论文标题
非线性PDES的统计力学方法
Non-linear PDEs approach to statistical mechanics of Dense Associative Memories
论文作者
论文摘要
密集的关联记忆（大坝）是用于模式识别任务的人工智能中的广泛模型；在计算上，事实证明，它们对对抗性输入和理论上具有鲁棒性，从而利用了旋转玻璃系统的类比，通常通过统计机械工具对其进行处理。在这里，我们基于非线性PDE开发分析方法来研究其功能。特别是，我们证明了涉及大坝分区函数和宏观可观察物的差异身份，可用于系统的定性和定量分析。这些结果可以更深入地理解大坝的基本机制，并为其研究提供跨学科的工具。
Dense associative memories (DAM), are widespread models in artificial intelligence used for pattern recognition tasks; computationally, they have been proven to be robust against adversarial input and theoretically, leveraging their analogy with spin-glass systems, they are usually treated by means of statistical-mechanics tools. Here we develop analytical methods, based on nonlinear PDEs, to investigate their functioning. In particular, we prove differential identities involving DAM partition function and macroscopic observables useful for a qualitative and quantitative analysis of the system. These results allow for a deeper comprehension of the mechanisms underlying DAMs and provide interdisciplinary tools for their study.
