AI Singularity Discovered

Key Takeaways

Hello community. So great that you are back today. Today today we're going to solve here the reasoning problem in AI. Okay let's go. So you know that structured reasoning over the natural language input remain the core challenge in AI. So what we have to do we have on the one hand an unstructured linguistic expression let's say in English. But what we want is a formal logical representation that simple code is able to solve. So it's simple. We just have to map language to logic. No, we don't want that the AI is operating on our linguistic expression on our language. We want the is operating here on logical code representation that we can verify with solver with tools. Now you know we already have been there in my last video and this is see the thumbnail here. We already said hey Google is doing this. it is doing here and it's extracting here from the Titan EI the plan calculate the cost increase the value calculate now the new value and then calculate the profit this is here a solution template for very specific problems context engineering and you can see this today if you go at let's say older models like here Amazon nova experimental for May you see if you give it a task it immediately starts here by a step-by-step solution Start with zero, press this, do this, and go forward. There is no reasoning happening. But look at the other problem. Look at the new Kim K2. You see what's happening. You give it a topic and then it starts with I want to understand the task. I want to understand the objectives of the task. And then it says okay, we need to reach floor 50 in less than 20 button presses. We need to finish with an energy reservoir of a particular label. We have some tokens to get. We have to collect at least two of the four code cards. We have some random traps that I have to avoid. And then it says, okay, I understood the task. I understood the objective, but where do I start? What are my boundary conditions of the system? This is like in theoretical physics when you said, okay, the initial state is I'm at floor zero. I have this amount of energy. I have this amount of tokens. I have no code cards. I'm aware that there are different flags that I can switch on and off during the game. And then having understood my current situation now the system starts with a strategy and a plan. This is what modern AI are doing. And you might say, hey, wow, this is already interesting because you see a separation of the understanding task to the pure calculation task. And yeah in my very last video when we talked about the differences of DSPI 3 to lean 4 you saw exactly what we are talking about. Yeah in the primary goal of DSPI it was to find the empirically best performing solution from an uncertain space. But this is not anymore good enough for us today. We want not an uncertain space. So what we do? Yeah we have a human prompt. This is what we start. And then you know all the huge LLM now they start to interpret your prompt and internally rewrite the human prompt according to the draining data capabilities that this LLM learned during its training phase. And then if for example if we go with a chain of sort a linear sequency of reasoning we have our reasoning models that you see are number one on all the performance charts here for AI. And in my last video, we went a step further from a chain of sword to a more complex planning. And today, today we take the next step in the eye development. And yes, you already have seen it. Maybe you didn't notice it, but you have seen it. In this video where I compared Sonnet 4 to03 to Gemini 2.5 Pro, I showed you that my human query text, my logical causal reasoning text was transformed by the AI systems into code and the solved the code base and came back with the result. So this is already happening today. But let's make this a little bit more clearer. We transfer human language to code to very specific code. Yes, it can be Python based. But there is something you should watch out for. So let's talk about this new approach. Language to logic, not context engineering, not prompt engineering. No, we take the very next step. Language to pure logic construct that we can solve with absolute clarity. Let's have a look how humans do it. What is a human expert doing if you want a real professional in its very narrow domain? It abstracts and models here the problem using here formal logic or some mathematical framework to predict here whatever it will define variables constrained and objective and then it will only after clearing this it will apply analytical or computational methods to solve them. If you design a new wing for an aeroplane, if you design I don't know autonomous driving certain components, you start here with an abstraction with a model that you can really try to understand all the dependencies and then you have in your supercomput your computational methods to solve it. Now we do the same with the eye. Now let's say you are human engineered and you have to optimize a factory output. You don't start like I have shown you here with the Amazon LLM step one, step two. No, you model the problem. You define variables, production rates that you have currently and you want to achieve constraints like the capacity, the max capacity of a machine, the raw material. This is a limited what you can buy. An objective is to maximize the profit and you have to consider all the