Causal composition: Structural differences among dynamically equivalent systems

“However, transfer entropy still relies on observational data, while a causal approach generally requires perturbational data [53] (although observational data is sufficient for causal inference in ER systems since they cycle through all their possible states).”

“This part is then said to “represent” the variable or stimulus as its informational content [14–17] (but see [18] for a critical discussion).”

“Due to recent advances in the field of artificial intelligence, there is a growing realization that the ability to predict what a system is going to do does not equal understanding how or why it behaves in a certain way, not even in hindsight (e.g., [66,67]).”

“A distinguishing feature of IIT as a theory of consciousness is that it starts from phenomenology itself, which is the one and only thing whose existence is directly evident to the experiencing entity [26].”

“This is quantified by Φ (“big phi”), the system-level integrated information [27].”

“More recently, machine-learning based techniques such as “decoding” have gained popularity [11,17,19] and have been utilized to investigate content-specific neural correlates of consciousness [20,21].”

“…will discuss: (1) Differences and similarities between the notion of composition portrayed in this work and accounts of information decomposition [39–42], (2) the role of composition with respect to a system’s capacity for autonomy and agency, and (3) the role of composition within IIT as a…”

“More recently, machine-learning based techniques such as “decoding” have gained popularity [11,17,19] and have been utilized to investigate content-specific neural correlates of consciousness [20,21].”

“More recently, machine-learning based techniques such as “decoding” have gained popularity [11,17,19] and have been utilized to investigate content-specific neural correlates of consciousness [20,21].”

“Agents, however, are open systems that interact dynamically and informationally with their environment [59].”

“[29–31], how to identify individuals and their causal borders [27,32–35], and how to characterize the compositional nature of phenomenal experiences [27].”

“Within this sample, we especially focus on the class of ergodic, reversible (ER) systems (see Section 5.6) , which cycle through all their possible states and thus specify the same, maximal amount of effective [36,37] and predictive information [38] (3 bits).”

“…integrated information measure proposed in [56], but rather by min While the role of composition in accounting for the quality of phenomenal experience (see Section 4.3) had already been recognized in earlier publications [57], it was not incorporated in the quantitative measure φ 2.0 [58].”

“This measure has been termed the effective information EI ( S ) of a discrete dynamical system S [36,37]. can be conveniently represented in terms of the system’s TPM, as it corresponds to the average D KL between the distribution specified by each row M rS = p ( V t | v rt − 1 ) in M S and p ( V t…”

“In this way, our approach is more closely related to proposed measures of causal information flow [44,54], but evaluated in a state-dependent manner, as the information specified by the subset in its current state about its causes and effects (see also [55]).”

“…integrated information measure proposed in [56], but rather by min While the role of composition in accounting for the quality of phenomenal experience (see Section 4.3) had already been recognized in earlier publications [57], it was not incorporated in the quantitative measure φ 2.0 [58].”

“information flow [44,54], but evaluated in a state-dependent manner, as the information specified by the subset in its current state about its causes and effects (see also [55]).”

“Most proposed empirical measures of information integration [56,74–77] do not evaluate φ in a state-dependent manner, but rather as a difference in conditional entropies or mutual information under a (bidirectional) system partition (but see [78], which includes state-dependent measures).”

“As described in detail in [25,27,31], the cause and effect repertoire of a subset X ⊆ S in state x t ⊆ v t can be obtained from the system’s transition probabilities (Equation (2)) by conditioning on x t and causally marginalizing the variables W t = V t \ X .”

“Traditionally, how well we can predict the behavior of a system is taken as a measure of how well we are able to model, and thus “understand”, the system [1] (but see [2–4]).”

“Proposed practical measures of integrated information, such as geometric integrated information φ G [56], decoder-based integrated information φ ∗ [75], or stochastic interaction (SI) [74,76], typically evaluate bidirectional partitions between sets of system elements, as described for φ 2.0 [58]…”

“This part is then said to “represent” the variable or stimulus as its informational content [14–17] (but see [18] for a critical discussion).”

