Abstract
Predictive processing casts perception, action, and learning as probabilistic inference. This paper asks when a Bayesian description identifies a mechanism. I distinguish computational description, algorithm, and physical implementation. Mechanism requires a causal mapping from physical transitions to inferential roles; behavioural fit cannot establish it. Priors range over model-supplied alternatives; observation does not reveal the organism’s individuation. Bayesian algorithms may be high-dimensional, continuous, nonparametric, and representation-growing. Every specified model has a fixed reachable closure; neither closure nor size decides mechanism. The question is which differences a proposed controller state treats as irrelevant. If histories assigned to that state respond differently to intervention because of timing, phase, contact, or field structure, the mapping omits part of the mechanism. A prospectively richer Bayesian or hybrid account may include those differences. High-dimensional systems and flexible model families often resist binary falsification when an experiment’s projection loses distinctions required by the claim. I therefore propose convergent tests of specified internal, coupled, and hybrid mappings. Results reject only a mapping within a declared task, scale, horizon, and margin; post-hoc revision creates a new hypothesis. The resource-bounded coupling hypothesis predicts that human-level transfer on contact-rich tasks depends on distinctions retained in organism–environment relations. An adaptive internal controller counts against it when transfer has no preregistered resource disadvantage, relational-history effects vanish in state-collision tests, the relational block adds no meaningful intervention-predictive value, and internal-realiser interventions have distinctive predicted effects. Existing evidence has not established a Bayesian mechanism for unconstrained embodied behaviour.
1 Introduction
Tie a drawstring while jogging. The hands find the cord ends by touch, work them into loops felt rather than seen, and pull with forces set by the fabric’s compliance, all while the trunk stabilises against each stride and the reference frame shifts underfoot. Predictive processing says this is inference. Few advocates would claim that the brain computes a posterior over knot topology in real time; the generative model they posit is implicit, distributed, and hierarchical. But the moving cord and fabric do not reveal whether the organism tracks keypoints, material modes, contact states, or something else. A theorist can build any of these into a probabilistic model, including a measure over a function space. A good fit does not show that the organism divides the situation in the same way. Bayesian models are not too small to describe a continuum, and a coupling account faces the same demand to identify its causal variables. Without a specification of structure, physical vehicles, and transformations, “the brain does inference” names the task and not yet the process that performs it (Clark, 2013; Hohwy, 2013; Friston, 2010).
Predictive processing connects perception, action, attention, learning, interoception, and psychiatric explanation to Bayesian statistics, control theory, and machine learning (Clark, 2013; Seth & Friston, 2016). Its usefulness does not establish that Bayesian inference is the neural mechanism. Describing a planet’s orbit as the stationary point of an action does not make the planet a computer of integrals; an exact description can leave the mechanism unidentified. A model is specified and tested by an observer, and the tissue implements it only if its causal organisation supports the relevant computational states and transitions. The same holds for cloth, air, and soft tissue: a workable probabilistic model of a system is not yet an inferential mechanism within it.
This paper makes two claims. The first concerns realisation. Every candidate controller state groups physical histories as equivalent for the transition being explained, within a declared tolerance and horizon. If relative phase, ordering, delay, field structure, or ongoing contact varies among histories assigned to the same state and changes their response to intervention, that state is too coarse. A realiser that preserves and uses those differences instantiates a richer state. This criterion applies whether the candidate state is high-dimensional, continuous, distributed, or representation-growing. Bayesian models may have very large or unbounded support and may enlarge their active representations online. Like every specified computational or dynamical model, they also have a fixed reachable closure under their allowable dynamics. Neither capacity nor formal fact identifies the physical organisation that performs the task. A biological subsystem implements a Bayesian algorithm only when its causal organisation realises the required states and transitions. Section 2.4 states this criterion.
The second claim is comparative and empirical. A regulator needs response variety sufficient for the disturbances it must absorb, given the outcomes it may tolerate (Ashby, 1956). Conant and Ashby proved, for optimal regulators in a deterministic setting, that such a regulator must be a model of the system it regulates (Conant & Ashby, 1970). Their theorem constrains the organisation a successful controller must embody, but does not say where that organisation is realised. It may reside in probabilistic states, in brain–body–environment relations, across both, or in another internal control architecture. Against that background I propose the resource-bounded coupling hypothesis: for preregistered contact-rich benchmark classes and declared budgets, human-level transfer depends on future-relevant distinctions retained in ongoing physical dynamics. The hypothesis predicts that preregistered organism–environment relational variables will make an independent contribution to predicting intervention outcomes beyond any tested internal controller state. It adds an economy claim to the structural criterion; dimensionality alone does not support it.
Both claims lead to prospective, framework-relative comparisons. A high-dimensional system is observed through selected measurements and variables, so no single result identifies or eliminates an entire mechanism family. The realisation tests instead ask whether nominated phase, residual structure, and adaptive operations remain causally active within a specified controller mapping. The resource comparison asks whether a declared state–input–update mapping supports human-level transfer without a preregistered resource disadvantage relative to a validated relation-dependent arm. Preregistration, not anatomy, fixes the tested boundary: body states count as internal unless they enter the relational block under test. Block equivalence is one screen: the nominated relations add no meaningful held-out intervention-predictive value beyond the declared controller states, sensory inputs, and updates under the upper-bound interval rule specified in Sect. 9. Task sufficiency additionally requires the transfer criterion, conditional state-collision evidence, and a mapping-specific intervention on the proposed internal realiser.
An adaptive Bayesian controller can count against the local coupling prediction; a non-Bayesian internal controller can do so without supporting a Bayesian mechanism. A hybrid is another possible outcome. Evidence comes from the joint pattern of transfer, intervention, residual structure, and adaptive operations rather than a task-breaking severance test. Section 9 requires the variables, mappings, margins, and horizons to be fixed prospectively. Any conclusion remains local to the nominated block, task, horizon, margin, and measurement framework.
The difficult cases are those in which action changes the active constraints. A fold creates a boundary condition; a pinch activates a constraint; a slip releases stored tension. An ambient configuration space can include every such possibility without explaining how the organism controls it. A representation-growing Bayesian algorithm may recruit variables adequate for prospective control online. A coupled system may retain and transform future-relevant distinctions without reconstructing them as inferential controller states. Constrained laboratory tasks often leave these mechanisms observationally equivalent because the experimenter has already selected a small set of task variables. Naturalistic tasks allow prospective, resource-matched comparisons.
Motor control makes this evidential burden especially visible. Motor theories often treat the body as a mechanism with surplus degrees of freedom, so that the same outcome can be reached through many configurations of muscle, joint, and posture (Bernstein, 1967). That inventory is a modelling choice about soft, history-dependent tissue under contact, not a complete description of it. Even within that model, real-time coordination under contact demands more than description. Bayesian sensorimotor learning, optimal feedback control, and active inference all treat action as a domain where uncertainty, prediction, and control interact (Körding & Wolpert, 2004; Todorov & Jordan, 2002; Friston et al., 2017). A mechanism-level theory of embodied behaviour should explain how the relevant variables are recruited and controlled under contact and feedback.
