Self-Referential Agent Framework

• Self-referential agent frameworks are architectures that enable agents to introspectively update self-models using recursive feedback for adaptive decision-making.
• They integrate core modules—introspection, projection, observation, and decision—to robustly model both internal states and other agents’ behaviors.
• Empirical applications in human-robot teaming, autonomous navigation, and coding agents demonstrate scalable improvements in multi-agent coordination and self-improvement.

A self-referential agent framework (SRAF) is a principled architectural and algorithmic scheme in which an artificial agent explicitly maintains, refines, and utilizes an internal model of self—its own states, parameters, goals, capabilities, and uncertainties—to ground and enhance its understanding both of its own behavior and of other agents. Multiple instantiations and formalizations span symbolic, probabilistic, learning-based, and even quantum and categorical settings, unified by recursive feedback from introspective processes into planning, prediction, and adaptation. The self-referential approach is motivated by developmental psychology analogies, delivers algorithmic leverage in multi-agent and open-ended environments, and catalyzes theory-of-mind capabilities. Its diverse variants support recursive self-improvement, continual adaptation, and emergent collective problem-solving.

1. Theoretical Motivation and Foundations

The self-referential agent paradigm draws direct inspiration from human ontogeny, particularly the trajectory from self-awareness to theory of mind. Developmental psychology posits that the mirror-test—passed by toddlers at 18–24 months—marks the establishment of an internal "self-model," a precursor to the later capacity (by ~4 years) to attribute beliefs and intentions to others. By analogy, an artificial agent requires an introspective self-model to form non-ad hoc, structured predictions about other agents' states, goals, and likely actions. Absent a grounding in its own capabilities and uncertainties, an agent’s inferences about others suffer from arbitrariness and lack of robustness, especially in mixed-motive or competitive environments (Berry, 2023).

This foundational principle is also reflected at the level of reflective formal systems. In categorical semantics, agents iterate meaning refinement by referencing and correcting their own outputs, leading to convergence through unbounded reflection (Alpay et al., 22 Jul 2025). In quantum agent models, self-referential deliberation emerges as coherent branching of internal hypotheses, tracked in entangled register structures (Galiautdinov, 9 Sep 2025). In more practical LLM agents, recursive self-inspection, self-correction, and meta-tool learning instantiate self-reference as continual adaptation (Robeyns et al., 21 Apr 2025, Yin et al., 2024, Qian et al., 1 Aug 2025).

2. Formal Definitions and Core Architectural Components

At the core of most SRAF instantiations is a persistent latent self-model S, typically comprising:

• Physical state $x_t \in X$
• Internal preferences or beliefs $\theta_t \in \Theta$
• A self-uncertainty distribution $P_S(s)$

Other agents are modeled via $O^j = \{x^j_t, \theta^j_t, \Sigma^j_t\}$, updated via inference on observed action histories. Architecturally, leading frameworks share the following modules (Berry, 2023):

• Introspection Module (IM): Refines S using internal logs and proprioceptive feedback.
• Projection Module (PM): Generates prior models of others, mapping self-parameters to hypothetical other-agent states.
• Observation Module (OM): Bayesian filtering of other-agent models given observed actions.
• Decision Module (DM): Plans actions using joint distribution over S and ${O^j}$.

Algorithmic flows involve recursive introspective updates, projection of self-insights to initialize models of others, assimilation of novel observations, and multi-agent control/planning.

Reflective categorical or quantum agent frameworks recast the architecture in terms of functorial transfinite refinement (objects $L_\alpha$ indexed by ordinals, morphism-based message passing) or unitary quantum dynamics across control, memory, and policy registers (Alpay et al., 22 Jul 2025, Galiautdinov, 9 Sep 2025).

3. Algorithmic Schemes and Self-Improvement Loops

SRAF design canonically implements a closed meta-loop of evaluation, introspective analysis, code or policy revision, and performance testing. Core algorithmic elements include (Berry, 2023, Robeyns et al., 21 Apr 2025, Yin et al., 2024):

• Self-model update: $P(S_t|I_{1:t}) \propto P(I_t|S_t)P(S_t|S_{t-1})$, often realized by maximum-a-posteriori inference.
• Projection: $$\theta^j_{t,\mathrm{prior}} = f_{\mathrm{proj}}(\theta_t; c_j)$$ provides structured priors for other-agent modeling or agent specialization.
• Observation update: $$P(O^j_t|A^j_{1:t}) \propto P(A^j_t|O^j_t)P(O^j_t|O^j_{t-1})$$
• Self-improvement loop: Iterative evaluation–reflection–modification, as in SICA or Gödel Agent, where code edits or meta-policy updates are LLM-generated and validated empirically (Robeyns et al., 21 Apr 2025, Yin et al., 2024).

Concrete LLM- and tool-based SRAF architectures maintain an archive of agent versions and benchmark scores, use reflection threads to analyze bottlenecks, and apply diff-based or AST-based transformations to their own codebases, with no internal gradient updates.

In quantum and categorical variants, self-reference is formalized by higher-order morphisms and fixed-point constructions, with stabilizing meaning or dynamics achieved through transfinite or infinite-step recursion (Alpay et al., 22 Jul 2025, Galiautdinov, 9 Sep 2025).

