Inter-Level Causation Mechanism

• Inter-Level Causation Mechanism is a framework that decomposes supervenience into multiple functions, with changes in index sequences selecting governing equations.
• It employs structured neural networks and feedback error minimization to reconcile higher-level causal influences with underlying neural processes.
• The model integrates dual-process theory by distinguishing fast, automatic feedback control (Type 1) from slower, conscious reordering of equations (Type 2).

Inter-level causation mechanism is a formal account of how a higher-level state can exert causal influence on a lower-level neural base without violating supervenience. In the model developed by Ohmura and colleagues, the supervenience level is not treated as a single macro-state but as a space of multiple supervenient functions, interpreted as neural networks, whose algebraic combination defines equations and hence a feedback error. A higher-level cause is then identified with a change in the index sequence that selects which functions are combined into which equations; lower-level neural states are subsequently altered by feedback control so that the error defined by those equations is reduced to zero. The same framework is used to connect mental causation, agency, consciousness, and dual-process theory by distinguishing a fast error-reducing process from a slower process that changes the equations themselves (Ohmura et al., 12 Feb 2026). Related research treats top-down causation as constraint-setting, reversal of information flow, macro-to-micro transfer entropy, or macro-scale strengthening of causal relations, but the present mechanism is distinctive in assigning the higher-level causal role to equation selection over supervenient functions (Walker et al., 2012, Ashikaga et al., 2017, Comolatti et al., 2022).

1. Supervenience, downward causation, and the problem of higher-level causes

The mechanism begins from a standard supervenience thesis: mental or higher-level events do not change without some change in the lower-base physical events, and wholes likewise supervene on their parts. This creates an immediate difficulty for downward causation. If a whole cannot change independently of its parts, then “the state of the whole,” treated as a single coarse-grained variable, cannot itself serve as an independent cause. In the authors’ formulation, a cause must be something on which one can, in principle, intervene independently of the effect, via some causal transmission mechanism (Ohmura et al., 12 Feb 2026).

The key move is to reject the idea that the supervenience level is exhausted by one macro-state. Instead, the supervenience level is composed of multiple supervenience–lower-base relations and multiple supervenient functions. A supervenient cause is not a brute whole-state but a change in the index sequence specifying which supervenient functions are algebraically combined into which equations. Because an index sequence can change prior to, and independently of, the neural changes required to realize the new equations, it is treated as a higher-level cause. The neural adjustment that reduces the resulting error constitutes the causal transmission mechanism.

This produces a non-reductive account of inter-level causation. Supervenience is preserved because supervenient functions and their equations still depend on neural implementation. At the same time, lower-base physical dynamics alone are not sufficient for behavioral determination; one must also specify which supervenience-level equations are currently in force. A closely related philosophical theme appears in work on laws and causation at different levels, where coarse-grained macro-dynamics can “mesh” or fail to mesh with micro-dynamics, yet remain causally and explanatorily significant (Butterfield, 2014).

2. Formal architecture: base level, supervenient functions, and index sequences

The model distinguishes a base, or subvenient, level and a supervenience level. For each index $i \in I$, with $I \subset \mathbb{N}$, the base-level state spaces are

$SUB_i \subset \mathbb{R}^{n_i}.$

The supervenience level consists of supervenient functions, typically of the form

$$SUP[N] : \mathbb{R}^m \times \mathbb{R}^m \times \dots \times \mathbb{R}^m \to \mathbb{R}^m,$$

interpreted as neural networks. Distinct indices correspond one-to-one to distinct supervenient functions or families of functions (Ohmura et al., 12 Feb 2026).

The link between levels is given by a bridge function $B : SUB \to SUP[N]$. For each $i$, there is a bridge function $b_i \in B$ such that

$$X_i = b_i(x_i), \qquad X_i \in SUP[N_i],\; x_i \in SUB_i,\; i \in I.$$

Here $x_i$ is a concrete neural state and $X_i$ is the corresponding supervenient function or functional state. This formalizes supervenience, but the model’s novelty lies in treating the supervenience level as a space of functions that can be algebraically combined.

A supervenience-level state is represented by index sequences. A sequence is written

$I \subset \mathbb{N}$0

and a full supervenience-level state is an array of such sequences,

$I \subset \mathbb{N}$1

Changing this array is the supervenient cause. The index sequences are therefore not merely labels; they determine which higher-level equations exist at a given time. A useful comparison can be drawn with factored space models, which also treat higher-level variables as deterministic functions over more basic structures, but there the emphasis falls on structural independence across levels of abstraction rather than on equation selection and feedback control (Garrabrant et al., 2024).

