Temporal action-effect prediction does not affect perceived loudness, but the sense of agency

Elisabeth Lindner, Tobias Schöberl, Andrea Desantis, Alexander Gail

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Elisabeth Lindner, Tobias Schöberl, Andrea Desantis, Alexander Gail. Temporal action-effect prediction does not affect perceived loudness, but the sense of agency. Consciousness and Cognition, 2025, 130, pp.103837. 10.1016/j.concog.2025.103837. hal-05042977

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# Temporal action-effect prediction does not affect perceived loudness, but the sense of agency

Elisabeth Lindner<sup>a,b,*</sup>, Tobias Schöberl<sup>a</sup>, Andrea Desantis<sup>c,d,e,1</sup>, Alexander Gail<sup>a,b,1</sup>

## ARTICLE INFO

### Keywords:

Agency

Perception

Action

Action-effect prediction

Prediction

Cancellation

## ABSTRACT

Motor theories propose that predicting sensory consequences of one's own actions reduces perception and neural processing of these action-effects, a phenomenon known as sensory attenuation, considered an implicit measure of agency. However, recent findings question the link between action-effect prediction and sensory attenuation. This study directly examined the link between temporal action-effect prediction and auditory sensory attenuation, alongside assessing self-reported agency. Participants experienced self-initiated auditory effects with varying latencies and compared their loudness to a reference tone, whose intensities were modulated to measure auditory discrimination. Results showed no change in perceived loudness across delays, while agency ratings decreased with longer delays. A second experiment controlled for hazard rate effects, confirming initial findings. Our results contrast previous behavioral findings from the tactile modality and conclusions drawn from auditory electroencephalography. We suggest reconsidering auditory sensory attenuation as a necessary consequence of action-effect prediction and as an implicit measure of agency.

## 1. Introduction

The perception of someone else tickling us versus the attempt of tickling ourselves for most is fundamentally different. The inability to provoke a tickling experience when trying to tickle ourselves is explained by the idea that we form a prediction on the sensory outcome of our own actions (Blakemore et al., 2000). The tactile input related to the tickling is compared to the predicted sensory effects of the touch, and if there is a match the sensory effects are canceled out or at least strongly attenuated. Whereas, if a supposedly friendly villain tickles us, the precise sensory information cannot be predicted and therefore leads to a rather salient percept, due to an increased residual between prediction and sensory input (prediction error).

Action-effect prediction is believed to be the outcome of a so-called forward model (Crapse & Sommer, 2008; Miall & Wolpert,

<footnote><sup>a</sup> Cognitive Neuroscience Laboratory, German Primate Center – Leibniz Institute for Primate Research, Kellnerweg 4, 37077, Germany</footnote>

<footnote><sup>b</sup> Faculty of Biology and Psychology, University of Göttingen, Wilhelm-Weber-Str. 2, 37073 Göttingen, Germany</footnote>

<footnote><sup>c</sup> The French Aerospace Lab ONERA, Département Traitement de l'Information et Systèmes, BA 701 13661 Salon Cedex AIR, 13661 Salon-de-Provence, France</footnote>

<footnote><sup>d</sup> Institut de Neurosciences de la Timone (UMR 7289), CNRS, Aix-Marseille Université, Faculté de Médecine, 27, boulevard Jean Moulin, F-13005 Marseille, France</footnote>

<footnote><sup>e</sup> INCC - Integrative Neuroscience & Cognition Center UMR 8002, CNRS, Université de Paris, 45 Rue des Saint-Pères, F-75006 Paris, France</footnote>

<footnote>* Corresponding author at: Cognitive Neuroscience Laboratory, German Primate Center – Leibniz Institute for Primate Research, Göttingen, Germany.</footnote>

<footnote>E-mail addresses: elindner@dpz.eu (E. Lindner), aerdna.desantis@gmail.com (A. Desantis), agail@dpz.eu (A. Gail).</footnote>

<footnote n="1">¹ Shared senior authorship.</footnote>
1996; Sperry, 1950; von Holst & Mittelstaedt, 1950; Wolpert, 1997). Supposedly, action-effect prediction and, accordingly, sensory attenuation help us to differentiate our own action effects from external stimuli and thereby to form a sense of agency. Sense of agency in this context refers to the attribution of having caused one's own motor acts and their effects in the external world (Haggard & Tsakiris, 2009). In this study, we ask whether temporal action-effect prediction leads to perceptual attenuation of auditory effects. Further, we assess if a subjectively experienced and reported sense of agency is linked to sensory attenuation.