boundary condition. Yeah. And after you define the formal framework that you absolutely understand it on a logical basis, you apply then an algorithm to find the solution. And guess what? AI is now doing the same. It's a beautiful marriage here of a linguistic understanding as an input but formal logic as the main part here of the calculation. So you see it's rather simple this new idea. It is what's already happening just a little bit more crystal clear. So this if you want has two layers of complexity it has to solve. At a higher complexity level, it has an optimization guided formulation LLM, an OF LLM, which is simply explained to transform here my natural language query, my task that I give to the eye into some structured formal models specifying here in this formal model the problem type, the variables, the constraint, the objective and everything. I make sure that in my formal model mathematical or logical model I have all the parameters that I need and then at a lower complexity level layer it is easy a logic generation LLM an LG LLM this now constructs here a logical representation like a rulebased workflow or constraintdriven solution path translate this into Python code which serves or Python solver that we have as a tool use for the eye which solves here or serves here as a universal symbolic workflow logic generation. So simple but of course you know before we do this we have to train every LLM that we use. So here we have now the problem. We have a high level optimization guided formalization LLM that we have to train for our domain knowledge and for our specific task and then we have to train a logic generation LLM. But how do we do this? Now the funny thing is you remember those layers have to interact and generate something new. So we have then also to train them jointly. So this means we are now faced with a bile level optimization algorithm for EI LLM. And you might say hey finally this thing gets more interesting not such a simple video about AI. Absolutely. But the moment you start they say yippee you know you just realize but wait what mechanisms I do have currently in the latest AI research to drain to train here formalization LLMs. Well, actually we only have one method reinforcement learning. This is the main method we have. No. So guess what? For the abstraction generation LLM, the formalization LLM, we will use a reinforcement learning. And you're not going to believe it since this is the only method we have for the logic generation LLM. We also will use reinforcement learning. But you know what's now the positive aspect? If we have to do the jointly optimization problem since we have here the same base training methodology, we can combine it very easily. So this is now what we're going to solve. If you're a little bit more on the mathematical side, never mind. So you see this are our two main equation that we have to solve. We have here at first the upper level the OFF LLM. How is here the optimization process for this LLM? And here we have the lower level LG the logic generation LLM. How is here the objective function updated? And you notice immediately hey wait there are terms missing in our formula. Yes of course in this particular paper I'm going to show you the latest AI research here on this topic. they use here objective for the reinforcement learning without the coolback liber penalities and this could be a critical term but let's just look at the theory let's understand what the authors published the result they achieved but keep in mind they are terms missing and you know from one of my last videos that coolback liel penalities if you compare probability distribution they are of extreme importance so careful might be missing out something from this particular publication. If you're not really familiar with the terms and with the little bit of mathematics we have here, I have a video where I explain everything for you. This is our main paper published July 11, 2025 by Tongji University. A beautiful paper here from language to logic, a bile level framework for structured reasoning. Finally, they hope that they have found here the solution for the next generation LLMs for a much better reasoning performance. But let's go in media race. Let's have a look at this and let's say okay let's have a look at the first LLM. This is our UF optimization guided formalization LLM. What is it doing? Well, what is the core task of it? It's a problem modeler. Its job is to ingest your messy my human natural hardly English language query and translate this into some pristine structured formal logic representation. This is not just a plan as I showed you here in this video and my last video. This is more. This is now the next step in the complexity. This is now a formal specification with all the parameters of the system. So for example the output is here a five tupil easy whatever we do in more or less we just work with tupils and matrix multiplication. So our elements of the tupil are a p the problem overview this is simply a concise summary of the task but then it gets absolutely fascinating the model type it is the category of the problem for example here satisfiability. So this is here let's say a constraint satisfaction problem where we have the logical inference how to solve it. This is done in the last I don't know 50 maybe 100 years in mathematical and in causal reasoning that we know how to handle and now suddenly we