A model of subjective report and objective discrimination as categorical decisions in a vast representational space

A model of subjective report and objective discrimination as categorical decisions in a vast representational space King Dehaene

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A model of subjective report and objective discrimination as categorical decisions in a vast representational space 2014 Philosophical Transactions of the Royal Society B: Biological Sciences 10.1098/rstb.2013.0204 King2014-a-model-of-subjective-report-and-objective-d King2014-a-model-of-subjective-report-and-objective-d.txt, the project's staged copy 4aca7956b7ac7fbfaf0587678a72bcb9640ba3b0 not-redistributable neuroscience

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0 spans located by searching the stored text for the quote's exact words, allowing any whitespace between them why a stimulus can be discriminated above chance while being reported as unseen, treated as two decisions over the same sensory vector under different sets of response classes Quotation withheld because this record is not cleared for redistribution. whether objective and subjective tasks can be described by the same inference principles, differing only in the nature and size of the decision space Quotation withheld because this record is not cleared for redistribution. a geometric decision model that reproduces six standard findings in conscious and unconscious perception without postulating a separate conscious process, and a new experiment confirming one of its predictions Quotation withheld because this record is not cleared for redistribution. mechanism Quotation withheld because this record is not cleared for redistribution. dissociation between subjective visibility report and objective discrimination (subliminal perception) Quotation withheld because this record is not cleared for redistribution. simulation simulation Quotation withheld because this record is not cleared for redistribution. mechanisms Objective and subjective tasks apply the same maximum-a-posteriori inference to the same input vector, but over different response classes; the different class sets carry different priors and hence different decision boundaries, so the two tasks can return conflicting answers. Quotation withheld because this record is not cleared for redistribution. mechanisms Internal noise makes some threshold trials yield shorter input vectors; short vectors both fall in the 'absent' region and sit nearer the X/Y discrimination boundary, so trials called unseen are automatically the ones discriminated worse. Quotation withheld because this record is not cleared for redistribution. mechanisms Evidence weak enough to be classified as unseen necessarily lies near the origin of the representational space, where the forced-choice psychometric curve is shallow, producing linear (rather than all-or-none) unconscious response profiles. Quotation withheld because this record is not cleared for redistribution. each task imposes its own set of response classes on the same continuous vector space, so two tasks can partition it differently and return different answers Quotation withheld because this record is not cleared for redistribution. the distance between the two stimulus classes can exceed their distance from the absent class, which is why discrimination survives where detection does not Quotation withheld because this record is not cleared for redistribution. internal variability alone makes half of physically identical threshold stimuli fall nearer the absent class and be reported unseen, and those samples sit closer to the discrimination border status: the paper's own words: can explain why Quotation withheld because this record is not cleared for redistribution. the variance of the representation is what turns the visibility sigmoid from stepwise to nearly linear Quotation withheld because this record is not cleared for redistribution. raising the prior for one stimulus lowers the visibility threshold for that stimulus alone, which is offered as the mechanism behind hysteresis effects Quotation withheld because this record is not cleared for redistribution. if attention changes the variance of the input, it can raise or lower visibility depending on how many trials are already reported unseen Quotation withheld because this record is not cleared for redistribution. The account of linear versus nonlinear visibility profiles rests on an internal-variance parameter that cannot be measured in existing experiments. Quotation withheld because this record is not cleared for redistribution. The model assumes a decision based on one static input vector rather than an accumulation of samples over time. Quotation withheld because this record is not cleared for redistribution. Most of the model's coverage of the literature is post hoc rather than predictive. Quotation withheld because this record is not cleared for redistribution. most of the account is retrospective, which is why a new experiment was run Quotation withheld because this record is not cleared for redistribution. the internal variance that drives the central prediction cannot be determined from existing experiments, so that part of the account remains speculative Quotation withheld because this record is not cleared for redistribution. six computational simplifications are declared in order: the cost function neglected, priors fixed in a given context rather than continuously updated, Gaussian distributions assumed, subjects assumed to have an accurate estimate of stimulus distributions, the same input vector entering different tasks, and stimulus evidence treated as a single discrete point Quotation withheld because this record is not cleared