Anticipated to substantially enhance communication efficiency, semantic communication emerges as a novel communication paradigm. Considering the constraints of wireless resources, it becomes crucial to design resource allocation schemes that ensure efficient data transmission in a semantic communication system. This paper proposes a resource allocation scheme that maximizes the energy efficiency of the entire semantic network, ensuring the performance of semantic tasks within the confines of limited wireless resources. Specifically, we begin by defining the energy efficiency measurement metrics in semantic communication systems and subsequently optimize it through the joint allocation of semantic symbols, bandwidth, and power. This problem is formulated as an optimization problem. Given the absence of a mathematical closed-form expression for semantic similarity, an effective solution to the problem is proposed via a whale optimization algorithm with a penalty strategy, targeting joint semantic symbols assignment and resource allocation. Simulation results substantiate the effectiveness and feasibility of the proposed scheme.

Existing deep learning methods for graph matching(GM) problems usually considered affinity learningto assist combinatorial optimization in a feedforward pipeline, and parameter learning is executed by back-propagating the gradients of the matching loss. Such a pipeline pays little attention to the possible complementary benefit from the optimization layer to the learning component. In this paper, we overcome the above limitation under a deep bidirectional learning framework.Our method circulates the output of the GM optimization layer to fuse with the input for affinity learning. Such direct feedback enhances the input by a feature enrichment and fusion technique, which exploits andintegrates the global matching patterns from the deviation of the similarity permuted by the current matching estimate. As a result, the circulation enables the learning component to benefit from the optimization process, taking advantage of both global feature and the embedding result which is calculated by local propagationthrough node-neighbors. Moreover, circulation consistency induces an unsupervised loss that can be implemented individually or jointly to regularize the supervised loss. Experiments on challenging datasets demonstrate the effectiveness of our methods for both supervised learning and unsupervised learning.