have the bridge between AI and everything we developed in the last 50 years before AI was there. Everything that we developed here for logic, all the NP hard solutions, now we can use them because now finally we say AI is not operating on the human language anymore. But now EI is operating here on something else. The next uh parameter here in the five tupal is of course the variables. Then we have our constraint and then we have our objective. So if you want you really define the system much more clearer than simply having my natural language query that I have. So make sure we have all the parameters, we have all the variables, we have all the constraint and please redefine the objective in a way that the can understand it. That's it. Let me give you an example here. This is your simple prompt. What you do with this? You transform it simply into this. For P you determine identity of these two persons. For T you define it is a set problem a boolean satisfiability problem. Then for C you have here the statement given in the prompt. And you see how easily it can be transformed and then just find the true values for this that satisfy all the constraint. In logic we have the mathematical apparatus to solve this immediately. If you want to learn more about SAT or the boolean satisfiability problem and all the specific classes as you see here on the left side here just Wikipedia just a good explanation great but let's talk about the second LLM that we have now the logic generator this is now where really the code comes into play now this is the solver this is the tool that we use where a lot of my viewers said hey why don't you use a prologue tool well remember in my last video we talked about lean 4 here as a solver for causal reasoning. This is where we are now. So this solver takes the perfectly structured model M from our OF LLM. So we take here the output of the layer and now the sole job of the logic generation LLM is generate a program to solve it. And I don't care what it is. Yeah, let's go with Python. We have a lot of um libraries in Python particular focused on this job. So let's say we go here with something Microsoft developed here. This is Z3. Remember the lessons in in Stanford theory.stanford edu Nikolai programming set 3. If you go there you have all the information resources logical interfaces signature terms of formula quantify. We have a complete library for this multiple libraries for this. So how does this particular problem that I just showed you here for the first LLM, how is now the code of the second LLM, the logic generation LLM for this example. Here you have it. This is it. This is a very simple system that any code environment can solve with real precision. This is not anymore about an EI arguing in next token prediction about something. This is the real classical code that we can calculate on a computer, not an auto reggressive transformer. So beautiful to use this. Now if you think about it, you say, wait a minute, this has a game theoretical background in mathematics. No. Yes, of course. And they even the orers tell us here yeah there's a steelback game where you have this leader and follower and you could see our UGF LLM here as the leader and the logic generation LLM here as the follower and then it is simply here the best possible outcome for the overall system and you can use here our ideas from game theory. The last 50 years what we developed in game theory, the code we developed in game theory now suddenly becomes available here for our EI that operates on pure logical objects and not on language anymore. Now this is interesting. Think about this. Let's talk about a technological singularity that is happening and I call it a soft technological singularity. But this has quite some potential now. So what we doing? We having here a modeler LM. This creates a formal blueprint. And then we have a solver LLM that executes this with code. Seems like a clever engineering solution for better reasoning. But you know if you think about it, it could theoretically become something far more profound. And what we actually looking at is a framework that goes, hey, language to logic in AI. This is not just a new method. This is also a blueprint for a soft technological singularity. And what do I mean by this? It is not runaway super intelligence that you see here from I don't know m or whatever companies trying to sell you this marketing. No, I mean something much more subtle and really domain specific to your case. No, this is now really a point where the machine generated logic becomes so complex and layered that it fundamentally outspaces here outpaces here the human comprehension becoming here new unfollowable form of discovery and I look at some of these mathematical logical sover and I can't read it I can't understand it it is pure abstract mathematics compressed into axioms and theorems that are the result of I don't know 20 30 50 years of mathematics but for me as a normal human being it is outside of the scope of my language and it is outside of the scope of my analytical understanding. But this is exactly what I want AI to become. A problem solver that can handle a complexity my human brain cannot handle. Every supercomput normal noni supercomput can calculate systems with thousand 10,000 parameters. No problem. No human brain can do this. And now let's finally focus here AI not on the human language as the object of