Cascades and Fields in Perceptual Psychophysics

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Cascades and Fields in Perceptual Psychophysics. Robert Anthony Mills Gregson. Psychophysics is by definition mappings between events in the environment and levels of human sensory responses. In this text the methods of nonlinear dynamics, employing trajectories developed for simpler sensory modelling, are extended to classes of problems which lie at the interface between sensation and perception.


A diversity of topics for which extensive empirical evidence exists are reformulated by writing their dynamics in terms of complex trajectories put into coupled lattices and into cascades of such lattices. Fundamental relationships between core processes of psychophysics in time and space, and recurrent quantitative or topological distortions of the physical world which arise in perception, are given a treatment which contrasts fundamentally with traditional linear equations in use since the 19th century.

Nonlinear Psychophysics Response Surface. From bottom to top: i a subset of low-level orientation-selective units with individual tuning curves around their preferred orientations black curves and their individual response to the input stimulus blue dashed curves ; ii population response profile blue distribution characterized by individual responses of low-level units and a uniform distribution of decisional readout weights green distribution in the absence of stimulus and decision history; iii the decoding of sensory evidence from a decisional unit computed through a weighted average of the population response multiplied by decisional weights gray distribution ; iv in a noise-free example and in the absence of stimulus and decision history, the decoded orientation relayed to the final response stage white triangle corresponds to the stimulus in input black triangle.

A gain change black curves attracts the new stimulus toward the orientation presented before, altering the population response profile blue dashed curves. Decisional weights are uniform and constant in this model green distribution. C The behavior of the Two-process model in trial n. A decisional template formed in the previous trial infiltrates the processing of new stimuli by altering the readout weights of low-level activity nonuniform green distribution.

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This way, decisional traces contrast the repulsive effect of low-level adaptation blue curves and distribution , leading to positive serial dependence. The decision unit then decoded and integrated the population profile into a final response the reported orientation.

The decoding stage occurred through a set of weights, mediating the readout of the decision unit from each orientation-selective cell [ 54 ]. Thus, orientation discrimination was modeled as a two-stage process: an initial response by a population of perceptual units and a later weighted decoding by a higher-level decisional unit. In the Gain model Fig 6B , serial dependence was produced by a gain change in the response properties of orientation-selective units [ 26 ]. Exposure to a tilted stimulus increased the sensitivity of low-level units coding the same and nearby orientations, and this in turn biased the population response to an incoming stimulus toward the orientation coded in the past.

Responses to Constrained Stimulus Sequences in Nonlinear Psychophysics

In this model, the decision unit decoded the population profile with uniform and constant weights; thus, serial dependence only emerged from trial-by-trial gain modulations at the level of orientation-selective neurons. In the Two-process model Fig 6C , serial dependence resulted from the interaction between low-level adaptation mechanisms and changes in decisional weights.

Contrarily to the Gain model, exposure to oriented stimuli inhibited the response of low-level units centered onto the same and nearby orientations. This, in turn, biased the population response to an incoming stimulus away from the present orientation [ 74 , 75 ], resembling negative aftereffects observed after both brief and prolonged adaptation periods [ 76 — 78 ]. The critical aspect of the Two-process model was the plasticity at the level of decisional weights. This way, opposite carryover effects were modeled at different stages of the processing stream, with negative aftereffects arising from low-level adaptation and attractive biases emerging from decisional traces.

Because the reweighting process favored the readout from orientation channels that were more informative in the recent past, this effect compensated for trial-by-trial adaptation at the lower level, leading to the positive serial dependence observed after behavioral responses. The reweighting process was triggered by the requirement—and execution—of a behavioral response, and therefore, no weight update followed the mere exposure to irrelevant stimuli.

The Two-process model provides a compelling account for the coexistence of both positive and negative dependencies in visual perception [ 30 , 56 ]; however, its plausibility and performance had to be evaluated and tested against the Gain model.


To this aim, we first compared the two models in a simulation of behavioral errors for the trial sequences used in Experiments 1 and 2. As a more stringent test, we then compared the predictions of the two models with the true pattern of errors made by participants in a new experiment. In this experiment Experiment 5; Fig 1B , 15 participants were presented with a sequence of Gabors in each single trial and were asked to report the orientation of the last stimulus after the sequence ended see Methods.

