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
Recent developments in AI have given rise to a new class of systems known as agentic AI. These systems are characterized by their ability to perceive, reason, and act with varying levels of complexity, extending human capabilities in unprecedented ways.
PDF version of this report is available at the bottom of this page.
Recent developments in AI have given rise to a new class of systems known as agentic AI. These systems are characterized by their ability to perceive, reason, and act with varying levels of complexity, extending human capabilities in unprecedented ways. While there isn’t a single definition of agentic AI—what is agreed upon is that agentic AI represents a significant leap.
OpenAI describes agentic AI systems as those that "can pursue complex goals with limited direct supervision." Researchers from Stanford, Microsoft, and UCLA characterize AI agents as "a class of interactive systems that can perceive visual stimuli, language inputs, and other environmentally-grounded data, and can produce meaningful actions." IBM views AI agents as "language model-powered entities able to plan and take actions to execute goals over multiple iterations," while Google DeepMind defines advanced AI assistants as "artificial agents with natural language interfaces, whose function is to plan and execute sequences of actions on behalf of a user—across one or more domains—in line with the user's expectations."
At Artificiality, we define agentic AI systems as those that can perceive, reason, and act with varying complexity to extend the human mind beyond our current experience. This definition emphasizes the trio of capabilities—perception, reasoning, and action—that we will use to frame various capabilities of AI agents later in this report.
The concept of AI agency AI is not entirely new, with roots tracing back to early systems like IBM's Deep Blue chess-playing system in 1997 and the debut of virtual assistants like Siri in 2011. However, recent years have seen a rapid acceleration in the development and deployment of increasingly sophisticated agentic AI systems. Early experiments like AutoGPT and BabyAGI caught the AI community’s attention while newer tools and platforms like Brevian, CrewAI, LangChain, and Qurrent provide the ability for individuals and organizations to develop their own AI agents.
We are focused on agentic AI because we believe a) it has the potential to have wide-ranging impacts on how we live and work, b) these technologies have the potential to both empower and disempower, and c) some level of agency is the future of AI. Giving machines the agency to perceive, reason, and act to accomplish goals might be quite useful with everyday tasks. But there is also the possibility for AI agents to wreak havoc if left unchecked. Since everyone with a computer now has the ability to create agentic AI, there may be little to no ability to control how and why these agents do what they do.
In this report, we will explore the key components of agentic AI systems, including perception, reasoning, and action. We'll examine how these capabilities can be combined in various ways to create AI agents with different roles and personas, from simple task executors to complex decision support systems. We'll also consider the realities of deploying agentic AI in real-world contexts, including the shift from designing for human customers to designing for AI agents themselves. Finally, we'll explore the challenges and opportunities of building multi-agent systems and the importance of assembling diverse, multidisciplinary teams to effectively develop and integrate agentic AI technologies.
If you thought that LLMs changed everything (which they did), agentic AI will change everything even more, even if its full instantiation is many years away.
“Can machines think? This should begin with definitions of the meaning of the terms ‘machine’ and “‘think.’”
—Alan Turing
The rapid development of agentic AI systems has sparked a need for new metaphors and mental models to comprehend their complexity. While these AI agents display intricate behaviors and interactions that surpass simplistic notions of machines, they remain fundamentally distinct from biological life.
When we describe advanced AI using terms traditionally reserved for living systems, we must recognize that this linguistic mapping does not imply that AI possesses life or subjective experiences like that of humans. Instead, this language of life, cognition, and behavior serves as a tool to help conceptualize the increasingly sophisticated capabilities of AI, which emerge from complex informational dynamics and goal-directed, optimized functions.
As AI agents become more adaptive, interactive, and autonomous, we recognize they occupy a novel space on a multidimensional continuum of possible complex systems, characterized by varying degrees of design versus emergence and mechanism versus cognition. Across this continuum, agentic AI may functionally mimic properties of life—such as perception, reasoning, and action—through rational architectures that enable them to pursue goals while interacting with complex environments.
However, we must emphasize that this functional resemblance to living systems does not equate to AI possessing existential choice, intentionality, phenomenological experience, or metacognition—qualities that characterize biological cognition and remain qualitatively distinct from the computational processes of artificial agents.
As we attempt to describe these new AI capabilities, we face the challenge of developing more precise definitions and conceptual frameworks to reason about the novel design space of agentic systems. In this report, we lay the groundwork for this task, aiming to maintain a balanced perspective that includes the use of appropriate metaphors. By doing so, we hope to provide intellectual clarity as we shape a future in which artificial agents and living cognitive systems interact in increasingly fluid and synergistic ways.