optimization but of something that makes sense in code. So whenever I try to convert here the machine code that I get back from the solver into my human language in order to understand here the logic I fail. But for any eyes, think about it, just a neural network, it is just another pattern and car in the eyes are perfect pattern matching machines. This now makes sense to apply AI on this particular structure. And you remember here this video AI no intelligence and I showed you here at 11 minutes 35 seconds here that AI system tried to discover here the true Newtonian law and this is what they discovered here from the transformer architecture and you see they failed completely. But you know why they fell completely? Because they were more or less operating here also in a linguistic space and not in a solver space. So this now becomes absolutely interesting because as AI moves on the next generation not to find and predict patterns in the human language but to find and predict patterns in pure machine logic in patterns that are there in the mathematical solver and maybe I can't understand this solver representation but AI is a neural network it just says okay it's a pattern I don't care what it is I don't want to understand it and maybe I don't have the possib ability to understand it but it's a pattern I can work with I can replicate and this is now interesting now there are three elements I would like to draw your attention to at first we have a kind of a decoupling of logic from the human language up until now all our AI system we're trying here yeah we're trained here on the human literature and on the human reading and the human whatever this here is interesting because language to logic starts by talking but its first and only goal is to escape here from this prison of the human language. It the first LLM says hey I want to get rid of the human language. I want to abstract away into a pure logical space where I have logic axum and theorems and pure mathematical formulas that I know are valid in my kernel. No human language anymore and it makes sense. Second, you have to have a self-arning element. Yeah. And here we have an autonomous improvement loop. And this is what I have to show you right next. The engine of acceleration of this language to logic idea is simply as I showed you this jointly by level reinforcement learning. This if you want by GRPO Allen algorithm for reinforcement learning. This has a simple elegance to it. And what we achieve and this is step number three. There's now a widening gap between a human and a machine cognition. This is where theoretically you could argue that a singularity now begins to form. The machine code for logic will not even be readable for a human being. We can try to transcribe it back into a human language. But the beauty and the elegance and the power of this particular logic representation in a complete different space is simply then gone. What an interesting idea by this new research paper. Let me show you what I mean with an example. Let's say we have now here from the OGF LLM. It builds now from my human blah blah blah. It builds now a logic model and this model has because I formulated it in a simple way maybe 50 parameters or 50 variables and it has 100 constraints that I maybe even didn't formulate in my human language because I was not aware that there exist but this is what I want AI to do to understand the situation go back go somewhere in the internet completely understand all system variables all system constraint temperature pressure whatever and understand that this has an effect. Let's say let's go with something controversial climate change. You have a complexity of a complete planet a dynamic from everything in a brilliant human mind and I hope you as a subscriber you are this brilliant human mind you can order this logic because it's just 50 variables and 100 constraint. So if you sit down on an afternoon this is okay for a human being but if we have now this self-improving engine we have let's say hundreds and thousands of generation of self-improvement and the system may decide to generate now a model for the global planet earth with 50,000 variables and more maybe than a million interrelated constraint that it found in the literature how vapor water land sunshine energy CO2 to how it all comes together and what are the cross relations. Now show me the human brain that can understand this complexity. And you see this is what I want AI to to be designed for. And now the solver code generates let's say I don't know 100k lines no problem who cares using here a complex theorem improver like let's go with the simplest sets three. So we the humans we develop this for years and years and we say hey we put all our logic in this construct of set three. So we give it here the right conditions and it can only calculate here according to our logical guidelines. So we hope that it executes here perfectly and provides you a groundbreaking new molecular structures for example and the answer is correct because it just works not on the human language but on mathematical theorems. So the proof is encoded in the logic of this but we I mean me personally I can no longer follow it. This is now a computation. I cannot say hey blackbox AI open up and show me your internal sorts. This is a complexity. Even if it would show me the generation of 1 million interrelated constraint in climate change, I'm