Contribution
A task-independent utility for adaptive agents, defined from the perception–action loop alone: the information-theoretic capacity of the agent’s “actuation channel terminating at the sensor” (eq. 3, p. 130).
Key insight
Count options, as mobility does in Othello, but count only those whose results the agent can perceive. “We define what an agent does solely in terms of what it perceives … it does not matter how much control or influence the agent appears to have from a ‘god’s eye view’” (p. 129). The neurosurgeon example: you may be able to make a neuron spike, “However, if you never directly or indirectly perceive the result, you will never know that you have control over the neuron” (p. 129), and it does not count.
Assumptions
- The loop as a causal Bayesian network S_t → A_t → R_{t+1} → S_{t+1} with R the rest of the system, time-invariant (Figure 1, p. 130).
- For empowerment the actions are redrawn as chosen “freely”, independent of the system’s state (the agent with “free will”, Figure 2): open-loop.
- Discrete variables; capacity computed by Blahut’s algorithm to 10⁻⁴ bit.
Key results
- Definition (eq. 3, p. 130): ℰ = C(p(s_{t+n} | aⁿ_t)) = max_{p(aⁿ)} I(Aⁿ_t; S_{t+n}), in bits; zero with no perceivable control. The sensor reading may be replaced by any function of variables downstream of A_t (the sensor sequence, or memory).
- Context (p. 130–131): the channel has state R; by the theory of channels with side information, “knowing the state of the channel may increase its capacity”, so a compact context approximating R can raise empowerment and can be built “from the data available on-board”. Not developed here.
- Two ways to maximize it (§2.3): go where p(s | aⁿ) is less noisy, or change the sensors and actuators.
- Sensor evolution (§3.2, Figure 3). 5 actions (stay or move to a von Neumann neighbour), sensors of ≤ 20 sampling points in a 21 × 21 square, fitness = 4-step empowerment − 10⁻³|S|. Best sensors: blobs near the source, arcs capturing bearing far from it; empowerment 4.322 bits at (0, 0) and (10, 0), 3.907 at (10, 10), 3.248 at (20, 0), 2.858 at (20, 10), 2.807 at (20, 20).
- Actuator evolution (§3.3, Figure 5). Fixed 16-state bearing sensor, ≤ 10 actions within 4 cells: 4.000 bits near the centre, 2.807 farther out; “much larger” variety of optimal actuators than of sensors; with longer jumps all six places reach 4 bits, “constrained by the capacity of the sensor”.
Claims
| id | claim | strength | support |
|---|---|---|---|
| C1 | Empowerment is a universal, agent-centric utility | weak | definitional universality; utility argued from examples |
| C2 | Empowerment counts only control the agent can perceive | strong | definition: capacity to its own sensor |
| C3 | Empowerment as fitness switches the sensor’s representation with the niche | moderate | one grid world, evolutionary search |
| C4 | Actuators are under less selective pressure than sensors | weak | one experiment; varied optima at equal fitness |
| C5 | Knowing the channel’s state can raise empowerment | strong | standard side-information result (cited) |
Concepts
- Empowerment — channel capacity from the agent’s n actions to its later sensor state.
- Actuation channel — p(s_{t+n} | aⁿ_t), the agent’s embodiment described by the effects of its actions on its sensors.
- Context — a variable approximating the channel’s state.
- Logical level — actions identified by their effects on the sensor, sensors by how they see actions (§2.3).
Connections
Ashby’s law of requisite variety and Touchette and Lloyd’s information limits of control; Gibson’s affordances; the authors’ information-flow work. Extended in Klyubin et al. 2008 (LIT-1951, NOTE-1514).
Bearing on the record
- CLAIM-354. Empowerment is a ready-made candidate for the claim’s
“viable reachability” dimension restricted to what the agent can tell
apart: the capacity of the channel from its actions to its later sensor
is the log of how many perceptibly different futures it can bring about,
with noise priced in. Two points for the claim:
- It is a scalar defined from the dynamics alone, with no task. That is the form the claim’s defeater names. But the 2005 definition prices no control cost, imposes no viability set and is open-loop, so it agrees at best with one of the claim’s dimensions; it does not collapse the profile. A neighbourhood empowerment that is equal for two agents whose reachable sets differ (the 4-bit ceiling set by the sensor, §3.3) is the claim’s non-nesting in a single number: equal capacity, different sets.
- The neurosurgeon point is the legibility restriction of the claim’s note of 2026-11-02, built into the definition: control the agent cannot read does not count. Empowerment is legibility-limited reachability in exactly the sense CLAIM-537 makes concrete, but measured by information rather than by sets.
- A21’s “controllability and observability together” (the registration of LIT-1951). Fair: the capacity is zero if the actions cannot move the sensor (uncontrollable) or the sensor cannot register the move (unobservable). It is an information measure, not a rank: a noisy channel with full rank has low empowerment.
- TERM-064. “What it does not matter … what other agents perceive” (p. 129) is legibility to oneself, not to a governing observer.
Limitations
- Universality is by definition; whether empowerment tracks what organisms value is argued from examples (sugar, social status, money).
- One toy world; evolutionary search with a small arbitrary penalty.
- Open-loop only; contextual empowerment is named, not developed.
Open questions
Whether closed-loop or context-dependent empowerment changes the sensor result; how to compute it on-board without a world model, which the 2008 paper takes up.