Draft v0.2Prepared for the Journal of Controversial Ideas2026

脳機能を模倣した多階層制御言語モデルの自然選択的学習法及びこれを用いた統合意識の作成について

Natural-Selection Learning in a Brain-Mimetic Multi-Level Control Model, and the Construction of Integrated Consciousness

— Integration is not enough: dissociability (Δ) as the missing axis —

Keywords: integrated information · IIT · dissociability · criticality · neuromodulation · synthetic neuroscience

Abstract

Integrated Information Theory (IIT) proposes that the quantity Φ — the degree to which a system's cause–effect structure cannot be decomposed into independent parts — characterizes what it is like to be that system. I argue that Φ conflates two distinct properties: operational inseparability (the system cannot be run in pieces) and descriptive irreducibility (the system's state cannot be enumerated and reconstructed part by part). A brain cannot be operated in fragments, yet if every cell's state were observable, the whole could in principle be listed and restored; nothing in Φ distinguishes this from a system that is irreducible in the stronger sense. I propose a complementary axis, dissociability (Δ): not whether a system is decomposed, but how strongly it tends to fall apart when its integrative drive is withdrawn. High-Φ systems divide into two classes that Φ alone cannot separate: monoliths, whose parts co-vary because they are enslaved to a single global mode, and brains, whose parts constantly tend toward independence and whose integration is an active, metabolically expensive achievement. I support this distinction with measurements from a small survival-driven hierarchical network ("Thelymitra"): its leading global mode absorbs 84% of response variance and its effective dimensionality is 1.4 (of a possible 29), yet 13.8 dimensions of stimulus information survive beneath that mode — the signature of a monolith, not a mind. The same system shows that sparse activation, which raises Δ by construction, more than doubles causally attributable learning. Δ reframes "operate near criticality" as a measurable design target, predicts the fragmentation observed under anesthesia, and yields an engineering rule: integration should be bought, not assumed.

1 Two kinds of irreducibility

IIT (Tononi 2004; Oizumi, Albantakis & Tononi 2014) identifies consciousness with integrated information: a system has high Φ when no partition of it leaves the whole's cause–effect structure intact. The intuition is powerful — a brain is not a heap — and Φ formalizes "not a heap" as irreducibility to parts.

But irreducibility is ambiguous between two readings:

  1. Operational inseparability. You cannot cut a brain in half and run the halves. True, and captured by Φ.
  2. Descriptive irreducibility. You cannot, even in principle, enumerate the states of the parts and reconstruct the whole from the list. This is what "the whole is more than the sum" would require — and it is false for any physical system whose micro-states are observable. If every neuron's state could be read, the brain's state could be listed and restored. Integration does not make a system's description non-enumerable; it makes its operation non-separable.

Φ measures the first property while its interpretive weight rests on the second. This gap is not merely philosophical. Doerig et al. (2019) showed that for any recurrent network with high Φ there exists a feed-forward network with identical input–output behavior and Φ ≈ 0 (the "unfolding argument"): Φ places no constraint on function. The critique below arrives at the same fault line from a different direction — and, unlike the unfolding argument, motivates a replacement measurement rather than only a rejection.

2 Dissociability

Define dissociability (Δ) informally as: the tendency of a system's parts to become independent when the drive that binds them is withdrawn.

Δ is not the inverse of Φ. Φ asks whether the system's information is decomposable now; Δ asks what the system would do if left alone. The two are orthogonal, giving a 2×2 taxonomy (Figure 1). Φ alone cannot distinguish the monolith from the brain: both are "highly integrated." Yet they are opposite as designs. A monolith's parts co-vary because they cannot do otherwise; nothing is achieved by their unity, and nothing can specialize. A brain's parts co-vary despite a standing tendency to dissociate, and the maintenance of unity is precisely the work the system does.