quite sure I'm not able to follow it in here mathematical precision. But any computer can do this. Any supercomput can do this. So this is kind of a soft singularity you see. And maybe it's even a theoretically a singularity we will approach. It's a world filled with black boxes of verifiable logic. All the LLMs, but they aren't black boxes because their rules are hidden. We reprogrammed here the logic for the operational system of the black boxes. So the code is right there. But now finally AI is doing what it was designed to do. The black boxes now reach a level of complexity that our human brains simply lack. We lack capacity to trace the execution. So this is now a point in the soft complexity theorem when verifiable is no longer auditable. So this means yes of course we can track the final results. We can run real physical experiment, chemical biological experiment but we cannot audit the logical derivation done in the pure machine logic code or we would have to translate it somehow back in human language but yeah try to communicate this. So the chain of reasoning is so vast and complex that now at this level it is fundamentally let's call it opaque to the human mind. What an interesting idea. So when I tell here my current language model to stop thinking in words but jump to pure logic abstraction mathematical structures. We doing more than just asking here for a better reason. Yes, of course we want the better reasoning, but we kind of setting them on a path from kind of autonomous logical evolution. And this is what I like in this publication. And that right there is a quiet, soft and a beautiful singularity we are building towards today. Okay, this was this now coming back. I told you step two of this is important. The jointly training here of our complexity. this reinforcement learning this GRPO that we know but now jointly at multiple levels. Now this is not interesting. Now it could truly interwoven or not at all if we have the right idea. So what we know we know the algorithm the GRPO beautiful is an explicit reward model. Great. We have not the problems with implicit DPO structured. This is the right way to go. GRPO and we have two policies. No, the OGF policy is what the goal is to generate the best possible problem model M in a causal reasoning space. And the LG policy is to take the model M generated here by the OGF policy and generate the best possible code. The solver go with prologue, go with Python libraries, go whatever you like lean for to solve it. And then you optimize it together. Okay, you might say how we do this? Well, we have a loop. What is the simplest thing? We have an alternating loop. So the final reward did the code produce the correct answer. We can verify this very easily is first used to update here the LG model. This is the reward function that we get back. Now and the average reward achieved here by the LG model for a given problem formalization M. then simply becomes you the reward signal for the OFF model. It's simple and trivial. No. So the OFF model is rewarded if it produces here a formalization, an abstraction that the code model can successfully solve by running now the Python code. And this joint optimization forces here the OGF to learn how to create clear and solvable logical structures in the abstraction thereby dramatically improving here the generalization and the accuracy this is such a beautiful simple idea I'm loving it yeah mathematics you say hey where's the ma mathematics I showed you already but again let's have a look at this so what is our objective function and our optimization here the solver our lower level. So this is here our code solver. So for a given problem Q and a formal model MI generated here by the OF LLM the LG policy is updated to maximize the expected advantage. Here we have our rewards integrated of its generated programs. OIG easy this is the optimization term and for the upper level objective oh function sorry there's the word missing. So how we optimize now the abstract modeler. So this is yeah a leader. It aims to maximize this objective here by anticipating the optimal response here from the logic generated code model and then you just combine it here in a clever way and you have here your level reward optimization with a simple feedback loop. And of course, if it's not working, if the OGF creates here some formal model M and the code LLM consistently fails to find here a code representation of this formal abstract representation leading now to a lower average reward structure. It's simply a negative update here for this particular OGF policy by creating here this non-working abstraction level. So you see this is exactly what we do in EI all the time. There's nothing special about it. We just combine the modules here in a very particular way. And you have also here from Tongji University a little bit before this is here published here November 2024. They also showed you here exactly the solution. So no wonder that now Tongji University came up with the new study because I don't know half a year ago they already found a solution for a three-level navigator for a bille reinforcement learning algorithm. Yeah. So if you want to see this in the code this is it. This is exactly what I already showed you now just here in the official publication. And you might say so only reinforcement learning now. Okay, by the way, yes, you are right. We also have and the authors