Perspective Latents as an Architectural Condition for Causal Emergence in Active Inference Agents

# Perspective Latents as an Architectural Condition for Causal Emergence in Active Inference Agents
Source: [https://arxiv.org/html/2607.20708](https://arxiv.org/html/2607.20708)
11institutetext:Active Inference Institute, Crescent City, CA, USA
11email:hjpae@activeinference\.institute###### Abstract

A recent line of work measures causal emergence in reinforcement learning agents through Integrated Information Decomposition, reporting thatΦr\\Phi\_\{r\}grows with training and tracks reward improvement\. For active inference, this raises the question of how reward\-free predictive organization relates to such information\-theoretic signatures\. I test this within an active inference agent whose architecture separates a fast perception latentzzfrom a slow global latentgg, whereggis driven by prediction error and structurally decoupled from policy gradients\. In a reward\-free environmental regime\-switching protocol,Φr\\Phi\_\{r\}concentrates ingg; its aggregate magnitude is largely architectural and decreases with training\. The substantive effect of learning becomes legible only at the atom\-compositional level: decoupling flips sign from negative to positive and becomes regime\-invariant under environmental change, while downward causation carries the regime\-dependent adjustment\. These results identifyggas the architectural locus ofΦr\\Phi\_\{r\}\-relevant temporal organization in an active inference agent, and argue against reading scalarΦr\\Phi\_\{r\}as a direct index of learned integration\.

## 1Introduction

Recent work has used Integrated Information Decomposition \(Φ\\PhiID\)\[[7](https://arxiv.org/html/2607.20708#bib.bib3),[8](https://arxiv.org/html/2607.20708#bib.bib4)\], an extension of the integrated information tradition\[[17](https://arxiv.org/html/2607.20708#bib.bib6),[1](https://arxiv.org/html/2607.20708#bib.bib7)\]into the causal emergence framework\[[4](https://arxiv.org/html/2607.20708#bib.bib5),[16](https://arxiv.org/html/2607.20708#bib.bib2)\], to analyze latent dynamics in trained reinforcement learning agents, reporting that the slow integrative organization measured byΦr\\Phi\_\{r\}grows with training and aligns globally with reward improvement\[[15](https://arxiv.org/html/2607.20708#bib.bib1)\]\. This positionsΦr\\Phi\_\{r\}as a candidate empirical signature of agentintegration: the extent to which an agent’s internal state predicts its own future as a coherent whole, rather than as a collection of independent parts\. Yet such analysis detects the slow integrative mode without specifying its architectural locus\. Hence I ask:what architectural locus, within a single agent, gives rise to the slow integrative mode thatΦr\\Phi\_\{r\}detects?

A natural candidate is suggested by an independent line of work onperspective latentsin active inference agents\. Phenomenological accounts of subjectivity have long emphasized that any subjective experience is oriented from a perspectival standpoint\[[5](https://arxiv.org/html/2607.20708#bib.bib14),[9](https://arxiv.org/html/2607.20708#bib.bib15),[19](https://arxiv.org/html/2607.20708#bib.bib16)\]\. This could be interpreted as a slowly evolving, history\-sensitive condition under which the world becomes given as meaningful, threatening, or unremarkable\. Recent active inference work has formalized analogous structures as slow latent variables that anchor an agent’s interpretive stance toward the world across time\. The architecture I adopt here introduces a slow latentgg, driven by environmental prediction error minimization and decoupled from policy gradients, and demonstrates thatggexhibits hysteresis under regime change and reorganizes perceptual encoding as a function of accumulated history\[[11](https://arxiv.org/html/2607.20708#bib.bib20),[12](https://arxiv.org/html/2607.20708#bib.bib21),[10](https://arxiv.org/html/2607.20708#bib.bib22)\]\. The present paper asks whetherggis the locus thatΦr\\Phi\_\{r\}detects\. Rather than re\-evaluating the behavioral phenotype of this agent, the present paper treats the inherited architecture as a fixed test case and asks whereΦr\\Phi\_\{r\}\-relevant temporal organization appears within it\.

This is tested in a reward\-free regime\-switching protocol, computingΦr\\Phi\_\{r\}over the fast perceptual latentzzand the slow perspective latentggacross 30 seeds\. Three controls anchor the analysis: \(1\) a within\-episode temporal shuffle \(isolating temporal structure\), \(2\) an untrained\-architecture baseline \(isolating learning\), and \(3\) a pre/post regime\-switch comparison \(testing atom\-level adaptivity\)\. To characterize the locus of integration further,Φr\\Phi\_\{r\}is also decomposed into three theory\-grounded atom groups, following\[[16](https://arxiv.org/html/2607.20708#bib.bib2)\]: \(i\) decoupling, \(ii\) downward causation, and \(iii\) part\-driven contributions\.

On the basis of the perspective framework, three predictions follow\. First, sinceggis a history\-sensitive Gated Recurrent Unit \(GRU\)\-gated latent in the architecture,Φr\\Phi\_\{r\}should concentrate onggrather than onzz\. Second, sinceΦr\\Phi\_\{r\}has been reported to grow with training under reward\-driven learning\[[15](https://arxiv.org/html/2607.20708#bib.bib1)\], a similar growth might be expected under the reward\-free prediction\-error objective used here, with trainedΦr​\(g\)\\Phi\_\{r\}\(g\)exceeding its untrained baseline\. Third, environmental regime shift should leave a measurable signature in the atom\-level composition ofΦr​\(g\)\\Phi\_\{r\}\(g\), consistent with the history sensitivity previously reported forgg\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\]\. The first and third predictions are confirmed by the analyses below\. The second yields a more informative reversal:Φr​\(g\)\\Phi\_\{r\}\(g\)does not simply grow with training, while the substantive effect of learning becomes visible only whenΦr\\Phi\_\{r\}is decomposed into its constituent atom groups\. Disentangling these atom groups reveals a structural transformation that scalarΦr\\Phi\_\{r\}alone cannot capture\.

#### Key Contributions\.

\(1\) Empirical locus\.Φr\\Phi\_\{r\}in a perspective architecture concentrates in the slow latentggrather than the fast latentzz\.\(2\) Architecture vs\. learning\.AggregateΦr​\(g\)\\Phi\_\{r\}\(g\)is largely supplied by the recurrent architecture itself; learning lowers this magnitude\.\(3\) Atom\-level dissociation\.Learning shifts decoupling from negative to positive and makes it approximately regime\-invariant, while downward causation remains regime\-adaptive\.