Sensory attenuation is not restricted to somatosensory modalities (Asimakidou et al., 2022; Bays et al., 2005; Kilteni et al., 2019; Kilteni & Ehrsson, 2022). It has also been reported for vision (e.g., Cardoso-Leite et al., 2010; Mifsud et al., 2018; see Schwarz et al., 2018 for a counter-example) and audition (e.g. Baess et al., 2011; Sato, 2009; Weiss et al., 2011) in phenomenology, i.e., perceived stimulus intensity, and for neural responses, i.e., attenuation of stimulus-triggered evoked potentials. It is still unclear, though, if and how the temporal contingency between action and auditory effect – and the predictability of the effect that results from this contingency – determines perceptual attenuation of the auditory effect and if it similarly influences the subjective experience of having caused it, i.e., the associated sense of agency.

Sensory attenuation is not an all-or-nothing phenomenon but can change gradually, for example, with varying latency of the action-effect (Bays et al., 2005; Blakemore et al., 1999; Cemeljic et al., 2025; Oestreich et al., 2016; Pinheiro et al., 2019; Van Elk et al., 2014). According to the forward model idea, different degrees of prediction would lead to different degrees of sensory attenuation. Our own actions mostly lead to effects in the outside world already while performing the action or immediately after, allowing and improving temporal prediction (Morillon & Baillet, 2017). While delayed action-effects are possible, they tend to violate our prediction the more the longer the latency is. For instance, when pressing the key on a piano, an immediate onset of the tone is expected, while a delayed onset would be surprising after we previously learned the temporal contingency. When sensory attenuation of action-effects is mediated by temporal prediction, then attenuation should be reduced with reduced predictability of longer latency action-effects. This may be the case because unpredicted late effects might capture our attention and increase the saliency to the level of externally caused stimuli (Bays et al., 2005; Blakemore et al., 1999; Oestreich et al., 2016; Pinheiro et al., 2019; Van Elk et al., 2014).

Reduced sensory attenuation with increased action-effect latency has been demonstrated especially in the form of (less) attenuated early sensory responses in electroencephalography (EEG; e.g., Elijah et al., 2016; Oestreich et al., 2016; Pinheiro et al., 2019; Van Elk et al., 2014). Perceptual sensory attenuation as a function of action-effect latency, instead, to our knowledge has only been shown in psychophysics experiments using tactile, not auditory stimuli (e.g., Bays et al., 2005, 2006; Blakemore et al., 1999; Cemeljic et al., 2025; Kilteni et al., 2019, 2021, 2023; Kilteni & Ehrsson, 2024; Knoetsch & Zimmermann, 2021). In our study, auditory perceptual attenuation and sense of agency were both tested as a function of action-effect latency in the auditory domain.

A link between auditory sensory attenuation and the sense of agency has been suggested by studies comparing action-effects generated by oneself (active condition) versus passive conditions with effects generated externally (e.g. Klaffehn et al., 2019; Sato, 2009; Weiss et al., 2011). Auditory sensory attenuation for active conditions has been reported. However, the comparison between active and passive conditions may in some cases be confounded by additional factors, such as differences in temporal control (see review of Hughes et al., 2013) or attentional allocation (Schröger et al., 2015). Other recent evidence points out that experiments comparing active versus passive conditions do not necessarily lead to auditory sensory attenuation for active stimuli (Cao & Gross, 2015; Myers et al., 2020; Thomas et al., 2022). Here, we use only active conditions and vary the sense of agency via effect latencies.