go the classical way with a supervised fine-tuning as the cold start. So they say to cold start here the OFF model. No, before it can learn through the reinforcement learning, they still believe it needs to know the basic syntax and the structure of a valid formal model M and they train it here supervised fine-tuning here on this particular topic. But you remember now supervised fine-tuning is nothing else than reinforcement learning with an F divergent and KA cliber terms. So yes, they have the classical supervised fine-tuning with the generation, the filtering, the ranking and the fine-tuning. But what if you don't have this? I mean, you have to design the training data. Now, careful because as I've shown you in this video about the new AF framework of a post-training innovation that supervised fine-tuning is in fact the DPO, there are further optimization that are not yet implemented in this new paper. But anyway let's have a look at the result. Let's say great we understand now the main idea what is the performance that we achieve. Now I only go for gross domain reasoning I go to this heavy stuff. Yeah. So language to logic here has for certain terms here for certain autologic problems 13% improvement for temporal test data set 11% improvement and for geometric prediction problem 17% improvement to the baseline this is quite impressive at least we are not at 3 or 4% like I shown you in my last video but we are 13 11 17 so yeah this is moving something and this is not yet here the best optimized version. This is just here the first try. Hey, can we do this? Yeah. And you see here for example here 35% higher than chain of sort. So he's yeah this is working now you have here all the formal data. Beautiful. And then the conclusion and I think this is nice. No because what we are talking about is structured systematic reasoning with large language model. And now they tell us listen we don't stay anymore in the language this is not the way forward for AI they say allowing here our LLMs to construct structured formal logic models and then generate executable symbolic workflow. This is the way forward. So this design captures here the underlying logic of complex problems more effectively to increase here the reasoning performance with LLMs. And this is exactly the same as I showed you at the beginning of this video when I did my logic causal test and I showed you that some of the models like 03 simply took my human text transformed it into a Python code solved it in code and gave me back the result. And this is the reason why you see no reasoning traces of 03. I just had to wait 5 7 12 minutes because it was doing all the calculation in the background. So some companies understood this and already implementing this. Some companies like Google with Gemini 2.5 Pro as I showed you in my video. I can do both. I can do a inherent parametric knowledge without coding where then I just take the slider push it to activate code execution and then the system will do it with a code execution in Python. So we have right now all the possibilities to see this and to learn and understand code is absolutely perfect. Just think about what you do here if you code I don't know whether you use cursor or you use Gemini code or you use here any other code IDE what a nice study now so July 14 here we go this is more or less today for me Tongi University a bille reinforcement learning approach cutting edge and ensures a tightly coupling between the modeling of a logic abstraction and a solving ing of this complexity by relying on code. And what's so nice is it this entangles here the primary understanding from solving and solving from tools with particular solver for particular topics and set and whatever you have. Yeah. And then the reward signal is now here designed in a way that it is kind of a communication channel between our complexity levels between our two different LLMs. No. So nicely designed. So you see you can have elegant simple solution if they're just done in a clever way. Yeah, I told you super fine tuning fundamentally doing the same thing as DPO optimizing your implicit reward function. So careful with FST if you want to do something out of domain. Some of you might say Python why Python. No, you don't have Python is just an example because it has such a rich ecosystem. So you can go here with different libraries. No, you have symbolic mathematics in Python for solving your equation or simplifying expression or go with set 3 from Microsoft. No, as I showed you, great constraint satisfaction problems, boolean satisfiability problems. They can formalize it. They can solve it. Maybe you go with prologue. My last video I showed you here with lean for as a pure mathematical proof solver. We have all this code already available. We just have to abstract away from the human language. So in general, what would I say about this? Oh, I like it. We have two LLMs, a model LLM that analyzes here the problem. This is my human query and translate it into a structural formal representation M. And then we have a solver llm takes this formal model m and generates some executable logical former solver code to find the solution. The core method why this works. So this selfarning approach is inherent in the system is a ble reinforcement learning with the reward function that works here on both LLMs. What a beautiful idea. If you like this kind of video, why not subscribe?