Toward a theory of evolution as multilevel learning

Thermodynamic consistency of autocatalytic cycles

Autocatalysis is seen as a potential key player in the origin of life, and perhaps more generally in the emergence of Darwinian dynamics. Building on recent formalizations of this phenomenon, we tackle the computational challenge of exhaustively detecting minimal autocatalytic cycles (autocatalytic cores) in reaction networks and further evaluate the impact of thermodynamic constraints on their realization under mass action kinetics. We first characterize the complexity of the detection problem by proving its NP-completeness. This justifies the use of constraint solvers to list all cores in a given reaction network, and also to group them into compatible sets, composed of cores whose stoichiometric requirements are not contradictory. Crucially, we show that the introduction of thermodynamic realism does constrain the composition of these sets. Compatibility relationships among autocatalytic cores can indeed be disrupted when the reaction kinetics obey thermodynamic consistency throughout the network. On the contrary, these constraints have no impact on the realizability of isolated cores, unless upper or lower bounds are imposed on the concentrations of the reactants. Overall, by better characterizing the conditions of autocatalysis in complex reaction systems, this work brings us a step closer to assessing the contribution of this collective chemical behavior to the emergence of natural selection in the primordial soup.

Maximum Entropy Production Principle of Thermodynamics for the Birth and Evolution of Life

Research on the birth and evolution of life are reviewed with reference to the maximum entropy production principle (MEPP). It has been shown that this principle is essential for consistent understanding of the birth and evolution of life. First, a recent work for the birth of a self-replicative system as pre-RNA life is reviewed in relation to the MEPP. A critical condition of polymer concentration in a local system is reported by a dynamical system approach, above which, an exponential increase of entropy production is guaranteed. Secondly, research works of early stage of evolutions are reviewed; experimental research for the numbers of cells necessary for forming a multi-cellular organization, and numerical research of differentiation of a model system and its relation with MEPP. It is suggested by this review article that the late stage of evolution is characterized by formation of society and external entropy production. A hypothesis on the general route of evolution is discussed from the birth to the present life which follows the MEPP. Some examples of life which happened to face poor thermodynamic condition are presented with thermodynamic discussion. It is observed through this review that MEPP is consistently useful for thermodynamic understanding of birth and evolution of life, subject to a thermodynamic condition far from equilibrium.

Purine Chemistry in the Early RNA World at the Origins of Life: From RNA and Nucleobases Lesions to Current Key Metabolic Routes

In early life, RNA probably played the central role and, in the corresponding RNA world, the main produced amino acids and small peptides had to react continuously with RNA, ribonucleos(t)ides and nucleobases, especially with purines. A RNA-peptide world and key metabolic pathways have emerged from the corresponding chemical modifications such as the translation process performed by the ribosome. Some interesting reactions of the purine bicycle and of the corresponding ribonucleos(t)ides are performed under plausible prebiotic conditions and described RNA chemical lesions are reviewed with the prospect to highlight their connection with some major steps of the purine and histidine biosynthetic pathways that are, in an intriguingly way, related through two key metabolites, adenosine 5'-triphosphate and the imidazole ribonucleotide 5-aminoimidazole-4-carboxamide ribonucleotide. Ring-opening reactions of purines stand out as efficient accesses to imidazole ribonucleotides and to formamidopyrimidine (Fapy) ribonucleotides suggesting that biosynthetic pathway' first steps have emerged from RNA and ribonucleos(t)ide damages. Also, are summarized the works on the formation and catalytic properties, under plausible prebiotic conditions, of N6-derivatives of the purine base adenine as potential surrogates of histidine in catalysis accordingly to their structural relationship.