## 2Experiment Methods

### 2\.1Agent Architecture and Simulation Environment

The agent implementation and its simulation environment are inherited directly from\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\], with no additions beyond the analysis\-side knobs\. In this agent, the perspective layer and the action policy layer are designed to be structurally separated, where the perspective layer answers to “What kind of world do I believe I am still in?”, while the policy layer answers to “What should I do right now?”\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\]\.

![Refer to caption](https://arxiv.org/html/2607.20708v1/x1.png)Figure 1:Agent architecture overview \(inherited from\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\]\)\.The fast perception latentztz\_\{t\}and the slow global “perspective” latentgtg\_\{t\}feed into the action policyπ\\pi, whilegtg\_\{t\}is structurally decoupled from policy gradients\. The present study analyzes theΦr\\Phi\_\{r\}structure of these latent trajectories\.Following the active inference principle, the agent learns to minimize its environmental prediction error\. Agents act in a reward\-free 2D gridworld of size15×915\\times 9with 3 distinct environmental niche\-like zones distinguished by zone\-specific observation noise of\(σ0,σ1,σ2=0\.6,0\.3,0\.05\)\(\\sigma\_\{0\},\\sigma\_\{1\},\\sigma\_\{2\}=0\.6,0\.3,0\.05\)\. Environmental prediction is therefore harder in the leftmost zone and easier in the rightmost, so the agent comes to prefer rightward over leftward motion\. Importantly, no reward signal is provided; the primary representational signal is one\-step prediction error on perceptual reconstruction\. This aligns with the active inference principle at the level of perception and world\-modeling, while policy selection is trained through a learned actor loss rather than via expected\-free\-energy minimization; however, note that the paper’s claims concern the perception and world\-modeling side of the architecture rather than action\-selection dynamics\.

The observation encoder maps the agent’s local surroundings \(the 8 neighboring tiles in the 2D gridworld\), together with the previous action encoded as a learned embeddingpt∈ℝ8p\_\{t\}\\in\\mathbb\{R\}^\{8\}\(over the 5 actions UP / DOWN / LEFT / RIGHT / STAY\), into a fast latentztz\_\{t\}\. Architecturally, what matters is the separation ofztz\_\{t\}, which serves the role of immediate perception, fromgtg\_\{t\}, which serves as a global\-scale “perspective” that registers and predicts the environment at the regime level\. It accumulates history through a damped GRU module updated from\(zt,pt\)\(z\_\{t\},p\_\{t\}\); the parameters of this pathway are trained through the one\-step prediction objective and thegtg\_\{t\}\-smoothness regularizer\. A state head composesztz\_\{t\},ptp\_\{t\}andgtg\_\{t\}into a policy statests\_\{t\}, which feeds a discrete action policyπ​\(at∣st\)\\pi\(a\_\{t\}\\mid s\_\{t\}\)over the 5 actions\. In all experiments, the dimensions are fixed atzt∈ℝ16z\_\{t\}\\in\\mathbb\{R\}^\{16\},pt∈ℝ8p\_\{t\}\\in\\mathbb\{R\}^\{8\},gt∈ℝ12g\_\{t\}\\in\\mathbb\{R\}^\{12\}, andst∈ℝ16s\_\{t\}\\in\\mathbb\{R\}^\{16\}\. An overview of the architecture is shown in Fig\.[1](https://arxiv.org/html/2607.20708#S2.F1)\.

Importantly,gtg\_\{t\}is structurally decoupled from policy gradients through stop\-gradient operators that sever the paths through which policy or actor losses could flow back intogtg\_\{t\}\. As a result,gtg\_\{t\}is largely shaped by global predictive coherence, rather than by actor\-side gradients\.

### 2\.2Training Protocol

Each seed is trained for48,00048,000environment steps withAdamoptimizer at learning rate3×10−43\\times 10^\{\-4\}on240240\-step episodes; this corresponds to200200episodes per seed, with the network weights including those producingztz\_\{t\}andgtg\_\{t\}carried across episode boundaries\. A total of 30 seeds were run\.

The training objective \(loss function\) follows\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\]and combines four terms:

ℒ=ℒpred\+wsmooth​ℒsmooth\+wactor​ℒactor−wentropy​ℋ​\(π\)\\mathcal\{L\}=\\mathcal\{L\}\_\{\\text\{pred\}\}\+w\_\{\\text\{smooth\}\}\\,\\mathcal\{L\}\_\{\\text\{smooth\}\}\+w\_\{\\text\{actor\}\}\\,\\mathcal\{L\}\_\{\\text\{actor\}\}\-w\_\{\\text\{entropy\}\}\\,\\mathcal\{H\}\(\\pi\)\(1\)whereℒpred\\mathcal\{L\}\_\{\\text\{pred\}\}is the one\-step prediction error on the perceptual reconstruction \(primary signal\),ℒsmooth\\mathcal\{L\}\_\{\\text\{smooth\}\}is a temporal smoothness regularizer ongtg\_\{t\},ℒactor\\mathcal\{L\}\_\{\\text\{actor\}\}is an actor\-style consistency cost applied through an exponential moving baseline with coefficientβ=0\.98\\beta=0\.98, andℋ​\(π\)\\mathcal\{H\}\(\\pi\)is the policy entropy\. Loss weights are inherited unchanged from\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\]:wsmooth=0\.25w\_\{\\text\{smooth\}\}=0\.25,wactor=0\.25w\_\{\\text\{actor\}\}=0\.25,wentropy=0\.001w\_\{\\text\{entropy\}\}=0\.001\. The actor term is gated on only after a12,00012,000\-step warmup, allowing the predictive backbone andgg\-dynamics to stabilize before actor\-side optimization is introduced\. Actor\-side gradients are blocked fromgtg\_\{t\}through the stop\-gradient operators, so that the actor objective shapesπ\\piandsts\_\{t\}but notgtg\_\{t\}itself\.