Integration Φ → Dissociability Δ → low high Sand / noise parts never cohere Heap independent parts Brain integration actively maintained, at cost Monolith parts enslaved to one global mode Thelymitra (measured, §3) raise Δ: sparsify, localize learning
Figure 1. Integration (Φ) and dissociability (Δ) are orthogonal. Φ alone cannot separate the two right-hand cells: a monolith and a brain are both "highly integrated," but for opposite reasons. The system measured in §3 sits in the monolith cell; the dashed arrow marks the interventions that move it upward.

The empirical signature of the difference is what happens when the binding is released: under deep anesthesia and slow-wave sleep, cortex fragments into local modules and long-range responses collapse — measured directly by the perturbational complexity index (Casali et al. 2013), which drops when a TMS pulse no longer propagates and re-integrates. Integration in brains is an achievement, paid for continuously (≈20% of resting metabolism for ≈2% of body mass), not a standing property.

2.1 Candidate operationalizations

Two normalizations are mandatory. First, Δ must be normalized by noise strength, or it degenerates into a thermometer. Second, Δ must be verified to be independent of whether the system happens to be integrated at measurement time — Δ is a disposition, not a state — otherwise it collapses back into ¬Φ.

3 A monolith, measured

The distinction is not hypothetical; I exhibit a system sitting squarely in the monolith cell, discovered by accident while debugging why it could not learn.

System. "Thelymitra" is a survival-driven network of 3,125 rate units arranged in a 5-level tree (branching factor 5). Only leaf units compute; interior nodes are passive relays that sum child messages upward and return the complement downward (a "post-office" hierarchy), with amplitude decaying as αL across L tree levels and a small number of long-range shortcut fibers (Figure 2). Learning is a three-factor Hebbian rule: node-perturbation noise, per-synapse eligibility traces, and a single diffuse scalar neuromodulator carrying homeostatic stress — no backpropagation anywhere. The system is evaluated by survival in a 2-D foraging environment (29 sensory channels) and by classical conditioning with mid-life reversal.

relay long-range fiber (few, decisive: §3, Finding 4 context) sensory motor 3,125 leaf units amplitude ×α per level one scalar neuromodulator, broadcast to every learning synapse
Figure 2. Thelymitra, schematic (depth compressed to three levels for display; the real system has five). Leaves compute; interior nodes are passive "post-office" relays. A handful of long-range fibers bypass the hierarchy. The third learning factor is a single scalar broadcast to all synapses — the eventual bottleneck (§3, Finding 3; §5).

Finding 1: one mode owns the system. Probing each of the 29 sensory channels and recording the population response of the motor region yields a response matrix whose effective dimensionality (participation ratio of squared singular values) is 1.4 — out of a possible 29 — at every stage: sensory region 1.40, whole network 1.41, motor region 1.41. The leading mode absorbs 84% of variance and carries no channel identity: whatever you show it, the whole network heaves in the same direction. Yet the information is not destroyed: removing the common mode raises the effective dimensionality to 13.8 at the sensory region and 13.7 at the motor region (Figure 3). Thirteen dimensions of stimulus identity ride, intact but enslaved, beneath one global heave. By any Φ-flavored intuition this system is beautifully integrated. It is in fact a monolith: low Δ, with unity achieved trivially rather than maintained meaningfully. Notably, the passive relay hierarchy itself was exonerated — it transmits all ~14 dimensions without loss; the collapse is a property of the collective dynamics, not the anatomy.

variance of responses 84% one global mode, no channel identity 16% (all 29 probes) effective dimensionality 29 channels (ceiling) 0 29 1.40 13.8 sensory 1.41 13.7 motor raw common mode removed
Figure 3. The monolith signature. Left: one global mode absorbs 84% of the variance of channel-probe responses and carries no channel identity. Right: effective dimensionality (participation ratio) of the response matrix is ~1.4 of a possible 29 at both sensory and motor regions; removing the common mode reveals ~14 intact dimensions beneath it. Mean of 3 seeds; seed-to-seed spread ±0.03.

