[Paper Review] A Quantifiable Information-Processing Hierarchy Provides a Necessary Condition for Detecting Agency

Brett J. Kagan, Valentina Baccetti+4 more|arXiv (Cornell University)|Jan 7, 2026

Free Will and Agency0 citations

TL;DR

The paper proposes a bottom-up, three-class hierarchy of information processing to identify necessary informational precursors of agency, with Class III (adaptive, self-modulating) as the highest order.

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.

Motivation & Objective

• Define a substrate-independent, bottom-up framework for inferring agency based on information processing dynamics.
• Introduce three ordered classes of information processing (I, II, III) that progressively incorporate memory and adaptation.
• Argue that Class III dynamics provide necessary (not sufficient) conditions for genuine agency across systems.
• Illustrate with neurophysiological and computational examples to show how input is transformed across classes.

Proposed method

• Formally define three classes of information processing with minimal mathematical representations: Class I: R(t)=α(t)I(t)+ε(t); Class II: R(t)=T[I(t)]+ε(t) with a fixed transformation T; Class III: R_t=T_t[I_t]+ε_t with adaptive T updated via G based on past outputs.
• Provide case examples: Class I thermostat with exogenous gain modulation, Class II ideal memristor with fixed non-linear transformation, Class III memristive bioreceptor with slow adaptive gain/bias modulation.
• Characterize memory and adaptivity by analyzing input–output trajectories and hysteresis in the IO plane under periodic driving; discuss memory indication via hysteretic loops and adaptation via shifting loops.

Figure 1: Information-processing classes and their relation to memory, adaptivity, and agency.

Experimental results

Research questions

• RQ1 What informational conditions are necessary for a system to exhibit agency across diverse substrates?
• RQ2 Can a three-class information-processing hierarchy capture memory and adaptivity as precursor features of agency?
• RQ3 Do real or simulated systems (thermostats, memristors, memristive bioreceptors) realize each class and how do their IO behaviours reflect memory/adaptivity?
• RQ4 Is Class III adaptation a necessary condition for agency, even if not sufficient?
• RQ5 How can substrate-independent, quantitative measures distinguish agency-relevant dynamics from mere behavioural capacity?

Key findings

• A three-class hierarchy of information processing is proposed, with Class III (adaptive) containing memory and self-modulation, offering a measurable precursor to agency.
• Class I systems are reactive and memoryless; Class II systems transform inputs with a fixed operator; Class III systems adapt their transformation rules over time based on history.
• Case studies (thermostat, ideal memristor, memristive bioreceptor) illustrate progression from memoryless to memory-enabled to adaptively modulating information processing.
• Memory emerges in IO-plane trajectories as hysteresis loops, increasing in complexity from Class I to Class III; adaptation is evidenced by shifting, deforming loops in Class III.
• The framework provides a substrate-independent, quantitative approach to identify informational precursors of agency, while acknowledging that these are necessary, not sufficient, conditions for true agency.

Figure 2: First-order thermostat response to a square wave: instantaneous, proportional switching between two fixed output levels; no memory or adaptation.