AI Agents, Mathematics, and Making Sense of Chaos
From Artificiality This Week * Our Gathering: Our Artificiality Summit 2025 will be held on October 23-25 in Bend, Oregon. The
We speculate on how the GPT store might act a market mechanism for discovering the most valuable use cases for AGI
Key points:
OpenAI's goal is to evolve GPTs to be more "agentic," the capability to perform sophisticated actions. The data and interactions within the GPT Store offers a market mechanism for discovering the most valuable use cases for AI by interpreting the proprietary, rare, dynamic, and contextual use by millions of users. This makes us wonder if the Store isn't just a random development or the pursuit of usage growth. Perhaps the true purpose of the GPT Store is to tap into the existing network characteristics of GPTs to develop their own kind of intelligence, perhaps even exhibit an emergent form of AGI, OpenAI’s most significant strategic goal.
While it's true that not all GPTs are created equal, it's even more crucial to understand that the connections between GPTs and users vary significantly. Data from conversation analysis reveals that only a few GPTs dominate in terms of usage.
This is a characteristic of complex networks known as power law distribution, where many nodes (in this case, most GPTs) have few links (conversations), while a few hubs have a multitude of links. Networks which show power law distributions are a signal that hubs have a significant influence on information flow and, consequently, the way the network behavior evolves over time.
Networks, such as app stores and the internet more generally, are governed by two laws: growth and preferential attachment. If a network is static, there is no opportunity for change. But if it is growing, a lot can happen. The first law says that growth matters a lot.
The second law—preferential attachment—says that growth isn’t random: the growth of new links is proportional to the number of links a chosen node already has. This is how an early start creates an advantage—an early node (app or website or GPT) has more links which then drives proportionately more links, ultimately creating a hub.
What is important is that information is captured in the links as well as in the nodes. You can move things around in relation to each other in uniquely flexible ways. In an app store, different app categories (like games, productivity, social media) are interconnected based on user preferences or functionalities. For example, a productivity app might be closely linked to a cloud storage app in terms of functionality and user overlap. It's early days so we don't know how GPT linkages might play out and what these links might tell us.
Power law distributions hint at underlying self-organization and emergent behavior. In networks where nodes display increasing agency—agentic GPTs for instance—this becomes particularly crucial. Humans call on GPTs, and on other humans by sharing or within GPT Teams. GPTs might call on other GPTs. User interactions and the inherent agency of GPTs collectively contribute to the network's emergent behavior.
To take advantage of the network as an emergent structure, we need both growth and competition. Competition drives evolution of the structure of a network through fitness—the relative strength of one node over another. Because the network is growing and there is competition between nodes for links, sometimes winners take it all. Conversely, new upstarts can topple a historically dominant hub in a kind of cascading failure of super-linking. But they have to be super-fit for this to happen (think TikTok-level fit).
In a GPT Store where GPTs are powerful, agentic AIs, the network structure would likely become more dynamic and complex. These agentic apps, which can constantly learn and adapt, could strengthen power law distributions. Perhaps a few highly adaptive and popular apps become super-hubs, dominating much of the network traffic and user interaction. Perhaps the system of competition and fitness mimics evolution and gives rise to emergent capabilities and complexity. This dynamic would accelerate other novel functionalities and user experiences, as these AI apps compete and evolve, driven by new data uploads, user preferences, and feedback.
In an app store with agentic AI apps, the insights gleaned from their interactions and evolution could significantly inform the development of a more general intelligence. As these AI apps adapt and compete, they generate vast amounts of data on dynamic human preferences, successful adaptation strategies, and effective learning processes. This information would be valuable for developing AI systems that are more intuitive, responsive, and capable of handling complex, real-world scenarios.
The dynamics within this network might mirror certain aspects of natural intelligence, such as learning from experience, which is crucial for the development of general AI. Perhaps this network topology would give rise to new learning algorithms themselves, similar to how grokking works, where generalization arises as a function of the structure of the network itself. This could lead to breakthroughs in AI's cognitive abilities, pushing it closer to human-like versatility and adaptability.
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