A key challenge is to develop more precise definitions and conceptual frameworks to reason about this novel design space of possible agentic systems, something we attempt to make a start on in this report. Our goal is to maintain a balanced perspective—including use of appropriate metaphors—which will provide intellectual clarity as we shape a future in which artificial agents and living cognitive systems interact in increasingly fluid and synergistic ways.
At the core of agentic AI systems are three key components: perception, reasoning, and action. Each of these capabilities can be present in an AI agent to varying degrees of complexity, allowing for the creation of systems with diverse skill sets and areas of specialization. By understanding how these components function and interact, we can better grasp the potential and limitations of agentic AI.
Perception
Perception refers to an AI agent's ability to interpret and make sense of its environment. This involves taking in data from various sensors or input channels and processing it to extract meaningful information. At a basic level, perceptual capabilities might include simple pattern recognition and feature extraction from structured data. However, as the complexity of an agent's perception increases, it can begin to handle more diverse, multi-modal sensory inputs and unstructured data.
Advanced perceptual capabilities in AI agents may include sophisticated spatial and visual reasoning, allowing them to navigate and interact with the physical world in more natural and intuitive ways. These systems can also demonstrate continuous adaptation and refinement of their perceptual models, learning from experience to better handle novel situations and environments.
As the complexity of an AI agent's perception grows, it can give rise to emergent properties and behaviors. The system may begin to exhibit a more holistic and contextual understanding of its environment, integrating multiple sources of information to form a coherent picture of the world around it.
Reasoning
Reasoning encompasses an AI agent's ability to process information, draw inferences, and make decisions based on the data it has gathered through perception. At a basic level, this might involve predominantly heuristic-based reasoning with a limited ability to handle complex or ambiguous problems. Such systems may rely on narrow, domain-specific planning and problem-solving strategies with minimal integration of spatial and visual reasoning.
As the complexity of an agent's reasoning increases, however, it can begin to demonstrate a more balanced integration of intuitive and deliberate reasoning processes. These advanced systems can tackle ill-defined, open-ended problems by employing flexible, adaptive problem-solving strategies that span multiple domains. They may also incorporate seamless integration of spatial and visual reasoning, allowing them to manipulate and draw insights from perceptual data in more sophisticated ways for more advanced planning and problem-solving..
At the highest levels of complexity, an AI agent's reasoning may begin to consider the broader context and complex system dynamics in which it operates. This could involve explicit modeling of the interconnections and feedback loops that shape the environment, as well as the ability to anticipate and adapt to emergent phenomena. The result is the emergence of genuinely intelligent decision-making capabilities that can rival or even exceed human reasoning in certain domains.
Action
Action refers to an AI agent's ability to interact with its environment and effect change based on its perceptual inputs and reasoning processes. At a basic level, this might involve executing simple, pre-defined action routines or motor skills with limited adaptability or learning from experience.
As the complexity of an agent's action capabilities increases, however, it can begin to demonstrate a more diverse and adaptive action repertoire. This might include sophisticated motor skills and behaviors that allow the agent to manipulate objects, navigate environments, and interact with humans in more natural and intuitive ways. Advanced action capabilities may also involve deliberate, goal-directed control of actions, with the ability to plan and execute complex sequences of behaviors to achieve desired outcomes.
Critically, the development of advanced action capabilities in AI agents often involves the integration of spatial and visual reasoning. By leveraging perceptual data to guide physical interactions, these systems can demonstrate a more embodied and situated form of intelligence that is grounded in the real world.
The three components of perception, reasoning, and action can be combined in various ways to create AI agents with different capabilities and specializations. We can think of these combinations as defining different agent personas, each with its own strengths, limitations, and potential applications.
For example, an AI agent with low complexity in all three components might function as a simple aide or assistant, carrying out basic tasks with minimal autonomy or adaptability. Such a system might be well-suited to handling routine data entry, scheduling, or customer service inquiries but would likely struggle with more open-ended or ambiguous problems.
In contrast, an agent with high complexity reasoning and action capabilities but low complexity perception might function as a navigator or decision support system. Such an agent could analyze complex datasets, generate novel insights, and propose solutions to strategic problems but would rely on human input for situational awareness and contextual understanding.
At the highest end of the complexity spectrum, we might imagine an AI agent with advanced capabilities across all three components—a "Wayfinder" persona that can navigate uncharted territories, devise innovative solutions to complex problems, and adapt to changing circumstances with a high degree of autonomy. Such a system would likely excel in domains requiring a combination of perceptual acuity, creative problem-solving, and situated action, such as leading complex projects or guiding strategic decision-making.
