Scientists have grappled with reconciling biological evolution^1,2 with the immutable laws of the Universe defined by physics. These laws underpin life’s origin, evolution and the development of human culture and technology, yet they do not predict the emergence of these phenomena. Evolutionary theory explains why some things exist and others do not through the lens of selection. To comprehend how diverse, open-ended forms can emerge from physics without an inherent design blueprint, a new approach to understanding and quantifying selection is necessary^3–5. We present assembly theory (AT) as a framework that does not alter the laws of physics, but redefines the concept of an ‘object’ on which these laws act. AT conceptualizes objects not as point particles, but as entities defined by their possible formation histories. This allows objects to show evidence of selection, within well-defined boundaries of individuals or selected units. We introduce a measure called assembly (A), capturing the degree of causation required to produce a given ensemble of objects. This approach enables us to incorporate novelty generation and selection into the physics of complex objects. It explains how these objects can be characterized through a forward dynamical process considering their assembly. By reimagining the concept of matter within assembly spaces, AT provides a powerful interface between physics and biology. It discloses a new aspect of physics emerging at the chemical scale, whereby history and causal contingency influence what exists.

Complexity of life forms on the Earth has increased tremendously, primarily driven by subsequent evolutionary transitions in individuality, a mechanism in which units formerly being capable of independent replication combine to form higher-level evolutionary units. Although this process has been likened to the recursive combination of pre-adapted sub-solutions in the framework of learning theory, no general mathematical formalization of this analogy has been provided yet. Here we show, building on former results connecting replicator dynamics and Bayesian update, that (i) evolution of a hierarchical population under multilevel selection is equivalent to Bayesian inference in hierarchical Bayesian models and (ii) evolutionary transitions in individuality, driven by synergistic fitness interactions, is equivalent to learning the structure of hierarchical models via Bayesian model comparison. These correspondences support a learning theory-oriented narrative of evolutionary complexification: the complexity and depth of the hierarchical structure of individuality mirror the amount and complexity of data that have been integrated about the environment through the course of evolutionary history.

Bayesian learning theory and evolutionary theory both formalize adaptive competition dynamics in possibly high‐dimensional, varying, and noisy environments. What do they have in common and how do they differ? In this paper, we discuss structural and dynamical analogies and their limits, both at a computational and an algorithmic‐mechanical level. We point out mathematical equivalences between their basic dynamical equations, generalizing the isomorphism between Bayesian update and replicator dynamics. We discuss how these mechanisms provide analogous answers to the challenge of adapting to stochastically changing environments at multiple timescales. We elucidate an algorithmic equivalence between a sampling approximation, particle filters, and the Wright‐Fisher model of population genetics. These equivalences suggest that the frequency distribution of types in replicator populations optimally encodes regularities of a stochastic environment to predict future environments, without invoking the known mechanisms of multilevel selection and evolvability. A unified view of the theories of learning and evolution comes in sight.

Efficient search in vast combinatorial spaces, such as those of possible action sequences, linguistic structures, or causal explanations, is an essential component of intelligence. Is there any computational domain that is flexible enough to provide solutions to such diverse problems and can be robustly implemented over neural substrates? Based on previous accounts, we propose that a Darwinian process, operating over sequential cycles of imperfect copying and selection of neural informational patterns, is a promising candidate. Here we implement imperfect information copying through one reservoir computing unit teaching another. Teacher and learner roles are assigned dynamically based on evaluation of the readout signal. We demonstrate that the emerging Darwinian population of readout activity patterns is capable of maintaining and continually improving upon existing solutions over rugged combinatorial reward landscapes. We also demonstrate the existence of a sharp error threshold, a neural noise level beyond which information accumulated by an evolutionary process cannot be maintained. We introduce a novel analysis method, neural phylogenies, that displays the unfolding of the neural-evolutionary process.

Complexity of life forms on Earth has increased tremendously, primarily driven by subsequent evolutionary transitions in individuality, a mechanism in which units formerly being capable of independent replication combine to form higher-level evolutionary units. Although this process has been likened to the recursive combination of pre-adapted subsolutions in the framework of learning theory, no general mathematical formalization of this analogy has been provided yet. Here we show, building on former results connecting replicator dynamics and Bayesian update, that (i) evolution of a hierarchical population under multilevel selection is equivalent to Bayesian inference in hierarchical Bayesian models, and (ii) evolutionary transitions in individuality, driven by synergistic fitness interactions, is equivalent to learning the structure of hierarchical models via Bayesian model comparison. These correspondences support a learning theory oriented narrative of evolutionary complexification: the complexity and depth of the hierarchical structure of individuality mirrors the amount and complexity of data that has been integrated about the environment through the course of evolutionary history.

The Bayesian framework offers a flexible language for the consistent modular assembly of statistical models used by both minds and machines. Another algorithmic domain capable of adaptation in potentially high-dimensional and uncertain environments is Darwinian evolution. The equivalence of their fundamental dynamical equations, replicator dynamics and Bayesian update, hints at a deeper algorithmic analogy. Here we show, based on a unified mathematical discussion of evolutionary dynamics and statistical learning in terms of Bayesian graphical models, that this is indeed the case. Building blocks of Bayesian computations, such as inference in hierarchical models, filtering in hidden Markov models, gradient likelihood optimization, and expectation-maximization dynamics of mixture models, map naturally to fundamental concepts of evolution: multilevel selection, quasispecies dynamics, phenotypic adaptation and ecological competition, respectively. We believe that these correspondences point towards a more comprehensive understanding of flavors of adaptive computation observed in Nature, as well as suggesting new ways to combine insights from the two domains in engineering applications.