### 2\.3Analysis Protocol

For analysis, the trained weights are used to record replay rollouts under the same environment\. Each replay episode runs forT=500T=500steps, and the first8080steps are discarded as warmup\. The architecture itself is identical between training and replay; only the regime\-switch instrumentation and the episode length \(T=500T=500vs\.T=240T=240\) differ\.

#### Replay conditions\.

Two conditions are analyzed: acontrolcondition, in which the zone variances are fixed throughout at the same values used during training, and aregime switchcondition, in which the observation noise of the environment zones are reversed from\(σ0,σ1,σ2\)=\(0\.6,0\.3,0\.05\)\(\\sigma\_\{0\},\\sigma\_\{1\},\\sigma\_\{2\}\)=\(0\.6,0\.3,0\.05\)to\(0\.05,0\.3,0\.6\)\(0\.05,0\.3,0\.6\)att=320t=320, defining a pre\-switch window of80<t≤32080<t\\leq 320and a post\-switch window oft\>320t\>320\. 10 rollout episodes per seed are collected per condition under stochastic action sampling, yieldingn=300n=300episodes per condition across3030seeds\. For regime\-switch analyses,Φr​\(g\)\\Phi\_\{r\}\(g\)and its atom\-group decomposition are computed separately on the pre\-switch window and the post\-switch window\.

#### Control analyses\.

Two additional controls separate contributions to the observed signals\. Awithin\-episode temporal shufflerandomly permutes the time index ofgtg\_\{t\}within each episode \(three independent shuffles averaged per episode\), preserving its marginal distribution while destroying all temporal order\. This separates the contribution of temporal structure from that of the marginal distribution\.

Anuntrained\-architecture baselineinstantiates the same architecture with the same hyperparameters but with fresh random initialization \(random seeds are distinct from those used for trained checkpoints\) and no training, with the replay protocol identical to the trained case\. This separates the contribution of learning from that of the architecture alone\.

#### Statistical analysis\.

Paired comparisons use Student’s pairedtt\-test on episode\-level estimates or within\-episode pre/post regime switch differences, and unpaired group comparisons use Welch’s unequal\-variancett\-test\. Effect sizes are reported as Cohen’sddwhere informative\. Allpp\-values are two\-sided, with significance assessed atα=0\.05\\alpha=0\.05\. Code and data are available at[https://github\.com/hjpae/perspective\-causal\-emergence](https://github.com/hjpae/perspective-causal-emergence)\.

### 2\.4Φr\\Phi\_\{r\}Calculation

To measure the temporal information structure of latent trajectories, I calculateΦr\\Phi\_\{r\}, which is an estimator based onΦ\\PhiID\[[7](https://arxiv.org/html/2607.20708#bib.bib3),[8](https://arxiv.org/html/2607.20708#bib.bib4)\], adapted from the implementation used in\[[15](https://arxiv.org/html/2607.20708#bib.bib1)\]\. This estimator is local and pointwise, i\.e\. atom values are computed at each time step, are permitted to take negative values, and are summarized by the median over time\. It therefore differs from the non\-negative synergistic\-channel construction that\[[16](https://arxiv.org/html/2607.20708#bib.bib2)\]uses to define causal decoupling as a scalar system\-level property\. In what follows, I borrow the atom taxonomy of\[[16](https://arxiv.org/html/2607.20708#bib.bib2)\]but not its non\-negativity constraint\. Thus, sign shifts in this study should be read as changes in the local pointwise contribution of the corresponding atom, rather than as changes in a Rosas\-style non\-negative index\. The purpose of this analysis is to ask whereΦr\\Phi\_\{r\}\-relevant temporal organization appears within the architecture, and how its composition changes with learning and regime shift\.

For a multivariate latent trajectoryX=\[x1,…,xT\]X=\[x\_\{1\},\\dots,x\_\{T\}\], withxt∈ℝdx\_\{t\}\\in\\mathbb\{R\}^\{d\}, the trajectory is first arranged as ad×Td\\times Tmatrix and standardized dimension\-wise using a corrected z\-score procedure, which injects small noise into near\-constant units before standardization\. A lag\-1 Gaussian mutual information matrixMMis then computed across latent dimensions, following the Gaussian copula approach to mutual information estimation\[[6](https://arxiv.org/html/2607.20708#bib.bib10)\]\. For each pair of dimensions, the lagged correlationri​jr\_\{ij\}is converted to Gaussian mutual information as:

Mi​j=−12​log⁡\(1−ri​j2\),Mi​i=0M\_\{ij\}=\-\\frac\{1\}\{2\}\\log\(1\-r\_\{ij\}^\{2\}\),\\quad M\_\{ii\}=0\(2\)Pairwise dependencies are retained only when significant under Bonferroni\-corrected testing atα=0\.05\\alpha=0\.05, and non\-significant entries are set to zero\. This matrix defines a weighted mutual information graph over latent dimensions\.

The thresholdedMMis then used to bisect the system\. Except where explicitly noted below, the Fiedler vector of the graph Laplacian associated withMM\[[2](https://arxiv.org/html/2607.20708#bib.bib9)\]provides an automatic minimum information bipartitionm​i​n​\(A\|B\)min\(A\|B\)of thedddimensions; if the Fiedler split is degenerate, the implementation falls back to an index\-based halving\. The standardized trajectoryX~\\tilde\{X\}is then collapsed onto a two\-node trajectoryY=\(YA,YB\)Y=\(Y\_\{A\},Y\_\{B\}\)by within\-partition averaging, determined as:

m​i​n​\(A\|B\)=Fiedler​\(L​\(M\)\);YA​\(t\)=1\|A\|​∑i∈AX~i​\(t\),YB​\(t\)=1\|B\|​∑i∈BX~i​\(t\)min\(A\|B\)=\\mathrm\{Fiedler\}\(L\(M\)\);\\quad Y\_\{A\}\(t\)=\\frac\{1\}\{\|A\|\}\\sum\_\{i\\in A\}\\tilde\{X\}\_\{i\}\(t\),\\quad Y\_\{B\}\(t\)=\\frac\{1\}\{\|B\|\}\\sum\_\{i\\in B\}\\tilde\{X\}\_\{i\}\(t\)\(3\)
This two\-node trajectoryYYis the input toΦ\\PhiID itself\. A localΦ\\PhiID latticeΠ​\(Y\)\\Pi\(Y\)is computed using Gaussian local entropy estimates and Möbius inversion, producing local atom valuesπa​\(t\)\\pi\_\{a\}\(t\)for each lattice atomaa\. Let𝒜r\\mathcal\{A\}\_\{r\}denote the subset of lattice atoms that contribute toΦr\\Phi\_\{r\}\. The episode\-levelΦr​\(X\)\\Phi\_\{r\}\(X\)is the median over time of the local sum, which could be expressed as:

πa​\(t\)=\[Π​\(Y\)\]a​\(t\);ϕr​\(t\)=∑a∈𝒜rπa​\(t\),Φr​\(X\)=mediant​ϕr​\(t\)\\pi\_\{a\}\(t\)=\[\\Pi\(Y\)\]\_\{a\}\(t\);\\qquad\\phi\_\{r\}\(t\)=\\sum\_\{a\\in\\mathcal\{A\}\_\{r\}\}\\pi\_\{a\}\(t\),\\quad\\Phi\_\{r\}\(X\)=\\mathrm\{median\}\_\{t\}\\,\\phi\_\{r\}\(t\)\(4\)
Throughout the results, I refer to this episode\-level scalarΦr​\(X\)\\Phi\_\{r\}\(X\)asaggregateΦr\\Phi\_\{r\}\. Here, “aggregate” means that the nineΦr\\Phi\_\{r\}\-relevant atom values have been summed locally and then summarized over time by the median\. It does not refer to averaging across episodes or seeds, which are reported separately as descriptive statistics\. Atom grouping is further discussed below\.

In the main analyses, I computeΦr\\Phi\_\{r\}separately forzzandgg\. For thesezz\-only andgg\-only analyses, the bipartition is selected automatically by the Fiedler procedure described above\. I also compute a diagnosticΦr\\Phi\_\{r\}on the joint trajectory\[z,g\]\[z,g\], forcing the bipartition to respect the architectural boundaryz\|gz\|g\. This forced split asks how much temporal organization is present across the perceptual\-perspective boundary, rather than how the Fiedler procedure would partition the concatenated latent space\. Because the central signal localizes togg, the main results focus on theggtrajectory and its atom\-level composition\.

#### Atom grouping\.

To interpret the composition ofΦr\\Phi\_\{r\}, I decompose eachgg\-trajectory into the nineΦr\\Phi\_\{r\}\-relevantΦ\\PhiID atoms and group them by their directional pattern on the two\-node partial information decomposition \(PID\) lattice\[[18](https://arxiv.org/html/2607.20708#bib.bib8)\]\. The nine atoms are those on the double\-redundancy lattice whose source and target both involve the two\-node partition induced by the Fiedler bisection; the atom taxonomy is that of\[[16](https://arxiv.org/html/2607.20708#bib.bib2)\], and the specific implementation of the pointwise decomposition follows\[[15](https://arxiv.org/html/2607.20708#bib.bib1)\]\. This grouping preserves the directional distinction of\[[16](https://arxiv.org/html/2607.20708#bib.bib2)\]: decoupling and downward terms correspond most directly to emergence\-related whole\-to\-whole and whole\-to\-part organization, whereas the part\-driven group closes the accounting of the fullΦr\\Phi\_\{r\}sum in the present estimator\. Because the bipartitions are produced by the Fiedler bisection, the labels of the individual parts might possess redundancy\. Hence, I report 3 topology\-level group sums rather than treating the 9 individual atom labels\.

The first group isdecoupling\(whole→\\towhole\), consisting of the single atom in which the whole at the present informs the whole at the future\. This is the atom most directly associated with whole\-as\-whole irreducibility\. The second group isdownward causation\(whole→\\topart\), consisting of the 3 atoms in which whole\-level present information contributes to future part\-level structure\. The third group ispart\-driven contribution\(part→\\towholeandpart→\\topart\), consisting of the remaining 5Φr\\Phi\_\{r\}\-relevant atoms, including bottom\-up and lateral part\-mediated terms\.

## 3Results

The results are organized around the progression from localization to interpretation\. First, I ask whereΦr\\Phi\_\{r\}\-relevant temporal structure appears within the inherited architecture\. Second, I test whether aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)is produced by learning or already supplied by the recurrent substrate\. Third, I decomposeΦr​\(g\)\\Phi\_\{r\}\(g\)into atom groups to determine what learning changes\. Finally, I examine whether the learned composition ofΦr​\(g\)\\Phi\_\{r\}\(g\)responds differently to environmental regime shift\. Taken together, these analyses position the perspective latentggas the locus at whichΦr\\Phi\_\{r\}\-relevant temporal organization can be decomposed and interpreted\.

### 3\.1Φr\\Phi\_\{r\}localizes to the perspectivegg, and depends on temporal order

![Refer to caption](https://arxiv.org/html/2607.20708v1/fig1_separation_and_shuffle.png)Figure 2:Φr\\Phi\_\{r\}localizes to the perspective latent and depends on temporal order\.Scatter points show individual episodes, the half\-violin shows the pooled distribution, and the horizontal bar marks the mean\.\(a\)\.Under the same replay condition,Φr​\(g\)\\Phi\_\{r\}\(g\)is129×129\\timeslarger thanΦr​\(z\)\\Phi\_\{r\}\(z\)\(meanΦr​\(g\)=1\.42\\Phi\_\{r\}\(g\)=1\.42±\\pmSD0\.560\.56, meanΦr​\(z\)=0\.011\\Phi\_\{r\}\(z\)=0\.011±\\pmSD0\.0210\.021\)\.\(b\)\.Within\-episode temporal shuffling ofggcollapsesΦr​\(g\)\\Phi\_\{r\}\(g\)from1\.42±0\.561\.42\\pm 0\.56to0\.009±0\.0040\.009\\pm 0\.004, a99\.4%99\.4\\%reduction\.For each trained seed,Φr\\Phi\_\{r\}was computed separately forzzandggon the post\-warmup portion of each rollout episode\. As shown in Fig\.[2](https://arxiv.org/html/2607.20708#S3.F2)\(a\), the two distributions are clearly separated\. Across300300trained episodes, meanΦr​\(g\)=1\.42\\Phi\_\{r\}\(g\)=1\.42±\\pmSD0\.560\.56, whereas meanΦr​\(z\)=0\.011\\Phi\_\{r\}\(z\)=0\.011±\\pmSD0\.0210\.021\(pairedt=43\.6t=43\.6,p<0\.0001p<0\.0001\)\. The inequality holds at the seed level for all3030trained seeds\.

