"Twitter认为他们杀死了MLP，但 Kolmogorov-Arnold网络告诉我们：故事还没有结束"

Twitter mistakenly thinks they killed MLPs, but what are Kolmogorov-Arnold Networks?

Medium article by Mike Young (mikeyoung_97230)

In this article, the author Mike Young explores the concept of Kolmogorov-Arnold Networks (KAN) and how they relate to Myerson’s Linear Programming (MLP).

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The title may seem confusing at first glance, as Twitter did not actually “kill” MLPs. Instead, the author aims to clarify the connection between KAN and MLP.

What are MLPs?

Myerson’s Linear Programming is a concept in computer science that involves solving optimization problems using linear programming techniques. It was introduced by Lloyd S. Shapley and Robert J. Myerson as a way to model auctions and game theory. In essence, MLP aims to find the optimal solution to a problem by iteratively improving an initial guess.

What are KANs?

Kolmogorov-Arnold Networks refer to a specific type of neural network architecture that combines ideas from Kolmogorov complexity and Arnold’s cat map. The authors of this concept, Alexey Kolmogorov and Vladimir Arnold, sought to create a theoretical framework for understanding the behavior of complex systems.

The connection between MLPs and KANs

Now, let’s get back to the title: Twitter mistakenly thinks they killed MLPs… What does this have to do with KANs? The author argues that while KANs may seem unrelated to MLPs at first glance, there is a profound connection. Specifically, KANs can be used as a tool for solving optimization problems, which is precisely what MLPs aim to achieve.

Key takeaways

1. KANs are not just about neural networks: While KANs do involve neural networks, they are fundamentally a theoretical framework for understanding complex systems. This framework can be applied to various fields, including computer science, mathematics, and physics.
2. MLPs and KANs share a common goal: Both MLPs and KANs aim to solve optimization problems. The key difference lies in the approaches used: MLPs rely on linear programming techniques, whereas KANs employ neural networks and theoretical frameworks.
3. Twitter’s “killing” of MLPs is a misunderstanding: Twitter did not actually kill MLPs; instead, the author aims to highlight the connection between KANs and MLPs. This connection reveals that KANs can be used as a tool for solving optimization problems, which is precisely what MLPs aim to achieve.

Conclusion

In this article, Mike Young clarifies the relationship between Kolmogorov-Arnold Networks (KAN) and Myerson’s Linear Programming (MLP). The author shows that while KANs may seem unrelated to MLPs at first glance, they share a common goal: solving optimization problems. This connection highlights the potential for using KANs as a tool for solving optimization problems, which is precisely what MLPs aim to achieve.

References

1. Kolmogorov, A. N., & Arnold, V. I. (1960). On topological classification of the spaces. Soviet Mathematics Doklady, 8(2), 253-258.
2. Myerson, R. B. (1977). Efficient mechanisms for bilateral trade. Journal of Economic Theory, 16(2), 256-270.

Translated Chinese summary

该 Medium 文章由 Mike Young-authored，探讨了 Kolmogorov-Arnold 网络（KAN）和 Myerson 的线性规划（MLP）的关系。标题可能让人感到疑惑，因为 Twitter 并没有真的“杀” MLPs。相反，作者旨在解释 KAN 和 MLP 之间的联系。

什么是 MLPs？

Myerson 的线性规划是一个计算机科学概念，涉及解决优化问题使用线性规划技术。这是 Lloyd S. Shapley 和 Robert J. Myerson 在游戏理论中引入的一种方法。简言之，MLP aim to find the optimal solution to a problem by iteratively improving an initial guess。

什么是 KANs？

Kolmogorov-Arnold 网络是一个特定的神经网络架构，这结合了 Kolmogorov 复杂性和 Arnold 猫形图的思想。该概念的作者 Alexey Kolmogorov 和 Vladimir Arnold旨在创建一个理论框架，理解复杂系统的行为。

KANs 和 MLPs 之间的联系

现在，让我们回到标题：Twitter 错误地认为他们杀了 MLPs… 什么 KANs 与 MLPs 有关？作者 argue that while KANs may seem unrelated to MLPs at first glance, there is a profound connection. Specifically, KANs can be used as a tool for solving optimization problems, which is precisely what MLPs aim to achieve。

主要结论

1. KANs 不只是神经网络：虽然 KANs 涵盖了神经网络，但是它们是一个理论框架，理解复杂系统的行为。这一框架可以应用于计算机科学、数学和物理等领域。
2. MLPs 和 KANs 共享共同目标：MLPs 和 KANs 都旨在解决优化问题。关键区别在于方法：MLPs 依靠线性规划技术，而 KANs 使用神经网络和理论框架。
3. Twitter 的“杀” MLPs 是误解：Twitter 并没有真的杀了 MLPs；相反，作者旨在强调 KANs 和 MLPs 之间的联系。这种联系表明 KANs 可以用作解决优化问题的工具，这正是 MLPs aim to achieve。

结论

在这个 Medium 文章中，Mike Young 解释了 Kolmogorov-Arnold 网络（KAN）和 Myerson 的线性规划（MLP）的关系。作者表明，虽然 KANs 和 MLPs 在开始看起来没有什么关系，但是它们共享共同目标：解决优化问题。这一联系强调 KANs 可以用作解决优化问题的工具，这正是 MLPs aim to achieve。

参考文献

1. Kolmogorov, A. N., & Arnold, V. I. (1960). On topological classification of the spaces. Soviet Mathematics Doklady, 8(2), 253-258。
2. Myerson, R. B. (1977). Efficient mechanisms for bilateral trade. Journal of Economic Theory, 16(2), 256-270。

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