Giovanni Pezzulo, Michael Levin
Achieving advanced machine intelligence remains a central challenge in AI research, often approached through scaling neural architectures and generative models. However, biological systems offer a broader repertoire of strategies for adaptive, goal-directed behavior – strategies that emerged long before nervous systems evolved. This paper advocates a genuinely life-inspired approach to machine intelligence, drawing on principles from biology that enable robustness, autonomy, and open-ended problem-solving across scales. We frame intelligence as flexible problem-solving, following William James, and develop the concept of “cognitive light cones” to characterize the continuum of intelligence in living systems and machines. We argue that biological evolution has discovered a scalable recipe for intelligence – and the progressive expansion of organisms’ “cognitive light cone”, predictive and control capacities. To explain how this is possible, we distill five design principles – multiscale autonomy, growth through self-assemblage of active components, continuous reconstruction of capabilities, exploitation of physical and embodied constraints, and pervasive signaling enabling self-organization and top-down control from goals – that underpin life’s ability to navigate creatively diverse problem spaces. We discuss how these principles contrast with current AI paradigms and outline pathways for integrating them into future autonomous, embodied, and resilient artificial systems.

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Tiago P. Peixoto, Leto Peel, Thilo Gross, Manlio De Domenico
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on “higher-order networks” that graph-based representations are fundamentally limited to “pairwise” interactions, requiring hypergraph formulations to capture richer dependencies. We clarify this issue by emphasizing two frequently overlooked facts. First, graph-based models are not restricted to pairwise interactions, as they naturally accommodate interactions that depend simultaneously on multiple adjacent nodes. Second, hypergraph formulations are strict special cases of more general graph-based representations, as they impose additional constraints on the allowable interactions between adjacent elements rather than expanding the space of possibilities. We show that key phenomenology commonly attributed to hypergraphs — such as abrupt transitions — can, in general, be recovered exactly using graph models, even locally tree-like ones, and thus do not constitute a class of phenomena that is inherently contingent on hypergraphs models. Finally, we argue that the broad relevance of hypergraphs for applications that is sometimes claimed in the literature is not supported by evidence. Instead it is likely grounded in misconceptions that network models cannot accommodate multibody interactions or that certain phenomena can only be captured with hypergraphs. We argue that clearly distinguishing between multivariate interactions, parametrized by graphs, and the functions that define them enables a more unified and flexible foundation for modeling interacting systems.

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Fernando Rodriguez-Vergara and Phil Husbands

Mathematics 2026, 14(3), 535

According to the Church–Turing thesis, the limit of what is computable is bounded by Turing machines. Following from this, given that general computable functions formally describe the notion of recursive mechanisms, it is sometimes argued that every organismic process that specifies consistent cognitive responses should be both limited to Turing machine capabilities and amenable to formalization. There is, however, a deep intuitive conviction permeating contemporary cognitive science, according to which mental phenomena, such as consciousness and agency, cannot be explained by resorting to this kind of framework. In spite of some exceptions, the overall tacit assumption is that whatever the mind is, it exceeds the reach of what is described by notions of computability. This issue, namely the nature of the relation between cognition and computation, becomes particularly pertinent and increasingly more relevant as a possible source of better understanding the inner workings of the mind, as well as the limits of artificial implementations thereof. Moreover, although it is often overlooked or omitted so as to simplify our models, it will probably define, or so we argue, the direction of future research on artificial life, cognitive science, artificial intelligence, and related fields.

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