The argument first separates the levels of Bayesian claim and states the realisation criterion. It then treats adaptive Bayesian algorithms as genuine mechanism candidates and weighs what current evidence establishes at each level. The cloth case illustrates why predictive fit leaves physical realisation underdetermined. Later sections apply the criterion to changing constraints and coupling, show why constrained laboratory designs leave competing mechanisms observationally equivalent, and derive resource-matched intervention tests.
2 Three Levels of Bayesian Claim
Marr (1982) separated the problem a system solves, the algorithm and representations it uses, and the physical implementation of that algorithm. Debates about the Bayesian brain move between these levels quickly, which is productive early in theory-building and costly when empirical claims are weighed. Three versions need to be kept apart.
2.1 Version 1: Computational-Level Description
The weakest version says organisms solve problems whose optimal solutions can be described in Bayesian terms. Perception is treated as unconscious inference (von Helmholtz, 1867); behaviour is compared with a rational observer; learning is described as belief updating under uncertainty (Knill & Pouget, 2004; Tenenbaum et al., 2011). This version is often valuable. Rational analysis reveals what information a task makes available, what an optimal observer would do with it, and where behaviour departs from that benchmark. It is also weakly constraining about mechanism: the same input–output function can be produced by explicit probabilistic inference, a learned heuristic, a control law, a recurrent network, or a tuned dynamical system. Rational analysis has nonetheless yielded real insight, often precisely because it explains behaviour through the structure of the task environment without recourse to mechanism. Its success leaves the algorithm unidentified.
2.2 Version 2: Algorithmic Approximate Inference
The second version says neural systems run a recognisable approximation to Bayesian inference: they maintain a generative model, estimate hidden causes, represent uncertainty, and update internal states under posterior constraint. Predictive coding is the most influential proposal—descending predictions meet ascending prediction errors, and precision weights set which errors count (Rao & Ballard, 1999; Friston, 2005; Lee & Mumford, 2003; Bastos et al., 2012). This claim carries obligations. An algorithmic account therefore specifies its representations and update scheme, the signatures that distinguish them from generic error reduction, and what would count against the mapping. Identifying the neural variables that realise those roles is the further obligation of Version 3. “Functionally equivalent to Bayesian inference” cannot be allowed to absorb every adaptive process; a thermostat, a spinal reflex, and a trained network all reduce error in some sense. They become Bayesian algorithms only if the probabilistic mapping imposes distinctive causal constraints.
2.3 Version 3: Implementational Predictive-Processing Circuitry
The implementational version assigns Bayesian roles to neural populations and circuit motifs: superficial pyramidal cells carry prediction errors, deep pyramidal cells carry predictions, precision is gain modulation, and a canonical microcircuit implements message passing (Bastos et al., 2012; Keller & Mrsic-Flogel, 2018). It is directly exposed to neuroscience and carries the highest evidential burden. Behavioural optimality or a fit to average responses does not meet that burden. Mechanism-level evidence requires the proposed neural quantities to have the right causal profile. A prediction-error signal must update the relevant state in the predicted way, a precision signal must reweight errors with uncertainty, and a generative model must constrain what the system can predict and how it fails.
2.4 The Realisation Criterion
Versions 2 and 3 attribute Bayesian organisation to the brain itself. They require algorithm-specific quantities to be causal parts of the process. An abstract computational state is an equivalence class over physical histories. A physical system realises that state only where variations grouped together leave the required abstract transition invariant within tolerance (Piccinini, 2015). If a proposed realiser instead preserves and uses those variations, the mechanistic mapping must include them in a richer state. Digital machines secure such equivalence classes through thresholds, clocking, registers, and reset conditions. A biological implementation may secure them differently, including through continuous or distributed dynamics. Support for the claim depends on tissue realising the probabilistic roles assigned to it; establishing that mapping requires evidence beyond behavioural fit.
3 Physical Realisation Across Bayesian Algorithms
A Bayesian mechanism claim must identify a particular algorithm and the physical organisation that realises it. Bayesian computation is not exhausted by one predictive-coding scheme, and no Bayesian algorithm requires a literal posterior register that the system consults. The Kalman filter is a Bayesian estimator for linear–Gaussian state-space models (Kalman, 1960; Roweis & Ghahramani, 1999). Particle filters represent a posterior with weighted samples; Markov chain Monte Carlo approximates expectations by stochastic exploration; variational methods optimise within a tractable family (Blei et al., 2017); and active inference minimises variational free energy under a generative model (Friston et al., 2017). Each proposal therefore has different candidate realisers: particles and resampling operations, samples, sufficient statistics, variational parameters, message-passing dynamics, population activity, synaptic weight distributions, or other causally specified vehicles.
Some Bayesian algorithms change the size and organisation of their active representation. Bayesian nonparametrics places priors over function spaces, unbounded component sets, or unbounded latent-feature arrays (Rasmussen & Williams, 2006; Orbanz & Teh, 2011; Teh et al., 2006; Griffiths & Ghahramani, 2011). Sequential variants instantiate new regimes and transition structures when the data warrant them (Fox et al., 2011a, b; Adams & MacKay, 2007). These algorithms can expand an active data structure while their learning rules and probabilistic semantics remain specified.
Bayesian neural networks make a different point. Fixed-architecture networks can learn task-dependent distributed features under uncertainty over weights (Blundell et al., 2015), while Bayesian evidence can guide comparison or pruning among candidate architectures (MacKay, 1992). Online component birth and in-network feature learning both show why a Bayesian algorithm need not use a static, pre-enumerated representation. Architecture comparison is ordinarily an outer-loop procedure; it counts as in-task adaptation only when the tested controller implements it prospectively.
This plurality determines what evidence can count against a Bayesian mechanism claim. The absence of an identifiable prediction-error unit does not refute sampling, population-code, or filtering accounts (Ma et al., 2006). Approximation is how Bayesian methods scale. Recognising a particular algorithm as Bayesian can explain its optimality conditions, constrain how uncertainty should propagate, and motivate new variants. The Kalman filter is a clear example. Evidence must therefore be assessed against the algorithm proposed and its distinctive causal organisation, not against predictive-coding vocabulary in general.
Formal closure supplies no useful dividing line between these candidates and dynamical descriptions. For a model with initial states \(S_0\) and allowable dynamics T, the reachable space \(S^*=\bigcup _{t\ge 0}T^t(S_0)\) is fixed once the model is specified. The same construction applies to a Bayesian algorithm, a recurrent network, and a coupled dynamical model. An algorithm may nevertheless create components, features, relations, or data structures as it runs. The causal-grain question asks whether its active state preserves the distinctions prospective control requires; formal closure does not answer that question. A Bayesian mechanism requires physical state-transition organisation corresponding to its particular inferential approximation and any claimed representation-growth operation.
4 What Current Predictive-Processing Evidence Establishes
Predictive processing has substantive empirical support. In multisensory cue combination, observers integrate visual, haptic, and auditory signals close to the reliability-weighted optimum a Bayesian observer would compute (Battaglia et al., 2003; Ernst & Banks, 2002). Sensorimotor adaptation tracks uncertainty as Bayesian accounts predict (Körding & Wolpert, 2004). The mismatch negativity and related expectation-suppression effects behave as prediction-error responses under models of expected regularities (Näätänen et al., 2007; Winkler et al., 2009). Attention can be modelled as precision modulation (Feldman & Friston, 2010; Summerfield & de Lange, 2014).