for redistribution. the hypothesis that the input vector remains unchanged and identically available for a series of successive judgements may turn out to be simplistic, given temporal decay, an attentional cue presented after the stimulus, the task set imposed by the first task, and the order in which two questions are presented Quotation withheld because this record is not cleared for redistribution. the model assumes a single input vector where sequential sampling models assume an accumulation, and extending it that way would be needed to predict reaction times Quotation withheld because this record is not cleared for redistribution. the assumption that the decision system is fully informed of the stimulus distributions is called undoubtedly an idealization, with a dynamic model whose likelihood functions, priors and costs are learned and may therefore be ill estimated offered as the route to human deviations from optimality Quotation withheld because this record is not cleared for redistribution. the predicted exceptions to the all-or-none pattern, at high variance or low signal to noise, remain untested Quotation withheld because this record is not cleared for redistribution. the MAP rule, which supplies the decision boundaries instead of their being assumed Quotation withheld because this record is not cleared for redistribution. likelihood distributions and a decision rule, moved from one axis into a multi-dimensional space Quotation withheld because this record is not cleared for redistribution. non-commuting projections, offered as a way to model why the order of two questions changes the answers Quotation withheld because this record is not cleared for redistribution. within-category compression and between-category separation as the definition to be met Quotation withheld because this record is not cleared for redistribution. two subjects excluded for failing to converge to a stable threshold eliminates: a threshold estimate that never settled, which would put an unmeasurable visibility level into the group analysis · outcome (stated by the tagger, no quotation): held Quotation withheld because this record is not cleared for redistribution. discrimination → visibility A DEPENDENCE, AND A SAMENESS CLAIM UNDERNEATH IT: the model predicts that linear and nonlinear response profiles ARISE FROM THE SAME DECISION MECHANISM, and that the discrimination profile of physically identical stimuli becomes increasingly nonlinear AS VISIBILITY INCREASES. No type expresses 'these vary together because one mechanism produces both'. Quotation withheld because this record is not cleared for redistribution. THE SAME INPUT UNDER TWO CLASS STRUCTURES GIVES TWO ANSWERS, AND BOTH ARE CORRECT: each task imposes, top-down, its own categorical structure on one continuous space, and distinct response classes may therefore lead to different conclusions Quotation withheld because this record is not cleared for redistribution. so a dissociation between what is discriminated and what is reported needs no second process - it is what one inference looks like when the question changes Quotation withheld because this record is not cleared for redistribution. THE BOUNDARIES ARE DERIVED, NOT POSITED: their placement is stated not to be an additional hypothesis but a consequence of choosing the most probable class Quotation withheld because this record is not cleared for redistribution. A WIDELY USED TERM WHOSE ORDINARY FORM IS WRONG: criterion suggests a single scalar value, and in this framework it is a set of task-specific boundaries dividing a space, which move when the task or the priors move Quotation withheld because this record is not cleared for redistribution. THE BIAS IS THE SIGNAL: a shift in visibility criterion reflects the subject's own priors and costs and is argued not to be an experimental confound to be discarded Quotation withheld because this record is not cleared for redistribution. THE CONTROL CREATES THE CONFOUND IT WAS MEANT TO REMOVE: equating discrimination by masking or by attention introduces physical differences between the visible and invisible stimuli, so the contrast may reflect the stimulus rather than the visibility Quotation withheld because this record is not cleared for redistribution. AND THE PAPER SAYS ITS OWN ARGUMENTS ARE RETROSPECTIVE before running a new experiment - the accommodation of six existing findings is not offered as the test Quotation withheld because this record is not cleared for redistribution. the target set is declared first: six empirical findings that any account should reproduce, listed before the model is built Quotation withheld because this record is not cleared for redistribution. AND THE ORDER OF THE QUESTIONS MAY CHANGE THE ANSWERS: successive judgements may project the vector onto a task-defined subspace, and projections do not commute Quotation withheld because this record is not cleared for redistribution. an explanation is removed rather than added: a linear-then-categorical pattern previously read as two processes is reproduced by one, with the extra kind declared unnecessary Quotation withheld because this record is not cleared for redistribution. claim_type: mechanism a second reading reaching the same value. Recorded: mechanism — note: a second reading reaching the same value from a different sentence. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. method: a Bayesian signal-detection model in a multi-dimensional feature space, simulated for six known findings, then tested behaviourally by morphing one bar between two digits at perceptual threshold and collecting identification and visibility on every trial a second reading DIFFERING from the recorded value. Recorded: simulation — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. phenomenon: subliminal perception: above-chance discrimination of a stimulus the subject reports not having seen a second reading DIFFERING from the recorded value. Recorded: dissociation between subjective visibility report and objective discrimination (subliminal perception) — note: a second reading, verbatim-verified, disagreeing with the value on the record. Not applied - a person decides. Quotation withheld because this record is not cleared for redistribution. builds-on → earlier proposals [8, 12] (including Lau's decision-theoretic account) Quotation withheld because this record is not cleared for redistribution. extends → de Gardelle et al. [47] Quotation withheld because this record is not cleared for redistribution. contradicts → Rahnev et al. [26] differs in: what drives the visibility rating: Rahnev has attention inducing a bias BY CHANGING THE INTER-TRIAL VARIANCE OF THE STIMULUS, where this model predicts AN INTERACTION BETWEEN THE VARIANCE AND INITIAL VISIBILITY THRESHOLD Quotation withheld because this record is not cleared for redistribution. critiques → accounts on which conscious perception is qualitatively different - more integrated, or dependent on higher-order metacognitive representations differs in: quantitative against qualitative: CONSCIOUS PROCESSES ARE QUANTITATIVELY MORE COMPLEX, INTEGRATED AND DIFFERENTIATED (Tononi and Edelman) against CONSCIOUS PERCEPTION IS QUALITATIVELY DIFFERENT FROM UNCONSCIOUS PERCEPTION, AS IT RELIES ON HIGHER ORDER METACOGNITIVE REPRESENTATIONS (Lau, Rosenthal) Quotation withheld because this record is not cleared for redistribution. explains-away → the reading of linear unconscious and categorical conscious priming as two distinct processes Quotation withheld because this record is not cleared for redistribution. critiques → the methodological position that subjective reports are unreliable and objective sensitivity measures should be preferred differs in: whether one measure reduces to the other: WE SHOW THAT SUBJECTIVE REPORTS CANNOT BE REDUCED TO OBJECTIVE MEASURES, against the position that OBJECTIVE MEASURES, FOR EXAMPLE DETECTION SENSITIVITY (d'), SHOULD BE FAVOURED Quotation withheld because this record is not cleared for redistribution. qualifies → Lau and colleagues' designs that equate discrimination across seen and unseen trials, which do so at the cost of physical stimulus differences differs in: what the design holds constant and what it lets vary: DISCRIMINATION PERFORMANCE IS EQUATED AT THE EXPENSE OF INTRODUCING PHYSICAL DIFFERENCES between the conditions, since masking and attention BOTH MAY CHANGE THE SIGNAL-TO-NOISE RATIO OF THE INCOMING EVIDENCE Quotation withheld because this record is not cleared for redistribution. contradicts → Rahnev and colleagues' account of attention as inducing a conservative visibility bias through inter-trial variance differs in: the same parameter as item 2: variance alone against AN INTERACTION BETWEEN THE VARIANCE AND INITIAL VISIBILITY THRESHOLD Quotation withheld because this record is not cleared for redistribution. builds-on → signal detection theory, extended from its usual one-dimensional depiction to multiple dimensions Quotation withheld because this record is not cleared for redistribution. extends → de Gardelle and colleagues' morphed-face priming result, replicated here with digits and an explicit visibility scale Quotation withheld because this record is not cleared for redistribution. task —causes→ classes task classes strength of the relation: 1 · note: THE WHOLE ARGUMENT: each task imposes, top-down, its own categorical structure on a continuous space, and distinct response classes may therefore lead to different answers about the same input Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span says each task imposes a categorical structure of classes; causes is loose. Quotation withheld because this record is not cleared for redistribution. response classes —part-of→ task response classes task strength of the relation: 1 · note: and a confidence judgement is just another set of classes, so there is one confidence per task rather than one confidence Audit 2026-09-28: DOUBTFUL - read against its span and kept, but confidence judgements add response classes to a task; part-of is loose. Quotation withheld because this record is not cleared for redistribution. identification —operationalised-as→ posterior probability identification posterior probability strength of the relation: 1 · note: three tasks over the same three classes: identification across all of them, discrimination with the absent class excluded, visibility as absent against not-absent Quotation withheld because this record is not cleared for redistribution. input vector —distinct-from→ sequential sampling input vector sequential sampling strength of the relation: 1 · note: a single point where the newer models use a trajectory, which is why this model says nothing about reaction times Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but the model assumes a SINGLE input vector, which sequential sampling models supersede; distinct-from is loose. Quotation withheld because this record is not cleared for redistribution. discrimination —contrasted-with→ detection discrimination detection strength of the relation: 1 · note: the distance between the two stimuli exceeds their distance from the absent class - in two dimensions by a factor of root two - so one can be significant when the other is not Quotation withheld because this record is not cleared for redistribution. unseen —distinct-from→ seen unseen seen strength of the relation: 1 · note: internal variability alone splits physically identical threshold trials, and the unseen half necessarily