So today was a rather fascinating day as we got Denny Joe, the person who is the founder and lead of the reasoning team at Google DeepMind, with a profound statement that fundamentally changes our understanding of Transformers. He stated that we have mathematically proven that Transformers can solve any problem, provided they are allowed to generate as many intermediate reasoning tokens as needed. Remarkably, constant depth is sufficient. So this is where we take a look at this paper they are referring to called Chain of Thought Empowers Transformers to Solve Inherently Serial Problems. So of course most of you know what Chain of Thought prompting is, but for those of you who don't, here's a quick example. Let's imagine you're asking a friend to help you plan a birthday party. With standard prompting, you might ask, What kind of party should I throw for my 30th birthday? and your friend might simply reply, You should have a beach barbecue. Now while that's helpful, you don't know why they suggested that or how they came to that conclusion. Now with Chain of Thought

prompting. You'd ask what kind of party should I throw for my 30th birthday, but this time you add, can you walk me through your thinking. And here's where your friend might respond, okay, let's think about this one. It's your 30th, so it should be something special but not too wild. Two, you love the outdoors and it's summertime. Three, you have a lot of friends, so you need space for everyone. Four, you enjoy casual relaxed environments. Five, cooking is one of your hobbies. And now putting all that together, I think a Beach barbecue would be perfect. You can enjoy the outdoors, have plenty of space for friends, keep it casual, and show off your grilling skills. Now this is Chain of Thought in action. Instead of just getting an answer, you see the reasoning process. It's like the difference between a teacher just marking your math homework right or wrong versus showing you how to solve the problem step by step. Now this approach helps in complex problem solving because it allows us to see and check each step of the AI's reasoning.

just like we can follow our friends' thought process in planning the party, it's especially useful when dealing with tricky questions where the reasoning is as important as the final answer. So, why is this stuff even important? It's because Transformers actually have inherent limitations with their design. So, for Transformers, Transformers are like the brain of modern AI language models. Think of them as incredibly smart text processors that can understand and generate human-like text. Now, Transformers have a unique superpower, and this is their ability to handle many pieces of information at the same time. It's like having a team of expert researchers who can all read different parts of a book simultaneously and then instantly share their understanding with each other. However, Transformers struggle with tasks that need to be done step by step, one after the other. For example, Transformers might struggle with a math problem that requires multiple steps to solve or a logic puzzle where each clue builds on the previous one. Their design is to look at everything at once, which is great for many tasks but not ideal for problems that need a chain of reasoning.

this limitation is why the Chain of Thought prompting is so important. It's like giving our Factory a blueprint that shows the step-by-step process for building a house. By encouraging the AI to show its work, we're helping it overcome its natural limitation with sequential tasks. Now, let's actually break down this statement and why it's truly groundbreaking regarding the paper Transformers solving any problem. When the authors state that Transformers can solve any problem, they are making a bold claim about the potential universality of Transformers as a computational model. Transformers have already proven their prowess in natural language processing and a variety of other tasks. However, their ability to solve any problem has always been viewed within certain limitations based on their design as parallel processing units. Now, to say that a Transformer can solve any problem implies that it has the potential to emulate the functionality of a general-purpose computer or, more technically, a Turing machine, provided it is configured correctly. This is a sweeping claim because it suggests that Transformers are not just specialized tools for text generation or language

understanding, but they could, in theory, be applied to any domain of computation, ranging from mathematical problem-solving to complex decision-making tasks. However, and here's where you should pay attention, there's a critical qualification in this claim: the Transformer needs to be allowed to generate as many intermediate reasoning tokens as needed. This caveat actually highlights the importance of intermediate reasoning in the problem-solving process. The implication here is that while Transformers can solve any problem, the solution may not be direct or immediate. Instead, it requires a gradual, step-by-step approach where the model builds up its understanding and solution iteratively using a sequence of intermediate steps. Now, let's talk about where he says, provided they are allowed to generate as many intermediate reasoning tokens as needed. The concept of intermediate reasoning tokens is central to this discussion and is what underpins the Chain of Thought mechanism. To understand this better, let's draw an analogy to human reasoning. When humans solve a complex problem, such as a mathematical proof or a logical puzzle, they do not jump directly to the answer.

