Deep Neural Networks (DNNs) have become an integral part of our daily lives, especially in vision-related applications. However, the conventional lossy image compression algorithms are primarily designed for the Human Vision System (HVS), which can non-trivially compromise the DNNs' validation accuracy after compression, as noted in \cite{liu2018deepn}. Thus developing an image compression algorithm for both human and machine (DNNs) is on the horizon. To address the challenge mentioned above, in this paper, we first formulate the image compression as a multi-objective optimization problem which take both human and machine prespectives into account, then we solve it by linear combination, and proposed a novel distortion measure for both human and machine, dubbed Human and Machine-Oriented Error (HMOE). After that, we develop Human And Machine Oriented Soft Decision Quantization (HMOSDQ) based on HMOE, a lossy image compression algorithm for both human and machine (DNNs), and fully complied with JPEG format. In order to evaluate the performance of HMOSDQ, finally we conduct the experiments for two pre-trained well-known DNN-based image classifiers named Alexnet \cite{Alexnet} and VGG-16 \cite{simonyan2014VGG} on two subsets of the ImageNet \cite{deng2009imagenet} validation set: one subset included images with shorter side in the range of 496 to 512, while the other included images with shorter side in the range of 376 to 384. Our results demonstrate that HMOSDQ outperforms the default JPEG algorithm in terms of rate-accuracy and rate-distortion performance. For the Alexnet comparing with the default JPEG algorithm, HMOSDQ can improve the validation accuracy by more than $0.81\%$ at $0.61$ BPP, or equivalently reduce the compression rate of default JPEG by $9.6\times$ while maintaining the same validation accuracy.

In recent years, the integration of mixture-of-experts (MoE) within large-scale foundation models has markedly advanced the machine learning field [24, 11, 53, 73, 41]. MoE architectures, known for their ability to efficiently handle diverse and complex datasets, have facilitated significant improvements in model performance without a proportional increase in computational demand. They address bottlenecks associated with traditional deep learning architectures by dynamically allocating resources to parts of the model for which they are most relevant [67, 56]. The Hierarchical Mixture of Experts (HMoE) model [12] is a special type of MoE architecture that is characterized by a layered structure of decision modules and expert networks that operate in tandem to refine decision-making at each level, optimizing the allocation of computational resources and enhancing specialization for complex tasks. Unlike the standard MoE, which typically involves a single gating network directing inputs to various expert networks, HMoE introduces multiple layers of gating mechanisms and experts. This hierarchical design divides the problem space recursively, allowing different experts to specialize in subspaces of the input space, leading to enhanced flexibility and model generalization [25, 5]. Figure 1 compares HMoE and standard MoE in processing multimodal input data. The hierarchical structure of HMoE makes it particularly effective at handling complex inputs, such as data that can be divided into semantically meaningful subgroups.

Mixture of Experts (MoE) offers remarkable performance and computational efficiency by selectively activating subsets of model parameters. Traditionally, MoE models use homogeneous experts, each with identical capacity. However, varying complexity in input data necessitates experts with diverse capabilities, while homogeneous MoE hinders effective expert specialization and efficient parameter utilization. In this study, we propose a novel Heterogeneous Mixture of Experts (HMoE), where experts differ in size and thus possess diverse capacities. This heterogeneity allows for more specialized experts to handle varying token complexities more effectively. To address the imbalance in expert activation, we propose a novel training objective that encourages the frequent activation of smaller experts, enhancing computational efficiency and parameter utilization. Extensive experiments demonstrate that HMoE achieves lower loss with fewer activated parameters and outperforms conventional homogeneous MoE models on various pre-training evaluation benchmarks. Codes will be released upon acceptance.

Due to domain shifts, machine learning systems typically struggle to generalize well to new domains that differ from those of training data, which is what domain generalization (DG) aims to address. Although a variety of DG methods have been proposed, most of them fall short in interpretability and require domain labels, which are not available in many real-world scenarios. This paper presents a novel DG method, called HMOE: Hypernetwork-based Mixture of Experts (MoE), which does not rely on domain labels and is more interpretable. MoE proves effective in identifying heterogeneous patterns in data. For the DG problem, heterogeneity arises exactly from domain shifts. HMOE employs hypernetworks taking vectors as input to generate the weights of experts, which promotes knowledge sharing among experts and enables the exploration of their similarities in a low-dimensional vector space. We benchmark HMOE against other DG methods under a fair evaluation framework -- DomainBed. Our extensive experiments show that HMOE can effectively separate mixed-domain data into distinct clusters that are surprisingly more consistent with human intuition than original domain labels. Using self-learned domain information, HMOE achieves state-of-the-art results on most datasets and significantly surpasses other DG methods in average accuracy across all datasets.