Could Artificial General Intelligence (AGI) solve/violate “no free lunch theorem”?
Imagine you’re at a buffet where there’s a variety of food to choose from. The “no free lunch theorem¹” is like saying you can’t have every dish without making choices and maybe sacrificing one dish for another. In a similar way, in the realm of solving complex problems in computers, you can’t have a one-size-fits-all solution that works perfectly for every situation.
In the context of computer algorithms and problem-solving, it means that for every algorithm’s strength or advantage in solving a specific kind of problem, there’s a corresponding weakness or inefficiency in solving another type of problem. It’s a reminder that in the world of computational solutions, you have to pick and choose what works best for the particular problem you’re trying to solve.
The formal proof² involves complex mathematical concepts, including probability theory, information theory, and combinatorial optimization. It shows that, on average, no specific optimization algorithm can perform better than random chance across all possible optimization problems. In other words, for every algorithm that performs well on a certain type of problem, there exists another problem for which the same algorithm will perform poorly.
The theorem emphasizes the importance of selecting appropriate algorithms or approaches tailored to the specific characteristics of the problem at hand, rather than relying on a universal, one-size-fits-all solution. Let’s consider a specific example from deep learning involving two different types of problems: image classification and language translation.
- Image Classification Problem: Algorithm X is a deep learning model (CNNs based architecture) specifically trained and optimized for accurately classifying images into various categories, such as recognizing different animals (cats, dogs, etc.).
- Language Translation Problem: Algorithm Y, a different deep learning model (Transformers based architecture), is specialized in translating sentences from one language to another, for instance, from English to French.
Now, if we take Algorithm X, which is excellent at image classification, and use it to perform language translation, it will not work. Conversely, if we use Algorithm Y, which is great at translation, to classify images, it would also fail.
In this example, the “free lunch” would be having a single algorithm that excels at both image classification and language translation without specialized training or tuning. The theorem reminds us that such a universal algorithm is not feasible, and we must tailor our approaches to the unique characteristics of each problem.
However, with the advancement of large language models or large models in general, such as GPT-4³ (Generative Pre-trained Transformer 4) and similar AI architectures, there’s a noteworthy shift in how we approach problem-solving within the domain of deep learning.
These large models, with millions or even billions of parameters, have shown a remarkable ability to generalize and perform well across a diverse range of tasks. This has led to the idea of “few-shot” or “zero-shot” learning, where these models can achieve reasonably good results on tasks they were not explicitly trained for, given a small amount of context or examples.
For instance, a large language model like GPT-3⁴, initially designed for natural language processing tasks, has demonstrated promising performance in tasks like translation, question-answering, text completion, and even simple arithmetic, despite not being specifically trained for these tasks.
This leads to a reexamination of the “no free lunch theorem” in the context of large models. While the fundamental theorem still holds true — there’s no universally superior algorithm across all possible problems — the emergence of these massive models blurs the lines. Large models exhibit a certain level of adaptability and generalization, challenging the notion that each problem requires a highly specialized approach.
However, in a hypothetical future where we envision access to infinite data from all corners of the universe, coupled with computation resources and energy beyond current imagination, and a neural network architecture boasting an infinite number of parameters, an intriguing paradigm shift occurs, which could, in this scenario, be referred to as Artificial General Intelligence⁵ (AGI).
In this boundless scenario, with such an AGI, the “no free lunch theorem” might take on a fascinating twist. An infinitely large neural network could, in theory, encompass a comprehensive representation of all possible patterns and knowledge in the universe. It becomes an ultimate universal approximator, capable of perfectly fitting any conceivable problem.
With infinite computation and energy, this neural network could be fine-tuned for each specific problem, seemingly violating the traditional constraints of the “no free lunch theorem”. It would adapt and specialize for each problem instance, achieving optimal performance across the entire spectrum of challenges.
However, we must acknowledge that even in this hypothetical scenario, fundamental philosophical and practical questions arise. Would a true, infinitely large neural network or AGI be achievable in reality, considering the laws of physics and practical engineering constraints? Would the notion of “infinite” data and resources challenge our understanding of information and computation at a fundamental level?
In the end, while we delve into this hypothetical realm, it’s essential to remember that the “no free lunch theorem” remains a fundamental principle that guides our understanding of problem-solving and the necessity of specialization and adaptability in our approach, even in the face of boundless possibilities. Moreover, it is exciting to imagine if or when convergence to such an AGI will occur in future. We will only see, or our future generations will.
I intend to closely follow what organisations like OpenAI, x.ai, etc. will achieve in this regard, and you should too if you liked my first (mini) blog.