The loop that disappears on paper

A recurrent system reuses a state-changing mechanism through time. A feed-forward system can replace that reuse with a longer chain of distinct copies. The final behaviour may survive, while the intervention geometry changes.

What recurrence adds before consciousness enters the story

Show a visual system a clean, isolated letter for a few milliseconds. A rapid cascade can carry edge information from early visual areas towards progressively more selective populations. Now place that letter inside clutter or cover half of it. The first cascade contains the same local fragments, but the system must decide which edges belong together, which surface continues behind the obstruction and which region is foreground. These are more than extra labels. They are constraints that later activity can send back to earlier representations.

Lamme and Roelfsema distinguished the initial feed-forward sweep from later horizontal and feedback interactions that change neuronal responses after the first pass.[1] This distinction began as a proposal about visual computation. Recurrent processing theory then gave it a stronger role: local recurrent interaction within sensory cortex was proposed as central to phenomenal consciousness, while wider access and report were treated as later additions.[2][3]

The important step is often skipped. Evidence that feedback improves grouping or difficult recognition does not yet show that feedback constitutes experience. It establishes that a circuit with return paths can implement a useful computation under some conditions. A claim about consciousness adds a bridge: that this organisation is not only useful for the task but is the property in virtue of which the visual content is experienced. Recurrent computation, recurrent correlates of report and recurrent constitution of experience are three different claims.

The smallest equation that reveals the issue

Consider one scalar state. At each moment, the system combines the current input with half of its previous state:

Start at zero and provide four inputs, each equal to one. The states are 1, 1.5, 1.75 and 1.875. A feed-forward chain with four copies can calculate exactly the same numbers. Copy two receives the output of copy one; copy three receives the output of copy two. Nothing about the final value identifies whether one mechanism was reused or four were arranged in sequence.

Change the causal question. After the second state, set the recurrent gain to zero. In the loop, the changed shared parameter governs every later transition, so the remaining states become 1 and 1. In a naive unrolled chain, changing only the edge corresponding to the second transition affects that location alone. The next copied edge still has gain 0.5. The trajectories diverge. A carefully mapped intervention can recover equivalence by setting every later copied gain to zero. That recovery is not a defeat. It exposes the missing clause: equivalence held only after a one-to-many intervention map was supplied.

flowchart LR
  A["One actor, four doubles and<br/>the scene that refuses to<br/>settle"] --> B["The loop that disappears on paper"]
  B --> C["What ordinary behaviour leaves<br/>undecided"]
  C --> D["Turn the loop into an<br/>intervention fingerprint"]
  D -. "re-test" .-> A
  classDef first fill:#0a1424,stroke:#087A98,stroke-width:2px,color:#e6f3ff
  classDef step fill:#0a1424,stroke:#3f7da0,stroke-width:1px,color:#e6f3ff
  class A first
  class B,C,D step

What ordinary behaviour leaves undecided

Visual evidence makes recurrence a serious mechanistic candidate, but it also shows why a single contrast between “early unconscious” and “late conscious” activity is too coarse.

The visual case is stronger and narrower than the slogan

Backward masking supplies a useful intervention. A target appears briefly, followed by another image that reduces or removes its visibility. In one influential EEG study, early target-related activity survived masking while later activity was strongly reduced. Fahrenfort, Scholte and Lamme interpreted this as a preserved feed-forward sweep followed by disrupted reentrant processing.[4] The result made the feed-forward and recurrent distinction experimentally tangible. It did not directly observe a labelled “feedback signal”, nor did masking selectively remove every possible recurrent path. The inference depended on a model of what masking changed.

Later work has sharpened the functional picture. Kar and colleagues identified “challenge” images for which primate object solutions emerged later in inferior temporal cortex than for matched controls. Standard feed-forward models predicted those late patterns poorly, while very deep feed-forward and shallower recurrent models did better.[6] The result supports extra iterative computation for some difficult images. It also contains the unfolding lesson in miniature: additional depth and recurrence can be functionally substitutable for a selected task.

Seijdel and colleagues varied the need for scene segmentation. Recurrent disruption mattered more when an object had to be separated from a complex scene than when recognition could rely on simpler local evidence.[7] This changes the useful question from “Is recurrence always required?” to “Which causal demand recruits it?” More recent combined EEG and fMRI work found that masking altered the geometry and persistence of visual representations, with effects in early visual cortex and later object-selective cortex at different times.[8] That result strengthens a process-level account: recurrence can change not only response magnitude but the form and duration of information represented.

A preregistered TMS study supplies a useful counterweight. Allen and colleagues perturbed visual processing at early and later times. Early stimulation affected both reportedly unseen residual discrimination and conscious perception, with conscious performance appearing more dependent on early processing than a simple theory predicted. Later stimulation was more associated with response criterion effects.[5] The study did not show that recurrence is irrelevant. It showed that mapping feed-forward activity to unconscious processing and recurrence to consciousness is too simple.

This is what mature evidence should look like. Masking, TMS, neural dynamics and model comparison jointly constrain possible mechanisms, yet each manipulation carries collateral effects. A theory earns progress by predicting where the dissociations should occur, which measurement should change first and which rival process could mimic the pattern. “Late” is not a mechanism, and “recurrent” is not a consciousness readout.