Hierarchical predictive coding connects these results through descending predictions, ascending errors, and precision-weighted updating (Bastos et al., 2012; Friston, 2005; Rao & Ballard, 1999). It also proposes mappings to cortical anatomy. Active inference extends the calculus to action (Friston et al., 2017). The phenomena are real and Bayesian models capture them well. Their evidential force depends on the level of claim.
Cue combination shows the gap between computational and algorithmic evidence. Near-optimal reliability weighting (Battaglia et al., 2003; Ernst & Banks, 2002) can also be produced by a learned rule that weights each cue using stored reliability without representing a posterior (Jones & Love, 2011). In standard two-cue designs the two accounts are not merely hard to tell apart; they are underdetermined by the design.
Auditory mismatch responses admit the same underdetermination. A deflection interpreted as prediction error is also predicted by stimulus-specific adaptation: frequency-tuned populations adapt to a repeated standard and respond more strongly to a rare deviant (Ulanovsky et al., 2003). Equiprobable many-standards controls (Jacobsen & Schröger, 2001) test whether the oddball effect exceeds simple adaptation, and cascade controls (Ruhnau et al., 2012) reduce sequence-context confounds. The remaining response is still interpreted differently by adaptation and deviance-detection models (May & Tiitinen, 2010; Näätänen et al., 2007).
In sensorimotor adaptation, error-driven learning with a fitted learning rate can reproduce trial-by-trial corrections attributed to uncertainty-weighted Bayesian updating. A Bayesian mechanism predicts that the learning rate should follow a Kalman gain as uncertainty is manipulated; many designs outside reliability-manipulation paradigms do not make that comparison (Shadmehr et al., 2010). These results establish uncertainty-sensitive behaviour and support Bayesian models in constrained settings. They provide less evidence that the brain’s own organisation realises the proposed probabilistic variables. A constrained design fixes the variables it will score, and rival mechanisms that agree on those variables cannot be separated by fit to them however much data is gathered. Discriminating evidence has to come from somewhere the design has not already decided: from intervention on independently specified physical variables, and from regimes the chosen scoring was not built around.
Motor-cortex trajectories have likewise been analysed fruitfully in dynamical and neural-manifold terms (Churchland et al., 2012; Gallego et al., 2017; Shenoy et al., 2013). Those analyses establish structured population dynamics, but do not test whether the same activity also realises prediction-error or posterior variables. They strengthen the case for direct causal comparison without deciding between the mappings.
5 From Description to Realisation
5.1 Redescription and Mechanism
Brains are evolved control systems with sensors and goals, so Bayesian descriptions of their behaviour are scientifically plausible. But a plausible description can be overlaid on a system without being realised by it. To identify a mechanism one must independently specify a causal mapping from physical organisation to inferential states and transformations.
This is more than a limit on what an observer can know. Incompatible ways of dividing the process into states can fit the same behaviour equally well, so additional fit on that same behavioural projection cannot select among them. They differ in which physical organisation carries the distinctions needed for the next action. That is a fact about the system, not about the observer’s confidence.
5.2 What it Takes to Implement a Computation
The implementation question is familiar in philosophy of computation. If any mapping from physical states to formal states were sufficient, every complex physical system would implement every automaton and implementation would explain nothing (Putnam, 1988; Searle, 1992). Nontrivial accounts require the physical causal structure to mirror the computation. The proposed realisers must be individuated by causal roles, support the relevant counterfactuals, and undergo transitions produced by the system rather than assigned after observing it (Chalmers, 1996; Piccinini, 2015).
These requirements are medium-independent. Continuous, distributed, and analog systems can satisfy them; Piccinini’s mechanistic account allows neural computation. The question is whether the brain’s physical organisation realises the quantities and operations of a particular Bayesian algorithm.
Digital machines protect their states with thresholds, clocking, and engineered tolerance, which is why binary logic can remain the same across silicon, relays, or fluidic devices. Clocking matters because it makes timing variation within the admissible window irrelevant to the registered transition: those temporal differences occupy one computational equivalence class. A continuous or oscillatory Bayesian mechanism is not excluded by this contrast. It must show either that phase and timing are among its realised inferential variables or that varying them within a proposed computational state leaves the algorithm’s counterfactual transitions invariant within tolerance. That cannot be assumed in tissue. Oscillatory phase changes which signals are available when (Buzsáki, 2006); weak extracellular fields can alter spike timing and network activity (Anastassiou et al., 2011; Fröhlich & McCormick, 2010); dendritic nonlinearities and neuromodulatory state alter circuit transformations (London & Häusser, 2005; Marder, 2012; Sacramento et al., 2018; Stuart & Spruston, 2015). Where those variations change what transition occurs or when, an abstraction that groups them together describes part of the mechanism rather than its complete causal state.
Dynamical approaches treat continuous organism–environment relations as causally organised parts of cognition (Beer, 2000; Chemero, 2009; van Gelder, 1995). A coupling mapping and a Bayesian mapping carry the same evidential burden. The Bayesian mapping must identify physical realisers of its inferential quantities and operations; the coupling mapping must identify the relations that carry anticipation and produce their predicted intervention signature. The field manipulations cited in the previous paragraph establish that phase and field variables can be causally relevant, but they are compatible with either a relational mechanism or a Bayesian implementation. For unconstrained embodied behaviour, the Bayesian mapping has not been established. Causal relevance alone does not establish the coupling mapping either. Section 7 develops that alternative, and Sect. 9 tests both mappings.
A predictive-processing account reaches mechanism level when its algorithm-specific variables and operations are specified independently of the data they explain, causally individuated, and manipulable through physical realisers.
6 Active Constraints in Embodied Tasks
6.1 Changing Active Constraints and Causal Grain
Cloth manipulation makes changing active constraints concrete. Gravity, friction, tension, folding, and self-contact alter the active contact graph and constraint manifold during control. These changes determine which actions are available next. The controller must become sensitive to the distinctions that matter at the speed required for action. It may recruit a probabilistic state adequate for prospective control under a specified growth rule. It may also exploit distinctions retained in the coupled cloth–hand–body dynamics without reconstructing them as prior, likelihood, and posterior. Current robotic methods make progress by choosing keypoints, latent material properties, graph structures, simulations, or task-specific constraints, but generalisation across real-world textiles and task variations remains difficult (Gu et al., 2023; Li et al., 2016; Longhini et al., 2025).
These changes occur within the physical system’s ambient closure. A continuum model of cloth may likewise use an ambient configuration space containing every admissible crease and a union over contact topologies. Formal closure therefore applies equally to Bayesian algorithms and dynamical descriptions: once a model is specified, its allowable dynamics fix its reachable closure. The mechanistic question is which constraints and relations become active within that closure and which physical distinctions the controller preserves.
Answering that question requires separating several objects. The scientific state variables describe the brain–body–environment system at a scale selected by the theorist. A candidate algorithm’s active representation consists of the features, latent variables, relations, or data structures it currently uses. The task variables are selected by the experimenter, and recorded neural variables form a further measurement layer. An adaptive Bayesian algorithm may enlarge its active representation while all of these remain inside a fixed formal closure. An ambient variable in the scientist’s model is not thereby a variable represented by the organism.
