Agency Gain: Neural, Economic & AI Perspectives

• Agency Gain is a multifaceted concept characterized by its role in enhancing prediction, learning, and control across neural, economic, and AI systems.
• In minimal neural systems, agency gain is measured as the reduction in prediction error when incorporating action-awareness, quantified via metrics like mean-squared error and mutual information.
• Different fields operationalize agency gain uniquely—from modulating slow plasticity in spiking models to realizing strategic mixed equilibria and empowerment in artificial agents.

Searching arXiv for papers on “agency gain” and related formulations to ground the article. arxiv_search query: "agency gain" max_results: 10 I’ll look up “agency gain” and closely related arXiv papers to anchor the terminology and citations. Agency gain denotes several distinct quantitative constructs used to characterize how agency enters prediction, learning, control, contract design, and human–machine interaction. In recent work on minimal neural systems, it is the predictive advantage of an action-aware model over an action-blind model, $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$. In a closely related spiking framework, the same signal becomes a multiplicative gain on slow plasticity, entering the update rule $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$. In combinatorial principal–agent theory, the term refers to the principal’s gain from being allowed to induce mixed-strategy rather than pure-strategy equilibria, formalized as the Price of Purity. In active-inference work, an analogous role is played by empowerment, the channel capacity between actions and anticipated observations (Ye, 4 Jun 2026, Han, 29 Jun 2026, Babaioff et al., 2014, Wilson et al., 25 Apr 2026).

1. Major meanings of the term

The literature uses “agency gain” in non-equivalent ways. Some usages are diagnostic, asking whether the system’s own action improves prediction. Others are developmental, asking whether that information is routed into durable structural change. Others are economic or sociotechnical, measuring the gain to a principal, institution, or human actor when agency is redistributed or amplified.

Domain	Formalization	Function
Minimal predictive systems	$$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$	Predictive signature of self-causation
Spiking developmental agents	$\mathrm{Agency}_t$ inside $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$	Gain on slow learning
Combinatorial agency	$\mathrm{POP}(t,c)$	Principal’s gain from mixed equilibria
Active inference	$\max_{p(a_t)} I(A_t; O_{t+1})$	Operational phenotype of agency

In the predictive-neural lineage, agency gain is explicitly the “predictive advantage of knowing one’s own action,” and the crucial distinction is between merely reading out that advantage and using it as a gain on plasticity (Ye, 4 Jun 2026, Han, 29 Jun 2026). In economics, the relevant quantity is not self-causation but the principal’s multiplicative payoff gain when contracts induce mixed equilibria rather than pure equilibria (Babaioff et al., 2014). In AI phenotyping and control, empowerment is used to distinguish zero-, intermediate-, and high-agency phenotypes by structural manipulations of a generative model (Wilson et al., 25 Apr 2026). This suggests a family resemblance rather than a single settled quantity.

2. Predictive agency gain in minimal neural systems

In minimal neural systems, agency gain is defined by comparing two next-observation predictors: a self-aware predictor conditioned on internal state and current action, and a self-blind predictor conditioned on internal state only. With mean-squared error, the time-local quantity is

$$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$

and the normalized prediction gap is

$$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$

Under Gaussian assumptions, the difference in MSE is approximately proportional to the conditional mutual information between action and next observation given history. The same work pairs this quantity with a spike ratio, defined as the ratio between self-aware prediction error under action disconnection and under normal operation; positive gain with a large spike is treated as meaningful agency, whereas positive gain with spike near $1$ is treated as mechanical compensation or artifact (Ye, 4 Jun 2026).

The implementation uses a single 192-dimensional GRU with multi-scale EMA, dual heads, and environments based on a 4-channel sinusoidal world and the Lorenz attractor. Agency gain appears only after four developmental conditions are satisfied in strict order: persistent state forming stable attractors, a causal action loop linking output to input, proprioceptive feedback that makes implicit causal knowledge explicit, and asynchronous awakening in which perceptual learning consolidates before action learning begins. The same study reports that only forward-sampled action selection yields meaningful agency gain. In the sinusoidal environment with trace, forward-sampled actions achieve pred gap $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$0 and spike $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$1; in the Lorenz environment, pred gap is $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$2 and spike $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$3. Two gradient-based alternatives degenerate: direct AG gradient yields pred gap $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$4, spike $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$5, and autocorrelation $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$6, while gradient disagreement yields pred gap $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$7, spike $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$8, and autocorrelation $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$9.