Neural network properties of hydrophilic polymers as a key for development of the general theory of evolution

The analysis of the existing literature demonstrates that in order to address the fundamental challenges associated with the origin of life, it is essential to consider this problem from a comprehensive perspective, specifically from the vantage point of the general theory of evolution of complex systems. From these positions, life should be regarded as a distinctive instance of an information storage and processing system that emerges naturally. Evolutionary processes should be examined from the vantage point of the coevolution of material and informational components, which has not been sufficiently emphasized hitherto. It is shown that a specific example in this respect is analogues of neural networks spontaneously formed in solutions of some hydrophilic polymers. Such systems lead to the formation of non-trivial information objects. A wide range of other examples is considered, proving that the processes occurring with the participation of hydrophilic polymers should be interpreted, among other things, from the point of view of formation of information objects, which, under certain conditions, influence the processes occurring at the molecular and supramolecular level. It is shown that it is reasonable to use the tools of classical dialectics to solve such fundamental problems as that of the origin of life.

Principles of Molecular Evolution: Concepts from Non-equilibrium Thermodynamics for the Multilevel Theory of Learning

We present a non-equilibrium thermodynamics approach to the multilevel theory of learning for the study of molecular evolution. This approach allows us to study the explicit time dependence of molecular evolutionary processes and their impact on entropy production. Interpreting the mathematical expressions, we can show that two main contributions affect entropy production of molecular evolution processes which can be identified as mutation and gene transfer effects. Accordingly, our results show that the optimal adaptation of organisms to external conditions in the context of evolutionary processes is driven by principles of minimum entropy production. Such results can also be interpreted as the basis of some previous postulates of the theory of learning. Although our macroscopic approach requires certain simplifications, it allows us to interpret molecular evolutionary processes using thermodynamic descriptions with reference to well-known biological processes.

Biothermodynamics of Hemoglobin and Red Blood Cells: Analysis of Structure and Evolution of Hemoglobin and Red Blood Cells, Based on Molecular and Empirical Formulas, Biosynthesis Reactions, and Thermodynamic Properties of Formation and Biosynthesis

Hemoglobin and red blood cells (erythrocytes) have been studied extensively from the perspective of life and biomedical sciences. However, no analysis of hemoglobin and red blood cells from the perspective of chemical thermodynamics has been reported in the literature. Such an analysis would provide an insight into their structure and turnover from the aspect of biothermodynamics and bioenergetics. In this paper, a biothermodynamic analysis was made of hemoglobin and red blood cells. Molecular formulas, empirical formulas, biosynthesis reactions, and thermodynamic properties of formation and biosynthesis were determined for the alpha chain, beta chain, heme B, hemoglobin and red blood cells. Empirical formulas and thermodynamic properties of hemoglobin were compared to those of other biological macromolecules, which include proteins and nucleic acids. Moreover, the energetic requirements of biosynthesis of hemoglobin and red blood cells were analyzed. Based on this, a discussion was made of the specific structure of red blood cells (i.e. no nuclei nor organelles) and its role as an evolutionary adaptation for more energetically efficient biosynthesis needed for the turnover of red blood cells.

Complexity and entropy of natural patterns

Complexity and entropy play crucial roles in understanding dynamic systems across various disciplines. Many intuitively perceive them as distinct measures and assume that they have a concave-down relationship. In everyday life, there is a common consensus that while entropy never decreases, complexity does decrease after an initial increase during the process of blending coffee and milk. However, this consensus is primarily conceptual and lacks empirical evidence. Here, we provide comprehensive evidence that challenges this prevailing consensus. We demonstrate that this consensus is, in fact, an illusion resulting from the choice of system characterization (dimension) and the unit of observation (resolution). By employing a complexity measure designed for natural patterns, we find that the complexity of a coffee-milk system never decreases if the system is appropriately characterized in terms of dimension and resolution. Also, this complexity aligns experimentally and theoretically with entropy, suggesting that it does not represent a measure of so-called effective complexity. These findings rectify the prevailing conceptual consensus and reshape our understanding of the relationship between complexity and entropy. It is therefore crucial to exercise caution and pay close attention to accurately and precisely characterize dynamic systems before delving into their underlying mechanisms, despite the maturity of characterization research in various fields dealing with natural patterns such as geography and ecology. The characterization/observation (dimension and resolution) of a system fundamentally determines the assessment of complexity and entropy using existing measures and our understanding.