This localization, however, is partly predictable from the architecture itself\.gtg\_\{t\}is a recurrent \(GRU\) latent, whileztz\_\{t\}is a feed\-forward encoding, so a temporal information measure is expected to find more structure inggthan inzzon architectural grounds alone\. The result is therefore best read as architectural localization, providing the anchor for the subsequent analyses: in this agent architecture, theΦ\\PhiID\-relevant signal is concentrated in the perspective latentggrather than in the immediate perceptual representationzz\.

A second question is whether the largeΦr​\(g\)\\Phi\_\{r\}\(g\)value reflects genuine temporal organization, or merely the marginal distribution ofgg\. To test this, within\-episode temporal shuffle was applied to eachggtrajectory, preserving its empirical marginal distribution while destroying temporal order\. As shown in Fig\.[2](https://arxiv.org/html/2607.20708#S3.F2)\(b\), this ablation collapsesΦr​\(g\)\\Phi\_\{r\}\(g\)from1\.42±0\.561\.42\\pm 0\.56to a near\-zero residual of0\.009±0\.0040\.009\\pm 0\.004, which marks a99\.4%99\.4\\%reduction \(pairedt=43\.6t=43\.6,p<0\.0001p<0\.0001\)\. The signal therefore depends on the temporal ordering of the latent trajectory rather than on its static distribution\.

These results establish the target of the remaining analyses\.Φr\\Phi\_\{r\}in this architecture is concentrated ingg, and the measured signal reflects temporal structure rather than a distributional artifact\. The more substantive question is whether learning changes theΦr\\Phi\_\{r\}structure, and which atom\-level components ofΦr\\Phi\_\{r\}are most affected\.

### 3\.2AggregateΦr​\(g\)\\Phi\_\{r\}\(g\)is supplied by architecture rather than learning

The localization result shown in Section 3\.1 does not by itself establish a learned effect\. Becausegtg\_\{t\}is a recurrent latent, high aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)could arise from the gated recurrent substrate itself, even before training\. To separate these contributions, I compareΦr​\(g\)\\Phi\_\{r\}\(g\)between trained and untrained agents under the same replay protocol\.

![Refer to caption](https://arxiv.org/html/2607.20708v1/fig2_magnitude.png)Figure 3:AggregateΦr​\(g\)\\Phi\_\{r\}\(g\)is larger in untrained than trained agents\.Raincloud format follows Fig\.[2](https://arxiv.org/html/2607.20708#S3.F2)\. Under the same replay condition, untrained agents show a higher meanΦr​\(g\)\\Phi\_\{r\}\(g\)value than trained agents \(mean±\\pmSD:2\.98±0\.912\.98\\pm 0\.91vs\.1\.42±0\.561\.42\\pm 0\.56\)\.The comparison highlights that the aggregate magnitude ofΦr\\Phi\_\{r\}is not the operative quantity that tracks learning\. Under the same replay condition, untrained agents show substantially higher aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)than trained agents \(Fig\.[3](https://arxiv.org/html/2607.20708#S3.F3)\):Φr​\(g\)=2\.98±0\.91\\Phi\_\{r\}\(g\)=2\.98\\pm 0\.91for untrained agents, compared with1\.42±0\.561\.42\\pm 0\.56for trained agents \(Welch’st=−25\.1t=\-25\.1,p<0\.0001p<0\.0001, Cohen’sd=−2\.05d=\-2\.05\)\. Thus, the recurrent architecture already produces substantialΦ\\PhiID\-relevant temporal structure inggprior to learning; learning lowers the scalar magnitude of this structure rather than increasing it\. While\[[15](https://arxiv.org/html/2607.20708#bib.bib1)\]reports a direction\-based alignment betweenΦr\\Phi\_\{r\}trajectories and reward improvement, the present cohort\-level comparison shows that a simple magnitude\-based reading ofΦr\\Phi\_\{r\}would misattribute the substantive change of learning\.

This result is important because it prevents aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)from being interpreted as a direct measure of learned temporal organization\. If scalarΦr\\Phi\_\{r\}were read in that way, the untrained agent would appear more integrated than the trained one\. The more plausible interpretation is that aggregate magnitude conflates different atom\-level contributions\. The substantive effect of learning must therefore be sought not in the amount ofΦr​\(g\)\\Phi\_\{r\}\(g\), but in its composition\. This motivates the atom\-group decomposition in the following section\.

### 3\.3Learning reorganizes the atom composition ofΦr​\(g\)\\Phi\_\{r\}\(g\)

The preceding result shows that aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)decreases after training\. This raises the possibility that the scalar summary masks a change in the underlying compositional structure\. To test this,Φr​\(g\)\\Phi\_\{r\}\(g\)is decomposed into the three atom groups defined in Section 2\.4, and the resulting composition between trained and untrained agents is compared \(Fig\.[4](https://arxiv.org/html/2607.20708#S3.F4)\)\. Note that aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)is computed as the median over time of the local sum of atoms, whereas the group means reported below are cohort means of episode\-level atom values; the two therefore need not sum identically\.