“Yet, understanding what caused the agent to perform a particular action typically requires extensive additional analysis and cannot be addressed in purely reductionist or holistic terms [31,69,70].”

“…measure of autonomy based on dynamical, informational, or causal criteria, agents can then be identified as subsystems that form local maxima of autonomy [27,32–34 , 65 Finally, when an agent interacts with its environment, we are often interested in why the agent performed a particular action.”

“…evaluate ϕ Ψ C / E ( v t ) , the difference in the cause/effect repertoire of v t before and after the partition Ψ (Equation (16)). φ H is closely related to φ 2.0 [58], and even more so to φ 2.5 as defined in [78], since φ 2.0 only takes constraints of v t onto the prior states of S into account.”

“More recently, machine-learning based techniques such as “decoding” have gained popularity [11,17,19] and have been utilized to investigate content-specific neural correlates of consciousness [20,21].”

“All quantities evaluated in this article were computed using custom-made python scripts (available upon request) based on PyPhi, the IIT python software package [72].”

“While these approaches recognize that subsets within the system may carry out different functional roles, they consider correlations between objects or events from an extrinsic point of view rather than the causal consequences within the system [10,20,22,23].”

“More recently, machine-learning based techniques such as “decoding” have gained popularity [11,17,19] and have been utilized to investigate content-specific neural correlates of consciousness [20,21].”

“This is demonstrated particularly well by recent computational studies involving simulated artificial agents with minimal cognitive architectures [15,23,68,69], whose behavior can easily be predicted.”

“As shown in [52], PID can also be applied to decompose transfer entropy, a directional measure of information transfer from a variable Y t to another variable X t + 1 , extended to the case of multiple sources.”

“…measures of integrated information, such as geometric integrated information φ G [56], decoder-based integrated information φ ∗ [75], or stochastic interaction (SI) [74,76], typically evaluate bidirectional partitions between sets of system elements, as described for φ 2.0 [58] and in [78].”

“While these approaches recognize that subsets within the system may carry out different functional roles, they consider correlations between objects or events from an extrinsic point of view rather than the causal consequences within the system [10,20,22,23].”

“Traditionally, how well we can predict the behavior of a system is taken as a measure of how well we are able to model, and thus “understand”, the system [1] (but see [2–4]).”

“This is demonstrated particularly well by recent computational studies involving simulated artificial agents with minimal cognitive architectures [15,23,68,69], whose behavior can easily be predicted.”

“As described in detail in [25,27,31], the cause and effect repertoire of a subset X ⊆ S in state x t ⊆ v t can be obtained from the system’s transition probabilities (Equation (2)) by conditioning on x t and causally marginalizing the variables W t = V t \ X .”

“To establish whether a (sub)set of elements forms a whole in an observer-independent manner, purely reductionist or holistic approaches are inadequate [33].”

“Moreover, the focus is put on prediction, rather than understanding [3].”

“For elements with one binary output, all input-output functions except for COPY and NOT logic-gates are necessarily convergent (multiple inputs may lead to the same output) and thus logically irreversible (see also [45] for a recent review on reversible cellular automata).”

“…argument—that a compositional perspective is necessary for understanding a system’s causal and information structure—should hold even in the case of an infinite state space and continuous time (see [46,47] for an initial approach to translate the principles of IIT to continuous dynamical systems).”

“EI(S) and 〈H(Vi,t+1)〉 are related to the differentiation measures D1 and D2 described in [73].”

“information flow [44,54], but evaluated in a state-dependent manner, as the information specified by the subset in its current state about its causes and effects (see also [55]).”

“…argument—that a compositional perspective is necessary for understanding a system’s causal and information structure—should hold even in the case of an infinite state space and continuous time (see [46,47] for an initial approach to translate the principles of IIT to continuous dynamical systems).”

“Traditionally, how well we can predict the behavior of a system is taken as a measure of how well we are able to model, and thus “understand”, the system [1] (but see [2–4]).”

“Of course, this example also raises the question of why ABC was determined to be a separate entity from the environment E in the first place [23,33,35,60–63].”