Reflexive neural circuits and the origin of language and music codes

Conscious activity is grounded in the reflexive self-awareness in sense perception, through which the codes signifying sensual perceptive events operate and constrain human behavior. These codes grow via the creative generation of hypertextual statements. We apply the model of Vladimir Lefebvre (Lefebvre, V.A., 1987, J. Soc. Biol. Struct. 10, 129-175) to reveal the underlying structures on which the perception and creative development of language and music codes are based. According to this model, the reflexive structure of conscious subject is grounded in three thermodynamic cycles united by the control of the basic functional cycle by the second one, and resulting in the internal action that it turn is perceived by the third cycle evaluating this action. In this arrangement, the generative language structures are formed and the frequencies of sounds that form musical phrases and patterns are selected. We discuss the participation of certain neural brain structures and the establishment of reflexive neural circuits in the ad hoc transformation of perceptive signals, and show the similarities between the processes of perception and of biological self-maintenance and morphogenesis. We trace the peculiarities of the temporal encoding of emotions in music and musical creativity, as well as the principles of sharing musical information between the performing and the perceiving individuals.

Life should be redefined: Any molecule with the ability to self-replicate should be considered life

Understanding the nature of life and its propensity for reproduction has long been a question that humans aspire to answer. Reproduction, a defining characteristic of life, fundamentally involves the replication of genetic material, be it DNA or RNA. The driving force behind this replication process has always intrigued scientists. In recent years, theories involving selfish genes, the RNA world, and entropic forces have been proposed by some scholars. These theories seem to suggest that life, as we know it, exists solely in Earth's environment and is based on a single type of genetic material, either DNA or RNA. However, if we broaden our definition of life to include any replicable molecules, we might be able to transcend traditional thought. This could potentially enhance our understanding of the impetus behind DNA replication and provide deeper insights into the essence of life.

Evolutionarily new genes in humans with disease phenotypes reveal functional enrichment patterns shaped by adaptive innovation and sexual selection

New genes (or young genes) are genetic novelties pivotal in mammalian evolution. However, their phenotypic impacts and evolutionary patterns over time remain elusive in humans due to the technical and ethical complexities of functional studies. Integrating gene age dating with Mendelian disease phenotyping, our research shows a gradual rise in disease gene proportion as gene age increases. Logistic regression modeling indicates that this increase in older genes may be related to their longer sequence lengths and higher burdens of deleterious de novo germline variants (DNVs). We also find a steady integration of new genes with biomedical phenotypes into the human genome over macroevolutionary timescales (~0.07% per million years). Despite this stable pace, we observe distinct patterns in phenotypic enrichment, pleiotropy, and selective pressures across gene ages. Notably, young genes show significant enrichment in diseases related to the male reproductive system, indicating strong sexual selection. Young genes also exhibit disease-related functions in tissues and systems potentially linked to human phenotypic innovations, such as increased brain size, musculoskeletal phenotypes, and color vision. We further reveal a logistic growth pattern of pleiotropy over evolutionary time, indicating a diminishing marginal growth of new functions for older genes due to intensifying selective constraints over time. We propose a "pleiotropy-barrier" model that delineates higher potentials for phenotypic innovation in young genes compared to older genes, a process that is subject to natural selection. Our study demonstrates that evolutionarily new genes are critical in influencing human reproductive evolution and adaptive phenotypic innovations driven by sexual and natural selection, with low pleiotropy as a selective advantage.