The cloth–air–hand continuum is not itself a Bayesian prior. A prior is a probability measure over alternatives defined within a specified measurable space. A hanging shirt, like a vortex in a science-centre tornado maker, is a single unstable, history-dependent trajectory. One can place a prior over such a system, and Bayesian nonparametrics does so routinely. Doing so overlays a probabilistic description on the process rather than locating one within it. The alternatives it ranges over come from the modeller’s choice of state space. That choice is not unique, and behavioural fit to the trajectory does not show which, if any, is realised by the controller.
Surface geometry can be imaged with little disturbance. Interior stress, contact force, and local flow are accessed through a measurement model at a chosen spatial and temporal scale, and instrumentation may alter the loading. Different admissible probe sets therefore individuate different hypothesis spaces, and several will fit the same handling behaviour. Describing the unmeasured process as an implicit generative model inherits one such individuation without showing that the organism’s causal organisation realises it. Relational descriptions are subject to the same limit, which is why both mappings are referred to the intervention tests of Sect. 9 rather than settled by description. The relational variables preregistered there are interface quantities—grasp force, contact tension, limb and cloth kinematics—that the task already loads. Their standing is decided by intervention, not by completeness of measurement.
Here “coarse” means a task-relative many-to-one mapping; it does not imply low dimensionality. The relational-block criterion specified in Sect. 9 tests the resource-bounded coupling hypothesis. Passing shows only that the block has no meaningful added intervention-predictive value for the declared task, horizon, and margin. It neither establishes task sufficiency nor shows that every physical difference within the candidate state is inert. Sections 9.2–9.4 test other nominated differences—phase and time course, residual structure, and representation growth—as parts of the broader realisation mapping.
Every recording is a finite-bandwidth, finite-resolution projection. Greater resolution can reduce practical uncertainty, but it does not by itself establish that observer-chosen variables are the equivalence classes realised by the controller. Where rival mappings agree on one projection, more data from that projection cannot select between them. The tests proposed below therefore compare causal invariance under intervention rather than attempt a complete reconstruction.
6.2 Predictive Adequacy, Causal Grain, and Representation Growth
A prior can be defined over possible flag trajectories, and a Bayesian model built from it may predict the flag accurately. That does not make the flag a Bayesian mechanism. The same distinction applies to the brain. Predictive accuracy establishes that a model is useful at a chosen scale; a Bayesian mechanism claim additionally requires evidence that the system’s physical organisation realises the proposed probabilistic states and transformations.
This distinction also governs what the model calls “noise.” In the flag, the term names cloth–air structure omitted by a model, not a separate model-independent component. Calling it noise does not make it causally irrelevant. Marginalising that structure is legitimate when the omitted distinctions meet the preregistered equivalence criterion: they make no meaningful independent contribution to predicting intervention outcomes at the explanatory scale. On formulations broad enough to count any system maintaining a statistical boundary as performing inference, the flag itself would qualify. Such generality does not distinguish the flag from the hand that catches it.
Suppose two cloth–air microstates project to the same coarse state and diverge under the same perturbation. A single-valued forecast that receives only the coarse state cannot identify both trial-specific futures. A probabilistic algorithm may deterministically return their conditional distribution. This is a limitation of the coarse state, not of Bayesian inference; the distribution may still be predictively adequate for the scored outcomes. Predictive adequacy and mechanistic attribution are separate conclusions. The conditional distribution belongs to the specified model unless an independent causal mapping shows how the controller realises it. It does not restore the omitted distinction driving the flag on a particular trial. The flag–air state carries that distinction forward in tension, curvature, and flow. It becomes a control resource only if the organism can access it and selective perturbation of that route changes performance.
The same causal-grain test applies to temporal variation. Two physical trajectories can occupy the same instantaneous or window-averaged controller state while differing in phase, sequence, or delay. If their intervention responses diverge, that state is too coarse for the transition. A posterior over their possible futures may still be predictively adequate for the scored outcomes. A Bayesian account may respond by refining the candidate state or placing phase, sequence, and delay in a richer realised state-transition organisation. Stochastic resonance gives one example of omitted variation that may remain causal: fluctuations entering a nonlinear substrate can improve signal transmission even though they do not encode the signal (Douglass et al., 1993; Faisal et al., 2008; Wiesenfeld & Moss, 1995). A fitted noise term without the intervention signatures preregistered in Sect. 9.2 remains descriptive. A Bayesian mechanism remains possible if the physical process realises the proposed inferential operation and predicts the same intervention signature.
Representation growth is one way for a candidate state to become richer. The mechanisms of Sect. 3 apply directly here: a nonparametric model can instantiate a new regime, re-segment a stream, or recruit a new latent feature as the data warrant, and a fixed-architecture network can reorganise its distributed features. Bayesian models can therefore expand their active representations without changing their ambient formal closure. Every computational proposal has allowable operations and inductive bias, specified through a base measure, program, architecture, growth rule, or some combination of these. A structured or compositional prior can generalise to a novel contact regime by recruiting or recombining representational elements. Such a model is a genuine mechanism candidate.
The empirical question is who or what performs the adaptation. Parameter updating changes values within the active model. Endogenous structure learning creates or removes components under the candidate algorithm’s own prospectively specified rule. Exogenous redesign occurs when the theorist changes the variables, factorisation, or grammar after seeing a new regime. The first two are compatible with a Bayesian mechanism, especially when the algorithm recruits structure online and remains calibrated. Reliance on the third shows that the tested model did not transfer without external repair.
6.3 Realising Representation Growth
Endogenous representation growth contributes to a mechanism only when the system physically realises the proposed updating and growth operations. A representation-growing Bayesian account must identify the vehicles of probabilistic updating and of the adaptive transformations it posits: component birth or retirement, distributed feature reorganisation, architecture change, or another specified transformation. The physical vehicles depend on the proposed algorithm; no single encoding is required.
Intervention provides the next test of the mapping. Under that mapping, perturbing a proposed uncertainty variable changes learning or action in the direction implied by the algorithm. Likewise, interfering with a proposed latent-birth operation specifically impairs adaptation when a new component is required. Evidence for the mapping also depends on its surviving changes in task and measurement rather than being reconstructed from each behavioural projection. Without these constraints, a representation-growing probabilistic model may fit the system while a non-probabilistic dynamical process generates the same behaviour.
Causal evidence that Bayesian structure learning helps a mapping meet the full task-sufficiency portfolio without a preregistered resource disadvantage would weaken the local coupling prediction. Such growth operations have not yet been individuated in the unconstrained regimes considered here.
7 Prediction Through Coupling
7.1 Anticipation Without Reconstruction
On a coupling mapping, prediction depends on the organism’s relation to the evolving environment. Two continuous high-dimensional systems can partially synchronise, entrain, or phase-lock. An internal neural–body system may then become predictive of an external system’s action-relevant modes without reconstructing those modes as internal controller states (Haken et al., 1985; Kelso, 1995; Lakatos et al., 2008). During sustained contact, tension, compliance, and reaction forces continuously carry task-relevant structure through the hand, allowing the coupled system to track a fold or slip as it develops. A skilled handler becomes tuned to a cloth’s accessible modes: the slow swing of a hanging garment, the way a fold propagates, the resistance that arrives in the grip. The organism need not inventory every fibre, fold, or vortex. Its internal dynamics are predictive because they remain coupled to the same evolving process.
