Mathematics Theory and Mathematical Methods for Deep Generative Artificial intelligence

Dear Colleagues,

The investigation of mathematics theory and mathematical methods on deep generative artificial intelligence represents a cutting-edge research frontier with the tremendous potential to provide impetus to generative artificial intelligence capabilities. Deep generative artificial intelligence techniques, such as representation learning, zero-shot, one-shot, and few-shot learning, self-supervise learning, pre-training, and knowledge distillation, generative adversarial network, normalizing model, and generative diffusion model have demonstrated striking text, language, voice, image, and video sensing and understanding capabilities, while deep generative artificial intelligence is skilled in modeling the commonsense knowledge. The corresponding mathematical theories and methods are relatively primitive and cannot adapt to the rapid development of deep artificial intelligence. The growth of deep artificial intelligence is limited, and there are many uncertainties and unsolved mysteries.

The field of deep generative artificial intelligence has matured considerably, offering a reliable vehicle for sensing and understanding knowledge underlying a large number of datasets, empirically providing decision-making capabilities. Unfortunately, it faces challenges in terms of the correctness and rationality of formal description and the theoretical verification of methods and learning procedures. In contrast, we believe that mathematics theory and mathematical methods can provide formal description for the neural network construction and learning processing and accurately discuss the generalization capabilities by parameterizing the generative model and the whole training and test procedures, entailing the resolution of technical challenges for deep generative artificial intelligence.

There are numerous hotspot research directions in mathematics theory and mathematical methods for deep generative artificial intelligence. These include the following: 1) qualitatively and quantitatively describing the hidden representations; 2) the formal description and theoretical verification of the whole learning, validation, and testing process for deep neural networks; and 3) the mathematical formal description and theoretical analysis of various emerging deep generative learning paradigms and models. This Special Issue aims to push the sharing and discussion of recent progress and future trends in the collaborative development of mathematics theory and mathematical methods on deep generative artificial intelligence.

Dr. Jianwei Liu
Guest Editor

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• feature representation learning
• exploring the existence and uniqueness for the optimal and most general representation of learning specific domain knowledge
• formal description and theoretical verification of the complete learning, validation, and testing process for deep neural networks (including inputting external data, mini-batch training process, validation process, and testing process)
• mathematics theory and mathematical methods for self-supervise learning
• mathematics theory and mathematical methods for zero-shot, one-shot, and few-shot learning
• mathematics theory and mathematical methods for the diffusion model
• mathematics theory and mathematical methods for causal reasoning
• the intrinsic transfer mechanism for pre-training and the intrinsic distillation mechanism for large models
• geometric methods for deep generative model
• thermodynamic and statistical physical models for deep generative model