![Refer to caption](https://arxiv.org/html/2607.20708v1/fig3_atom_decomposition.png)Figure 4:Learning reorganizes the atom composition ofΦr​\(g\)\\Phi\_\{r\}\(g\)\.Atom\-group decomposition in untrained and trained agents under the same replay condition, with300300episodes per cohort\. Dotted line indicatesy=0y=0\. Cohort means are indicated as horizontal line, and also printed above each panel\.\(a\)\.Decouplingcomponent shifts from negative in untrained agents to positive in trained agents\.\(b\)\.Downward causationcomponent is reduced by roughly a factor of three after training\.\(c\)\.Part\-driven contributionremain small in both cohorts\.Thedecouplingcomponent changes in a distinctive way \(Fig\.[4](https://arxiv.org/html/2607.20708#S3.F4)\(a\)\)\. In untrained agents, decoupling is negative on average \(mean−0\.51\-0\.51\), with positive seed\-level means in only9/309/30seeds\. After training, the mean shifts to\+0\.12\+0\.12, with positive seed\-level means in22/3022/30seeds \(Δtrained−untrained=\+0\.64\\Delta\_\{\\mathrm\{trained\-untrained\}\}=\+0\.64, Welch’st=8\.6t=8\.6, Cohen’sd=0\.70d=0\.70,p<0\.0001p<0\.0001\)\. The change in absolute magnitude is smaller than for downward causation, but it is distinctive in sign shift\. Positive decoupling indicates that the whole\-to\-whole atom contributes positively to the aggregateΦr\\Phi\_\{r\}, whereas negative decoupling indicates an offsetting contribution\. The shift from negative to positive decoupling therefore marks a qualitative change in the direction of the whole\-to\-whole contribution toΦr​\(g\)\\Phi\_\{r\}\(g\)\.

The largest change in magnitude occurs in thedownward causationcomponent \(Fig\.[4](https://arxiv.org/html/2607.20708#S3.F4)\(b\)\)\. Untrained agents show a large downward contribution \(mean\+3\.41\+3\.41\), whereas trained agents show a substantially smaller value \(mean\+1\.22\+1\.22;Δtrained−untrained=−2\.18\\Delta\_\{\\mathrm\{trained\-untrained\}\}=\-2\.18, Welch’st=−21\.2t=\-21\.2, Cohen’sd=−1\.73d=\-1\.73,p<0\.0001p<0\.0001\)\. The high aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)in untrained agents is therefore mainly carried by whole\-to\-part terms, and training reduces this dominant downward component\.

Thepart\-driven contributionalso shows a small but statistically significant decrease \(Fig\.[4](https://arxiv.org/html/2607.20708#S3.F4)\(c\);\+0\.14\+0\.14in untrained agents,\+0\.08\+0\.08in trained agents;Δtrained−untrained=−0\.05\\Delta\_\{\\mathrm\{trained\-untrained\}\}=\-0\.05, Welch’st=−8\.6t=\-8\.6, Cohen’sd=−0\.70d=\-0\.70,p<0\.0001p<0\.0001\)\. Its absolute magnitude is smaller than the other two groups in both cohorts, indicating that the architecture\-versus\-learning distinction is not primarily carried by bottom\-up or lateral part\-mediated terms\.

The aggregate result in Section 3\.2 can therefore be reinterpreted in compositional terms\. Untrained recurrent dynamics produce high scalarΦr​\(g\)\\Phi\_\{r\}\(g\), dominated by downward whole\-to\-part contributions and accompanied by negative decoupling\. Learning reduces the dominant downward causation and shifts decoupling positive, while leaving part\-driven contributions small in both cohorts\. In short, learning reorganizes the atom\-level composition ofΦr​\(g\)\\Phi\_\{r\}\(g\)\.

### 3\.4LearnedΦr​\(g\)\\Phi\_\{r\}\(g\)shows regime\-specific atom dynamics

The next question is whether the learned composition ofΦr​\(g\)\\Phi\_\{r\}\(g\)remains stable under environmental change, or instead reorganizes when the observation\-noise regime switches\. Since prior work showed thatggexhibits hysteresis under regime change\[[11](https://arxiv.org/html/2607.20708#bib.bib20)\], I ask here how the atom\-level composition ofΦr​\(g\)\\Phi\_\{r\}\(g\)responds to the regime switch\. Throughout this section,Δ\\Deltais reported aspost−pre\\mathrm\{post\}\-\\mathrm\{pre\}, while pairedtt\-values are computed on the pre\-vs\-post difference, so their sign is the opposite ofΔ\\Delta\.

![Refer to caption](https://arxiv.org/html/2607.20708v1/fig5_atom_sensitivity.png)Figure 5:Atom\-level pre\-to\-post regime switch composition\.Each panel shows one atom group, separated by cohort and pre/post switch window\. Scatter points show individual episodes, half\-violins show the pooled distributions, and horizontal bars mark means\. In trained agents, decoupling and part\-driven contributions remain approximately stable, while downward causation decreases\. In untrained agents, all three groups shift across the regime switch, including a positive shift in decoupling and a large decrease in downward causation\.The atom\-level decomposition clarifies what changes under the regime switch \(Fig\.[5](https://arxiv.org/html/2607.20708#S3.F5)\)\. In trained agents, the decoupling component is almost unchanged from pre\- to post\-switch \(Δ=\+0\.04\\Delta=\+0\.04, pairedt=−1\.2t=\-1\.2,p=0\.23p=0\.23\), and the part\-driven component is likewise stable \(Δ=\+0\.01\\Delta=\+0\.01, pairedt=−1\.9t=\-1\.9,p=0\.06p=0\.06\)\. The main trained change is instead a decrease in downward causation \(Δ=−0\.23\\Delta=\-0\.23, pairedt=6\.6t=6\.6,p<0\.0001p<0\.0001\)\. Thus, the whole\-to\-whole component ofΦr​\(g\)\\Phi\_\{r\}\(g\)remains stable across the regime switch, while the whole\-to\-part component adjusts to the new environmental regime\.

Untrained agents show a broader and less selective response\. Decoupling shifts upward from negative to positive values \(Δ=\+0\.51\\Delta=\+0\.51, pairedt=−7\.0t=\-7\.0,p<0\.0001p<0\.0001\), downward causation decreases strongly \(Δ=−1\.36\\Delta=\-1\.36, pairedt=14\.2t=14\.2,p<0\.0001p<0\.0001\), and the part\-driven component also changes significantly despite its smaller scale \(Δ=−0\.05\\Delta=\-0\.05, pairedt=4\.9t=4\.9,p<0\.0001p<0\.0001\)\. In other words, the untrained recurrent substrate has high aggregateΦr​\(g\)\\Phi\_\{r\}\(g\), but its atom\-level organization is broadly regime\-sensitive\. By contrast, training confines the regime\-dependent response mainly to downward causation while leaving decoupling approximately invariant\.

