无网络的AI
AI without networks
AI总结：
本文提出一种无网络、无参数、透明的生成式Hilbert框架，通过推广数据插值方法实现机器学习，并在鱼群行为建模、倒立摆与logistic映射控制及Riemann Zeta函数零点预测中验证了其有效性。
摘要：
当代人工智能（AI）立足于两大支柱：大规模训练数据语料库和具有大量参数的人工神经网络（ANN）。数据语料库用于表征世界的复杂性和异质性。网络的作用则较不透明，因为网络参数和输出对训练数据和输入的依赖关系难以捉摸。这引发了从技术科学到法律伦理等一系列问题。我们提出假设：完全可以在不使用网络的情况下实现一种透明的机器学习方法。通过推广一种无参数、统计一致的数据插值方法（我们对其进行了详细的理论分析），我们开发了一个融合生成建模的无网络AI框架。我们用来自三个不同学科——动物行为学、控制理论和数学——的例子来展示这一框架。将我们的生成式Hilbert框架应用于小型鱼群游动轨迹，其表现优于最先进的传统数学行为模型和当前基于ANN的模型。我们通过将倒立摆和受驱logistic映射稳定在不稳定不动点附近，展示了基于纯数据插值的控制。最后，我们通过预测Riemann Zeta函数的零点展示了一个数学应用，取得了与transformer网络相当的性能。我们并不是说所提出的框架总能优于网络，因为过参数化网络可以进行插值。然而，我们的框架在理论上可靠、透明、确定性且无参数：值得注意的是，它不需要任何计算昂贵的训练，不涉及优化，没有模型选择，并且易于复现和移植。我们还提出了一种基于该框架的易于计算的信用分配方法，以帮助应对生成式AI带来的伦理法律挑战。
英文摘要：
Contemporary Artificial Intelligence (AI) stands on two legs: large training data corpora and many-parameter artificial neural networks (ANNs). The data corpora are needed to represent the complexity and heterogeneity of the world. The role of the networks is less transparent due to the obscure dependence of the network parameters and outputs on the training data and inputs. This raises problems, ranging from technical-scientific to legal-ethical. We hypothesize that a transparent approach to machine learning is possible without using networks at all. By generalizing a parameter-free, statistically consistent data interpolation method, which we analyze theoretically in detail, we develop a network-free framework for AI incorporating generative modeling. We demonstrate this framework with examples from three different disciplines - ethology, control theory, and mathematics. Our generative Hilbert framework applied to the trajectories of small groups of swimming fish outperformed state-of-the-art traditional mathematical behavioral models and current ANN-based models. We demonstrate pure data interpolation based control by stabilizing an inverted pendulum and a driven logistic map around unstable fixed points. Finally, we present a mathematical application by predicting zeros of the Riemann Zeta function, achieving comparable performance as a transformer network. We do not suggest that the proposed framework will always outperform networks as over-parameterized networks can interpolate. However, our framework is theoretically sound, transparent, deterministic, and parameter free: remarkably, it does not require any compute-expensive training, does not involve optimization, has no model selection, and is easily reproduced and ported. We also propose an easily computed method of credit assignment based on this framework, to help address ethical-legal challenges raised by generative AI.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