sits closer to the discrimination border Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span explains why some identical stimuli are reported unseen; distinct-from is loose. Quotation withheld because this record is not cleared for redistribution. variance —causes→ sigmoid variance sigmoid strength of the relation: 1 · note: the parameter that turns the visibility function from stepwise to nearly linear is the variance in representational space, not a change of process Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span names a parameter driving the sigmoid's slope; causes 'sigmoid' is loose. Quotation withheld because this record is not cleared for redistribution. attention —causes→ visibility attention visibility strength of the relation: 0.8 · note: and the disagreement with the rival account is stated as a testable difference rather than an interpretation Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the span predicts how attention affects visibility ratings; causes states a prediction. Quotation withheld because this record is not cleared for redistribution. RETRACTED (AN ATTRIBUTED PROPOSAL, AND THE CONTAINMENT IS A CATEGORY CONFUSION) · global workspace —part-of→ conscious perception global workspace conscious perception RETRACTED: AN ATTRIBUTED PROPOSAL, AND THE CONTAINMENT IS A CATEGORY CONFUSION. The edge is 'global workspace --part-of--> conscious perception'. The span: 'These areas have been proposed to form A “GLOBAL WORKSPACE”…'. A workspace is a proposed ARCHITECTURE in which conscious information is held - it is not a PART of conscious perception, and the sentence attributes the proposal to others rather than asserting it. — strength of the relation: 0.8 · note: the neural sketch is left explicitly as future work, with prefrontal, anterior temporal and parietal areas as the categorical decision system Audit 2026-09-28: DOUBTFUL - read against its full span and kept, but these areas 'HAVE BEEN PROPOSED to form' a global workspace that contributes to conscious perception; part-of is loose. Quotation withheld because this record is not cleared for redistribution. t-test t-test Quotation withheld because this record is not cleared for redistribution. standard deviation standard deviation Quotation withheld because this record is not cleared for redistribution. model fitting (binomial / logistic psychometric fit) model fitting (binomial / logistic psychometric fit) Quotation withheld because this record is not cleared for redistribution. correlation (coefficient of determination) correlation (coefficient of determination) Quotation withheld because this record is not cleared for redistribution. d’ d’ Quotation withheld because this record is not cleared for redistribution. binomial binomial Quotation withheld because this record is not cleared for redistribution. t 16 t 16 Quotation withheld because this record is not cleared for redistribution. A single Bayesian/signal-detection decision framework, differing only in the response classes each task imposes, reproduces the standard dissociation between objective discrimination and subjective report. Quotation withheld because this record is not cleared for redistribution. The decision model suffices to account for several classical characteristics of conscious and unconscious perception. Quotation withheld because this record is not cleared for redistribution. Geometrically, the two-dimensional model implies that discrimination sensitivity exceeds detection sensitivity, which is why above-chance discrimination can coexist with chance-level detection. Quotation withheld because this record is not cleared for redistribution. In a new experiment with morphed digits at threshold, subjects identified the digit above chance even at the lowest visibility rating. Quotation withheld because this record is not cleared for redistribution. The steepness of the identification sigmoid rose systematically with reported visibility, as the model predicted. Quotation withheld because this record is not cleared for redistribution. Unseen trials produced a near-linear relation between morph level and response, whereas seen trials produced a near step-function, all-or-none pattern. Quotation withheld because this record is not cleared for redistribution. Because one decision process yields both response profiles, no qualitative difference between conscious and unconscious processing need be postulated. Quotation withheld because this record is not cleared for redistribution. SIX EMPIRICAL FINDINGS ARE DECLARED IN ADVANCE as the set any account must reproduce, before the model is introduced Quotation withheld because this record is not cleared for redistribution. each task is taken to impose its own class structure on one continuous space, so distinct response classes can give different answers about the same input Quotation withheld because this record is not cleared for redistribution. the conscious percept is modelled as the most probable class among all classes, with negative classes such as I did not see anything included Quotation withheld because this record is not cleared for redistribution. THE DECISION BOUNDARIES ARE DERIVED RATHER THAN POSITED - their placement is explicitly not an additional hypothesis Quotation withheld because this record is not cleared for redistribution. SIX SIMPLIFICATIONS ARE LISTED IN ORDER: no cost function, fixed priors, Gaussian distributions, a calibrated observer, a task-invariant input vector, and a single point rather than a trajectory Quotation withheld because this record is not cleared for redistribution. a degraded stimulus can fall in the unseen region and still be discriminated above chance when the choice excludes the absent class Quotation withheld