If auditory sensory attenuation as a consequence of action-effect prediction is indeed linked to the sense of agency, both phenomena should similarly be affected by variable levels of action-effect prediction, independent of which behavioral factors modulate prediction. Modulation of sensory attenuation with temporal delays of action-effects at the physiological level has been reported especially in EEG, and at the perceptual level only for the tactile modality. Here, we investigate, first, whether the latency effect for perceptual sensory attenuation also exists in the auditory modality, and, second, how perceptual sensory attenuation relates to the sense of agency in the same task and participants.

## 2. Materials and stimuli

We adapted an established action-effect paradigm in which participants were invited to create a tone (standard tone) by pressing a key on a computer keyboard (Desantis et al., 2012; Reznik et al., 2015; Sato, 2009; Weiss et al., 2011). After a short interval, a second tone (comparison tone) appeared, which varied slightly in intensity across trials, and participants were asked to indicate which of the two tones they perceived as louder. It has previously been shown that tones created in the active condition (keypress) were perceived as less intense (sensory attenuation) than in the passive condition (no keypress, just listening) (Sato, 2009; Weiss et al., 2011). To avoid possible confounds resulting from differences between active and passive conditions, we sought to modulate prediction and sensory attenuation by including variable levels of temporal predictability with different delays between keypress and associated standard tone. We expected that tones closest in time to the action should be perceived as attenuated compared to tones with larger delays. To test whether this putative effect co-varies with the sense of agency, participants were asked to rate their feeling of agency after every trial. We hypothesized decreasing levels of agency with increasing tone delays, co-varying with sensory attenuation.

The experiment was conducted in a soundproof, dark, and electromagnetically shielded chamber (Desone Modulare Akustik, Berlin, Germany). Matlab (version R2015b) with Psychophysics toolbox 3.0.14 (Brainard, 1997; Kleiner et al., 2007; Pelli, 1997) was used for the presentation of the task on a 22.5-inch calibrated monitor (ViewPixx/EEG Inc.; resolution = 1440x980 pixels, refresh rate = 120 Hz). Participants performed the task while sitting at a distance of 91 cm from the screen and resting their heads on a chinrest. Auditory stimuli were delivered via on-ear headphones (Sennheiser HD100), that passively reduced external noise, consisting of 1000 Hz pure tones between 72 and 76 dB (steps of 1 dB) sound-pressure level (SPL) with a duration of 100 ms (with a ramp-up and ramp-down of 5 ms). SPL levels were calibrated before experimental testing, using an artificial ear (artificial ear: Brüel & Kjær, Copenhagen –
Type 4152; precision sound level meter: Brüel & Kjær, Copenhagen – Type 2203, octave filter set: Brüel & Kjær, Copenhagen – Type 1613). The visual stimulus, serving as a fixation circle (i.e., an empty black circle of 0.7 visual angle degrees) was displayed on a mid-grey background. Fluorescent tape was attached to all relevant keys on the computer keyboard, i.e., the keys with the numbers 1 to 7 on top of the keyboard “Q” and “E”, “enter” and “space”.

## 2.1. Participants

We tested a total of 51 participants without any known relevant health conditions. 26 (12 males, mean age = 28.65 [SD = 12.51], 2 left-handed) and 25 (7 males, mean age = 27.96 [SD = 9.18], 0 left-handed) participants were tested in experiment 1 and experiment 2, respectively. A power analysis conducted on pilot data from a related variant of an auditory attenuation experiment, which additionally included negative SOAs, suggested that already a minimum of 15 independent participants should be sufficient to obtain an effect (power = 0.8, effect size *f* = 0.47, correlation among repeated measures = 0; using G*Power; Faul et al., 2007). We increased this number to approx. 25 participants per each experiment for better statistical power.