Because previous decisions were always interleaved with a sequence of new stimuli before the next to-be-reported orientation, this paradigm offered an ideal situation in which previous stimuli and decisions were dissociated and both positive and negative serial dependence could emerge. B Predictions of the two models in the context of Experiment 5. The Gain model left plot showed consistent dependencies on the last nonreported stimulus in the sequence, with no persisting effect of the orientation reported in the past.

The Two-process model right plot revealed the opposite effect of repulsive adaptation for nonreported stimuli and attractive serial dependence for the perceptual decision and related stimulus one trial in the past. As expected, the Gain model predicted positive serial dependence for the preceding stimulus in the sequence but no persisting influence of the orientation reported in the previous trial, i. On the contrary, previous stimuli and perceptual decisions had opposite effects on the errors generated by the Two-process model: although adaptation at the low level caused repulsive biases, prior decisional weights attracted the representation of incoming stimuli Fig 7B.

In order to select which data-generating process provided a better approximation of the mechanisms underlying serial dependence, we compared the outcomes of both models with the actual data from Experiment 5. The behavioral results resembled almost exactly the predictions made by the Two-process model Fig 8A and 8B. A—B In excellent agreement with the predictions of the Two-process model A , the observed results of Experiment 5 B revealed the opposite effects of previous stimuli nonreported and perceptual decisions reported on current perception.

C Almost all stimuli in the last nonreported sequence exerted a repulsive effect. D In the context of this experiment, where past decisions and stimuli were orthogonal, opposite biases from previous decisions and sensory signals dominated single perceptual reports with almost equal contribution. This clear-cut result provided strong evidence in favor of a hierarchical view of serial dependence, and in addition, it showed that decisional traces affect current perceptual decisions even when interleaved with new stimuli.

The fact that the lingering effect of perceptual decisions persisted across time, even after streaks of intervening stimuli, is in line with the idea that positive serial dependence emerges from the inertia of a high-level decision unit, which operates in a stimulus-independent manner. An interesting question is therefore whether decisional traces, once formed, become mere abstractions of a biased sensory experience or still preserve some low-level properties of the sensory evidence upon which they are based.

In the present experiment Experiment 6 , we focused on the role of stimulus contrast on serial dependence by perceptual decisions. The aim was 2-fold: 1 to evaluate the contribution of the actual and previous sensory evidence, as determined by the stimulus contrast, and 2 to further address whether decisional traces only rely on perceptual reports the orientations confirmed with the response bar or their impact varies with the strength of the previously decoded stimulus.

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More specifically, if positive serial dependence requires weak sensory signals and the mere absence of adaptation [ 29 , 43 ], then it should increase for streaks of low-contrast stimuli and should decrease or even turn negative for streaks of high-contrast stimuli; contrarily, if attractive biases are due to persistent traces in decisional circuits that counteract adaptation, then the stronger the perturbation of the circuit was e.

A High-contrast inducer stimuli increased the impact of previous decisions on the processing of low-contrast stimuli. To further characterize this interaction between the contrast of previous and present stimuli, we then estimated the magnitude of serial dependence at the single-subject level in order to compare four conditions of interest in a full factorial design.

Thus, decisional traces are stronger after high-contrast stimuli, and their attractive influence increases in relation to weak stimuli. To generalize our findings to domains other than orientation perception, we performed a further experiment Experiment 7 in which the task required participants to reproduce the average size of an ensemble of circles see Methods and Fig 10A. Perceptual averaging, also defined as statistical representation or ensemble coding [ 79 , 80 ], refers to the ability of our perceptual system to extract global statistics, such as the mean or variability, from sets of similar stimuli, thus providing a coarse gist of complex visual scenes.

It has been recently shown that ensemble coding occurs in space as well as in time and, consequently, the perceived statistics of an ensemble depends on its global properties in the immediate past [ 31 ].

