The distortion-perception (DP) tradeoff reveals a fundamental conflict between distortion metrics (e.g., MSE and PSNR) and perceptual quality. Recent research has increasingly concentrated on evaluating denoising algorithms within the DP framework. However, existing algorithms either prioritize perceptual quality by sacrificing acceptable distortion, or focus on minimizing MSE for faithful restoration. When the goal shifts or noisy measurements vary, adapting to different points on the DP plane needs retraining or even re-designing the model. Inspired by recent advances in solving inverse problems using score-based generative models, we explore the potential of flexibly and optimally traversing DP tradeoffs using a single pre-trained score-based model. Specifically, we introduce a variance-scaled reverse diffusion process and theoretically characterize the marginal distribution. We then prove that the proposed sample process is an optimal solution to the DP tradeoff for conditional Gaussian distribution. Experimental results on two-dimensional and image datasets illustrate that a single score network can effectively and flexibly traverse the DP tradeoff for general denoising problems.

By extracting task-relevant information while maximally compressing the input, the information bottleneck (IB) principle has provided a guideline for learning effective and robust representations of the target inference. However, extending the idea to the multi-task learning scenario with joint consideration of generative tasks and traditional reconstruction tasks remains unexplored. This paper addresses this gap by reconsidering the lossy compression problem with diverse constraints on data reconstruction, perceptual quality, and classification accuracy. Firstly, we study two ternary relationships, namely, therate-distortion-classification (RDC)andrate-perception-classification (RPC). For both RDC and RPC functions, we derive the closed-form expressions of the optimal rate for binary and Gaussian sources. These new results complement the IB principle and provide insights into effectively extracting task-oriented information to fulfill diverse objectives. Secondly, unlike prior research demonstrating a tradeoff between classification and perception in signal restoration problems, we prove that such a tradeoff does not exist in the RPC function and reveal that the source noise plays a decisive role in the classification-perception tradeoff. Finally, we implement a deep-learning-based image compression framework, incorporating multiple tasks related to distortion, perception, and classification. The experimental results coincide with the theoretical analysis and verify the effectiveness of our generalized IB in balancing various task objectives.

Coded distributed computing can reduce the communication load for distributed computing systems by introducing redundant computation and creating multicasting opportunities. However, the existing schemes require delicate data placement and output function assignment, which is not feasible when distributed nodes fetch data without the orchestration of a master node. In this paper, we consider the general systems where the data placement and output function assignment are arbitrary but pre-set. We propose two coded computing schemes, One-shot Coded Transmission (OSCT) and Few-shot Coded Transmission (FSCT), to reduce the communication load. Both schemes first group the nodes into clusters and divide the transmission of each cluster into multiple rounds, and then design coded transmission in each round to maximize the multicast gain. The key difference between OSCT and FSCT is that the former uses a one-shot transmission where each encoded message can be decoded independently by the intended nodes, while the latter allows each node to jointly decode multiple received symbols to achieve potentially larger multicast gains. Furthermore, based on the lower bound proposed by Yuet al., we derive sufficient conditions for the optimality of OSCT and FSCT, respectively. This not only recovers the existing optimality results but also includes some cases where our schemes are optimal while others are not.

Balancing diverse task objectives under limited rate is crucial for developing robust multitask deep learning (DL) models and improving performance across various domains. In this paper, we consider the lossy compression problem with human-centric and task-oriented metrics, such as perceptual quality and classification accuracy. We investigate two ternary relationships, namely, the rate-distortion-classification (RDC) and rate-perception-classification (RPC). For both RDC and RPC functions, we derive the closed-form expressions of the optimal rate for both binary and Gaussian sources. Notably, both RDC and RPC relationships exhibit distinct characteristics compared to the previous RDP tradeoff proposed by Blau et al. Then, we conduct experiments by implementing a DL-based image compression framework, incorporating rate, distortion, perception, and classification constraints. The experimental results verify the theoretical characteristics of RDC and RPC tradeoffs, providing information-theoretical insights into the design of loss functions to balance diverse task objectives in deep learning.

In this paper, we consider the general heterogeneous MapReduce system, where the file placement and Reduce function assignment are arbitrary but pre-set among all nodes (i.e., can not be designed by schemes). The storage and the computational capabilities for different nodes are not necessarily equal. We propose a universal CDC scheme, namely One-Shot Coded Transmission (OSCT), and establish the upper bound of the optimal communication load. The OSCT scheme encodes intermediate values into message blocks, each of which can be immediately and independently decoded by multiple intended nodes. We carefully design the bit-length of each message block to increase the multicasting gain. Furthermore, we provide a sufficient condition under which our scheme is optimal. To the best of our knowledge, this is the first work to investigate the general MapReduce problem with fixed data placement and Reduce function assignment.