Before the experiment, all participants provided written informed consent and attested to possessing normal or corrected vision and hearing and no history of neurological or psychiatric disorders. Additionally, they affirmed abstaining from drugs, medication, or dependency on alcohol prior to the experiment. The methodology and objectives of the study received approval from the local ethics committee of the Georg-Elias-Mueller-Institute for Psychology, University of Goettingen and adhered to the principles of the Declaration of Helsinki.

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Experimental Design. A: Participants were asked to cause a tone (standard) by pressing a key and compare its loudness to a comparison tone, that followed shortly after. The standard tone could appear with a SOA of 0, 50, 200 or 600 ms in experiment 1, or with a SOA between 0 and 1378 ms in experiment 2, after the keypress. At the end of the trial, an agency rating was requested from the participant. B: Hazard rate of SOA in experiment 1. C: Hazard rate of SOA in experiment 2. Grey bars represent SOAs excluded from further analysis (see section 4.1) using the cutoff represented by grey dotted line.</figcaption></figure>
# 3. Experiment 1

## 3.1. Procedure – Experiment 1

The experimental design (Fig. 1A) adopted elements of previous studies (Desantis et al., 2012; Reznik et al., 2015; Sato, 2009; Weiss et al., 2011). The experiment comprised 360 valid trials (see below) divided into 18 blocks of 20 trials. Each trial started with information (white letters on the screen) on the number of accomplished trials from total trials and the request to press the space bar to start the trial. An empty black fixation circle appeared in the middle of the screen, which remained until the end of the trial. Participants then could press the key on a keyboard with the letter “P” using their right index finger.

In Experiment 1, the keypress was followed by a tone (standard tone) of 74 dB at a stimulus onset asynchrony (SOA) of either 0 ms, 50 ms, 200 ms, or 600 ms (mean over all trials = 213 ms). We used different SOAs of the tone to probe perceived loudness for different levels of temporal prediction. The different SOAs had equal chances of appearance and were presented in randomized order. Each SOA appeared 18 times for each of the five tone levels of the later comparison tone (see below).

A second tone (comparison tone) was presented after a random interval between 1200 to 1600 ms following the first tone. The intensity of the second tone ranged from 72 to 76 dB, in steps of 1 dB. Thus, this tone could be either less or more intense than the first tone. Each block of trials contained all 4x5 combinations of SOA and tone intensity, in random order. Participants were asked to judge which tone was perceived as being louder. The key “Q” or “E” had to be pressed with a finger of the left hand if the first or second tone, respectively, was judged louder. These two keys were marked with the number “1” and “2” on the keyboard to indicate to which tone they correspond.

Finally, a request for an agency rating was displayed on the screen, reading: “How strongly do you have the feeling that you caused the first tone? “(in German: “Wie stark haben Sie das Gefühl, dass Sie den ersten Ton verursacht haben?”) with a scale from 1 to 7 from “Not at all” (“Überhaupt nicht”) to “Completely” (“Absolut”). By typing the respective number on the keyboard and pressing “enter” participants could proceed to the next trial, which again started with the display of the completed number of trials and the current block number. If the participant accidentally indicated an agency judgment outside the indicated range, an error message appeared on the screen and the trial was aborted. Error trials were repeated at the end of the experiment.

A trial was considered valid if the participant initiated it by pressing the space bar, triggered the standard tone by pressing the “P” key, responded to the loudness judgment task by pressing the appropriate key, and completed the agency rating within the specified range. There were no time constraints for any part of the trial, and all keys unrelated to the experiment were disabled during the trial prior to the agency judgement to prevent accidental input.

Before the experiment, participants read and had the opportunity to discuss the written instructions. They then completed a short training. The instructions indicated that the first tone in each trial could either be created by the participant or by the computer and that there would be no right or wrong answer on the agency judgment. After half of the blocks, participants were invited to take a short break, as indicated on the screen.