instead, they go through a series of intermediate steps. Each step is reasoned out based on the results or insights obtained from the previous steps. These intermediate steps, which might involve breaking down the problem into smaller sub-problems or formulating partial solutions, are crucial for arriving at the final answer. Similarly, for Transformers to solve complex problems, they need to be capable of generating these intermediate reasoning steps, which in the context of AI are referred to as tokens. Each token represents a part of the model's thought process or reasoning chain that builds upon the previous tokens. This chain is not predefined or fixed; it can be dynamically constructed based on the problem at hand and the specific reasoning path the model takes. The Chain of Thought technique is essentially about guiding the model to think step by step rather than attempting to leap directly to the solution. Instead of providing just an answer, the model outputs a series of intermediate tokens that outline its reasoning process. This approach not only provides a more interpretable way to understand how the model reaches a

decision, but it also dramatically expands the types of problems the Transformer can handle. It's like giving the model the ability to explain its work as it goes along, which is crucial for solving more intricate and challenging problems that cannot be addressed through simple parallel computation. Now let's talk about the last part, which is the most surprising. Constant depth is sufficient in the realm of neural networks. Depth refers to the number of layers in the model. The depth of a network is often equated with its capacity to learn complex representations of data. More layers generally mean more complex features can be learned; therefore, deeper models have been the go-to solution for tackling harder problems because they have more computational power to process and abstract data in multiple steps. However, deeper models also come with increased computational cost, more memory usage, and longer training times. They are more complex to design, optimize, and maintain, which poses practical challenges in deploying them in real-world scenarios. Hence, the idea that a Transformer with a constant fixed and relatively small number of layers, meaning it doesn't get

deeper as the problems get more complex. If it could still solve any problem, it is quite radical. So, in summary, what the authors are saying is that you don't need to stack more and more layers onto a Transformer to increase its problem-solving capability. Instead, if you enable the model to generate as many intermediate steps (tokens) as necessary, it can achieve the same computational outcomes. This is because these intermediate steps effectively unroll the complexity over time rather than embedding it in a deep stack of layers. The constant depth allows the model to compute one step of the reasoning process at a time, but by generating a sequence of such steps, it can build up to solve very complex problems. So, how does this actually change our understanding of AI? This concept challenges the conventional wisdom that deeper models are inherently better for more complex tasks. Instead, it suggests that we can build highly capable models that remain shallow but leverage the power of generating intermediate reasoning steps to perform sequential computation. The mathematics behind this claim, as explained in the paper, draws on

the concept of circuit complexity. The authors use circuit complexity to explain why K is so powerful. They show that without Co Transformers can only solve problems that belong to simpler classes like ac0, which are solvable in parallel without needing much sequential computation. However, when K is introduced, the class of problems that Transformers can solve expands dramatically. With coot, a Transformer can simulate the behavior of circuits that solve problems in the P poly class. This is a vast improvement because it encompasses a wide range of problems that require both parallel and serial computation. Now, I do believe that this post went quite viral as on a first glance, the statement that Transformers can solve any problem under certain conditions does sound ambitious and might lead some to think about the potential for artificial general intelligence. However, it is important to clarify what the authors are actually saying in the context of this paper and whether this really implies AGI or not. When the authors state that Transformers can solve any problem, they are specifically referring to the theoretical capabilities of Transformers to simulate certain types of computations when

equipped with the Chain of Thought mechanism and allowed to generate as many intermediate steps as needed. This means that in theory, Transformers can perform any computation that a circuit of arbitrary size can perform, given enough time and steps. This is a significant finding that demonstrates the flexibility and power of Transformers enhanced by K. So does this mean that Transformers with Chain of Thought are AGI? I mean, not really, but it's still pretty insane. So let's actually take a look at things in more detail. DET. The claim made by the authors is primarily about the theoretical expressiveness of Transformers. In theory, they show that Transformers with a Chain of Thought can compute anything that can be represented by a Boolean Circuit of polynomial size. This theoretical result is akin to saying that a Transformer could simulate any computational process, given enough steps. However, this is not the same as saying a Transformer can operate with the broad intelligence, adaptability, and understanding that we associate with AGI. The author's claim can be likened to saying that these Transformers have a form of computational universality in