'Snakes and ladders' in paleoanthropology: From cognitive surprise to skillfulness a million years ago

A paradigmatic account may suffice to explain behavioral evolution in early Homo. We propose a parsimonious account that (1) could explain a particular, frequently-encountered, archeological outcome of behavior in early Homo - namely, the fashioning of a Paleolithic stone 'handaxe' - from a biological theoretic perspective informed by the free energy principle (FEP); and that (2) regards instances of the outcome as postdictive or retrodictive, circumstantial corroboration. Our proposal considers humankind evolving as a self-organizing biological ecosystem at a geological time-scale. We offer a narrative treatment of this self-organization in terms of the FEP. Specifically, we indicate how 'cognitive surprises' could underwrite an evolving propensity in early Homo to express sporadic unorthodox or anomalous behavior. This co-evolutionary propensity has left us a legacy of Paleolithic artifacts that is reminiscent of a 'snakes and ladders' board game of appearances, disappearances, and reappearances of particular archeological traces of Paleolithic behavior. When detected in the Early and Middle Pleistocene record, anthropologists and archeologists often imagine evidence of unusual or novel behavior in terms of early humankind ascending the rungs of a figurative phylogenetic 'ladder' - as if these corresponded to progressive evolution of cognitive abilities that enabled incremental achievements of increasingly innovative technical prowess, culminating in the cognitive ascendancy of Homo sapiens. The conjecture overlooks a plausible likelihood that behavior by an individual who was atypical among her conspecifics could have been disregarded in a community of Hominina (for definition see Appendix 1) that failed to recognize, imagine, or articulate potential advantages of adopting hitherto unorthodox behavior. Such failure, as well as diverse fortuitous demographic accidents, would cause exceptional personal behavior to be ignored and hence unremembered. It could disappear by a pitfall, down a 'snake', as it were, in the figurative evolutionary board game; thereby causing a discontinuity in the evolution of human behavior that presents like an evolutionary puzzle. The puzzle discomforts some paleoanthropologists trained in the natural and life sciences. They often dismiss it, explaining it away with such self-justifying conjectures as that, maybe, separate paleospecies of Homo differentially possessed different cognitive abilities, which, supposedly, could account for the presence or absence in the Pleistocene archeological record of traces of this or that behavioral outcome or skill. We argue that an alternative perspective - that inherits from the FEP and an individual's 'active inference' about its surroundings and of its own responses - affords a prosaic, deflationary, and parsimonious way to account for appearances, disappearances, and reappearances of particular behavioral outcomes and skills of early humankind.

Evolution at the Origins of Life?

The role of evolutionary theory at the origin of life is an extensively debated topic. The origin and early development of life is usually separated into a prebiotic phase and a protocellular phase, ultimately leading to the Last Universal Common Ancestor. Most likely, the Last Universal Common Ancestor was subject to Darwinian evolution, but the question remains to what extent Darwinian evolution applies to the prebiotic and protocellular phases. In this review, we reflect on the current status of evolutionary theory in origins of life research by bringing together philosophy of science, evolutionary biology, and empirical research in the origins field. We explore the various ways in which evolutionary theory has been extended beyond biology; we look at how these extensions apply to the prebiotic development of (proto)metabolism; and we investigate how the terminology from evolutionary theory is currently being employed in state-of-the-art origins of life research. In doing so, we identify some of the current obstacles to an evolutionary account of the origins of life, as well as open up new avenues of research.

Toward the Relational Formulation of Biological Thermodynamics

Classical thermodynamics employs the state of thermodynamic equilibrium, characterized by maximal disorder of the constituent particles, as the reference frame from which the Second Law is formulated and the definition of entropy is derived. Non-equilibrium thermodynamics analyzes the fluxes of matter and energy that are generated in the course of the general tendency to achieve equilibrium. The systems described by classical and non-equilibrium thermodynamics may be heuristically useful within certain limits, but epistemologically, they have fundamental problems in the application to autopoietic living systems. We discuss here the paradigm defined as a relational biological thermodynamics. The standard to which this refers relates to the biological function operating within the context of particular environment and not to the abstract state of thermodynamic equilibrium. This is defined as the stable non-equilibrium state, following Ervin Bauer. Similar to physics, where abandoning the absolute space-time resulted in the application of non-Euclidean geometry, relational biological thermodynamics leads to revealing the basic iterative structures that are formed as a consequence of the search for an optimal coordinate system by living organisms to maintain stable non-equilibrium. Through this search, the developing system achieves the condition of maximization of its power via synergistic effects.

