OpenAI 发布解决昨日长期困扰研究人员的三个块块式数学问题。 一个是惊讶地否定了"衡量时间假说(ETH)"，这是计算机科学中一个持久的假设，它对我们理解什么是难以计算的有着很大的作用。
与以前来自前沿实验室的证明一样，科学界也以惊愕和沮丧的混合方式作出反应。 Anthropic数学家勒文特·阿尔波赫(Levent Alpöge)建议，OpenAI是用先前已有的工作来建立其解决方案的，数小时后，Anthropic之后，发布自行反驳ETH.
然而，OpenAI的过程正在演变。 这一次，实验室对所涉及的三个学科中的每一个学科的发布结构都不同：数学家们把工作丢在了GitHub上；计算机科学家们组成了一个工作组，要求公开分享证明，OpenAI资助一个会议来讨论这些证明；物理学家们组成了一个工作组来决定他们的结果如何是发布。
麻省理工学院的Ryan Williams教授是一位计算机科学家，他正在组织他的领域对新发现的反应。 威廉姆斯的工作重点是这些计算复杂性的问题，他批评了OpenAI过去的做法，称今年10月早些时候它的证据倾倒是“DDOS攻击数学家 ”。
然而，他同意与前沿实验室合作，以帮助牧羊人提出对现场至关重要的想法，他告诉了TechCrunch. 实验室要求他与UC圣迭戈计算机科学家罗素·伊帕格利亚佐和拉马莫汉·帕图里一起帮助解释解决方案，后者于1999年首次发表了ETH.
他们的第一步是发布一封公开信，呼吁对这些问题感兴趣的科学家提供反馈，并讨论围绕AI对其工作的贡献的规范。
“[OpenAI的证明某些部分也许可以说是例行公事，但是是的，有两个或三个外观外观的部分，而正是这些部分让我觉得，哇，这是整个社区需要共同解决的问题，”威廉姆斯告诉了TechCrunch。
你和P对NP有关系吗？
ETH是被称为P vs NP的更广泛的一类问题的一部分，它拥有数十年来的计算机科学动画和许多其他领域。 从减少的角度来说，研究者们正在试图理解，任何能够轻易核实(NP)的解决方案(P)也能轻易解决(P)的问题。
一个简单的例子是游戏Sodoku：一个谜题的解决方案一旦到位，就可以快速验证，但找到解决方案需要时间。 这种动态在一系列重要问题上是真实的，其洞察力支撑着密码系统：当您有编码消息的密钥时，您可以打开它，但实际上破解一个有效的代码需要太长的时间才能有用。
然而，科学家尚未证明是否始终如此。 “P = NP表示，不仅在数独解决方案存在时，“P = NP 主张，对于每一个你能够快速核实的问题都是如此——如果你能够快速核实，你可以快速解决。 因此，这似乎太好，不是事实。”
所以大多数科学家都认为P Q NP。 ETH为此提供了证据。 基本上称，即使是最快的计算机算法也需要指数化的更多时间来寻找一个解决方案，因为变量的数量会随着特定类别的棘手逻辑谜题而增长。
来自OpenAI和Anthropic的声称是他们的模型提出了算法，在"次责任"时间解决这些谜题，意思比以前认为可能的速度更快。 如果是真的，他们可能已经证明了EFT是虚假的——从科学角度反驳了它——也许为一般执行P=NP的算法开辟了一条路径。
“每个计算机科学家也许应该对P=NP的可信度增加一点加权，但一个人的加权可能有所不同，” Williams 称。 “我确实认为，这引起了很多我们所认为的直觉的疑问，这些直觉是。.....多么容易理解的。 我也认为，这或许也不是最后的答案。 我认为OpenAI的算法不可能是你们可以得到的最佳算法。
计算机科学家今后的工作
如果人工智能实验室的声称已经证明这是错误的
“这就是我要求或推动OpenAI支持召开关于这个会议的部分原因——它将影响许多研究者的工作，我们需要找出，除了理解算法，接下来会发生什么。 我们必须明白，与我们以前相比，基金会应该如何改变？”
在科学关切之前，还有网络安全问题。 威廉姆斯·称认为，改进后的算法可能意味着依赖于某些密钥大小的加密系统可以被认为是破损的。 因此，他向OpenAI科学提出的第一个问题之一是，Dan Roberts“如果他们检查过这是否影响到任何密码系统。.....现在有什么不安全的情况吗？他们有理由相信这并不意味着任何间歇。
这一新的科学发现的AI范式仍然是在进行中的工作，但威廉姆斯·称尽管有真正的担忧，他还是很乐观，特别是对培养下一代科学家。 作为一个从事高水平数学的计算机科学家，也许使他的调整比纯数学家更容易。
然而，他称 AI却在“强迫人们对他们所从事的工作更加雄心勃勃
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OpenAI released solutions to three blockbuster math problems that have long vexed researchers yesterday. One was a surprise rejection of the Exponential Time Hypothesis (ETH), a durable assumption in computer science that plays a large role in how we understand what is difficult to compute.
