A Quantifiable Information-Processing Hierarchy Provides a Necessary Condition for Detecting Agency

TL;DR

The paper addresses how to define agency in heterogeneous substrates by proposing a bottom-up framework based on information-processing order. It formalizes three classes—Class I: $R(t)=\alpha(t)I(t)+\varepsilon(t)$; Class II: $R(t)=\mathcal{T}[I(t)]+\varepsilon(t)$; Class III: $R_t=\mathcal{T}_t[I_t]+\varepsilon_t$, with $\mathcal{T}_{t+1}=\mathcal{G}(\mathcal{T}_t,R_t)$—and argues that genuine agency requires third-order adaptivity. Through three case studies (thermostat, ideal memristor, memristive bioreceptor), it demonstrates that memory and adaptivity manifest in input–output trajectories and can be quantified via rolling regression and zero-crossing lag. The framework offers substrate-independent criteria with ethical and neuroscience relevance, clarifying when a system exhibits minimal agency and guiding future research into autonomous information processing.

Abstract

As intelligent systems are developed across diverse substrates - from machine learning models and neuromorphic hardware to in vitro neural cultures - understanding what gives a system agency has become increasingly important. Existing definitions, however, tend to rely on top-down descriptions that are difficult to quantify. We propose a bottom-up framework grounded in a system's information-processing order: the extent to which its transformation of input evolves over time. We identify three orders of information processing. Class I systems are reactive and memoryless, mapping inputs directly to outputs. Class II systems incorporate internal states that provide memory but follow fixed transformation rules. Class III systems are adaptive; their transformation rules themselves change as a function of prior activity. While not sufficient on their own, these dynamics represent necessary informational conditions for genuine agency. This hierarchy offers a measurable, substrate-independent way to identify the informational precursors of agency. We illustrate the framework with neurophysiological and computational examples, including thermostats and receptor-like memristors, and discuss its implications for the ethical and functional evaluation of systems that may exhibit agency.

Figures (10)

• Figure 1: Information-processing classes and their relation to memory, adaptivity, and agency.
• Figure 2: First-order thermostat response to a square wave: instantaneous, proportional switching between two fixed output levels; no memory or adaptation.
• Figure 3: Ideal memristor response to a square wave. The output current reflects the slow evolution of the internal state, so each input transition leaves a carry-over in the next cycle; the mapping is fixed, but the response depends on recent history.
• Figure 4: Memristive bioreceptor under square-wave drive. The output exhibits memristive transients and gradual changes in sensitivity and offset driven by slow activity averages, indicating that the input–output mapping is itself adapting over time.
• Figure 5: Input-Output trajectories for the three example systems, all driven by a sinusoidal input. The thermostat (left) produces two fixed gain lines corresponding to the constant gain values $\alpha_\mathrm{on}$ and $\alpha_\mathrm{off}$ (On and Off state), showing an instantaneous, memoryless response. The ideal memristor (centre), exhibits a stationary voltage-current loop, where points at earlier times (darker blue) are retraced by later ones (lighter yellow), indicating memory without adaptivity. The MBR (right) shows a loop that gradually shifts and deforms over time, (colour scale indicates absolute time within the final 50 s of simulation), demonstrating memory with adaptivity