A central implication of this formulation is that agency gain, so defined, is a predictive and causal-discriminative quantity. It says that knowing the action improves prediction, and that this advantage collapses when the action’s causal link is severed. It does not by itself specify how the system’s durable parameters should change. That developmental limitation becomes the explicit target of subsequent work.

3. Agency gain as a gain on slow plasticity and durable behavioral structure

A later spiking study reproduces the agency comparator but changes the role of the signal. The agent computes agency from the prediction-error margin between the taken action’s forward model and the best alternative model; after normalization this becomes $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$0. The key update is

$$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$1

implemented on a Nengo LIF/PES substrate as a gain on the PES error for slow decoders. If any factor is near zero, the product is near zero, and the event performs no slow work. The paper calls this multiplicative structure a veto: only self-owned, self-caused, and salient events are allowed to modify the durable slow store (Han, 29 Jun 2026).

This developmental reinterpretation yields a clean dissociation. In the agency bridge experiment, the Ye-style readout-only agent and the full slow-credit agent share the same architecture for the agency comparator and achieve essentially matched agency gain, $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$2 versus $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$3, with paired difference $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$4 and $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$5. The only difference is whether the self-credit term updates slow behavioral parameters. After unload, the readout-only condition has $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$6 and self-preserving behavior $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$7, whereas the full condition has $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$8 and unloaded self-preservation $$A = \mathrm{Err}_{\mathrm{world}} - \mathrm{Err}_{\mathrm{self}}$$9. The same matched-gain dissociation appears in the 24-dimensional partially observed scale-up, where agency gain remains statistically matched, with paired $\mathrm{Agency}_t$0, but post-unload self-preservation is $\mathrm{Agency}_t$1 for the full model and $\mathrm{Agency}_t$2 for controls.

The paper formalizes the effect through a behavioral potential $\mathrm{Agency}_t$3, with Gibbs policy

$\mathrm{Agency}_t$4

and basin depth

$\mathrm{Agency}_t$5

In the simple linear case with a single dominant rival, basin deformation obeys

$\mathrm{Agency}_t$6

so basin deformation equals net self-credit work. The learning-rate $\mathrm{Agency}_t$7 is an actuation gain, but the sign of $\mathrm{Agency}_t$8—and thus which basin deepens—is determined by the credit form. Multiplicative credit,

$\mathrm{Agency}_t$9

enforces eventwise veto; additive pooling,

$$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$0

leaks credit to events that fail one factor and can misroute plastic work.

The empirical consequence is durable residue after unload. On the spiking substrate, full agency-gated credit yields learned_full self-preservation $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$1, learned_unloaded $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$2, and residue fraction $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$3. Resetting slow decoders after unload collapses self-preservation to $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$4, no_efference gives $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$5, no_agency gives $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$6, owner_shuffled gives $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$7, and a counterfactual condition with no real harm contingency gives $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$8. In continual learning under exogenous interference, multiplicative self-credit retains old tasks with final post-unload accuracy approximately $$\mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t$$9, forgetting approximately $\mathrm{POP}(t,c)$0, and robustness approximately $\mathrm{POP}(t,c)$1, without replay buffer, task IDs, or EWC-style task-boundary protection; additive credit and no-agency controls collapse to $\mathrm{POP}(t,c)$2–$\mathrm{POP}(t,c)$3 final accuracy after unload. On this account, agency gain is not merely an epistemic readout. It matters developmentally only when it is used as a multiplicative gain on slow plasticity.

