Goal-Directed State Representation

• Goal-directed state representation is a framework that constructs state abstractions based on an agent’s goals, selectively encoding features relevant to targeted outcomes.
• It emphasizes observer-dependent abstraction and controlled entropy management by compressing experience trajectories into goal-equivalent classes.
• This approach informs the design of AI systems by balancing representation granularity with computational efficiency to enable purposeful, adaptive action.

Goal-directed state representation refers to the formulation, learning, and use of state abstractions in which the features, boundaries, and semantics of the state are determined by an agent’s goals, rather than by an objective, fixed description of the environment. This view holds that which aspects of experience are encoded in a state depend on their relevance to achieving a particular target, whereby a state is constructed as a concept reflecting equivalence with respect to the agent’s aims or preferences. Rather than treating state spaces as absolute and environment-derived, the goal-directed perspective reveals them to be contextually shaped, compressed, and even observer-dependent constructs, central to both natural and artificial agents’ capacity for purposeful action and adaptive learning.

1. Observer-Dependence and the Role of Abstraction

In physical and computational systems, the boundaries and identities of agents are not intrinsic but are determined by an observer’s abstraction. The observer acts as a "tailor" who selects which degrees of freedom (variables, memory registers, or sensory dimensions) are part of the "agent" under consideration, and which are to be excluded or treated as environment (Samengo, 2017). For example, in Maxwell’s demon scenarios, whether the demon's memory is included in the description of the thermal system determines whether the observed subsystem appears to locally reduce entropy and thus exhibits goal-directed behavior. The act of ascribing a goal to a subsystem thus depends on how information loss or transfer is modeled: the observer deliberately ignores or compresses certain details, and in doing so, enables a many-to-one mapping from initial to final states—a signature of goal-seeking dynamics.

This observer-dependence is central: a goal-directed state representation emerges not as an objective characteristic of the world, but as a result of selective modeling which emphasizes economy (ignoring inessential details) and efficiency in prediction or control.

2. Information Flow, Entropy, and Reversibility

Goal-directed state representations typically compress many possible initial conditions into equivalence classes that converge (under agent behavior) to target outcomes. This is reflected mathematically in mappings from sets of initial states to goal states that are non-injective and thus result in loss of information about initial conditions. In physical terms, the agent system appears to locally decrease entropy, but since the fundamental laws are reversible, this is achieved only by exporting the "missing" information to untracked degrees of freedom outside the agent (e.g., as waste heat or external records) (Samengo, 2017).

A general principle emerges: entropy decrease inside a goal-ascribed subsystem must be accounted for by information transfer or "garbage" collection in the rest of the total system, as per Landauer's principle (minimum energy cost per erased bit is $k_B T$). In computational systems, this is analogous to the requirement for reversible computation to account for all information discarded in state transition functions.

3. Constructing Goal-Directed Agents and Intentionality

Agents, in this view, are not immutable entities but observer-dependent constructs. "Agency" arises when the observer or designer chooses a boundary for the agent such that it achieves a particular objective, by properly accounting for the system’s information balance and specifying what is to be tracked or ignored (Samengo, 2017).

The process of constructing a goal-directed state representation is thus a problem of abstraction—drawing boundaries so that a subsystem’s entropy reduction is visible against the background of transferred "unobserved" information. Intentionality (the "aboutness" or directedness of agency) is not an intrinsic property, but rather an efficient modeling device arising from recurrent observation that similar initial conditions produce convergent goal outcomes.

This abstraction underlies both evolved biological systems and human cognitive modeling: minds ascribe intentionality where it helps predict regularities, explain observed compression of initial variability, or model their own goal-seeking behavior (as in the unity of the self).