because this record is not cleared for redistribution. and this is not a response bias - the simulation is Bayes-optimal and still produces the dissociation Quotation withheld because this record is not cleared for redistribution. the geometry gives discrimination a root-two advantage over detection in two dimensions, so one can be significant while the other is not Quotation withheld because this record is not cleared for redistribution. internal variability alone explains why about half of physically identical threshold trials are reported unseen, and why those trials discriminate worse Quotation withheld because this record is not cleared for redistribution. THE TERM CRITERION IS RECONSTRUCTED: it suggests a single scalar value, and here it is a task-specific set of boundaries that move when the task or the priors move Quotation withheld because this record is not cleared for redistribution. three distinct mechanisms are offered for equating discrimination while visibility varies, each with its own manipulation to test it Quotation withheld because this record is not cleared for redistribution. the slope of the visibility sigmoid is driven by the variance of the representation, so all-or-none and graded patterns come from one process Quotation withheld because this record is not cleared for redistribution. and that part is marked speculative, because internal variance cannot be determined from existing experiments Quotation withheld because this record is not cleared for redistribution. in a hysteresis paradigm, subjects reported letters as more visible in the descending than in the ascending sequence, once they knew the letter's identity Quotation withheld because this record is not cleared for redistribution. and the account is immediately qualified, since subjects also learn the sequence structure and would expect more absent trials at its ends Quotation withheld because this record is not cleared for redistribution. with a discriminating prediction attached: the same sequences should shift the bias but leave discrimination unchanged Quotation withheld because this record is not cleared for redistribution. attention modelled as a variance change can raise or lower visibility depending on how many trials are already reported unseen Quotation withheld because this record is not cleared for redistribution. which is stated as a testable disagreement with the rival account rather than an interpretation of it Quotation withheld because this record is not cleared for redistribution. THE PAPER STATES THAT ITS ARGUMENTS SO FAR ARE RETROSPECTIVE and runs a new experiment for that reason Quotation withheld because this record is not cleared for redistribution. the prediction under test is that identical stimuli give increasingly nonlinear discrimination as visibility rises Quotation withheld because this record is not cleared for redistribution. the continuum is built by varying the contrast of a single bar between two digits, so one physical dimension carries two categories Quotation withheld because this record is not cleared for redistribution. stimuli were held at perceptual threshold so that a fixed stimulus produced both seen and unseen reports Quotation withheld because this record is not cleared for redistribution. contrast was set per subject by staircase to about 70 percent accuracy, and two subjects who would not converge were excluded Quotation withheld because this record is not cleared for redistribution. the visibility scale was validated against target-absent trials before being used Quotation withheld because this record is not cleared for redistribution. THE RESULT: choices tracked bar contrast at every visibility level, and the sigmoid steepened significantly as visibility rose Quotation withheld because this record is not cleared for redistribution. three predictions verified - above chance throughout, rising with visibility, and increasingly nonlinear with visibility Quotation withheld because this record is not cleared for redistribution. AND NO QUALITATIVE DIFFERENCE HAD TO BE POSTULATED between conscious and unconscious processing to get it Quotation withheld because this record is not cleared for redistribution. an earlier result read as two processes - unconscious analogue against conscious discrete - is reproduced by one Quotation withheld because this record is not cleared for redistribution. conscious percepts are held to a borrowed definition of categorical perception, with three separate signatures promised in a companion paper Quotation withheld because this record is not cleared for redistribution. perception is framed as a massive classification problem, with a picture-naming task involving tens of thousands of classes Quotation withheld because this record is not cleared for redistribution. subjective reports are argued not to be reducible to objective measures nor to second-order confidence Quotation withheld because this record is not cleared for redistribution. THE BIAS IS THE SIGNAL: a criterion shift reflects the subject's own priors and costs and is argued not to be discarded as a confound Quotation withheld because this record is not cleared for redistribution. THE CONTROL CREATES A CONFOUND: equating discrimination by masking or attention introduces physical differences between visible and invisible stimuli Quotation withheld because this record is not cleared for redistribution. the predicted exceptions to the all-or-none pattern remain untested Quotation withheld because this record is not cleared for redistribution. the assumption that one vector serves several successive tasks is supported by a four-guess experiment, and its limits are named Quotation withheld because this record is not cleared for redistribution. including