Evolutionarily new genes in humans with disease phenotypes reveal functional enrichment patterns shaped by adaptive innovation and sexual selection

New genes (or young genes) are structural novelties pivotal in mammalian evolution. Their phenotypic impact on humans, however, remains elusive due to the technical and ethical complexities in functional studies. Through combining gene age dating with Mendelian disease phenotyping, our research reveals that new genes associated with disease phenotypes steadily integrate into the human genome at a rate of ~ 0.07% every million years over macroevolutionary timescales. Despite this stable pace, we observe distinct patterns in phenotypic enrichment, pleiotropy, and selective pressures between young and old genes. Notably, young genes show significant enrichment in the male reproductive system, indicating strong sexual selection. Young genes also exhibit functions in tissues and systems potentially linked to human phenotypic innovations, such as increased brain size, bipedal locomotion, and color vision. Our findings further reveal increasing levels of pleiotropy over evolutionary time, which accompanies stronger selective constraints. We propose a "pleiotropy-barrier" model that delineates different potentials for phenotypic innovation between young and older genes subject to natural selection. Our study demonstrates that evolutionary new genes are critical in influencing human reproductive evolution and adaptive phenotypic innovations driven by sexual and natural selection, with low pleiotropy as a selective advantage.

A Variational Synthesis of Evolutionary and Developmental Dynamics

This paper introduces a variational formulation of natural selection, paying special attention to the nature of 'things' and the way that different 'kinds' of 'things' are individuated from-and influence-each other. We use the Bayesian mechanics of particular partitions to understand how slow phylogenetic processes constrain-and are constrained by-fast, phenotypic processes. The main result is a formulation of adaptive fitness as a path integral of phenotypic fitness. Paths of least action, at the phenotypic and phylogenetic scales, can then be read as inference and learning processes, respectively. In this view, a phenotype actively infers the state of its econiche under a generative model, whose parameters are learned via natural (Bayesian model) selection. The ensuing variational synthesis features some unexpected aspects. Perhaps the most notable is that it is not possible to describe or model a population of conspecifics per se. Rather, it is necessary to consider populations of distinct natural kinds that influence each other. This paper is limited to a description of the mathematical apparatus and accompanying ideas. Subsequent work will use these methods for simulations and numerical analyses-and identify points of contact with related mathematical formulations of evolution.

Entropic Dynamics in a Theoretical Framework for Biosystems

Central to an understanding of the physical nature of biosystems is an apprehension of their ability to control entropy dynamics in their environment. To achieve ongoing stability and survival, living systems must adaptively respond to incoming information signals concerning matter and energy perturbations in their biological continuum (biocontinuum). Entropy dynamics for the living system are then determined by the natural drive for reconciliation of these information divergences in the context of the constraints formed by the geometry of the biocontinuum information space. The configuration of this information geometry is determined by the inherent biological structure, processes and adaptive controls that are necessary for the stable functioning of the organism. The trajectory of this adaptive reconciliation process can be described by an information-theoretic formulation of the living system's procedure for actionable knowledge acquisition that incorporates the axiomatic inference of the Kullback principle of minimum information discrimination (a derivative of Jaynes' principle of maximal entropy). Utilizing relative information for entropic inference provides for the incorporation of a background of the adaptive constraints in biosystems within the operations of Fisher biologic replicator dynamics. This mathematical expression for entropic dynamics within the biocontinuum may then serve as a theoretical framework for the general analysis of biological phenomena.