computer science. A Turing machine is a universal model of computation that can simulate any other machine given the correct instructions. However, being able to perform any computation does not mean it has understanding, awareness, or the ability to autonomously pursue goals like a human. Even if Transformers can emulate a Turing machine's functionality in principle, this does not mean they possess general intelligence. Sadly, AGI requires the integration of many cognitive abilities: learning, perception, reasoning, planning, and more that work seamlessly across a variety of tasks. The fact that Transformers with CoE can solve complex problems by generating intermediate reasoning steps does actually show that these models are more powerful than previously thought. However, their ability to solve problems still heavily depends on how well they are guided or prompted. Without proper prompting and structure, these models can fail spectacularly. Now, current Transformers, even with CoT, do not possess the metacognitive abilities to autonomously break down new problems, understand novel contexts without large-scale data, or dynamically adjust their strategies in the way an AGI would need to. So, overall, whilst this paper is an

AGI. It certainly is a large step towards it, and it's incredible because it mathematically proves that Transformers, when using Chain of Thought, can solve any type of problem that can be represented by a certain kind of logic circuit known as POI in computer science. And think of it this way: imagine Transformers are like problem-solving machines. Before, we knew they could solve some tricky problems when guided step by step, but we didn't know just how powerful they could become. This paper shows that with enough steps in their reasoning process, like a detailed checklist, they can handle extremely complex problems, not just easy ones. It's like discovering that your calculator can secretly perform advanced calculus as long as you let it show all the steps. Another major finding is that Transformers don't need a lot of layers to solve complex problems if they use Chain of Thought. Traditionally, we thought that deeper models with more layers were always better at handling difficult tasks because they could process more information. This paper shows that even Transformers with a small fixed number of layers, constant

depth can solve very hard problems as long as they are allowed to think step by step. This is like saying you don't need a huge complex computer to solve a big problem; you just need a small clever computer that can carefully follow a long list of instructions. So, before this research, Transformers were seen mainly as good at doing things in parallel, solving many parts of a problem at once, like sorting a deck of cards quickly by having multiple people each sort apart. They weren't considered good at solving problems that need careful step-by-step thinking. This paper changes that view. It shows that with Chain of Thought, Transformers can handle both types of problems: the quick parallel ones and the more complex sequential ones that require reasoning through several steps. This makes Transformers much more versatile than we thought. They can be guided to think out loud and work through problems that need deeper logical thinking, like a human would. Now, some of you might be wondering how this compared to OpenAI's recent research with their new model, OpenAI1. You've probably heard that OpenAI1 ranks

incredibly high on tough challenges like competitive programming, code forces, and also ranks among the top 500 in a qualifier for the USA Math Olympiad, and even outperforms humans with PhDs in science problems. Now, these are impressive feats, but how does all this tie into what we're talking about with Chain of Thought and Transformers? Well, both OpenAI's new research and the recent paper on Chain of Thought are built around the same core idea: teaching AI to think step by step rather than just spitting out an answer. The recent paper provides the theory behind why this works. If you guide AI through a series of reasoning steps, it can solve much harder problems. OpenAI shows this idea in action. Its success in programming, math, and science isn't because it's just bigger or has more data; it's because it has been trained to think more like humans do, breaking down problems into steps. So, this is why this is such a shift. Both the paper, Google DeepMind, and OpenAI's research suggest a shift in how we should build AI in the

future. Instead of just focusing on making models bigger, the key is to make them better thinkers. This means more focus on how we train them to reason and solve problems step by step, which can lead to more efficient, powerful, and versatile AI.

Googles New AI Research Is Incredible! (The Sky Is the limit....)

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Googles New AI Research Is Incredible! (The Sky Is the limit....)

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