Taxonomy of Self-Evolving Techniques

• The taxonomy of self-evolving techniques is a categorization of computational methods that autonomously adapt and optimize using evolutionary dynamics and meta-level feedback.
• It systematically classifies methods based on evolutionary algorithms, algebraic rewriting frameworks, adaptive population topology, and self-supervised taxonomy expansion.
• Key metrics, such as Physical Complexity and clustering efficiency, provide quantifiable insights into emergent self-organization across diverse digital and agentic systems.

Self-evolving techniques comprise a broad class of computational methods in which the system autonomously adapts, restructures, or optimizes itself via mechanisms such as evolutionary dynamics, meta-adaptation, self-supervision, or continual feedback-driven restructuring. These techniques draw conceptual foundations from biological evolution, information theory, formal rewriting systems, adaptive architectures, and recent advances in agentic and neural systems. The taxonomy of self-evolving techniques has grown to encompass evolutionary algorithms, digital ecosystems, self-modifying agents, self-supervised taxonomy expansion, organic computing architectures, and more, each with specific mathematical, algorithmic, or structural models to characterize the self-evolution process.

1. Evolutionary Dynamics in Digital Ecosystems and Agent Populations

Digital ecosystems represent a primary paradigm in which self-evolving techniques are formalized as evolutionary multi-agent systems (MASs) wherein the self-organization of agent populations—defined through replication, mutation, recombination, and local selection—gives rise to emergent global order (0803.2675). Self-organization is quantified by the emergence of structured, non-random patterns among agents evolving under internal Darwinian selection.

Physical Complexity, an extension from biological information measures, serves as the primary macroscopic indicator. For a fixed-length agent population, Physical Complexity is defined as:

$C = \ell - \sum_{i=1}^\ell H(i)$

where $\ell$ is the sequence length and $H(i)$ is the Shannon entropy at site $i$, defined as:

$H(i) = -\sum_{d \in D} p_d(i) \log_{|D|} p_d(i)$

for alphabet $D$. The extension to variable-length populations introduces a computable length $\ell_V$ and analogous entropy-based terms.

An Efficiency metric $E = C_V / C_{VP}$, with $C_{VP} = \ell_V$, measures clustering—the degree to which population diversity collapses into high-fitness, coherent organizations. This formalism distinguishes between self-evolving systems by their evolutionary operators (selection, recombination, mutation), sequence representations (fixed vs. variable-length), and their move toward clustering or maintaining diversity.

2. Algebraic and Rewriting Frameworks for Autonomous Self-Evolution

Formal algebraic frameworks for self-evolving problem solvers are typified by the use of net block homomorphisms, renetting systems, and abstraction hierarchies to enable recursive self-modification of system structure (Tirri, 2013).

• Net block homomorphism generalizes the standard notion of homomorphism by allowing entire subnetworks (blocks) to be abstracted into atomic units, supporting high-order structural reconfigurations:

$h(t) = h_p(s)(h(p_i), h(p_j))$

where $t$ is a net with in/out arities $p_i$, $p_j$, and $h_p$ abstracts blocks.

• Renetting systems (RNS) are context-sensitive rewriting systems over arbitrary graph structures (nets), enabling solution generation via rule preforms, abstracting away from standard tree-based grammars.
• Saturation via equivalence classes and iterative abstraction closures produce hierarchical abstraction algebras, ensuring that solutions obtained at one abstraction level generalize to entire classes of equivalent problems, while preserving decidability:

$S_{R}^{\#} = S_{R}^{*} \cap IRR(R)$

(where $S_R^*$ is the closure under rewriting system $R$, $IRR(R)$ the irreducible normal forms).

This framework enables a taxonomy based on levels of abstraction (from ground to memory to meta-levels), the operational power of renetting systems, and the decidability properties of the evolving solution set.

3. Adaptive Evolutionary Algorithms and Population Topology

Adaptation in evolutionary computation is not restricted to parameter tuning but extends to the topology and interaction structure of populations (0907.0516). The Event Takeover Value (ETV) is introduced as a genealogical metric, quantifying the impact of individuals on future population dynamics. Empirically, ETV sizes often follow a power-law distribution, reflecting that most individuals have limited influence while a minority can found evolutionary "lineages" with long-term consequences.

Self-organizing topology evolutionary algorithms (SOTEA) allow not only genetic operators but the social network of interactions to adapt:

• Nodes (individuals) may rewire their connections during reproduction and competition.
• "Epistatic fitness" makes the fitness of an individual relative to its local neighborhood, thus explicitly coupling network structure with evolutionary dynamics.

Experimental comparisons show these topologically-adaptive EAs outperform both panmictic and static-grid EAs on multimodal tasks, preserve greater genetic diversity among elite individuals, and enable parallelized search.

4. Self-Adaptation and Meta-Level Improvement in Organic Computing

Organic computing introduces a hierarchical view where systems self-improve not only by adaption at the resource or application level but by evolving the very logic and mechanisms of adaptation themselves (Niederquell, 2018).