Finding 2: the monolith cannot acquire conditional behavior. In the survival environment, learning produced only unconditional bias shifts (mean radius, danger exposure) and never state-conditional policy ("when damaged, retreat"), across four added mechanisms (orienting wiring, interoceptive shortcuts, gain modulation, compartmentalized neuromodulation) — each verified to operate correctly, none changing the outcome. A system with ~1.4 usable dimensions can only learn "more of this direction"; there is no room for "this, when that."

Finding 3: apparent learning decomposed into erasure plus reversal. Using reversal conditioning with a causality-broken control (the neuromodulator replaced by its own value from 37 steps earlier — distribution and magnitude preserved, causal link cut), total "reversal" splits into two components: erasure of prior learning, which occurs equally with and without the causal link, and true opponent re-learning, which requires it (Figure 4). In the survival environment the causal component was zero in 4 of 4 comparisons: everything that had looked like learning was erasure — random weight drift washing out initialization bias. Measures that reward outcome improvement are systematically fooled by erasure; only causally attributed learning counts.

0 −0.24 +0.18 avoidance differential (A − B) full three-factor rule crosses zero: true re-learning causality broken stops near zero: erasure only weights frozen no change before reversal after reversal (arrowhead)
Figure 4. Decomposing "reversal learning." Each arrow runs from the pre-reversal avoidance differential to the post-reversal value (means of 3 matched seeds). The causality-broken control erases prior learning as effectively as the full rule but barely crosses zero (swing ratio 1.42 vs 2.30); frozen weights change nothing. Erasure needs weight motion but no causal signal; opponent re-learning needs both.

Finding 4: raising Δ raises causal learning. Enforcing sparse activation (top-5% of units active per step) — which increases Δ by construction, since fewer units co-fluctuate — raised the causally attributable reversal from +0.400 to +1.004 in the same task, the largest single improvement of any intervention tested. Likewise, scaling from 625 to 3,125 units left total reversal nearly unchanged (+0.42 → +0.53, the kind of null that "size doesn't matter" conclusions are made of) while the causal component grew five-fold (+0.049 → +0.242) — visible only after subtracting erasure (Figure 5).

sparsification (raise Δ) +0.400 +1.004 dense top-5% reversal, three-factor rule scale 625 → 3,125 units 0.42 0.53 total reversal 0.049 0.242 causal component ×5 erasure hides the scale effect until subtracted 625 | 3,125 625 | 3,125
Figure 5. Interventions that raise Δ raise causally attributable learning. Left: restricting activity to the top-5% of units more than doubles reversal under the full rule (matched task and seeds). Right: quintupling network size barely moves total reversal — but the causal component (matched-seed difference from the causality-broken control) grows five-fold. Outcome metrics dominated by erasure mask both effects.

These are measurements on one small synthetic system, and I claim no more than existence: at least one highly-"integrated" system is a monolith, its pathology is invisible to integration measures, and it is legible — and improvable — in terms of Δ.

4 Relation to existing measures

Δ has respectable relatives, none of which occupies its position. Newman's modularity Q is structural and static; Δ is dynamical and dispositional. Markov-stability and spectral-gap analyses characterize diffusion timescales on a fixed graph but include no notion of withdrawing an integrative drive. Metastability and chimera indices (Kelso; Shanahan) capture the coexistence of integration and segregation but are confined to phase-oscillator descriptions. The perturbational complexity index (Casali et al. 2013) is, in effect, perturbational Δ executed in the clinic — its empirical success (tracking anesthesia, sleep, and disorders of consciousness where Φ is incomputable) is indirect evidence that the dissociative axis is the operative one. Closest of all is Integrated Information Decomposition (Mediano, Rosas et al. 2021), which splits Φ into redundancy, unique information, and synergy; the 84% common mode above is pure redundancy in ΦID terms. Δ can be read as the dynamical, dispositional face of that decomposition: redundancy-dominated systems are low-Δ monoliths; synergy requires parts that could be otherwise. The claim of novelty is therefore limited and precise: treating the tendency to dissociate — not the failure to decompose — as the primary axis, measurable by drive-withdrawal, and normative for design.

