Synthetic Gradient Optimization-Based Implicit Amortized Bayesian Meta-Learning for Few-Shot Pumi Spectrographic Image Recognition

Meta-learning provides a promising solution to the issue of insufficient training samples in Pumi spectrogram recognition. However, capturing model uncertainty remains a critical challenge, particularly for tasks influenced by lexical ambiguities. To overcome this problem, we propose a novel method, Synthetic Gradient Optimization-Based Implicit Amortized Bayesian Meta-Learning (SGO-IABML), which captures model uncertainty by evaluating posterior distributions within a hierarchical Bayesian framework, thereby facilitating few-shot Pumi spectrogram recognition. Specifically, SGO-IABML reformulates meta-learning as a bi-level variational inference problem, leveraging information bottleneck principles. At the lower level, a generative inference module is developed to implicitly model task-specific variational posteriors, thereby enhancing the model’s expressiveness. Given the lack of analytical forms for implicit distributions, we derive the Fenchel-Bayesian Bound Theorem to measure the divergence between arbitrary distributions. For the meta-learning of variational parameters, SGO-IABML constructs a synthetic gradient optimizer, integrating prior gradient information to facilitate rapid adaptation to new tasks. At the upper level, the model is calibrated by estimating the local geometry of the posterior distribution, utilizing the Generalized Gauss-Newton Matrix to capture the directional sensitivity of the loss function. Comprehensive experimental results on Pumi spectrograms demonstrate that SGO-IABML achieves state-of-the-art performance in generalization, calibration, expressiveness, versatility, and cross-domain adaptability. Furthermore, ablation studies confirm the contribution of each component to the overall performance improvement.