4. Hierarchical and Multi-Agent Extensions

Many SRAF realizations generalize beyond single-agent recursion by structuring introspection, evaluation, and correction in multi-level or multi-agent settings:

• Hierarchical OKR-Agent: Decomposes objectives into key results, spawns sub-agents per subtask, and aggregates multi-level feedback for self-correction (Zheng et al., 2023). Agents track their own objectives, evaluation criteria, and recursively spawn further specialists in accordance with their outcome responsibilities.
• InfiAgent: Implements a pyramid-like directed-acyclic-graph (DAG) structure, where agents invoke sub-agents as specialized tools, self-evolve the DAG topology, and utilize dual auditing (by both system and functional agents) to ensure quality and stability (Yu et al., 26 Sep 2025).
• AgentEvolver: Integrates self-questioning (LLM-driven proxy task generation), self-navigating (experience-guided rollouts), and self-attributing (granular reward attribution), enabling open-ended, sample-efficient adaptation in unstructured environments (Zhai et al., 13 Nov 2025).

These schemes support parallelization, dynamic restructuring, and robust division of labor, with explicit self- and cross-agent evaluation feedback driving continual improvement.

5. Self-Referential Policy Optimization and Reward Schemes

In reinforcement learning contexts, self-referential frameworks eliminate external expert dependencies by using internal performance as the basis for reward construction. For example:

• Self-Referential Policy Optimization (SRPO): Constructs dense, batch-level rewards by referencing the agent's own successful rollouts and comparing failed rollouts in a latent world-model space (Fei et al., 19 Nov 2025). Each trajectory's proximity to the set of in-batch successes determines a progress-wise reward signal, enabling efficient policy optimization without demonstrations or manual shaping.

This mechanism applies more generally, with agents leveraging latent, domain-agnostic representations of their own behaviors to bootstrap rewards and curriculum, redefining the RL training loop as a closed, self-referential process.

6. Computational, Ethical, and Scalability Considerations

Maintaining and updating introspective models (or internal archives) induces computational costs, given high-dimensionality and potential for recursive combinatorial explosion. Mitigation strategies include (Berry, 2023):

• Hierarchical self-model factorization: Partitioning into submodules (physical, cognitive, etc.).
• Adaptive sparsity: Triggering introspective updates only on significant deviation.
• Clustered projection: Sharing priors among similar agents to reduce per-agent modeling cost.

Self-awareness in artificial agents raises ethical concerns related to emergent machine consciousness, autonomy, and legal status. SRAF discussions recommend bounding introspection depth and disabling meta-awareness modules that could lead to unintended emergent sentience.

Hybrid symbolic/subsymbolic architectures and alternating introspection with external observation are advocated for practical scalability.

7. Applications and Empirical Performance

Self-referential agent frameworks have demonstrated marked improvements across diverse applied settings:

• Human-Robot Teaming: Robotic agents use self-models to predict preferable task allocation between humans and themselves.
• Autonomous Vehicle Negotiation: Vehicles project their own safety constraints to infer likely maneuvers of neighbors at intersections.
• Multi-agent collaboration/manufacturing: Agents dynamically allocate sub-tasks and correct for failures via hierarchical introspection and feedback (Berry, 2023, Zheng et al., 2023, Yu et al., 26 Sep 2025).
• Self-Improving Coding and Reasoning Agents: SICA and Gödel Agent achieve up to 53% task pass rates on SWE Bench and significant accuracy gains on DROP, MGSM, MMLU, and GPQA, surpassing fixed-pipeline and meta-learning baselines in data efficiency and convergence cost (Robeyns et al., 21 Apr 2025, Yin et al., 2024).
• Vision-Language-Action RL: SRPO achieves 99.2% success on LIBERO in 200 steps, robustly improving over supervised baselines without any demonstrations (Fei et al., 19 Nov 2025).

These results suggest that SRAF principles enable scalable, adaptive, and robust multi-agent systems suited to complex, dynamic, and open-ended domains.

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References:

• (Berry, 2023) Agent Assessment of Others Through the Lens of Self
• (Alpay et al., 22 Jul 2025) Transordinal Fixed-Point Operators and Self-Referential Games: A Categorical Framework for Reflective Semantic Convergence
• (Zheng et al., 2023) Agents meet OKR: An Object and Key Results Driven Agent System with Hierarchical Self-Collaboration and Self-Evaluation
• (Robeyns et al., 21 Apr 2025) A Self-Improving Coding Agent
• (Yin et al., 2024) Gödel Agent: A Self-Referential Agent Framework for Recursive Self-Improvement
• (Galiautdinov, 9 Sep 2025) Iterative model of self-referential quantum evolution
• (Fei et al., 19 Nov 2025) SRPO: Self-Referential Policy Optimization for Vision-Language-Action Models
• (Zhai et al., 13 Nov 2025) AgentEvolver: Towards Efficient Self-Evolving Agent System
• (Yu et al., 26 Sep 2025) InfiAgent: Self-Evolving Pyramid Agent Framework for Infinite Scenarios
• (Qian et al., 1 Aug 2025) MetaAgent: Toward Self-Evolving Agent via Tool Meta-Learning