decay, retro-cueing, task set and the order of the questions Quotation withheld because this record is not cleared for redistribution. AND PROJECTIONS DO NOT COMMUTE, so question order could change the answers - left open as a possible addition Quotation withheld because this record is not cleared for redistribution. the single-vector assumption is contrasted with sequential sampling models, which is what would be needed for reaction times Quotation withheld because this record is not cleared for redistribution. the ideal-observer assumption is named as an idealization, with learned and miscalibrated priors offered as the route to deviations from optimality Quotation withheld because this record is not cleared for redistribution. the classic one-dimensional depiction of signal detection theory is argued to miss the interaction between features, classes and tasks Quotation withheld because this record is not cleared for redistribution. the vast representational space is placed in posterior unimodal and multimodal sensory areas, whose role may be to augment the dimensionality of sensory inputs and turn decisions into linearly separable problems Quotation withheld because this record is not cleared for redistribution. with the global workspace named as the candidate for the categorical decision system Quotation withheld because this record is not cleared for redistribution. vast representational space vast representational space Quotation withheld because this record is not cleared for redistribution. categorical structure of classes categorical structure of classes Quotation withheld because this record is not cleared for redistribution. forced-choice discrimination forced-choice discrimination Quotation withheld because this record is not cleared for redistribution. visibility judgement visibility judgement Quotation withheld because this record is not cleared for redistribution. subliminal perception subliminal perception Quotation withheld because this record is not cleared for redistribution. representational space representational space Quotation withheld because this record is not cleared for redistribution. criterion criterion Quotation withheld because this record is not cleared for redistribution. categorical perception categorical perception Quotation withheld because this record is not cleared for redistribution. identification identification Quotation withheld because this record is not cleared for redistribution. sequential sampling sequential sampling Quotation withheld because this record is not cleared for redistribution. parameter λ parameter λ Quotation withheld because this record is not cleared for redistribution. identification performance identification performance Quotation withheld because this record is not cleared for redistribution. subjective visibility subjective visibility Quotation withheld because this record is not cleared for redistribution. target contrast target contrast Quotation withheld because this record is not cleared for redistribution. visibility visibility Quotation withheld because this record is not cleared for redistribution. discrimination discrimination Quotation withheld because this record is not cleared for redistribution. variance variance Quotation withheld because this record is not cleared for redistribution. prior probability prior probability Quotation withheld because this record is not cleared for redistribution. evidence evidence Quotation withheld because this record is not cleared for redistribution. n = 17 — number of subjects contributing to the reported results (two of nineteen were excluded) Quotation withheld because this record is not cleared for redistribution. 29% males, age: 25 ± 5 — composition of the volunteer sample recruited for the experiment Quotation withheld because this record is not cleared for redistribution. 67.7% — identification accuracy on unambiguous targets, confirming the staircase hit its ~70% goal Quotation withheld because this record is not cleared for redistribution. 36.7 versus 16.9% — proportion of trials given the lowest (0%) visibility rating on target-absent versus target-present trials Quotation withheld because this record is not cleared for redistribution. √2 — the factor by which discrimination sensitivity exceeds detection sensitivity in the two-dimensional version of the model Quotation withheld because this record is not cleared for redistribution. 1000 trials divided into 25 blocks — total trial count per subject in the main experiment Quotation withheld because this record is not cleared for redistribution. r ²(15) = 0.79 — strength of the relation between reported visibility level and the steepness of the identification sigmoid Quotation withheld because this record is not cleared for redistribution. 50% — the share of physically identical threshold trials reported unseen through internal variability alone Quotation withheld because this record is not cleared for redistribution. 36.7 versus 16.9% — use of the zero-visibility response on target-absent against target-present trials, the check that the scale was used properly Quotation withheld because this record is not cleared for redistribution. r ²(15) = 0.79 — the increase in sigmoid slope with visibility rating - the tested prediction Quotation withheld because this record is not cleared for redistribution. 70% — the accuracy the per-subject staircase targeted before the experiment began Quotation withheld because this record is not cleared for redistribution.

The full text of this article is not redistributable, so it is not included here. The evidence sentences are withheld with it; the tag layer and its grounding status remain. The article itself is at https://doi.org/10.1098/rstb.2013.0204.