4. Operational agency gain in contemporary AI systems

Several recent AI literatures operationalize increasing agency through structurally different metrics. In active inference, the core phenotype is empowerment, defined as the channel capacity between actions and future observations,

$\mathrm{POP}(t,c)$4

Within a T-maze POMDP, this distinguishes zero-, intermediate-, and high-agency phenotypes: trap states have empowerment approximately $\mathrm{POP}(t,c)$5 bits, the ambiguous initial state has approximately $\mathrm{POP}(t,c)$6 bit, and after an epistemic cue the agent reaches maximal $\mathrm{POP}(t,c)$7 bits. The same paper argues that epistemic foraging under expected free energy naturally raises empowerment, and that as agency increases, governance must shift from external constraints to internal modulation of prior preferences (Wilson et al., 25 Apr 2026).

In long-horizon LLM agents, agency gain is measured behaviorally through persistent, tool-using, multi-stage performance. One software-evolution approach mines chain-of-PR trajectories averaging $\mathrm{POP}(t,c)$8k tokens and $\mathrm{POP}(t,c)$9 tool calls, and fine-tuning GLM-4.6 on $\max_{p(a_t)} I(A_t; O_{t+1})$0 such samples yields a $\max_{p(a_t)} I(A_t; O_{t+1})$1 relative gain on Toolathlon, improving from $\max_{p(a_t)} I(A_t; O_{t+1})$2 to $\max_{p(a_t)} I(A_t; O_{t+1})$3, while also raising SWE-bench from $\max_{p(a_t)} I(A_t; O_{t+1})$4 to $\max_{p(a_t)} I(A_t; O_{t+1})$5, $\max_{p(a_t)} I(A_t; O_{t+1})$6-Bench retail from $\max_{p(a_t)} I(A_t; O_{t+1})$7 to $\max_{p(a_t)} I(A_t; O_{t+1})$8, SciCode-MP from $\max_{p(a_t)} I(A_t; O_{t+1})$9 to $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$0, and the overall average from $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$1 to $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$2 (Jiang et al., 2 Feb 2026). A related study argues for an “Agency Efficiency Principle,” according to which machine autonomy emerges not from data abundance but from strategic curation of high-quality agentic demonstrations. Using $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$3 trajectories, LIMI reaches $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$4 on AgencyBench, compared with $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$5 for GLM-4.5, $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$6 for Kimi-K2-Instruct, $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$7 for DeepSeek-V3.1, and $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$8 for Qwen3-235B-A22B-Instruct; it also reports a $$\mathcal{A}(t)=\mathrm{Err}_{\mathrm{world}}(t)-\mathrm{Err}_{\mathrm{self}}(t),$$9 improvement over models trained on $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$0 samples (Xiao et al., 22 Sep 2025).

In dialogue, agency is operationalized through Intentionality, Motivation, Self-Efficacy, and Self-Regulation. On a dataset of $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$1 human–human collaborative interior-design conversations containing $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$2 annotated designer–snippet instances, automatic and human evaluations indicate that models expressing stronger versions of these features are more likely to be perceived as strongly agentive. For generated dialogues, an ICL-Agency prompting strategy reaches Agency $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$3, Intentionality $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$4, Motivation $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$5, Self-Efficacy $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$6, and Self-Regulation $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$7, exceeding instruction-only, generic ICL, and fine-tuning baselines (Sharma et al., 2023). Across these AI settings, agency gain is measured not by a single universal scalar but by increased causal control, sustained tool-mediated competence, or richer agentive expression.

5. Economic and sociotechnical interpretations

In combinatorial principal–agent theory, agency gain is formalized as the principal’s payoff advantage when mixed-strategy Nash equilibria can be induced under hidden actions. With success function $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$8, costs $$\mathrm{pred\ gap}=\frac{\mathrm{Err}_{\mathrm{world}}-\mathrm{Err}_{\mathrm{self}}}{\mathrm{Err}_{\mathrm{world}}}.$$9, optimal mixed equilibrium $1$0, and optimal pure profile $1$1, the Price of Purity is

$1$2

Here $1$3, and $1$4 means no gain from mixed strategies. The paper gives explicit OR-technology examples with gains of about $1$5 and $1$6, proves that supermodular or increasing-returns technologies have $1$7, and derives bounds such as $1$8 for two-agent technologies with identical costs and $1$9 when the technology is anonymous (Babaioff et al., 2014). In this literature, agency gain is a contractual surplus generated by strategic randomization under hidden effort.

