Frame-Dependent Agency

• Frame-dependent agency is a concept describing how the measurement and attribution of agency change with the choice of analytical, physical, or organizational reference frames.
• It is applied in contexts such as reinforcement learning, quantum theory, decision modeling, and social sciences, impacting empirical assessments and system design.
• By identifying predictive gaps and dual frame effects, this concept drives novel approaches for modeling goal-directed behavior and emergent collective dynamics in complex systems.

Frame-dependent agency refers to the phenomenon that the attribution, measure, or operational definition of agency—commonly conceived as a system’s capacity to steer outcomes toward goals—depends in a constitutive way on the choice of reference frame. This dependency arises across physical, decision-theoretic, cognitive, social-scientific, and educational contexts, with profound consequences for philosophical analysis, empirical measurement, and system design. The frame in question may be a partitioning of variables (boundary specification), a coarse-graining map, an observer’s epistemic conventions, a modeler’s analytic lens, or an agent’s own internal structure for generating macroscopic behavior. Frame-dependence is not merely perspectival or epistemic: key formal properties, empirical statistics, and even the operational facts about agency-bearing systems provably shift or bifurcate with changes in analytic, physical, or organizational frame.

1. Formal Foundations: Reference Frames and the Structure of Agency

Frame-dependent agency arises whenever attributions of agency are made relative to a reference frame that selects boundaries, interprets causal sources, frames norms, or defines adaptivity criteria.

A reference frame may be specified in several mathematically precise senses:

• In reinforcement learning (RL), a frame is embodied in the partition of state variables into internal and external sets—i.e., the agent–environment cut. For an MDP $M = \langle S, A, P, R, \gamma \rangle$ and boundary $B$, the optimal policy $\pi^*_B$ and the value function $V^\pi_B$ both depend on $B$. Changing $B$ alters these objects, leading to operationally distinct agency assessments (Abel et al., 6 Feb 2025).
• In Promise Theory, an agent is a source/sink of promises; a super-agent is a collection of agents under coarse-graining. Promises at different scales may merge, vanish, or introduce new "irreducible" collective intentions, with the agent’s identity—elementary or composite—resolving differently at each scale (Burgess, 2015).
• In intrinsic dynamical accounts, frame dependence appears as internal vs. external coarse-grainings: the system's own map $\phi_S : X_t \mapsto V_t^S$ and the observer's map $\phi_O : X_t \mapsto V_t^O$. The system’s dynamics ($F_S$) and observer's model ($F_O$) thus define distinct informational frames, with divergences in their predictive capacity—termed the "predictive gap" $\Delta$ (Horibe et al., 7 Dec 2025).

A central insight is that the mere existence of behavior, structure, or outcomes is insufficient for frame-invariant agency; it is the analytic, semantic, and operational commitments inherent in a frame that ground agenthood.

2. Necessary Components of Agency and Their Frame-Dependence

Standard accounts (e.g. Barandiaran et al., 2009; Moreno, 2018) require four properties for agency: individuality (well-defined boundary), source of action (internal causal origin), normativity (goal-directedness), and adaptivity (responsive change). Each is intrinsically frame-dependent (Abel et al., 6 Feb 2025):

• Individuality: The agent boundary is not objectively fixed. Shifting the cut between internal and external variables (as in the thermostat example) fundamentally alters whether the system is judged as an agent.
• Source of Action: Attribution of causal origins to internal mechanisms, as opposed to the environment or other agents, requires a selected causal decomposition; different graphical models or variable partitions yield incompatible agent assignments.
• Normativity: Goals inferred via inverse RL (or similar methods) rely on priors and conventions (e.g., Occam’s razor), which form part of the analytic frame. Different priors induce different reward attributions, changing the conclusion regarding goal-directedness.
• Adaptivity: The scope and metric of adaptation (which behavioral differences are meaningful) are determined by the input reference class and coarse-graining. By adjusting the class or abstraction, a system can be deemed adaptive or not.

These dependencies are not merely philosophical; they are mirrored in formal properties such as boundary-dependent Bellman errors in RL, irreducibility criteria in coarse-grained dynamical systems, and loss of agency signals in semantic spacetimes (Horibe et al., 7 Dec 2025, Burgess, 2015).

3. Frame-Dependent Agency in Physics and Quantum Theory

Physical treatments bring extreme clarity to the operational implications of frame-dependence. In relativistic Wigner-friend scenarios, the very notion of a measurement record—and hence the agency of the measuring system ("friend")—is frame-dependent. For instance, the basis in which a macroscopic outcome is "declared" (encoded onto qubits) differs depending on the choice of inertial frame: one observer sees a record of a $\sigma_z$ measurement, another, following a Lorentz boost, finds a $\sigma_x$ record. These records are not related by Lorentz transformation but represent genuinely frame-dependent agency: the friend's operational act (measuring and declaring) is indexed to the simultaneity slice (temporal frame) employed (Allam et al., 2023).