3. Error functions and the causal transmission mechanism

The central transmission mechanism is inter-level feedback control. The model introduces an error-function space $I \subset \mathbb{N}$2 consisting of maps

$I \subset \mathbb{N}$3

There is a mapping

$I \subset \mathbb{N}$4

which sends an index sequence $I \subset \mathbb{N}$5 to an error function $I \subset \mathbb{N}$6. For an array of index sequences $I \subset \mathbb{N}$7, the corresponding array of error functions is

$I \subset \mathbb{N}$8

These error functions are generated by algebraic expressions over the supervenient functions. Choosing a different sequence $I \subset \mathbb{N}$9 changes which equations are in force (Ohmura et al., 12 Feb 2026).

The feedback error itself is written

$SUB_i \subset \mathbb{R}^{n_i}.$0

and inter-level feedback control aims to satisfy

$SUB_i \subset \mathbb{R}^{n_i}.$1

This formalizes the causal chain. A higher-level change in $SUB_i \subset \mathbb{R}^{n_i}.$2 alters the definition of the error, that is, the equation set or error landscape. A lower-level change in neurons, synapses, activations, and other neural states alters the current value of the error for the fixed equation set. Inter-level causation is realized when a supervenience-level change modifies the error structure and lower-level dynamics then move toward satisfaction of the new equations.

The resulting picture is asymmetric but bidirectionally constrained. The supervenience level shapes which constraints count; the lower-base level determines how, and how well, those constraints are realized. This differs from frameworks that define top-down causation directly by changes in macro-to-micro information flow, such as transfer-entropy analyses of biological or cardiac systems, because the present model locates the higher-level cause in a change of equation-defining indices rather than in a summary information-flow measure (Ashikaga et al., 2017). It also differs from phenomenological approaches in which higher-level actions are defined as selective changes in local mechanisms, although both share an emphasis on mechanism change rather than coarse description alone (Janzing et al., 2022).

4. Dual laws and the integration with dual-process theory

The theory introduces a dual-laws model with two distinct sets of dynamics. Dynamics 1 governs lower-base neural states, including activations and synaptic strengths, under the influence of feedback error, bodily input, and environmental input. Dynamics 2 governs the selection and modification of index sequences $SUB_i \subset \mathbb{R}^{n_i}.$3, thereby generating supervenient causes. The formal update at the higher level is

$SUB_i \subset \mathbb{R}^{n_i}.$4

The lower level then adjusts so that, for fixed $SUB_i \subset \mathbb{R}^{n_i}.$5,

$SUB_i \subset \mathbb{R}^{n_i}.$6

through negative feedback error reduction (Ohmura et al., 12 Feb 2026).

This dual architecture is identified with the two processes of dual-process theory. Type 1 is the continuous inter-level feedback control that adjusts neurons and synapses to reduce error for a fixed index sequence. It is described as fast, automatic or efficient, often unconscious, and capable of predictive control, though predictiveness is not taken as its defining feature. Type 2 is the discrete modification or selection of equations through changes in index sequences. It is discrete because it operates by selection or reordering of index sequences or sets of index sequences, symbolic because it operates over algebraically structured equations, slower and more effortful than Type 1, and typically consciousness-dependent in humans.

Both processes target the same feedback error, but Type 2 can redefine that error by changing the equations themselves. This supplies an internal interpretation of familiar conflict cases in dual-process theory. “Intuitive” and “logical” responses correspond to different equation sets: Type 1 may be reducing error relative to one set of embodied equations while Type 2 selects a conflicting set, such as linguistically codified logical norms. Type 2 is then required not merely to continue control but to restructure what counts as control.

The model also claims to explain why Type 1 must be relatively fast and why Type 2 must be discrete and symbolic. If Type 2 changed equations too quickly, no stable goal-directed behavior could emerge. The formalism itself does not require human Type 2 processing to be sequential; the sequentiality characteristic of human explicit reasoning is instead attributed to the linguistic system, especially inner speech and explicit symbolic reasoning. Compared with hierarchical dual-process accounts associated with Carruthers and Frankish, the present framework is said to provide a common feedback error minimized by both processes and a mathematical structure for inter-level causation (Ohmura et al., 12 Feb 2026). A plausible implication is that it occupies a different explanatory niche from multiscale causal-emergence frameworks that measure how causal power is distributed across scales rather than specifying a common error minimization mechanism (Jansma et al., 3 Oct 2025, Comolatti et al., 2022).