Human–machine network research uses the term differently. Increasing machine agency through automation can strengthen human agency when responsibility is shared and task allocation aligns with respective strengths. Case studies in air traffic management, crisis management, and crowd evacuation describe automation as enabling human actors to move from local procedural decisions toward larger, more critical, tactical, or strategical decisions, and characterize automation as a needed prerequisite of innovation and change. The effect is explicitly non-zero-sum: more machine agency can increase what humans can do and achieve in the network (Følstad et al., 2017).

A more critical AI-society literature treats agency gain as a distributive and governance problem. One paper uses Bratman-style planning theory, relational agency, empowerment, and Markov or causal blankets to argue that AI reshapes agency by expanding or contracting actors’ capacities to form goals, beliefs, plans, and successful actions; it also analyzes “attacks on agency” via sabotage of action success, planning, desire formation, belief formation, and available options (Swarup, 2 Feb 2025). Another argues that intent-aligned AI can still deplete human long-term agency, and proposes a formal notion of agency-preserving AI–human interactions based on forward-looking agency evaluations, together with a research program on benevolent game theory, algorithmic foundations of human rights, mechanistic interpretability of agency representation, and reinforcement learning from internal states (Mitelut et al., 2023). The sociotechnical question is therefore not only whether agency is gained, but whose agency is amplified, at what temporal scale, and under what governance.

6. Conceptual boundaries, selfhood, and open controversies

Several broader theoretical programs treat agency as graded and structurally variable, which in turn makes “agency gain” a matter of increasing complexity, controllability, or self-organization. A minimalist account in physics defines an agent as an information-processing system characterized by modelling activity with respect to its surrounding environment, geared towards successive interaction. It proposes that agency scales with the complexity of the agent’s data models, internal structure, temporal integration, counterfactual capacity, and probabilistic sophistication. Rovelli’s physical account instead treats agency as the breaking of an approximation under which dynamics appears closed, formalizes macroscopic branching by histories $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$00, and ties the information generated by choice,

$$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$01

to entropy production via

$$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$02

On that view, agency is a mechanism that transforms low entropy into information (Barzegar et al., 2023, Rovelli, 2020).

Autotelic and embedded-agency work pushes the issue from goal generation to self-generation. One recent synthesis represents autotelic agency by the tuple

$$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$03

where $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$04 is policy, $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$05 a goal space, $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$06 a goal distribution, $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$07 a resource functional, $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$08 a viability set, $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$09 a boundary, and $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$10 a self-model. Embeddedness is treated as necessary but not sufficient for autotelic agency, because the same global dynamics can admit many valid Markov-blanket partitions and thus many candidate selves (Sarkar, 18 Jun 2026). A logical treatment of cohesive group agency likewise shifts agency gain from individuals to structured assistance between strict subgroups. For a group $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$11, cohesive agency is witnessed by a cohesion network $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$12 whose realized edges are successful-assistance relations, and group bringing-it-about is reduced to conjunctions of such assistance formulas (Troquard, 2 Nov 2025). These accounts relocate agency gain from simple control to the construction of selves, scales, and social fabrics.

A final controversy concerns the relation between agency and consciousness. The developmental spiking and GRU papers explicitly state that no claim of consciousness is made (Han, 29 Jun 2026, Ye, 4 Jun 2026). By contrast, a phenomenological-IIT approach argues that the maximally irreducible cause–effect structure, with level $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$13, captures both the degree and the phenomenal quality of agency, and proposes monitoring AI systems by $$\Delta \theta_{\mathrm{slow}} = \eta \cdot \mathrm{Own}_t \cdot \mathrm{Agency}_t \cdot \mathrm{Salience}_t \cdot \phi(a_t,o_t)$$14 and by the shape of the corresponding MICES to distinguish altruistic from malicious dispositions (Das, 9 Feb 2025). The literature therefore separates at least three questions: whether a system can detect its own causal influence, whether that information durably shapes its behavior, and whether any such agency has phenomenal character. This suggests that “agency gain” is best understood as a plural technical term whose interpretation depends on the surrounding theory of prediction, plasticity, control, contract design, or selfhood.