When two dynamical systems are coupled sufficiently, their states can come to stand in a fixed functional relation: the state of one is determined by the state of the other for as long as the coupling holds. Weaker coupling gives partial versions of the same relation. On a distinctively relation-dependent mapping, the declared internal state–input mapping does not exhaust the relation’s intervention-predictive contribution. Prediction is explained partly through the relation itself. That is the sense in which anticipation here is not reconstruction, and it is narrower than the claim that the organism somehow accesses the environment’s future.
Entrainment supplies a competing process hypothesis. A neural–body system may track an environment’s slow modes because its dynamics are physically locked to them, without an independently realised probabilistic representation. Applied fields can change spike timing and population coordination (Anastassiou et al., 2011; Fröhlich & McCormick, 2010), giving phase and field variables a causal role. Those variables might still realise samples, uncertainty, or another inferential quantity.
A coupled predictive system can also be modelled as approximate filtering, and the model may be excellent. It supports a Bayesian mechanism claim only when physical states realise the algorithm’s probabilistic roles and their transformations implement conditioning or its approximation. The realiser need not be a stored distribution; an implicit or distributed encoding may qualify if the mapping has the required causal and counterfactual organisation. An adaptive account must also identify the physical operation corresponding to its particular form of adaptation.
Both accounts therefore need a prospective physical mapping. A Bayesian mapping identifies inferential vehicles, declared sensory inputs, and transformations. A coupling mapping specifies which organism–environment relations carry anticipation, how they are measured independently of the outcome, and what intervention signature they add beyond ordinary sensorimotor exchange. Evidence counts against the coupling mapping when its preregistered relational block meets the local equivalence criterion against a validated rival mapping or when interventions on its nominated relations lack the predicted residual signature. Breaking a task-constitutive contact and observing failure is not such a test; every embodied controller requires a causal route through its plant. The two descriptions may pick out compatible levels of one mechanism, and the same comparisons may support that conclusion.
The coupling proposal makes a structural claim about where future-relevant distinctions are carried. The resource-bounded coupling hypothesis adds a separate claim about cost. It predicts that maintaining a task-sufficient internal state across novel regimes takes more sensing, memory, update time, or energy than using the same body–environment relations directly, because coupling lets the body and environment carry part of the memory and transformation. Those physical resources are not free and must be counted within a declared system boundary.
The intervention comparisons of Sect. 9.2 follow from these alternative mappings. On a relation-dependent mapping, changing the nominated relation should produce an effect not exhausted by the declared sensory inputs and plant consequences of a rival mapping. An internal mapping predicts the response entailed by its specified state–input dynamics; a hybrid predicts contributions from both. Time course supplies one signature when the mappings predict different horizons. Where those horizons overlap, it does not discriminate.
7.2 Phase and Field Structure in Neural Implementation
The causal-grain test applies within neural tissue as well as across organism–environment relations. Predictive-coding accounts are often presented as nodes exchanging messages through a hierarchy, an abstraction that is useful and fits feedforward and feedback anatomy (Bastos et al., 2012; Friston, 2005). Such accounts can include oscillatory implementation. When a proposed message-passing state collapses phase and time into averaged messages, however, it groups together transient bursts, phase-specific communication, and changing population states involved in working memory and cortical coordination (Breakspear, 2017; Buzsáki, 2006; Lundqvist et al., 2018). The mapping must then show that those differences are causally inert for the transition or include them in its realised state.
Some authors assign representational roles to field structure distributed beyond the synaptic graph (Pinotsis & Miller, 2022, 2023; Pinotsis et al., 2023). These papers motivate a field-level representation hypothesis; relating extracellular field measurements to their cellular generators still requires care (Buzsáki et al., 2012). Relative phase, coherence time, phase slips, amplitude–phase coupling, and oscillator offsets can change which signals are available and when. When a proposed message-passing state identifies trajectories that differ in their phase- or coherence-dependent intervention response, the mapping has quotiented out a causal part of the mechanism.
Field evidence establishes the causal relevance of physical variables. A Bayesian account that assigns them an inferential role must specify and test that mapping.
8 Predictive Processing as Projection
When observation is confined to variables selected for a constrained task, a complex adaptive system can look Bayesian. Experimental design, measurement, and analysis choose a small set of variables from the brain–body–environment trajectory. Ecological interface design shows how such selection can make the constraints of a complex work domain perceptually available so that an operator can act effectively (Vicente & Rasmussen, 1992). Its success does not show that the underlying plant or operator is organised by the same partition. A constrained experiment can likewise make the experimenter’s chosen variables sufficient for prediction without showing that the organism uses that partition. Precision-like cue weighting, mismatch responses, and uncertainty-sensitive trial-by-trial updates can each arise from more than one mechanism (Ernst & Banks, 2002; Näätänen et al., 2007; Summerfield & de Lange, 2014). Bayesian and non-Bayesian mechanisms can therefore produce the same pattern in the observed variables. This is the laboratory form of the cloth case: fit to a selected projection does not identify how the system is organised. Relational descriptions inherit the same limit. Behavioural fit in constrained tasks therefore underdetermines algorithm and implementation (Bowers & Davis, 2012; Jones & Love, 2011; Marcus & Davis, 2013).
That underdetermination limits falsification itself. A high-dimensional physical process reaches an experiment only through a chosen measurement, representation, and decision rule. A sufficiently flexible model family can answer a failed fit by adding latent variables, changing a factorisation or approximation, or revising its growth rule. A finite result can reject the mapping specified before testing; it cannot reject every Bayesian or dynamical redescription constructed afterward. This does not immunise a particular claim: a post-hoc repair is a new mapping. It means that evidence in this regime should converge across projections, scales, transfers, and interventions rather than be compressed into a single binary verdict.
Broad formulations of the free-energy principle extend this descriptive reach. Any self-organising system with a suitable state partition can be described as minimising variational free energy (Friston, 2010). This generality may constrain explanations at the computational level, but it supplies little information about which algorithm a particular nervous system runs. Algorithmic hypotheses need additional variables, transformations, and failure conditions; implementation claims need physical mappings.
Markov blankets illustrate the difference between a partition in a scientific model and causal organisation in the system. A scientist may partition variables in a physical model of the brain–body–environment system into internal, external, and blanket states. A Bayesian brain theory makes the separate claim that physical states of the organism realise latent variables representing environmental causes. These levels can change independently: the organism’s latent representation may grow while the scientist’s physical variables and blanket partition remain fixed. An ambient variable available to the scientist is not thereby an inferential state available to the organism.
A conditional-independence partition in a chosen scientific model does not by itself establish a causal seam in the system or show that internal physical states realise beliefs about external causes. The scale and variables defining the partition must be independently motivated, and the proposed internal, external, and blanket states must survive the relevant interventions. Bruineberg et al. (2022) make the same distinction for blankets themselves, separating an instrumental partition that earns its place as a modelling tool from a realist partition asserted as a boundary of the system. The formalism alone does not license the second. A blanket can organise a useful model without yet identifying a Bayesian mechanism.