In quantum gravity regimes, as formalized through the deformation of classical symmetries by quantum groups (e.g., $SU_q(2)$), the spatial reference frame becomes fundamentally agent-dependent. Each agent chooses a "sharp" direction (quantization axis), and all points orthogonal to that axis become irreducibly fuzzy. Thus, different agents, by selecting different axes, reconstruct spatial geometry with incommensurate cones of uncertainty—there is no absolute notion of space, only agency-dependent fuzziness (Amelino-Camelia et al., 2022).

4. Frame-Dependent Agency in Decision Theory and Social Sciences

Frame dependence generalizes beyond physical and biological systems. In decision theory, the frame-dependent random utility model (FRUM) extends classical RUM by allowing alternatives to acquire an additional bonus via inclusion in a designated frame (e.g., being displayed or labeled). The choice function $U_F(x)$ depends explicitly both on the alternative and the frame $F$, generating empirically distinct revealed preferences. Behavioral axioms such as Independence of Irrelevant Framed Alternatives (IIFA) and associated Block–Marschak polynomials formally capture and test for frame-dependence in choice data (Cheung et al., 31 Jan 2025).

In educational research, the perception and measurement of faculty agency are shown to hinge on analytic framing. The teaching-method-centered paradigm (which tracks adoption/adaptation of named methods) contrasts with an asset-based agentic paradigm (which focuses on teaching values, internal pedagogical principles, and self-determined choices). The same faculty behaviors are alternately interpreted as "low-agency" or "high-agency" depending on the analytic lens—constituting a paradigm-level case of frame-dependent agency (Strubbe et al., 2019).

5. Coarse-Graining, Emergence, and Scale-Dependence

Promise Theory and coarse-graining approaches demonstrate how agency transforms under changes of resolution or scale—a form of frame-dependence that is neither purely spatial nor semantic but operational. When aggregating agents into a super-agent, internal promises (actions, commitments) may become hidden, while composite or emergent promises may arise at the new scale. Only external agents with access to directories (index structures) can resolve fine-grained agency within the super-agent; otherwise, agency assessment contracts to the externally visible interface. This results in the possibility of "emergent" agency at the super-agent level that does not correspond to any micro-level component (Burgess, 2015).

A plausible implication is that emergent semantic or dynamic continuity in quasi-continuous lattices (for instance, in distributed computing, neural tissue, or social collectives) is itself a frame-dependent phenomenon, requiring explicit mapping between observational and intrinsic frames.

6. Predictive Gaps and Quantification along the Agency Spectrum

Frame-dependent agency is not only descriptive but admits a rigorous quantitative structure. The predictive gap $\Delta$ partitions into an internal component (difference between intrinsic prediction and realization within the system's own frame) and an external component (irreducibility of the system’s macro-dynamics to any fixed observer model). Teleological systems (bacteria, humans) maximize both gaps; purely designed systems (VAEs, LLMs) are engineered to minimize the external gap. This decomposition formalizes the distinction between genuine, system-generated teleology and observer-imposed normativity (Horibe et al., 7 Dec 2025).

The following table summarizes agency types along this quantitative spectrum:

System Type	Internal Gap ($\Delta_{\rm int}$)	External Gap ($\Delta_{\rm ext}$)	Agency Characterization
Teleological (biological)	Nonzero	Nonzero	Autonomously generated constraints
Structural (designed)	Possible	≈0	Externally specified objectives
Passive	0 or undefined	0 or illusory	No internal agency

7. Implications, Methodological Consequences, and Open Problems

Recognition of frame-dependent agency has critical implications:

• All empirical and operational measures of agency must specify the analytic, physical, or semantic frame being used. Ambiguity or neglect of frame choice leads directly to category errors and spurious attributions, as in the misassessment of adaptive capacity or normativity.
• Evaluation and design of artificial agency (in RL, autonomous control, distributed systems) require not only robust performance within a fixed frame but also explicit consideration of how agency metrics shift with the frame (Abel et al., 6 Feb 2025).
• In cognitive and social domains, participatory sense-making and emergent coordination derive from the persistent gaps and non-reducible divergences between interacting agents’ frames, producing collective variables constrained by downward causation at the higher level (Horibe et al., 7 Dec 2025).
• In quantum and relativistic contexts, measurable facts, declared records, and even the notion of locality can be fundamentally contingent on the agent's operational frame, contesting the existence of frame-invariant "observer-independent" reality (Allam et al., 2023, Amelino-Camelia et al., 2022).

Future directions include the development of formal theories of reference frames for agency, frame selection principles (e.g., based on predictive sufficiency or simplicity), meta-learning of frames, and frameworks for quantifying and comparing robustness of agency attributions under frame shifts. In educational and social contexts, a shift toward asset-based agentic paradigms—explicitly attentive to intrinsic motivation, reflective choice, and local context—offers alignment with the foundational necessity of frame-dependent analysis (Strubbe et al., 2019).

In sum, frame-dependent agency is a general and structurally necessary feature of agency across domains, and any mature science or engineering of agency must operationalize and formalize its role at every level of system analysis.