This is the main mechanistic result of the analysis: learning does not create aggregateΦr​\(g\)\\Phi\_\{r\}\(g\); the recurrent architecture already supplies it\. Instead, learning changes howΦr​\(g\)\\Phi\_\{r\}\(g\)is composed and how that composition responds to environmental change\. In trained agents, the decoupling component shifts positive under learning and remains stable across the switch, whereas downward causation carries the main regime\-dependent adjustment\. These distinctions are invisible ifΦr\\Phi\_\{r\}is treated only as a scalar magnitude\.

## 4Discussion

This study asked whereΦr\\Phi\_\{r\}\-relevant temporal organization appears inside a reward\-free active inference agent, and whether its scalar magnitude is sufficient to interpret the perspective latentgg\. The localization ofΦr\\Phi\_\{r\}inggis partly expected, sinceggis the GRU\-based latent whereaszzis a fast perceptual encoding\. The more important finding is that the untrained baseline shows high aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)can be supplied by the recurrent substrate alone\. ScalarΦr\\Phi\_\{r\}therefore cannot be read as a straightforward index of learned perspective\-like organization; it localizes a relevant temporal signal, but its meaning depends on how that signal is compositionally structured\.

Learning reorganizes the composition of this temporal signal\. In untrained agents, high aggregateΦr​\(g\)\\Phi\_\{r\}\(g\)is dominated by downward whole\-to\-part contributions and accompanied by negative decoupling\. After training, aggregate magnitude decreases, but decoupling shifts positive and remains stable across regime change, while downward causation carries the main regime\-dependent adjustment\. In sum, learning does not createΦr​\(g\)\\Phi\_\{r\}\(g\)from nothing; instead, it transforms a high\-magnitude recurrent signal into a more structured configuration in which whole\-to\-whole and whole\-to\-part components play distinct roles\. Hence, the atom\-level decomposition is essential for identifying what learning actually changes\.

This connects to prior work that treats subjective perspective as a history\-sensitive orientation rather than as a reward function or policy variable\[[11](https://arxiv.org/html/2607.20708#bib.bib20),[12](https://arxiv.org/html/2607.20708#bib.bib21),[10](https://arxiv.org/html/2607.20708#bib.bib22)\]\. In this framework,ggis introduced as a candidate structural locus through which the same environmental input is organized and perceived in history\-dependent ways\. The present analysis adds an information\-dynamic layer to that proposal\. It shows that learning givesgga distinctive atom\-compositional profile: the whole\-to\-whole component becomes positive and remains approximately invariant under regime shift, while downward causation carries the main regime\-dependent adjustment\. The atom\-level decomposition therefore captures, in information\-dynamic terms, what learning does toggwithin this architecture\.

This point is relevant for active inference more broadly\. Active inference provides a principled account of perception, action, and policy selection without externally imposed reward\[[3](https://arxiv.org/html/2607.20708#bib.bib11),[13](https://arxiv.org/html/2607.20708#bib.bib12),[14](https://arxiv.org/html/2607.20708#bib.bib13)\]\. It is therefore natural to ask whether such reward\-free predictive organization can also support perspective\-relevant internal structure\. In that context, the present results argue against interpretingΦr\\Phi\_\{r\}by magnitude alone\. Prediction training produces temporally organized latent dynamics, but the relevant question is how those dynamics are compositionally organized\. Specifically,Φr\\Phi\_\{r\}should be evaluated by whether it separates stable whole\-level organization from adaptive whole\-to\-part engagement\.

However, the interpretation should be kept deliberately modest\.Φr\\Phi\_\{r\}is not presented here as a standalone measure of perspectival orientation in any phenomenologically rich sense\. At most, the present results show that this quantity tracks a particular information\-dynamic signature within a trained recurrent system\. This follows from the minimal setting in which the analysis was conducted\. The simulation uses a minimal gridworld\. Moreover, the atom grouping is a topology\-level decomposition of a reduced two\-node system under GaussianΦ\\PhiID assumptions, not a complete description of all internal causal structure\. Most importantly, the current design cannot separate effects of perspective\-specific organization from effects of learned recurrence in general\. Such distinction would require targeted architectural ablations, for example removing the stop\-gradient separation so thatggis trained under actor\-side objectives, or comparing against different recurrent latents that lack the perspective\-specific coupling used here\. Several of these limitations are the subject of ongoing work, which includes variance\- and autocorrelation\-matched baselines that isolate temporal structure from smoother recurrent dynamics, a partition\-stability audit of the Fiedler bipartition across cohorts, an intermediate\-checkpoint analysis of when the atom composition reorganizes during training, and a targeted stop\-gradient ablation\.

Nevertheless, the central conclusion holds despite these limitations: aggregateΦr\\Phi\_\{r\}localizes the relevant temporal signal, while atom composition reveals what learning actually changes\. For active inference and related approaches to perspective\-relevant internal organization, this suggests that such structures should be sought in the compositional organization of temporally extended information flow\.