9 Empirical Commitments
These studies are not a binary tribunal for Bayes, coupling, or the high-dimensional brain. Each experiment selects a measurement map, a representation of the resulting data, and a decision rule. It therefore evaluates a projection of the process. Section 9.1 tests the local resource-bounded coupling prediction within one declared benchmark and budget. Sections 9.2–9.4 test specified realisation mappings by intervening on proposed inferential and relational variables, examining causal structure omitted by a candidate state, and separating endogenous adaptation from exogenous redesign. A failed prediction counts against the mapping fixed before testing, not against every richer member of its family. A later repair is a new hypothesis.
A comparison is informative only where the nominated signal is readable at the tested scale, the measurement projection preserves the distinctions needed to evaluate the claim, and proponents share the local framework defining variables and outcomes. When any condition fails, the experiment may still constrain future models, but a binary rejection is misleading. Ensemble patterns, independent projections, and multiscale convergence then carry more weight.
Within each declared framework, comparisons use the same local equivalence criterion. Each study preregisters a held-out score appropriate to its outcome, such as log predictive density or error in a predicted intervention contrast. It also fixes a minimum meaningful improvement and an uncertainty procedure valid for out-of-sample comparisons of nested models. Proponents of the rival mappings agree on the minimum before data collection and justify it in the preregistration. A candidate variable adds independent intervention-predictive power only when the lower bound of the prespecified confidence or credible interval for its added held-out value exceeds that minimum after rival variables and matched controls are included. It has no meaningful independent power under the equivalence criterion only when the corresponding upper bound falls below the minimum. An interval crossing the minimum is inconclusive. Block equivalence is assessed on the preregistered relational variables jointly because correlated variables may contribute little alone but matter together. Claims about individual variables use a preregistered multiplicity procedure. Equivalence is local to the measurement map, outcome, horizon, and margin; it is one screen in the task-sufficiency portfolio, not proof that the unmeasured process contains no further causal structure.
Predictive screening alone is insufficient because an internal state may be a downstream record continually refreshed by the relation under test. The portfolio therefore includes matched state-collision trials. Within a preregistered tolerance, trials are matched on the candidate controller state, current declared sensory input, overt task state, and plant variables outside the nominated relational block. They differ in nominated relational history and then receive the same task-preserving perturbation. The mapping predicts a conditional transition distribution from that state and the ensuing declared input sequence. A residual effect of relational history above the meaningful margin, after that sequence is matched or conditioned on, shows that the mapping has grouped causally distinct histories. Absence of such an effect satisfies only the state-collision component; it contributes to task sufficiency only alongside the transfer criterion, block equivalence, and a mapping-specific intervention on the proposed internal realiser.
Natural collisions may be rare in continuous high-dimensional states. The protocol therefore preregisters the state metric and tolerance, which plant variables are nuisance controls and which constitute the relational contrast, the randomisation, reset, cloning, or matching procedure used to construct that contrast, minimum common support, and power for the equivalence margin. Variables in the nominated relational block cannot be matched away. Engineered controllers can often be cloned or reset exactly. If adequate contrasts cannot be constructed, the result is non-adjudicating rather than evidence for or against the mapping.
The tests compare preregistered causal mappings. A Bayesian mapping assigns inferential roles to specified physical states, sensory inputs, and transformations; a coupling mapping assigns an additional control role to specified organism–environment relations; and a hybrid assigns roles to both. A fourth possibility is a non-Bayesian internal controller whose mapping meets the full task-sufficiency portfolio while the tested Bayesian and coupling variables each meet the equivalence criterion. A coupled physical system may itself realise a Bayesian algorithm, so coupling and Bayesian computation are not exclusive alternatives.
Adaptive capacity belongs to the tested mechanism only when its rule is specified prospectively. A Bayesian rival therefore includes its generative program, structural prior, approximate update, and any latent creation or removal rule before testing. A nonparametric controller may add features, regimes, or contact relations online; a fixed-architecture Bayesian neural network may reorganise its distributed features under weight uncertainty. Human changes to the variables, factorisation, or grammar after a novel regime appears are exogenous redesign and do not support the original mapping. The same standard applies to changes in a coupling account’s relational variables or learning rule.
9.1 A Resource-Matched Test of the Coupling Hypothesis
Dynamic manipulation of deformable, self-contacting objects is a useful stress test because contact topology and material constraints change during control. Every tested controller must be prospectively specified at a level that yields variables and intervention predictions; probabilistic candidates additionally commit to a representation and measure whose adequacy the task then probes. Robotic systems have made substantial progress, but many methods remain specialised to particular textiles, task families, or physical variations (Gu et al., 2023; Li et al., 2016; Longhini et al., 2025). Performance alone cannot decide among the mappings because sensing, actuation, compliance, data, and sim-to-real transfer are major confounds.
All arms remain embodied and may use continuous sensory input and action. The candidate internal mapping comprises its controller states, declared sensory inputs, update and growth operations, and output mapping. The preregistered relational block contains the additional organism–environment relations claimed to carry control beyond that mapping. The comparison is not an internal controller against an absent environment. Removing contact, vision, or another task-constitutive channel and observing failure would break the task for any controller and would not distinguish mechanisms.
A fair experiment compares controllers instantiating inferential, relational, hybrid, and non-Bayesian internal mappings on the same plant and task environment. Sensing, actuation, compliance, training experience, and resource budgets are matched across arms. A preregistered system boundary specifies how sensors, memory, computation, body dynamics, and environmental structure are counted. Extra sensors or actuators, engineered compliance, and external memory are charged to the arm that uses them. Reports include controller memory, sensing bandwidth, update latency, and whole-system time and energy. The test then introduces novel materials, unfamiliar garment geometries, and unannounced contact changes during a timed task; these novel conditions are the held-out regimes.
Because the cost claim is comparative, success under one common cap is not enough. Controllers are evaluated across preregistered resource levels. The protocol either fixes a justified aggregate cost or sets componentwise equivalence margins and reports the resulting performance–resource Pareto frontiers. A resource advantage requires matched task performance under that rule; it cannot be inferred merely from the failure of a particular rival implementation.
Human-level transfer means meeting each preregistered non-inferiority margin against a human benchmark, for success rate and for completion time with failed trials scored at the task time limit, in each held-out regime. Each margin fixes how far a controller may fall short of the benchmark and still count as matching it. The human cohort, protocol, margins, and resource-accounting rules are specified before testing, and the human and controller ledgers are reported separately.
This benchmark bears on the resource-bounded coupling prediction. It asks whether a declared controller mapping remains sufficient as active constraints change, relative to the preregistered relational block, and whether that sufficiency carries a resource premium relative to a validated relation-dependent arm. Evidence counts against the prediction when at least one preregistered adaptive internal controller achieves human-level transfer with no preregistered resource disadvantage, the relational block meets the equivalence criterion across held-out interventions, state-collision trials show no residual relational-history effect under the conditional comparison above, and interventions on the proposed internal realiser have the predicted signature. An adaptive Bayesian controller may supply that convergent pattern. A non-Bayesian internal controller may do so without supporting a Bayesian mechanism. Either result defeats the local prediction for the nominated block, task, horizon, margin, budget, and cost rule; it does not identify the mechanism family beyond that framework.