As with previous proof-drops from the frontier lab, scientific communities responded with a mixture of thrill and dismay. Anthropic mathematician Levent Alpöge suggested that OpenAI was basing its solutions from pre-existing work, and hours later, Anthropic subsequently released its own refutation of ETH.
However, OpenAI’s process is evolving. This time, the lab structured its releases differently for each of the three disciplines involved: Mathematicians got the work dropped on GitHub; the computer scientists formed a working group, asked for the proofs to be shared publicly and OpenAI to fund a conference to discuss them; the physicists formed a working group that will determine how their result will be released.
MIT Professor Ryan Williams is the computer scientist who is organizing his field’s response to the new finding. Williams, whose work focuses on these questions of computational complexity, has criticized OpenAI’s approach in the past, calling its proof dump earlier this October a “DDOS attack on mathematicians.”
However, he agreed to collaborate with the frontier labs in order to help shepherd ideas that are vital to the field, he told TechCrunch. The lab asked him to help interpret the solution, along with UC San Diego computer scientists Russell Impagliazzo and Ramamohan Paturi, who first published the ETH in 1999.
Their first step was to release an open letter calling for feedback from scientists interested in these problems and a discussion of the norms around AI contributions to their work.
“Some parts [of OpenAI’s proof] are, maybe you could say routine, but then yes, there are two or three alien-looking parts, and it’s exactly these parts that that I saw that made me think, wow, this is something that the whole community needs to work on together,” Williams told TechCrunch.
Are you down with P vs NP?
The ETH is part of a broader class of problems known as P vs NP, which has animated computer science and many other fields for decades. Reductively, researchers are trying to understand if any problem whose solution can be easily verified (NP) can also be easily solved (P).
A simple example is the game Sodoku: Once a solution to a puzzle is in place, it can be quickly verified, but finding the solution is time-consuming. That dynamic is true across a range of important problems, and the insight underpins cryptographic systems: When you have the key to an encoded message, you can reveal it, but actually cracking an effective code takes too long to be useful.
However, scientists have yet to prove whether that is always true. “P = NP is saying that, not only can you verify Sudoku solutions when they exist, you can just generate them,” Williams said. “P = NP is asserting that this is true for every single problem you can verify quickly — if you can verify it quickly, you can solve it quickly. So this just seems too good to be true.”
That’s why most scientists assume that P ≠ NP. ETH provided evidence for that. It basically says that even the fastest computer algorithm needs exponentially more time to find a solution as the number of variables grow in a specific class of tricky logic puzzle.
The claims from OpenAI and Anthropic is that their models have come up with algorithms that solve those puzzles in “sub-exponential” time, meaning faster than the speeds previously thought possible. If true, they may have proven the EFT to be false — refuted it, in scientific terms — and maybe opened up a path for algorithms that generally perform P = NP.
“Every computer scientist should probably put a little more weight on the plausibility of P = NP, but one’s weight may vary,” Williams said. “I do think that it kind of calls into question a lot of the intuitions that we thought we had about … how tractable [hard NP problems] are. I also think that this is probably not the final answer either. I don’t think that OpenAI’s algorithm could possibly be the best algorithm you can get.”
The work ahead for computer scientists
The durability of ETH has lead to it being included in many scientific papers over the past decade that will need to be revisited if the AI labs claims that they’ve proven it wrong holds up, Williams said.
“This is partly why I was asking or pushing OpenAI to support a conference on this — it’s going to affect many researchers’ works, and we need to figure out, okay, what happens next besides understanding the algorithms. We need to understand, how should the foundations change compared to what we had before?” he said.
Before scientific concerns, there are cybersecurity questions. Williams said that an improved algorithm could imply that cryptographic systems relying on certain key sizes could be considered broken. So one of the first questions he asked OpenAI science lead Dan Roberts “was if they had checked that this affects any crypto systems … is anything insecure now? And apparently, they checked, and they were reasonably confident that this didn’t … imply any breaks.”
This new AI paradigm of scientific discovery is still a work in progress, but Williams says he is optimistic despite real concerns, particularly about training the next generation of scientists. Being a computer scientist who does high level math has perhaps made the adjustment easier for him than for pure mathematicians.
Still, he says AI is “forcing people to be a little more ambitious about the kind of work that they do, and to think more deeply about, okay, if all the things I used to work on are now low hanging fruit for AI, how can I raise the bar for the kind of scientific questions I want to ask?”
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