## References

- \[1\]L\. Albantakis, L\. Barbosa, G\. Findlay, M\. Grasso, A\. M\. Haun, W\. Marshall, W\. G\. P\. Mayner, A\. Zaeemzadeh, M\. Boly, B\. E\. Juel, S\. Sasai, K\. Fujii, I\. David, J\. Hendren, J\. P\. Lang, and G\. Tononi\(2023\)Integrated information theory \(IIT\) 4\.0: formulating the properties of phenomenal existence in physical terms\.PLOS Computational Biology19\(10\),pp\. 1–45\.External Links:[Document](https://dx.doi.org/10.1371/journal.pcbi.1011465)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4)\.
- \[2\]M\. Fiedler\(1973\)Algebraic connectivity of graphs\.Czechoslovak Mathematical Journal23\(2\),pp\. 298–305\(eng\)\.External Links:[Link](http://eudml.org/doc/12723)Cited by:[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.p3.6)\.
- \[3\]K\. Friston, T\. FitzGerald, F\. Rigoli, P\. Schwartenbeck, and G\. Pezzulo\(2017\-01\)Active inference: a process theory\.Neural Computation29\(1\),pp\. 1–49\.External Links:[Document](https://dx.doi.org/10.1162/NECO%5Fa%5F00912)Cited by:[§4](https://arxiv.org/html/2607.20708#S4.p4.2)\.
- \[4\]E\. P\. Hoel, L\. Albantakis, and G\. Tononi\(2013\)Quantifying causal emergence shows that macro can beat micro\.Proceedings of the National Academy of Sciences110\(49\),pp\. 19790–19795\.External Links:[Document](https://dx.doi.org/10.1073/pnas.1314922110)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4)\.
- \[5\]E\. Husserl\(2001\)Logical investigations i\-ii\.Routledge\.Note:Translated fromLogische Untersuchungen I\-IICited by:[§1](https://arxiv.org/html/2607.20708#S1.p2.5)\.
- \[6\]R\. A\.A\. Ince, B\. L\. Giordano, C\. Kayser, G\. A\. Rousselet, J\. Gross, and P\. G\. Schyns\(2017\)A statistical framework for neuroimaging data analysis based on mutual information estimated via a gaussian copula\.Human Brain Mapping38\(3\),pp\. 1541–1573\.External Links:[Document](https://dx.doi.org/https%3A//doi.org/10.1002/hbm.23471)Cited by:[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.p2.5)\.
- \[7\]P\. A\. M\. Mediano, F\. Rosas, R\. L\. Carhart\-Harris, A\. K\. Seth, and A\. B\. Barrett\(2019\)Beyond integrated information: a taxonomy of information dynamics phenomena\.External Links:1909\.02297,[Link](https://arxiv.org/abs/1909.02297)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4),[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.p1.3)\.
- \[8\]P\. A\. M\. Mediano, F\. E\. Rosas, A\. I\. Luppi, R\. L\. Carhart\-Harris, D\. Bor, A\. K\. Seth, and A\. B\. Barrett\(2025\)Toward a unified taxonomy of information dynamics via integrated information decomposition\.Proceedings of the National Academy of Sciences122\(39\),pp\. e2423297122\.External Links:[Document](https://dx.doi.org/10.1073/pnas.2423297122)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4),[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.p1.3)\.
- \[9\]M\. Merleau\-Ponty\(2013\)Phenomenology of perception\.Routledge\.Note:Translated fromPhénoménologie de la perceptionCited by:[§1](https://arxiv.org/html/2607.20708#S1.p2.5)\.
- \[10\]H\. Pae\(2026\)Body\-grounded perspective formation and conative attunement in artificial agents\.External Links:2605\.16728,[Link](https://arxiv.org/abs/2605.16728)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p2.5),[§4](https://arxiv.org/html/2607.20708#S4.p3.3)\.
- \[11\]H\. Pae\(2026\-05\)Minimal computational preconditions for subjective perspective in artificial agents\.Proceedings of the AAAI Symposium Series8\(1\),pp\. 309–315\.External Links:[Document](https://dx.doi.org/10.1609/aaaiss.v8i1.42559)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p2.5),[§1](https://arxiv.org/html/2607.20708#S1.p4.11),[Figure 1](https://arxiv.org/html/2607.20708#S2.F1.11.1),[Figure 1](https://arxiv.org/html/2607.20708#S2.F1.12.1),[§2\.1](https://arxiv.org/html/2607.20708#S2.SS1.p1.1),[§2\.2](https://arxiv.org/html/2607.20708#S2.SS2.p2.15),[§2\.2](https://arxiv.org/html/2607.20708#S2.SS2.p2.16),[§3\.4](https://arxiv.org/html/2607.20708#S3.SS4.p1.7),[§4](https://arxiv.org/html/2607.20708#S4.p3.3)\.
- \[12\]H\. Pae\(2026\)Same world, differently given: history\-dependent perceptual reorganization in artificial agents\.External Links:2604\.04637,[Link](https://arxiv.org/abs/2604.04637)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p2.5),[§4](https://arxiv.org/html/2607.20708#S4.p3.3)\.
- \[13\]T\. Parr, G\. Pezzulo, and K\. J\. Friston\(2022\)Active inference: the free energy principle in mind, brain, and behavior\.MIT Press\.Cited by:[§4](https://arxiv.org/html/2607.20708#S4.p4.2)\.
- \[14\]G\. Pezzulo, T\. Parr, and K\. Friston\(2024\)Active inference as a theory of sentient behavior\.Biological Psychology186,pp\. 108741\.External Links:[Document](https://dx.doi.org/10.1016/j.biopsycho.2023.108741)Cited by:[§4](https://arxiv.org/html/2607.20708#S4.p4.2)\.
- \[15\]F\. Pigozzi and M\. Levin\(2026\)The causally emergent alignment hypothesis: causal emergence aligns with and predicts final reward in reinforcement learning agents\.External Links:2605\.06746,[Link](https://arxiv.org/abs/2605.06746)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4),[§1](https://arxiv.org/html/2607.20708#S1.p4.11),[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.SSS0.Px1.p1.5),[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.p1.3),[§3\.2](https://arxiv.org/html/2607.20708#S3.SS2.p2.11)\.
- \[16\]F\. E\. Rosas, P\. A\. M\. Mediano, H\. J\. Jensen, A\. K\. Seth, A\. B\. Barrett, R\. L\. Carhart\-Harris, and D\. Bor\(2020\-12\)Reconciling emergences: an information\-theoretic approach to identify causal emergence in multivariate data\.PLOS Computational Biology16\(12\),pp\. 1–22\.External Links:[Document](https://dx.doi.org/10.1371/journal.pcbi.1008289)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4),[§1](https://arxiv.org/html/2607.20708#S1.p3.4),[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.SSS0.Px1.p1.5),[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.p1.3)\.
- \[17\]G\. Tononi\(2008\)Consciousness as integrated information: a provisional manifesto\.The Biological Bulletin215\(3\),pp\. 216–242\.External Links:[Document](https://dx.doi.org/10.2307/25470707)Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p1.4)\.
- \[18\]P\. L\. Williams and R\. D\. Beer\(2010\)Nonnegative decomposition of multivariate information\.External Links:1004\.2515,[Link](https://arxiv.org/abs/1004.2515)Cited by:[§2\.4](https://arxiv.org/html/2607.20708#S2.SS4.SSS0.Px1.p1.5)\.
- \[19\]D\. Zahavi\(2005\)Subjectivity and selfhood: investigating the first\-person perspective\.Bradford Book/MIT Press\.Cited by:[§1](https://arxiv.org/html/2607.20708#S1.p2.5)\.