## 3.2. Psychometric analysis – Experiment 1

To test for perceptual sensory attenuation as a function of action-effect latency and to investigate its relationship to a sense of agency, we measured the proportion of trials in which the second tone was rated louder than the first tone. This fraction was calculated for each SOA and each participant as a function of the intensity of the second tone. After pooling the data over all participants, for each SOA we fitted psychometric functions with a maximum-likelihood procedure with a cumulative normal distribution using the Palamedes toolbox in MATLAB (Prins & Kingdom, 2018).

The point of subjective equality (PSE) was extracted from each individual fit. The PSE describes the intensity at which the comparison tone was rated as louder than the first tone in 50 % of the trials according to the fitted data. It reflects the perceived loudness of the first tone under the different SOA conditions. Lower PSEs compared to higher PSEs would reflect attenuation of the loudness of the first tone. We pooled the data across participants before fitting to prevent data loss as some individual participant-level fits did not meet the goodness-of-fit criteria (see supplementary information – S1).

We conducted permutation tests to analyze the effect of SOA on the PSE. To do this, the labels for the SOA conditions were shuffled across the dataset, creating a random relationship between participants’ loudness judgment and SOA condition. A psychometric function was then calculated on this randomized dataset, a process that was repeated 10,000 times. Each iteration involved calculating the difference in PSE between each SOA condition. These differences represent data under the null hypothesis, which posits that variations in PSE across SOA conditions are due to random chance or sampling variability. To determine if SOA influences PSE in our data, we calculated p-values as the proportion of permuted absolute differences between SOA that were equal to or larger than the absolute differences observed in our data. A p-value below the critical alpha-level of 0.05 (Bonferroni corrected for multiple comparisons) was considered to indicate a significant difference between experimental conditions.

Because we could not reject the null hypothesis that the PSEs across the different levels of SOA are equal, we sought to estimate the extent to which our data favored the null model over the alternative hypothesis by computing Bayes factors (BFs). We focused on the difference in PSEs between the shortest (SOA1) and longest SOA (SOA4), as this comparison yielded the smallest p-value in our permutation tests and was the closest to significance.

First, we estimated the mean difference between the PSEs and the corresponding standard error of the mean for the two conditions of interest (SOA1 and SOA4) using bootstrapping. The BFs were then computed in the following way (cf. Colling, 2021; Rouder et al., 2009): We computed BFs as the ratio of the marginal likelihood given a null model and the marginal likelihood given an alternative
model. Each marginal likelihood was obtained by integrating the product of the likelihood function (the probability of the data given a parameter value) and a prior (a function reflecting prior beliefs about the probability distribution of a parameter) from minus to plus infinity.

The likelihood function was modeled as a normal distribution with mean $\mu$ and standard deviation $SE$ as obtained from bootstrapping. For the prior of the null model, we used a point prior at 0 difference. For the prior of the alternative model, we used a Cauchy distribution reflecting prior beliefs about the probability of PSE difference (cf. Rouder et al., 2009). The probability density function of the Cauchy distribution is given by

$$F(x) = \frac{r}{r^2 + (x - l)^2} * \frac{1}{\pi}$$

<figure><img src="image_5.png" /><figcaption>Fig. 2. Perceptual discrimination and agency ratings as function of SOA. A: Psychometric functions for proportion of “second tone louder” responses for all conditions of SOA over levels of comparison tone fitted on pooled data across participants for experiment 1 (left) and experiment 2 (right). B: Boxplots and outliers of bootstrapped PSE for experiment 1 (left) and experiment 2 (right). C: Boxplots and outliers (black) of agency ratings and ratings per participant (color) for experiment 1 (left) and experiment 2 (right). Agency ratings were averaged over all dB levels.</figcaption></figure>
with *l* = 0 and *r* = 0.707. This scaling of the distribution is default in common applications and is thought to reflects suitable assumptions when medium effect sizes are expected (JASP team, 2024); notice that our computation was based on the numerical mean difference in decibel between the PSEs in the two conditions, not on effect size. However, this scaling of the Cauchy should be appropriate for medium effect sizes in our case as well, because the presumed standard deviation of the internal representation, the just noticeable difference (JND), in the present study were close to 1 dB. Effect sizes should therefore be close to the mean difference in decibel).

