是什么让人们认为神经网络比现有模型具有更强的计算能力？
我在维基百科上读到，在任意实数/有理数域上定义的神经网络函数（以及算法模式和推测的“反递归”模型）比我们今天使用的计算机具有更多的计算能力。当然，这是俄语维基百科（ru.wikipedia.org）的一个页面，可能没有得到适当的证明，但这并不是此类谣言的唯一来源。
现在，我真正不明白的是：如何才能字符串重写机（神经网络与图灵机一样都是字符串重写机；只是编程语言不同）比通用的 U 机更强大？
是的，描述性工具确实不同，但事实是此类的任何函数都可以（容易或不容易）变成合法的图灵机。我错了吗？我错过了什么重要的事情吗？
人们这样说的原因是什么？我确实知道不可判定性的现象如今已被广泛接受（尽管根据我所读到的内容并没有得到一致证明），但我并没有真正看到神经网络能够解决该特定问题的最小机会。
插件：根据我读过的内容，没有得到一致的证明 - 我的意思是你可能想看看 A. Zenkin（俄罗斯数学家）在 90 年代中期之后的论文，他在其中令人信服地假设 G. Cantor 的概念是错误的，包括超限集、不可数集、对角化方法（图灵用于证明不可判定性的方法）以及其他可能的方法。就连 Goedel 的不完备定理也仅在 21 世纪就以正确的方式被证明了。这只是为了将 Zenkin 的工作添加到帖子中，因为我不知道这些知识在 CS 社区中有多广泛，所以如果这看起来确实很愚蠢，请原谅我。
谢谢你！
I've read in Wikipedia that neural-network functions defined on a field of arbitrary real/rational numbers (along with algorithmic schemas, and the speculative `transrecursive' models) have more computational power than the computers we use today. Of course it was a page of russian wikipedia (ru.wikipedia.org) and that may be not properly proven, but that's not the only source of such.. rumors
Now, the thing that I really do not understand is: How can a string-rewriting machine (NNs are exactly string-rewriting machines just as Turing machines are; only programming language is different) be more powerful than a universally capable U-machine?
Yes, the descriptive instrument is really different, but the fact is that any function of such class can be (easily or not) turned to be a legal Turing-machine. Am I wrong? Do I miss something important?
What is the cause of people saying that? I do know that the fenomenum of undecidability is widely accepted today (though not consistently proven according to what I've read), but I do not really see a smallest chance of NNs being able to solve that particular problem.
Add-in: Not consistently proven according to what I've read - I meant that you might want to take a look at A. Zenkin's (russian mathematician) papers after mid-90-s where he persuasively postulates the wrongness of G. Cantor's concepts, including transfinite sets, uncountable sets, diagonalization method (method used in the proof of undecidability by Turing) and maybe others. Even Goedel's incompletness theorems were proven in right way in only 21-st century.. That's all just to plug Zenkin's work to the post cause I don't know how widespread that knowledge is in CS community so forgive me if that did look stupid.
Thank you!
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从我所做的少量研究来看，大多数关于反图灵系统的主张，或者康托的对角化证明的不正确性等，我们可以说，在合法的数学圈子里都是“有争议的”。像“crank”这样的词经常被使用。
显然，强有力的丘奇-图灵论点尚未得到证实，但正如您所指出的，确实没有充分的理由相信人工神经网络构成了超越一般递归/UTM/lambda 演算/等的计算能力。
From what little research I've done, most of these claims of trans-Turing systems, or of the incorrectness of Cantor's diagonalization proof, etc. are, shall we say, "controversial" in legitimate mathematical circles. Words like "crank" get thrown around frequently.
Obviously, the strong Church-Turing thesis remains unproven, but as you pointed out there's really no good reason to believe that artificial neural networks constitute computational capabilities beyond general recursion/UTMs/lambda calculus/etc.
从理论的角度来看，我认为你是绝对正确的——神经网络几乎没有提供什么新的或不同的东西。
从实践的角度来看，神经网络只是将解决方案转换为并行执行自然且容易的形式的一种方式，而图灵机本质上是顺序的，并行执行其序列相对困难。事实上，过去几十年来，CPU 开发中所做的大部分工作基本上都是在寻找并行执行代码的方法，同时保持代码按顺序执行的错觉。现代CPU中的很多硬件都致力于维持这种错觉，而并行执行变得明确的程度在很大程度上表明维持这种错觉已经变得异常昂贵。
From a theoretical viewpoint, I think you're absolutely correct -- neural networks provide very little that's new or different.
From a practical viewpoint, neural networks are simply a way of casting solutions into a form where parallel execution is natural and easy, whereas Turing machines are sequential in nature, and executing their sequences in parallel is relatively difficult. In fact, most of what's been done in CPU development over the last few decades has basically been figuring out ways to execute code in parallel while maintaining the illusion that it's executing in sequence. A lot of the hardware in a modern CPU is devoted to maintaining that illusion, and the degree to which parallel execution has become explicit is mostly an admission that maintaining the illusion has become prohibitively expensive.
任何“证明”康托尔的对角线方法不起作用的人都只能证明他们自己的无能。比照。 Wilfred Hodges 的一位编辑回忆起一些毫无希望的论文对于这些尝试出了什么问题，他给出了令人惊讶的同情解释。
您可以提供超图灵神经网络的推测性描述，就像您可以提供其他类型的超图灵计算机的推测性描述一样：超级计算是可能的这一想法没有任何不连贯的地方，并且对机械超级计算机的推测性描述已经在超级计算机被规定具有无限精细的雕刻，为停止机器编码一个神谕：这种机器的存在与牛顿力学一致，尽管不是量子力学。相反，丘奇-图灵论点说它们无法被建造，并且有两个理由相信丘奇-图灵论点是正确的：
要点是丘奇-图灵论题的真实性是一个经验事实，而不是一个数学事实，我们可以确信它是真实的，但不是确定性的。
Anyone who "proves" that Cantor's diagonal method doesn't work proves only their own incompetence. Cf. Wilfred Hodges' An editor recalls some hopeless papers for a surprisingly sympathetic explanation of what kind of thing is going wrong with these attempts.
You can provide speculative descriptions of hyper-Turing neural nets, just as you can provide speculative descriptions of other kinds of hyper-Turing computers: there's nothing incoherent in the idea that hypercomputation is possible, and speculative descriptions of mechanical hypercomputers have been made where the hypercomputer is stipulated to have infinitely fine engravings that encode an oracle for the Halting machine: the existence of such a machine is consistent with Newtonian mechanics, though not quantum mechanics. Rather, the Church-Turing thesis says that they can't be constructed, and there are two reasons to believe the Church-Turing thesis is correct:
The main point is that the truth of the Church-Turing thesis is an empirical fact, and not a mathematical fact. It's one that we can have confidence is true, but not certainty.
从外行人的角度来看，我发现
From a layman's perspective, I see that
您可能对 S. Franklin 和 M. Garzon 的神经可计算性感兴趣。有一个 在 Google 上预览。它讨论了神经网络的计算能力，并指出有传言神经网络比图灵机更强大。
You may be interested in S. Franklin and M. Garzon, Neural computability. There is a preview on Google. It discusses the computational power of neural nets and also states that it is rumored that neural nets are strictly more powerful than Turing machines.