Evidence supports the coupling prediction when a portfolio converges. A validated relation-dependent mapping must achieve human-level transfer with the preregistered resource advantage over every tested internal mapping that also reaches that transfer. An internal mapping can reach that transfer while the relational block still adds intervention-predictive value. If no tested internal mapping reaches that transfer, the resource comparison is non-adjudicating rather than evidence of an advantage. The relational block must add independent held-out intervention-predictive power, and state-collision trials must show a residual relational-history effect above the meaningful margin. Interventions on nominated relations must also produce the predicted signature beyond effects already carried by the declared sensory inputs and plant dynamics. Hardware, data, or sim-to-real failures support neither mapping. Because every result remains projection- and framework-relative, no item in this portfolio alone identifies the mechanism, and failure of one specified Bayesian controller does not falsify adaptive Bayes as a family.
9.2 Selective Perturbation of Rival Realisers
Each account must specify its candidate physical variables, measurement mapping, state-collision tolerance and matching variables, the split between plant nuisance controls and the relational contrast, treatment of the ensuing declared input sequence, and intervention signature before testing. The proxies cannot be selected from the same behavioural effect they are meant to explain. Where feasible, a factorial design should perturb the proposed internal inferential realiser and the additional organism–environment relation separately, with controls matched for sensory energy, plant consequences, and overt task state.
The Bayesian mapping gains support when effects track its proposed realiser as its declared state–input dynamics predict and the relational block meets the equivalence criterion. The coupling mapping gains support when the preregistered relational variable adds a reproducible intervention signature beyond the inferential mapping and ordinary sensory and plant effects. Independent contributions from both support a hybrid. Evidence supports another internal controller, potentially a non-Bayesian one, when its mapping meets the full task-sufficiency portfolio while the tested Bayesian and coupling variables each meet the equivalence criterion. If both proposed mappings meet the equivalence criterion and no validated alternative remains, neither is supported.
An intervention discriminates among mappings only where they prospectively predict different signs, dose–response functions, mediation patterns, timing, or state transitions. An impairment shared by the rivals establishes causal relevance, not Bayesian or coupling identity. Generic disruption of a proposed realiser therefore does not by itself identify the mechanism.
Breaking a causal medium and observing failure is not a selective intervention on a mechanism. Grasp force, contact tension, and limb–cloth kinematics may be task-constitutive for every controller. A discriminating intervention must alter the nominated informational or temporal relation while preserving the ordinary task and declared sensorimotor channel, or model the unavoidable sensory and plant consequences and test for the mapping’s residual signature. If that separation cannot be achieved, the experiment does not adjudicate.
Where the design permits, the timing of an intervention effect matters as well as its size. A relation-dependent mapping predicts a direct contribution on its preregistered coupling timescale. An internal mapping predicts the response implied by its declared state–input dynamics. That horizon must be fixed in advance. A filter with high process noise may respond as quickly as a relational mechanism, so overlapping horizons do not distinguish the accounts. The timescale, prediction horizon, and meaningful margin must be justified before data collection from the nominated relation and rival process model.
Oscillatory phase provides one way to separate candidate mechanisms while holding the overt task constant. Rhythmic sensory stimulation can perturb entrainment while nominal task variables are held fixed (Lakatos et al., 2008), and coherence-based accounts motivate treating phase as a candidate causal variable (Fries, 2005). Direct electrical approaches such as transcranial alternating current or intracranial stimulation require modality-specific targets and controls. A phase effect alone is not discriminating because a predictive-processing account may propose that phase realises precision or temporal expectation.
Where stochastic resonance is proposed, the account should preregister the noise-intensity range, the expected non-monotonic response, and any proposed collective mediator. Failure to recover the predicted optimum or a posited mediation effect counts against that coupling mapping. The result remains compatible with a Bayesian mechanism that prospectively predicts and physically mediates the same interaction. Contact and tension perturbations permit the same comparison in manipulation tasks.
9.3 Causal Structure in Model Residuals
Large-scale recordings during spontaneous behaviour show behaviourally relevant structure spread across population activity (Stringer et al., 2019). Linear covariance spectra can miss curved low-dimensional manifolds, so nonlinear manifold methods, decoding, and perturbation are also required (Cunningham & Yu, 2014).
Fit a predictive-processing model, including its representation-growth rule where relevant, to dense recordings during naturalistic behaviour and examine the structure it does not capture. Here “residual” means a modelling residual, not noise in the system. If the residual predicts behaviour, mediates an intervention, or organises dynamics independently of the proposed Bayesian realisers, then the current model has omitted causal structure. The omission matters mechanistically when the account classified that structure as irrelevant or when its causal effect dissociates from the model’s probabilistic variables.
A causal residual bears on the tested mapping under the prospective conditions above; it does not decide the status of Bayesian computation as a family. The tested algorithm may recruit a new latent component and predict the residual’s effect if its specified growth rule states what triggers recruitment, how the update proceeds, and what intervention signature the new structure predicts. It should also identify residuals treated as irrelevant or lower-level. The mapping loses support when a causally organised residual appears and neither its active model nor its specified growth rule predicts the intervention effect, even if an analyst can add a latent variable later, or when interventions change behaviour while its proposed inferential realisers remain intact. It survives that test only if the residual’s added intervention-predictive effect remains below the preregistered meaningful margin, the mapping prospectively predicts it as implementation-level variation that leaves the declared transition invariant within tolerance, or its specified growth rule captures the effect prospectively.
9.4 Separating Adaptation From Redesign
Prospective tests separately record the three kinds of change distinguished in Sect. 6.2 and report how often each occurs. Repeated reliance on exogenous redesign counts against the particular mapping being tested. It does not falsify the encompassing model family, but the redesigned account is a new hypothesis and cannot be credited with the original prediction.
The same prospective standard applies to coupling. Its relational variables and intervention signatures must be specified before the test. The tested coupling mapping loses support when a task-preserving intervention on its proposed relations lacks the predicted residual signature, when those relations meet the equivalence criterion for no meaningful added intervention-predictive power beyond a validated rival mapping, or when the theorist repeatedly changes the preregistered relational variables after a contrary result. A dynamical fit cannot absorb unexplained structure more freely than a Bayesian fit.
Compare model classes across a task-complexity gradient and report predictive calibration, transfer, intervention accuracy, resource use, and the frequency of human redesign. The comparison should include predictive-processing and active-inference models (Bastos et al., 2012; Friston, 2005; Friston et al., 2017), optimal-control models (Todorov & Jordan, 2002), recurrent and reservoir dynamical models (Jaeger & Haas, 2004; Maass et al., 2002; Sussillo & Abbott, 2009; Vyas et al., 2020), and coupled-oscillator models (Breakspear, 2017; Haken et al., 1985; Kelso, 1995).
Prospective generalisation of probabilistic growth operations supports a representation-growing Bayesian mapping only when interventions on their proposed physical realisers have the predicted effects.