“Yet, understanding what caused the agent to perform a particular action typically requires extensive additional analysis and cannot be addressed in purely reductionist or holistic terms [31,69,70].”

“Several subsequent publications have aimed at improving upon this proposal of a partial information decomposition (PID) by refining the notion of redundancy and of synergy between variables [40–42 Our approach differs from PID measures in several ways.”

“In neuroscience, information theoretical approaches [8–13] are utilized to identify the presence of information about some external variable or stimulus in a specific part of the system.”

“Of course, the system’s causal powers can be fully unfolded, and revealed dynamically, by extensive manipulations and observations of subsets of system units because they are implicitly captured by the system’s causal model and ultimately by its transition probability matrix [36].”

“Systems with lower phi may be qualitatively different from systems with higher phi (Albantakis, 2017; Albantakis and Tononi, 2019), being less capable of state-dependent adaptation—and thereby learning—which may drastically limit their intelligence and agency.”

“Given the former definitions, the stochastic system S corresponds to a causal network where ppst`1|stq “ ppst`1|dopstqq [12,18,19].”

“” In this case, it has already been proven that systems with different internal structures and hence different predicted experiences, can have identical input/ output (and therefore identical reports or inferences about report) (Albantakis and Tononi 2019).”

“In this sense, IIT also goes beyond quantification, providing a conceptual account of how qualia contribute to a given experience (Albantakis et al. 2019; Haun and Tononi 2019; Albantakis and Tononi, 2019).”

“The use of a uniform distribution of intervention states is required to accurately capture its full cause–effect power [11,12].”

“In that sense, recent work explores very small networks showing how the compositional definition of measures like Φ can yield very different results than the non-compositional mechanism-level measures ϕ [26].”

“In IIT, causation is neither reductionist nor holistic but compositional: the IIT analysis considers the intrinsic causes and effects of every subset within a system and quantifies their irreducibility as φc/e(m) [5].”

“This allows reliably disentangling causal dependencies p(y|do(θ)) from mere statistical ones p(y|θ) [21].”

“A system’s effective information is correlated with its intrinsic information ( ∑ ϕ ) for binary random networks, as shown in [16].”

“This perspective is shared by other causal frameworks [8,36,37], where the TPM is taken as the basic object encoding the causal model.”

“ective in multiple ways. First, the IIT formalism provides a 16 complete account of a system’s causal structure, including irreducible higher-order mechanisms constituted of multiple system elements (Albantakis and Tononi, 2019). IIT’s quantitative notion of irreducibility here supplants the reductionist assumption th…”

“2020) and spatiotemporal grain of analysis (Leung and Tsuchiya 2022), as well as whether causal interactions matter over dynamical properties (Albantakis and Tononi 2019).”

“4 True, Φ may reveal the presence of an irreduc - ible cause-effect structure, but it does not explain what causes what, as IIT-inspired measures of causal strength claim (Albantakis et al., 2019).”

“As argued in [67,106], causal structure also matters for delineating the borders of a system from its environment, and for identifying whether the system under observation is in fact one system as opposed to multiple.”

“It suggests a correspondence between the qualitative forms of conscious experiences and the qualitative forms of cause – effect relationships between neurons [7 – 11].”

“This disagreement is known in Integrated Information Theory (IIT) as incongruence (Albantakis and Tononi, 2019).”

“As demonstrated by a series of simple example systems, IIT allows for funcGonal equivalence without phenomenal equivalence (Albantakis and Tononi 2019; Albantakis, Barbosa, et al. 2023; Hanson and Walker 2019; 2020).”

“Additionally, the physical state of the substrate instantiating maximal Φ, for the same token, presents a maximal cause-and-effect composition (for the details of the link between measures of integrated information and causality in an interconnected network, one may see [1,2]).”

“Effective information (EI) quantifies the causal power of a system at a given level of description: is the average output distribution under the uniform intervention, computed by injecting maximum-entropy noise into V t − 1 (do-calculus style) [4, 18].”