Evolution is driven by natural autoencoding: reframing species, interaction codes, cooperation and sexual reproduction

The continuity of life and its evolution, we proposed, emerge from an interactive group process manifested in networks of interaction. We term this process survival of the fitted. Here, we reason that survival of the fitted results from a natural computational process we term natural autoencoding. Natural autoencoding works by retaining repeating biological interactions while non-repeatable interactions disappear. (i) We define a species by its species interaction code, which consists of a compact description of the repeating interactions of species organisms with their external and internal environments. Species interaction codes are descriptions recorded in the biological infrastructure that enables repeating interactions. Encoding and decoding are interwoven. (ii) Evolution proceeds by natural autoencoding of sustained changes in species interaction codes. DNA is only one element in natural autoencoding. (iii) Natural autoencoding accounts for the paradox of genome randomization in sexual reproduction-recombined genomes are analogous to the diversified inputs required for artificial autoencoding. The increase in entropy generated by genome randomization compensates for the decrease in entropy generated by organized life. (iv) Natural autoencoding and artificial autoencoding algorithms manifest defined similarities and differences. Recognition of the importance of fittedness could well serve the future of a humanly livable biosphere.

Learning by Population Genetics and Matrix Riccati Equation

A model of learning as a generalization of the Eigen's quasispecies model in population genetics is introduced. Eigen's model is considered as a matrix Riccati equation. The error catastrophe in the Eigen's model (when the purifying selection becomes ineffective) is discussed as the divergence of the Perron-Frobenius eigenvalue of the Riccati model in the limit of large matrices. A known estimate for the Perron-Frobenius eigenvalue provides an explanation for observed patterns of genomic evolution. We propose to consider the error catastrophe in Eigen's model as an analog of overfitting in learning theory; this gives a criterion for the presence of overfitting in learning.

Dissipation + Utilization = Self-Organization

This article applies the thermocontextual interpretation (TCI) to open dissipative systems. TCI is a generalization of the conceptual frameworks underlying mechanics and thermodynamics. It defines exergy with respect to the positive-temperature surroundings as a property of state, and it defines the dissipation and utilization of exergy as functional properties of process. The Second Law of thermodynamics states that an isolated system maximizes its entropy (by dissipating and minimizing its exergy). TCI's Postulate Four generalizes the Second Law for non-isolated systems. A non-isolated system minimizes its exergy, but it can do so either by dissipating exergy or utilizing it. A non-isolated dissipator can utilize exergy either by performing external work on the surroundings or by carrying out the internal work of sustaining other dissipators within a dissipative network. TCI defines a dissipative system's efficiency by the ratio of exergy utilization to exergy input. TCI's Postulate Five (MaxEff), introduced here, states that a system maximizes its efficiency to the extent allowed by the system's kinetics and thermocontextual boundary constraints. Two paths of increasing efficiency lead to higher rates of growth and to higher functional complexity for dissipative networks. These are key features for the origin and evolution of life.

Energy-harnessing problem solving of primordial life: Modeling the emergence of catalytic host-nested parasite life cycles

All life forms on earth ultimately descended from a primordial population dubbed the last universal common ancestor or LUCA via Darwinian evolution. Extant living systems share two salient functional features, a metabolism extracting and transforming energy required for survival, and an evolvable, informational polymer-the genome-conferring heredity. Genome replication invariably generates essential and ubiquitous genetic parasites. Here we model the energetic, replicative conditions of LUCA-like organisms and their parasites, as well as adaptive problem solving of host-parasite pairs. We show using an adapted Lotka-Volterra frame-work that three host-parasite pairs-individually a unit of a host and a parasite that is itself parasitized, therefore a nested parasite pair-are sufficient for robust and stable homeostasis, forming a life cycle. This nested parasitism model includes competition and habitat restriction. Its catalytic life cycle efficiently captures, channels and transforms energy, enabling dynamic host survival and adaptation. We propose a Malthusian fitness model for a quasispecies evolving through a host-nested parasite life cycle with two core features, rapid replacement of degenerate parasites and increasing evolutionary stability of host-nested parasite units from one to three pairs.