10 Implications and Discussion
10.1 Broader Significance
The problem extends beyond predictive processing. Neural networks, latent-variable models, dynamical systems, and control-theoretic models can all fit high-dimensional data while leaving mechanism underdetermined. Each candidate should face the same requirements: prospectively specified structure, out-of-sample prediction, transfer, and intervention on its proposed realisers. Dynamical terminology receives no exemption. Similar identification problems arise in molecular and cellular biology when continuous physical processes are represented by discrete interaction networks: protein folding runs on a continuous energy landscape and chromosome organisation on continuous polymer dynamics, while contact maps and interaction graphs are useful discrete summaries of both (Dill & MacCallum, 2012; Fudenberg et al., 2016). In each case, a useful variable becomes mechanistic evidence only when the substrate supports the causal role assigned to it.
Engineered digital machines use thresholds, clocking, gain, and reset to protect selected state equivalence classes. These operations consume physical resources and therefore belong in the experimental ledger alongside sensing bandwidth, memory, update latency, actuation, and body–environment dynamics. Under specified assumptions, Landauer’s principle bounds the mean heat dissipated by logically irreversible erasure (Bennett, 1982; Landauer, 1961). It does not price every cost of state protection, establish a general energy advantage for coupling, or set a threshold below which dynamics become indeterministic. Nothing in it requires a biological realiser to protect states in the same way.
The resource question is which distinctions an implementation must stabilise as controller states and which remain causally available in ongoing dynamics. A Bayesian realiser can be continuous, stochastic, and distributed. It may make lower-level timing differences irrelevant to its computational transitions; another mechanism may leave relative phase, delay, and ongoing coupling among the variables that produce those transitions. Biological systems may stabilise some variables while retaining other future-relevant distinctions in continuous, thermally perturbed coupling. Stochastic resonance shows that fluctuations can alter a reliable collective response (Douglass et al., 1993; Faisal et al., 2008; Wiesenfeld & Moss, 1995). A mechanistic account must identify which distinctions are protected as computational equivalence classes, which remain causally available in the substrate, and whether a proposed Bayesian or hybrid mapping includes the latter in its realised state-transition organisation. A full thermodynamics of that distinction lies beyond this paper.
10.2 Implications for AI
The realisation distinction also applies to artificial systems. Some are organised around probabilistic objectives; recurrent, reservoir, and continuous-time models are often described through dynamical trajectories. These model-level descriptions do not automatically identify the physical computation. A neural ordinary differential equation running on digital hardware is realised through protected numerical states even though its mathematical description is continuous. Biological phase, field, and coupling variables have demonstrated effects on spiking and behaviour, while algorithm-specific probabilistic realisers remain to be established for unconstrained embodied behaviour. Tests should therefore target the proposed computational variables directly. Fast embodied control may benefit from coupled-dynamics organisation, probabilistic representation growth, or both. In an artificial system, access to engineered state definitions and interventions can constrain the realisation mapping more directly, though a causal mapping is still required.
10.3 Scope
This paper concerns mechanism attribution in unconstrained embodied behaviour. Bayesian models remain powerful tools for analysing uncertainty, perception, decision-making, and learning, and approximate Bayesian mechanisms are plausible in domains such as cue integration and sensorimotor learning. Their support may be enormous or unbounded, their active representations may grow, and their physical realisers may be continuous and distributed. Formal closure applies to every specified computational or dynamical model, so it supplies no limitation specific to Bayes. Probabilistic computation and coupling may also form one hybrid mechanism.
A Bayesian brain mechanism requires a causal mapping to physical vehicles and transformations that realise its inferential and adaptive operations. Physical evolution does not select a canonical prior–likelihood–posterior factorisation merely by admitting a successful probabilistic description. The vehicles may be continuous, distributed, or relation-dependent; the mechanism claim depends on their causal organisation.
High-dimensional systems and flexible model families often resist decisive binary falsification when the selected projection does not preserve the distinctions required by the claim. The paper therefore makes concrete mappings, not Bayes or coupling in the abstract, empirically vulnerable. A mapping that fails cannot be repaired by adding variables, changing its factorisation, or redescribing its physical realiser after the result and still claim the original prediction. The revised mapping may be worth testing, but it is a new hypothesis.
The resource-bounded coupling hypothesis has narrower scope. It applies only to preregistered benchmark classes and budgets and predicts that human-level transfer depends on future-relevant distinctions retained in ongoing physical dynamics, with relational variables adding independent intervention-predictive power beyond a declared controller mapping and a validated relation-dependent arm showing a resource advantage. A representation-growing Bayesian controller counts against that local prediction only when it achieves transfer without a preregistered resource disadvantage, the relational block meets the equivalence criterion, conditional state-collision comparisons show no residual relational-history effect, and its proposed realisers produce distinctive predicted effects. A non-Bayesian internal controller can produce the same local defeat without supporting a Bayesian mechanism. Either result establishes task sufficiency only for that framework, while neural realisation remains a separate burden. Coupling accounts face the same prospective standard for their relational variables.
10.4 Limitations
Recordings during fully naturalistic behaviour remain difficult, and dimensionality estimates depend on scale, behaviour, preprocessing, and modelling assumptions. Linear covariance measures can miss curved low-dimensional structure. Dynamical models can also become flexible curve-fitters, so they must specify their relational variables and failure conditions prospectively. Predictive-processing theories range from concrete process proposals to broad normative principles. A broad principle may legitimately describe a dynamical system as inference at the computational level, but it identifies a mechanism only when it adds algorithmic and causal constraints.
Some of those limits are practical, and better instruments will ease them. A separate structural limit arises when rival mappings remain observationally equivalent on the chosen measurement projection: more samples from that projection cannot select between them. Interventions supply additional projections but do not provide a theory-neutral view of the whole high-dimensional process. Specific prospective mappings can lose support; no finite battery eliminates every richer redescription in a flexible family. Current evidence therefore motivates convergent comparison rather than a single decisive verdict.
10.5 Conclusion
A prior over a contact-rich continuum is an individuation the modeller supplies, not one the observed trajectory determines. Placing that prior over the process can yield a powerful description without locating an inferential mechanism within it. Formal closure settles neither the realisation question nor which control strategy is at work.
The structural question concerns causal grain. A controller state proposed as sufficient apart from nominated ongoing relations is a quotient of a temporally extended physical process. It is adequate relative to the distinctions tested only where the phase, timing, and relational differences it groups together are inert for the declared task, tolerance, and horizon. When a tested difference changes what signals are available and when, the mapping must include it in a richer realised state-transition organisation. A continuous, adaptive Bayesian realiser or a hybrid can include those differences; the original quotient alone does not close the realisation gap.
The resource-bounded coupling hypothesis adds a local economy prediction: within declared benchmark classes and budgets, ongoing relations carry distinctions that no tested controller mapping preserves economically. An adaptive internal controller counts against that prediction only when it meets the full task-sufficiency portfolio without a preregistered resource disadvantage. If that controller is non-Bayesian, the result does not support a Bayesian mechanism. This is a local result within one measurement framework, not a binary verdict on high-dimensional Bayes or coupling. Evidence for mechanism must converge across transfer, intervention, residual structure, adaptation, and physical realisation in neural tissue.
Data Availability
Not applicable; this is a theoretical paper and no datasets were generated or analysed.
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Todd, I. Bayesian Descriptions are not Mechanisms: Predictive Processing and the Realisation Gap in Embodied Neural Dynamics. Minds & Machines 36, 45 (2026). https://doi.org/10.1007/s11023-026-09801-z
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DOI: https://doi.org/10.1007/s11023-026-09801-z