Key strategies include:

• Three Layer Architecture (3LA): Segregating component control, change management, and goal management, to decouple application concerns from adaptation logic.
• Dynamic Control Loops (DCL): Meta-adaptation via runtime-modifiable control loops (collect, analyze, decide, act).
• Organic Traffic Light Control (OTC): A reflective architectural layer uses evolutionary algorithms to evolve classifiers used by a reactive learning layer (Learning Classifier System).
• Models@Runtime for Meta-Adaptation: Evolution targets the model and adaptation logic itself, enabling the system to cope with unforeseen circumstances by fundamentally revising its operational logic.

Taxonomically, organic computing situates self-evolving techniques across the "when", "why", "where", "what", and "how" dimensions of the Krupitzer taxonomy, enabling systematic comparison and hybridization.

5. Self-Evolving Neural and Agentic Systems

Recent advances focus on autonomous agentic systems and neural architectures capable of self-evolution through a variety of feedback mechanisms and adaptation modes. This class includes both biologically-motivated neural systems and large-scale AI agents in open-ended domains.

Neural Evolution and Self-Supervision

• Evolving self-taught and self-supervised neural networks deploy dual-module architectures, with an Action Module (control/policy) and Reinforcement Module (self-generated intrinsic feedback), yielding gradient-based self-adjustment without explicit external rewards (Le, 2019, Le, 2019).
• The Baldwin Effect emerges: synergy between evolution (shaping an inductive bias to be learnable) and intra-life learning yields superior adaptation and generalization compared to evolution or self-teaching alone. Mathematical abstraction is provided by backpropagation using the self-generated error between modules.

Agentic Systems and Adaptive Agent Architecture

• Foundational taxonomies for self-evolving agents enumerate "what to evolve" (policy/model parameters, prompt/context, tools, architectures), "when to evolve" (intra/inter-test-time), and "how to evolve" (reward, imitation, population-based methods) (Gao et al., 28 Jul 2025).
• Formal recursive transformations capture self-evolution via:

$$f(\Pi, \tau, r) = \Pi' = (\Gamma', \{\psi_i'\}, \{C_i'\}, \{\mathcal{W}_i'\})$$

where $\Pi$ denotes the agent system, $\tau$ the trajectory/history, and $r$ external or self-generated feedback.

• Agent systems employ mechanisms such as prompt optimization (iterative rewriting, textual gradients), memory evolution (salient fact management), autonomous tool creation, and architectural evolution (single-agent self-improvement, multi-agent co-evolution).
• Practical instantiations occur in code generation, GUI management, finance, and healthcare, with evaluation protocols spanning adaptivity, retention (catastrophic forgetting), generalization, efficiency, and safety using domain-specific and cross-domain benchmarks (Fang et al., 10 Aug 2025).

6. Self-Supervised Taxonomy Expansion and Knowledge System Evolution

Contemporary knowledge systems rely on automated, self-supervised taxonomy completion and expansion methods (Shen et al., 2020, Yu et al., 2020, Jiang et al., 2022). These systems use the structure of existing taxonomies to generate natural supervision signals, enabling continual expansion without human intervention.

• TaxoExpan employs position-enhanced graph neural networks (GNNs) and InfoNCE-based contrastive losses for noise-robust, self-supervised learning, integrating local structural information for hierarchical expansion.
• STEAM utilizes multi-view co-training (distributed embeddings, contextual paths, lexico-syntactic features) for multi-class node attachment prediction, sampling "mini-paths" as anchor structures.
• TaxoEnrich integrates structure-semantic representations via taxonomy-contextualized embeddings, sequential encoders for vertical structure, and query-aware aggregation of sibling context.

These frameworks provide robust, scalable algorithms for self-evolving organizational structures, maintaining up-to-date knowledge representations under dynamic domain requirements.

7. Domain-Specific and Bio-Inspired Evolutionary Taxonomies

Research has produced comprehensive taxonomies paralleling the classification in biology, organizing algorithms by inspiration domain: Animalia (birds, insects, mammals, fishes), Bacteria, Fungi, Plants, Protista, and Viruses (Torres-Treviño, 2021). Each subclass encompasses algorithmic templates based on observed group behaviors (e.g., flocking, foraging, predation) and reproductive/migratory patterns.

Evolutionary adaptation in these approaches often entails population-based optimization, self-organization, and adaptive memory. While the theoretical underpinnings are less formalized than in algebraic or agentic frameworks, the bio-inspired taxonomy provides a structural lens for cataloguing self-evolving techniques and highlights the emergence of robustness, diversity, and scalability as recurrent themes.

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In sum, the taxonomy of self-evolving techniques organizes a pluralistic field: from entropy-based measures in digital ecosystems, algebraic abstraction mechanisms, adaptive population topologies, and organic architectures, to the modern agentic frameworks for neural and multi-agent systems evolving via multi-modal feedback. The field is unified by an emphasis on quantifiable self-organization, meta-level adaptation, recursive abstraction, and continual feedback-driven improvement, each correspondingly formalized within mathematical or algorithmic models matched to the domain and application context.