOS ’23),)

   Deformable Convolutional Networks (DCN) have been proposed as a powerful tool to boost the representation power of Convolutional Neural Networks (CNN) in computer vision tasks via adaptive sampling of the input feature map. Much like vision transformers, DCNs utilize a more flexible inductive bias than standard CNNs and have also been shown to improve performance of particular models. For example, drop-in DCN layers were shown to increase the AP score of Mask RCNN by 10.6 points while introducing only 1% additional parameters and FLOPs, improving the state-of-the art model at the time of publication. However, despite evidence that more DCN layers placed earlier in the network can further improve performance, we have not seen this trend continue with further scaling of deformations in CNNs, unlike for vision transformers. Benchmarking experiments show that a realistically sized DCN layer (64H×64W, 64 in-out channel) incurs a 4× slowdown on a GPU platform, discouraging the more ubiquitous use of deformations in CNNs. These slowdowns are caused by the irregular input-dependent access patterns of the bilinear interpolation operator, which has a disproportionately low arithmetic intensity (AI) compared to the rest of the DCN. To address the disproportionate slowdown of DCNs and enable their expanded use in CNNs, we propose DefT, a series of workload-aware optimizations for DCN kernels. DefT identifies performance bottlenecks in DCNs and fuses specific operators that are observed to limit DCN AI. Our approach also uses statistical information of DCN workloads to adapt the workload tiling to the DCN layer dimensions, minimizing costly out-of-boundary input accesses. Experimental results show that DefT mitigates up to half of DCN slowdown over the current-art PyTorch implementation. This translates to a layerwise speedup of up to 134% and a reduction of normalized training time of 46% on a fully DCN-enabled ResNet model. 

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