5. Consciousness, agency, and embodied belief networks

The dual-laws model is also presented as a theory of self-determining agency. Dynamics 2, the process that changes index sequences, is identified with the agentive “I.” Those changes count as supervenient causes because they precede and constrain lower-base dynamics through feedback control. The paper states that this satisfies Barandiaran et al.’s conditions for agency: individuality, because Dynamics 2 is agent-specific and not observer-relative; asymmetric causation, because supervenience-level interventions precede lower-base changes; and normativity, because lower-base control is explicitly goal-directed through feedback error minimization (Ohmura et al., 12 Feb 2026).

Consciousness is not simply identified with the supervenience level. Rather, Type 1 processes structure sensory information into forms available to consciousness, conscious content influences the operation of Dynamics 2, and Dynamics 2 changes index sequences, which then alter lower-base neural activity and behavior. The causal loop therefore runs from neural dynamics and supervenient equations to neural activity correlated with conscious experience, from conscious content to the “I,” and then from the “I” back to neural dynamics through changes in $SUB_i \subset \mathbb{R}^{n_i}.$7. Conscious states affect behavior indirectly by changing which equations are selected.

The same section of the theory interprets equations as beliefs. Equations define equivalence relations; if they induce bodily actions that make them true, they can be viewed as desires. A network of such equations forms an embodied belief network. Two types are distinguished. Classical embodied beliefs are derived from perceptual experience, pre-linguistic, bodily embedded, and present in non-human animals. Linguistic beliefs are embodied beliefs that encode and are influenced by language, are accessible to consciousness through inner speech and external symbolic expression, and provide the discrete meaningful structure associated with advanced Type 2 processing.

To represent competition among equations, the set of supervenient functions may be given a group structure, with a binary operation, identity, and inverses. The paper gives the example of moving right and moving left as inverse elements. Identity and inverse elements then permit mutually exclusive equations and counterfactual structure. Exclusivity alone would merely block selection of conflicting equations, so associative relations are added to allow parallel selection of mutually exclusive equations. The resulting unresolved feedback error is the setting in which Type 2 reasoning becomes necessary.

6. Neighboring formulations, scope, and unresolved issues

The inter-level causation mechanism belongs to a broader family of attempts to formalize macro-to-micro efficacy. In evolutionary and biological contexts, top-down causation has been described as a change in causal structure associated with a reversal in the dominant direction of information flow (Walker et al., 2012). In cardiac dynamics, inter-scale transfer entropy has been used as a surrogate for downward causation between macroscopic and microscopic descriptions, with downward flow found to be smaller than upward flow (Ashikaga et al., 2017). Causal-emergence research has argued that macro descriptions can strengthen causal relations by reducing indeterminism and degeneracy, and that this is widespread across many measures of causation (Comolatti et al., 2022). Factored space models were introduced to represent deterministic relationships at all levels of abstraction and to relate structural independence to statistical independence in hierarchies of abstraction (Garrabrant et al., 2024). These approaches are adjacent rather than equivalent: the present model is distinguished by defining higher-level causes as changes in index sequences and by locating the transmission mechanism in inter-level error feedback.

The framework is explicitly limited in several respects. It assumes a network of equations at the supervenience level, including associative and exclusive relations, but does not specify how that network is learned or formed via neural processes. It defines Dynamics 2 abstractly as changing index sequences, but leaves open the concrete algorithm by which equations are selected, modified, and stabilized. It is presented as a causal and mathematical framework rather than an implemented cognitive architecture, and the empirical separation of Type 1 and Type 2 is acknowledged to be difficult because real brain processes likely involve both simultaneously and share neural circuitry. The proposal that Type 2 requires consciousness is tied to current empirical trends concerning semantic integration and complex association, but is left open to further testing. The authors also note possible future use in neuro-symbolic AI, while emphasizing that concrete implementations remain future work (Ohmura et al., 12 Feb 2026).

Within that scope, the mechanism is intended to provide conditions under which inter-level causation is possible. Its defining claim is that a higher-level cause can be made coherent if the supervenience level is decomposed into multiple supervenient functions, if changes in their index sequences are treated as independently variable supervenient causes, and if lower-level neural dynamics serve as the feedback-controlled transmission mechanism that reduces the resulting error. This yields a unified formal skeleton in which consciousness, agency, and dual-process theory are treated as different aspects of one inter-level causal architecture.