Mathematical Optimization and Advanced Algorithms in Few-Shot and Zero-Shot Learning

Dear Colleagues,

The rapid advancement of Artificial Intelligence and Computer Vision has traditionally relied on the availability of massive, fully annotated datasets. However, learning in low-data regimes—specifically through few-shot learning (FSL) and zero-shot learning (ZSL)—remains a critical frontier. Overcoming the "data-hungry" nature of deep learning is essentially a complex mathematical challenge. It requires constructing robust mapping functions from limited support sets to query sets, synthesizing unseen class distributions via generative models, and performing rigorous structural alignment across diverse modalities.

This Special Issue in Mathematics aims to bridge the gap between pure/applied mathematics and advanced machine learning algorithms. We seek to explore the rigorous mathematical foundations that drive modern visual perception and low-data learning. Theoretical formulations, such as topological data analysis, manifold geometry in representation learning, probabilistic bounds in Generative Adversarial Networks (GANs), and the algebraic properties of continuous-time state space models (e.g., Mamba architectures) are of particular interest. By leveraging advanced mathematical tools like graph theory, optimal transport, and information theory, we can unlock new theoretical guarantees and performance bounds for cross-modal feature fusion.

We invite researchers to submit original research papers and comprehensive reviews that emphasize the mathematical modeling, algorithmic optimization, and theoretical analysis of AI systems operating under data constraints.

Topics of interest include, but are not limited to:

• Mathematical Foundations of Low-Data Regimes: Metric space learning, optimization landscapes, and generalization bounds for few-shot and zero-shot learning.
• Probabilistic and Generative Modeling: Optimization strategies, convergence analysis, and latent space geometry in GANs, VAEs, and diffusion models for unseen data generation.
• Geometry and Topology in AI: Manifold learning, capacity optimization, and geometry-aware frameworks for visual retrieval and representation.
• Graph Theory and Cross-Modal Alignment: Graph neural networks, structural alignment equations, and complex network analysis for multi-modal feature fusion.
• Algebraic and Continuous-Time Models: Mathematical properties, differential equations, and optimization of state space models (e.g., Vision Mamba) in machine learning.
• Information-Theoretic Approaches: Entropy bounds, mutual information maximization, and optimal transport in knowledge-driven open-world perception.

We look forward to receiving your contributions.

Dr. Yang Liu
Guest Editor

Manuscript Submission Information

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• few-shot learning (FSL)
• zero-shot learning (ZSL)
• mathematical foundations of machine learning
• manifold learning
• information theory
• graph theory
• graph neural networks
• generative modeling
• representation learning