Phase transitions in evolutionary dynamics

Sharp changes in state, such as transitions from survival to extinction, are hallmarks of evolutionary dynamics in biological systems. These transitions can be explored using the techniques of statistical physics and the physics of nonlinear and complex systems. For example, a survival-to-extinction transition can be characterized as a non-equilibrium phase transition to an absorbing state. Here, we review the literature on phase transitions in evolutionary dynamics. We discuss directed percolation transitions in cellular automata and evolutionary models, and models that diverge from the directed percolation universality class. We explore in detail an example of an absorbing phase transition in an agent-based model of evolutionary dynamics, including previously unpublished data demonstrating similarity to, but also divergence from, directed percolation, as well as evidence for phase transition behavior at multiple levels of the model system's evolutionary structure. We discuss phase transition models of the error catastrophe in RNA virus dynamics and phase transition models for transition from chemistry to biochemistry, i.e., the origin of life. We conclude with a review of phase transition dynamics in models of natural selection, discuss the possible role of phase transitions in unraveling fundamental unresolved questions regarding multilevel selection and the major evolutionary transitions, and assess the future outlook for phase transitions in the investigation of evolutionary dynamics.

Overcoming the limits of natural computation in biological evolution toward the maximization of system efficiency

The goal-directedness of biological evolution is realized via the anticipatory achievement of the final state of the system that corresponds to the condition of its perfection in self-maintenance and in adaptability. In the course of individual development, a biological system maximizes its power via synergistic effects and becomes able to perform external work most efficiently. In this state, defined as stasis, robust self-maintaining configurations act as attractors resistant to external and internal perturbations. This corresponds to the local energy–time constraints that most efficiently fit the integral optimization of the whole system. In evolution, major evolutionary transitions that establish new states of stasis are achieved via codepoiesis, a process in which the undecided statements of existing coding systems form the basis for the evolutionary unfolding of the system by assigning new values to them. The genetic fixation of this macroevolutionary process leads to new programmes of individual development representing the process of natural computation. The phenomenon of complexification in evolution represents a metasystem transition that results in maximization of a system’s power and in the ability to increase external work performed by the system.

Melting temperature prediction using a graph neural network model: From ancient minerals to new materials

The melting point is a fundamental property that is time-consuming to measure or compute, thus hindering high-throughput analyses of melting relations and phase diagrams over large sets of candidate compounds. To address this, we build a machine learning model, trained on a database of ∼10,000 compounds, that can predict the melting temperature in a fraction of a second. The model, made publicly available online, features graph neural network and residual neural network architectures. We demonstrate the model's usefulness in diverse applications. For the purpose of materials design and discovery, we show that it can quickly discover novel multicomponent materials with high melting points. These predictions are confirmed by density functional theory calculations and experimentally validated. In an application to planetary science and geology, we employ the model to analyze the melting temperatures of ∼4,800 minerals to uncover correlations relevant to the study of mineral evolution.

Toward a theory of evolution as multilevel learning

We apply the theory of learning to physically renormalizable systems in an attempt to outline a theory of biological evolution, including the origin of life, as multilevel learning. We formulate seven fundamental principles of evolution that appear to be necessary and sufficient to render a universe observable and show that they entail the major features of biological evolution, including replication and natural selection. It is shown that these cornerstone phenomena of biology emerge from the fundamental features of learning dynamics such as the existence of a loss function, which is minimized during learning. We then sketch the theory of evolution using the mathematical framework of neural networks, which provides for detailed analysis of evolutionary phenomena. To demonstrate the potential of the proposed theoretical framework, we derive a generalized version of the Central Dogma of molecular biology by analyzing the flow of information during learning (back propagation) and predicting (forward propagation) the environment by evolving organisms. The more complex evolutionary phenomena, such as major transitions in evolution (in particular, the origin of life), have to be analyzed in the thermodynamic limit, which is described in detail in the paper by Vanchurin et al. [V. Vanchurin, Y. I. Wolf, E. V. Koonin, M. I. Katsnelson, Proc. Natl. Acad. Sci. U.S.A. 119, 10.1073/pnas.2120042119 (2022)].