By understanding the interplay of perception, reasoning, and action in agentic AI systems, we can begin to map out the landscape of possible agent personas and skill sets. This, in turn, allows us to more effectively match AI capabilities to real-world problems and applications, ensuring that we are deploying these powerful tools in ways that maximize their potential while minimizing risks and unintended consequences.
Aide
Trailblazer
Navigator
Pathfinder
Lookout
Voyager
Oracle
Wayfinder
Today, AI agents are designed with three structures or architectures: single agents, multiple agents in a vertical hierarchy, and multiple agents in a horizontal hierarchy. Single agent structures are generally less complex, as they focus on individual tasks and actions. Multi-agent structures are generally more complex, as they involve communication and potential emergent behaviors among the agents.
The organizational structure of multiple agents is proving to be important. Vertical structures offer centralized control but can have information bottlenecks as all agents have to communicate through the “boss.” Horizontal structures offer more flexibility but can get weighed down by communication overhead and emergent behaviors. For instance, research has shown that agents in horizontal architectures can spend 50% of their time giving orders to each other and exchanging niceties like saying “how are you?”
Perhaps this is proof that LLMs trained on vast quantities of conversational text will learn to mimic water cooler chat. While chit-chat is important for human bonding, it’s likely just a waste of time and compute for machines.
Comparison of Single Agents vs Multi-Agents
Advantages and Disadvantages of Single Agents, Vertical Multi-Agents, and Horizontal Multi-Agents
What happens when your customers start to adopt AI agents to “get things done,” including searching for new products, purchasing products, and interacting with customer service agents? Your customer service will no longer solely consider human customers. Your marketing messages will no longer solely focus on human reception. Even your SEO might no longer solely focus on Google Search but on the countless AI agents that each individual human uses to find things on the Agentic Web.
As AI agents become more sophisticated, they may replace human customers in a wide range of interactions. This shift will require companies to fundamentally rethink their approach to customer experience design—shifting from customer experience (CX) to agent experience (AX).
Why would we want AI agents to handle these interactions and experiences for us? First, agents are able to do things we might value: process vast amounts of information, make objective decisions, and provide highly personalized experiences based on comprehensive user data. Second, the future of the internet (what we call the Agentic Web) will be overwhelmed by AI-generated content that humans will not be able to process—it will only be readable by machine. That means we will need AI agents to “read” the internet for us since the internet will be made by machines, for machines. Third, agents promise freedom—freedom from the devices where they work for us.
The adoption of AI agents is likely to begin with low-interaction utilities, such as bill payments and simple service inquiries. These transactions often involve standardized processes and require minimal personal input, making them well-suited for automation. As AI agents demonstrate their effectiveness and reliability in handling these tasks, consumers may become more comfortable entrusting them with more complex interactions. Imagine an AI agent that you use to purchase products on Amazon. Gone are the days of sifting through reviews and wondering if you might have missed something that’s important to you. An AI agent’s capability to process and analyze vast amounts of data might be increasingly important as the quantity of comments and reviews increases, written by AI.
It’s important to note here that we are unaware of authentication methods for AI agents that will be required for e-commerce companies, financial institutions, and regulators to approve of AI agents conducting transactions. But that gap is likely just a moment in time. As VeriSign’s authentication services grew out of the need to secure website connections, services to authenticate AI agency will likely be developed too.
It’s not possible to know how far this transition to agentic customers will go and over what time frame. But, no matter what, this future requires shifting focus from CS to AX. How might you design your company’s external experience to appeal to AI agents that are acting on behalf of humans?
Designing for AX requires a fundamentally different approach than traditional CX design. Rather than treating interactions as linear, predictable exchanges of information, AX design must account for the complex, emergent dynamics that arise when your organization’s agents interact with your customer’s agents. This means designing interfaces and interactions that are not only intuitive and user-friendly for humans, but also for AI agents.
Designing for AI agents also means being prepared for unintended consequences and unexpected behaviors that may arise from agent-agent interactions. This requires building in safeguards, monitoring mechanisms, and governance structures that can detect and respond to emergent risks or harms, while also enabling beneficial forms of emergence and adaptation to occur. And this requires building entirely new safety mechanisms—for both your organization and your customers.
It’s important to note that these design methods do not exist today. This is an important focus for Artificiality. We worry that the early and easy answers like oversight, override, transparency, explainability, accountability, while essential, will not be sufficient as AI is able to handle more complexity with more agency. And that is happening faster than anyone thought.
As a start, we offer a framework of seven design considerations, differentiated between a human (CX) and a machine (AX).
The Artificiality Weekend Briefing: About AI, Not Written by AI