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These results were discussed as evidence of a spatiotemporal continuity field in visual perception that promotes objects stability and coherence over time. However, based on the evidence reported thus far, it is plausible that serial dependence in summary statistic is due to the same persistence of decisional templates that we have characterized for orientation processing. A Example of one trial in the ensemble coding task of Experiment 7.

Participants viewed an ensemble of 16 dots in one of the four quadrants and had to report the average size by adjusting the size of a response dot. B Example of one trial with four items in the working memory task of Experiment 8.

Participants had to memorize the size of each dot and reproduce the diameter of the dot indicated by a retro-cue black X. The diameter was reported by adjusting the length of a central bar, which was randomly oriented on each trial. To test this hypothesis, we predicted errors in the reported average size of 15 new participants with two different multilevel linear models, following the approach of our Experiments 1 and 2. Before model comparison, errors were corrected for several confounds that typically affect size adjustment responses see Methods. As an alternative to the Two-process account, one can argue that positive history biases arise during the retention of perceptual or decisional information in a temporary memory storage where persistent traces may interfere i.

Although our results appear consistent with decisional inertia in reading-out sensory information, as a final step we found it worthwhile to rule out this alternative interpretation. To this aim, in two versions of this final experiment Experiment 8a and 8b , we evaluated the persistence of previous decisions when visual working memory was filled with new items see Methods. With this method, visual working memory was constantly filled with new and more recent representations e. If serial dependence is due to representations in working memory, then more recent traces should have stronger impact on perceptual errors than previous decisions.

The content of visual perception is strongly permeated by information lingering from the past. In the present study, we demonstrated that vision is shaped by two contrasting forces arising from the history of physical stimuli and perceptual decisions. Our work, based on multilevel modeling and cross-validation approaches, provides a thorough and comprehensive characterization of visual serial dependence from which we derived the following conclusions: 1 There are two contrasting forces that, at any given moment, interact in shaping our perception, biasing the appearance of visual stimuli toward or away from the past; 2 repulsive forces, resembling low-level adaptation, dominate after stimuli that require no perceptual decision; and 3 attractive forces on perception emerge during serially dependent perceptual decisions.

This comparison was performed in the first two experiments and supported by additional analysis in Experiments 7—8 and showed, without ambiguity, that serial dependence in visual perception is explained by the history of perceptual decisions that are required for behavioral responses. This indicated that response-induced history biases are independent of stimulus uncertainty and persist even when the perceptual resolution of stimuli increases. In a following step, we hypothesized that serial dependence occurs exclusively after stimuli passed through a complete perceptual and decisional processing.

The results of Experiment 3 revealed the opposite effects of stimulus and response history: after catch trials, in which a perceptual decision was withheld because of task instructions, past stimuli evoked repulsive biases on subsequent orientation judgments; after response trials, however, adjustment errors were systematically attracted toward previous decisions. It is reasonable, however, that in all these experiments a decision about the relevant stimulus attributes was formed and persisted from trial to trial.

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In fact, stimulus-related decisions are required for relational orthogonal judgments and may reflect the default strategy in tasks in which the demand for a response is uncertain [ 82 ], but responding is the most likely case [ 26 , 43 ]. Hence, if positive serial dependence arises from persisting internal representations required to perform the task, from trial to trial, it is no surprise that the presence or type of response plays no role.

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In line with this idea, here we demonstrated that the same opposite pattern of history biases can be gleaned from discriminative tasks requiring forced-choice responses. The results of our Experiment 4, without adjustment responses, are indeed of critical relevance for two main reasons: 1 They rule out any possibility that our findings may be due to orientation bias confounds in adjustment responses [ 43 , 65 ], and 2 they prove that attractive and repulsive history biases alter directly the sensitivity of our perceptual system and thus the appearance of stimuli.

Previous sensory signals may indeed act as an internal reference model against which incoming stimuli are compared [ 83 ]. Repulsive biases may contribute to the refinement of trial-by-trial internal references that maximize the system sensitivity during discriminative tasks. Decisional processes, on the other hand, build upon the gathering of sensory evidence over time [ 84 ]. Although our findings may not directly resolve this inconsistency, an interpretation in terms of decision inertia can be proposed.

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