5 Predictions and consequences

  1. Optimal Δ is intermediate, and is the criticality condition. Too high is sand, too low is a monolith; the balance point of binding and dissociation is a critical point. The neural-avalanche literature (Beggs & Plenz 2003) then falls out as systems tuned to optimal Δ, and "operate near criticality" becomes a measurable target instead of a slogan.
  2. Anesthetics reduce measured Φ via unmasking of native Δ, predicting that agents with similar Φ-reduction but different mechanisms should differ in fragmentation dynamics (rate, module boundaries) in ways PCI-style protocols can resolve.
  3. Learning capacity scales with Δ at fixed Φ. In any redundancy-dominated network, interventions that raise Δ (sparsification, inhibition, decorrelation) should increase causally attributable learning even when they leave task-outcome metrics unchanged — as observed above.
  4. Engineering rule: buy integration, don't assume it. An artificial brain should be built from parts that natively dissociate (heterogeneous time-constants, sparse activity, local learning signals), with integration added as an explicit, costed mechanism — the opposite of the default in most neural architectures, whose dense shared dynamics start monolithic.

6 Limitations

Δ inherits a granularity problem: it is defined relative to a partition into modules. IIT escapes partition-choice by minimizing over all partitions and pays with incomputability; Δ accepts a designated partition (anatomical or developmental) and pays with partition-relativity. In systems with a natural hierarchy this is cheap; in general it is a genuine weakness. Second, the empirical section rests on one synthetic system of 3,125 units; the monolith diagnosis there is solid, but the generalization to biological cortex is conjecture constrained by the anesthesia/PCI literature rather than established by it. Third, the four operationalizations of §2.1 have not been shown to agree; their concordance on model systems is the obvious next measurement.

7 Conclusion

"The whole is more than the sum of its parts" has been asked to do two jobs: to say that a system cannot be run in pieces, and to say that it cannot be understood in pieces. Φ formalizes the first and borrows the authority of the second. Once the two are separated, a complementary quantity becomes visible: the standing tendency of the parts to go their own way, against which integration must be earned. On this view a brain is not a maximally integrated object. It is a barely contained disintegration — and the containing is the point.

References

Beggs, J. M., & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. Journal of Neuroscience, 23(35).

Bellec, G., et al. (2020). A solution to the learning dilemma for recurrent networks of spiking neurons. Nature Communications, 11, 3625.

Casali, A. G., et al. (2013). A theoretically based index of consciousness independent of sensory processing and behavior. Science Translational Medicine, 5(198).

Doerig, A., Schurger, A., Hess, K., & Herzog, M. H. (2019). The unfolding argument: Why IIT and other causal structure theories cannot explain consciousness. Consciousness and Cognition, 72.

Kelso, J. A. S. (2012). Multistability and metastability: understanding dynamic coordination in the brain. Philosophical Transactions of the Royal Society B, 367.

Mediano, P. A. M., Rosas, F. E., et al. (2021). Towards an extended taxonomy of information dynamics via Integrated Information Decomposition. arXiv:2109.13186.

Newman, M. E. J. (2006). Modularity and community structure in networks. PNAS, 103(23).

Oizumi, M., Albantakis, L., & Tononi, G. (2014). From the phenomenology to the mechanisms of consciousness: IIT 3.0. PLoS Computational Biology, 10(5).

Shanahan, M. (2010). Metastable chimera states in community-structured oscillator networks. Chaos, 20(1).

Tononi, G. (2004). An information integration theory of consciousness. BMC Neuroscience, 5(42).

Methods details, code, and raw measurements for the Thelymitra system are available from the author. All reported effect sizes are from ≥2 random seeds with matched-seed controls; the causality-broken control preserves the neuromodulator's distribution while breaking only its temporal causality. Figures use the Okabe–Ito colorblind-safe palette: blue = Φ-side quantities (raw / integrated), vermilion = Δ-side quantities (dissociated / causal).