The unfolding argument changes the burden

Suppose a theory predicts that a particular recurrent network is conscious because of its causal structure. For any fixed number of time steps, construct a feed-forward network by copying the recurrent unit once per step and connecting the copies in sequence. The unrolled network can reproduce the recurrent network’s input-output relation over that horizon. If the theory predicts a different conscious status for the two, while every report remains the same, how can an experiment decide between them?

Doerig and colleagues used this construction to argue that causal-structure theories face a dilemma. If consciousness tracks reported function, an unfolded feed-forward counterpart should receive the same verdict. If the verdict instead tracks internal recurrence despite identical behaviour, the theory risks insulating its prediction from the evidence used to infer experience.[9] The argument targeted integrated information theory and recurrent processing theory, but its force is broader: it asks whether a theory’s privileged organisation can be varied while the evidence for consciousness is held fixed.

Replies attack different premises. Tsuchiya, Andrillon and Haun argue that a science of consciousness need not restrict itself to behaviour and can test internal causal structure.[10] Kleiner formalises the problem and rejects the premise that brain activity cannot legitimately enter theory testing.[11] Usher argues that static input-output equivalence does not guarantee equivalence of temporal trajectories or responses to structural perturbations.[12] Hanson and Walker show that the verdict depends on the level of computational description at which inference and prediction are fixed.[13]

These replies do not license a retreat to “the brain is different inside”. Internal measurements become probative only when the theory predicts them before seeing the result and connects them to the evidence used to infer a conscious content. Otherwise every architectural difference can be narrated as important after the fact. The right response is therefore not to choose behaviour or mechanism. It is to specify the relation among behaviour, mechanism and intervention.

Equivalence is a contract, not an adjective

Output equivalence asks whether systems return the same answer for selected inputs. Finite trajectory equivalence adds a mapping between internal states over a specified horizon. Intervention equivalence asks whether corresponding changes produce corresponding trajectories. Open-ended adaptive equivalence asks whether the systems continue to match while their parameters, environments or policies evolve.

The grades are nested in ambition, not guaranteed by one another. Two systems may match every tested answer and still diverge after a state reset. They may match internal trajectories under ordinary input yet differ after a synaptic perturbation. They may match every finite episode built in advance but fail when a fifth scene arrives. The unfolding challenge is decisive against architecture labels presented as explanations; it is not a ban on testing causal dynamics.

Turn the loop into an intervention fingerprint

A causal theory should say how a matched pair separates when the same scientific question is asked of each system. The intervention fingerprint makes that question explicit.

From architectural preference to predicted scar

A fingerprint is not a list of components. It is a patterned response to controlled changes. For recurrence, the relevant pattern includes when a perturbation begins, where it is applied, how it propagates through state and which observables recover or fail. A loop and an unfolded fan may have identical baseline behaviour, yet a change to a shared recurrent weight becomes a distributed family of changes in the fan. That difference is scientifically useful only if the mapping is fixed in advance.

The proposed protocol compares a recurrent candidate with a feed-forward rival at the strongest equivalence grade feasible. It then applies interventions that target the theory’s claimed mechanism. The output is a matrix of effect sizes across time, state, behaviour and internal measurement. The pattern is the intervention fingerprint. A theory earns organisation-specific support when its predicted fingerprint survives matched performance, matched resources, mapped perturbations and rival explanations.

The intervention-fingerprint protocol

1. Declare the candidate boundary. Name the components, external stores, sensors, report channel and experimenter-controlled apparatus. A feedback path outside the boundary cannot silently count as an internal loop.
2. Fix the comparison horizon. State the number of processing steps, presentation duration or interaction window. A finite unrolling is only promised over that horizon.
3. Match the ordinary task. Equalise performance across a registered input family, including easy, difficult and shifted cases. Record residual differences rather than declaring models “matched” from one aggregate score.
4. Map states and resources. Specify which recurrent state corresponds to which feed-forward activations, and compare parameter count, depth, energy, latency or sample exposure where those matter to the claim.
5. Register the intervention map. For each lesion, pulse, reset, delay or noise injection in one system, specify its counterpart in the other. State whether one physical change maps to one copied site or a family of sites.
6. Measure a trajectory. Capture time-resolved behaviour, internal representational geometry, recovery, error propagation and confidence. A final answer discards the pattern the theory is supposed to explain.
7. Build rival generators. Test whether depth, extra compute, altered criterion, attention, masking artefact, resource mismatch or an external controller can produce the same fingerprint.
8. Type the conclusion. A positive result permits an organisation-specific mechanism claim within the assay. It does not permit “the system is conscious”. A negative result lowers confidence in the claimed recurrence-specific mechanism under the registered conditions.

A realistic configured-system comparison

Consider two visual models trained on the same synthetic scenes. The recurrent model has a shallow ventral-like stack with a feedback connection from an object layer to an earlier segmentation layer. The feed-forward rival replaces three recurrent updates with three additional blocks. Both classify isolated and cluttered objects at the same accuracy, use comparable multiply-accumulate operations and expose matched intermediate dimensions.