4. Compression, Selective Representation, and Trade-offs

State representations in goal-directed systems emerge as a result of trade-offs between the granularity of representation and the cost or complexity of policy updates (Amir et al., 20 Jun 2024). The agent (or observer) abstracts away differences in experience trajectories that are irrelevant for goal attainment—this is formalized via equivalence relations over experience histories (see "telic states" below). Deliberate ignorance (coarse-graining or merging equivalence classes below some discrimination threshold, ε) prevents overfitting to unimportant details, and allows the agent to optimize for both flexibility (faithful, fine-grained distinctions) and efficiency (tractable, robust computations).

From an information-theoretic perspective, this trade-off resembles a rate–distortion problem: finer goal-directed state representations (lower ε) increase the complexity (measured, for instance, by KL divergence bound on policy change (Amir et al., 20 Jun 2024)), whereas coarser abstractions admit simpler policy adjustments between telic states.

5. Telic States and Goal-Equivalence

A central theoretical construct is the "telic state" (Amir et al., 20 Aug 2025, Amir et al., 2023, Amir et al., 20 Jun 2024): the equivalence class of experience distributions considered equivalent with respect to a goal. Formally, denoting the space of all experience distributions as Δ(𝓗), a goal g induces a binary preference relation ≽₍g₎, and two distributions A, B ∈ Δ(𝓗) are said to be goal-equivalent (A ∼₍g₎ B) if they are ranking-wise indistinguishable for g. The telic state space 𝒮₍g₎ is then defined as: $\mathcal{S}_g = \Delta(\mathcal{H}) / \sim_g$ where /∼₍g₎ indicates equivalence under the goal.

Goal-directed learning then consists in steering the agent's current policy-induced experience distribution towards the targeted telic state, as measured by a divergence metric such as KL divergence: $$\theta_{t+1} = \theta_t - \eta \nabla_\theta D_{KL}(P^*_i \Vert P_{\pi(\theta)})$$ where $P^*_i$ is the information projection of $P_{\pi}$ onto the telic state $S_i$ (Amir et al., 20 Aug 2025, Amir et al., 2023).

This paradigm shifts state abstraction from environmental or feature-driven clustering to goal-induced compression, in which categories of experiences are formed solely on their value for attaining goals (e.g., the same object may be classified by "edibility" or "warmth" depending on the current need).

6. Self-Observation, Recursion, and the Boundary Problem

The self in goal-directed state representation is a special case, as it is both the observer/constructor of goal-seeking agents and the object of such attribution. This "strange loop" (Samengo, 2017) is instantiated when the brain models and predicts its own actions by compressing its internal degrees of freedom (i.e., ignoring subpersonal neural details irrelevant to self-ascribed goals) to implement a unified, agentic self. The subjective experience of agency and purpose is a direct consequence of the same selective, boundary-drawing process applied when modeling external agents. From a modeling viewpoint, this recursion underscores the inherently observer-relative nature of all goal-directed state abstractions.

7. Implications and Consequences for AI and Modeling

This perspective has several implications:

• State representations in both natural and artificial agents should be learned and adapted with respect to specific goals, not prespecified as fixed or ground-truth entities (Amir et al., 2023, Amir et al., 20 Aug 2025).
• The "meaningfulness" of a state reduction (i.e., information compression) must be judged by observing whether entropy decreases with respect to the goal; such reductions are only real in a representation where certain aspects are tracked and others ignored.
• Goal-directed reasoning in AI, such as hierarchical planning, feature selection, and policy abstraction, can be systematically designed by partitioning experience spaces (or observation/action spaces) into telic states aligned with goal equivalence criteria. This approach unifies descriptive (predictive) and prescriptive (evaluative) components of models under the guiding force of the agent's active goals.
• The boundary problem—how and where to "cut" the system for the purpose of modeling agency—cannot be objectively solved, but must be tailored to the task and the observer’s intent.
• This theory also guides how one should interpret entropy and information flow in open systems: information is never "lost," but only partitioned outside the observer’s chosen boundaries, consistent with thermodynamic and computation-theoretic principles.

This unified, observer-relative, goal-directed approach to state representation has significant consequences for building adaptive intelligent systems, designing interpretable models, and understanding intentional action across biological and synthetic agents.