Ordinary evaluation yields a tie. The fingerprint assay adds four interventions. First, pulse the early segmentation state at one moment and measure how the disturbance persists. Second, delay the feedback message or its mapped feed-forward edge. Third, reset the recurrent state between glimpses and reset the corresponding copied activations. Fourth, selectively corrupt an object hypothesis and ask whether early feature geometry is revised towards the wrong object.

The recurrent theory predicts a distinctive pattern. Late object evidence should alter earlier segmentation geometry, and a feedback delay should shift that revision in time. State reset should remove cross-glimpse accumulation. Corrupting the late hypothesis should produce a structured, not random, error in the earlier representation. The feed-forward rival may reproduce every effect if the intervention mapping includes the right copied paths. If it does, the experiment has learned something valuable: recurrence was not the uniquely explanatory property. If it cannot without changing the registered system or adding an online controller, the organisation-specific claim strengthens.

Executable lab: lesion the loop, then choose the mapping

The lab below implements the scalar system from Part one. It is deliberately small enough to inspect. Change the recurrent gain, the intervention step and the intervention mode. In the baseline mode, the recurrent loop and unrolled fan match. A state pulse also matches because it has an obvious one-to-one state mapping. A shared-weight lesion diverges from a one-copy lesion because one reused parameter corresponds to several temporal copies. Choose the distributed lesion and equivalence returns.

function simulate({ gain, lesionAfter, pulse, mode }) {
  const input = [1, 1, 1, 1, 1, 1];
  const recurrent = [];
  const feedforward = [];
  let hr = 0;
  let hf = 0;

  for (let t = 0; t < input.length; t += 1) {
    const after = t > lesionAfter;
    const atPulse = mode === "pulse" && t === lesionAfter + 1;

    const recurrentGain =
      (mode === "local" || mode === "distributed") && after ? 0 : gain;

    let fanGain = gain;
    if (mode === "local" && t === lesionAfter + 1) fanGain = 0;
    if (mode === "distributed" && after) fanGain = 0;

    hr = recurrentGain * hr + input[t] + (atPulse ? pulse : 0);
    hf = fanGain * hf + input[t] + (atPulse ? pulse : 0);

    recurrent.push(hr);
    feedforward.push(hf);
  }

  return { recurrent, feedforward };
}

stateDiagram-v2
  [*] --> Claim
  state "What recurrence adds before<br/>consciousness enters the story" as Claim
  state "A loop unfolded into a<br/>temporal fan" as Test
  state "The four doubles" as Revision
  Claim --> Test: expose mechanism
  Test --> Decision: evidence survives
  Test --> Revision: rival survives
  Revision --> Claim: narrow or rebuild
  Decision --> [*]

Where the fingerprint can lie

A difference after intervention is not automatically evidence for recurrence. It can be manufactured by an unfair horizon, an unmatched resource, a poor site correspondence or a compensating process placed outside the declared system.

Finite fans have an expiry condition

An unrolled feed-forward network is built for a chosen number of steps. Give it four inputs and four copies suffice. Ask for a fifth update and the recurrent system reuses its mechanism, while the fan needs another copy. This does not prove that recurrence computes something impossible for feed-forward systems. The fan can be extended. It does show that the equivalence statement contains a construction cost and a horizon. Those terms matter when the environment does not announce episode length in advance.

Rapid plasticity sharpens this boundary. A fixed recurrent network follows different state trajectories while retaining one input-output rule. A plastic recurrent network can change the rule itself as a function of history. O’Reilly-Shah, Selvitella and Schurger formally argue that a single static feed-forward unfolding made at one time will diverge as the recurrent system’s parameters change.[14] Their conclusion is deliberately limited. The result bounds the original fixed-parameter unfolding construction. It does not establish that recurrence, plasticity or process is necessary for consciousness. A dynamically rebuilt or otherwise adaptive feed-forward realisation may still track the system, but it no longer has the original static form.

This suggests a fourth equivalence grade rather than a victory declaration. Open-ended adaptive equivalence must state whether both systems receive the same history, update under comparable rules and remain within declared resource limits. A theory that depends on rapid plasticity also owes an empirical prediction at the timescale of the conscious episode. Adding plasticity after the challenge is known is not enough.

Four rival generators of a “recurrence effect”

Damage load is the simplest rival. Lesioning a shared recurrent parameter may affect many temporal uses, while lesioning one feed-forward edge affects one use. The recurrent system looks more fragile because the intervention was larger in functional reach. A distributed fan lesion may remove the difference.

Depth and compute form a second rival. Hard images often benefit from more nonlinear transformations. A recurrent model obtains them by reuse; a deep model obtains them spatially. If the recurrent system receives more effective compute or easier optimisation, its advantage does not isolate feedback as the cause.

Measurement and report form a third. A late perturbation can alter criterion, confidence, motor preparation or memory for the stimulus without changing the visual content in the way the theory claims. Time-resolved internal measures help, but they require an independently motivated bridge to the target content.

Compensation forms a fourth. A controller may detect a perturbation and reroute processing. The observed resilience then belongs to the larger control system, not necessarily to the local architecture being compared.