Agency judgments were extracted for each SOA condition and stimulus intensity for each participant. Averaged agency judgments were modeled in a two-way repeated measures ANOVA with factors Tone Intensity and SOA. Greenhouse-Geisser corrections were applied to ANOVAs when the assumption of sphericity was violated and corrected p-values are reported along with original degrees of freedom and partial eta-squared (e.g. Harrison et al., 2021; Jones et al., 2013; Mizuhara & Uhlhaas, 2021). Additionally, pairwise t-tests were calculated post-hoc for significant ANOVA results, Bonferroni corrected for multiple comparisons.

### 3.3. Results – Experiment 1

We tested if the perceived loudness of the acoustic action effect varied with its latency after the keypress. We did not observe such an effect. Across individuals, probability of perceiving the comparison tone as louder than the standard tone increased in a sigmoidal fashion as a function of the intensity of the comparison tone (Fig. 2A, average goodness of fit (R²) for SOA0 = 1, SOA50 = 1, SOA200 = 1, SOA600 = 1). Yet, this probability did not depend on the SOA (Fig. 2A). Permutation testing revealed that the differences between SOA conditions did not differ significantly to randomized data after correction for multiple comparisons (minimal p-value: 0.29; Fig. 3). This means, the psychometric data does not indicate an attenuation that depends on SOA. However, before correcting for multiple comparisons, we observed a significant difference between PSE at 0 ms and PSE at 600 ms compared to the randomized data (p = 0.048) with a lower PSE for the latest SOA condition. Our Bayes factor analysis resulted in moderate evidence ($BF_{S01} > 3$) for the null hypothesis over the alternative hypothesis (difference between SOA1 and SOA4). The obtained Bayes factors are $BF_{10} = 0.33$ and $BF_{01} = 3.06$.

This suggests that instead of causing sensory attenuation for early action effects, SOA may not impact loudness perception or could even lead to attenuation for later SOAs.

In contrast to PSEs, the agency ratings showed a significant main effect of SOA (F(3, 75) = 41.40, p < 0.001, $\eta_p^2 = 0.62$; Greenhouse-Geisser corrected), with ratings decreasing with longer SOA (Fig. 2C). Pairwise t-tests revealed that ratings differed between all pairs of SOA (maximal p < 0.001, Bonferroni corrected). This means, that the longer the latency of the acoustic action effect, the less participants rate the effect as a consequence of their own action.

This strong dependency of agency on SOA and lack of dependency of loudness perception on SOA may suggest that agency rating effects were independent of sensory attenuation, as would have to be reflected in PSEs if present.

## 4. Experiment 2

In experiment 1, perceptual sensory attenuation was absent between every SOA and, therefore, was also not modulated as a function of SOA. Rather than finding an attenuation for early action effects, later action effects generated a trend towards reduced loudness perception, although this was not significant after correcting for multiple comparisons. One explanation for a missing effect might be the influence of a conditional probability of tone occurrence. The heightened predictability of the first tone due to temporal prediction of the action effect when immediately following the keypress might have been counter-balanced by hazard-rate effects. The

<figure><img src="image_6.png" /><figcaption>**Fig. 3.** Boxplots for permuted PSEs (black) and original PSE (yellow) for differences between conditions of SOA for experiment 1 (left) and experiment 2 (right).</figcaption></figure>
hazard function describes the conditional probability of the occurrence of an event at a specific point in time, given that it has not yet occurred. It increases with time if the absolute probability of occurrence is homogeneous across a time interval of finite duration (Lange, 2013; Näätänen, 1970; Nobre et al., 2007), as it was the case for the standard tone in experiment 1. As a consequence, the hazard rate for the action-effect was low for short SOAs and increased with higher SOAs. It has been shown that the hazard rate influences reaction times, for example, with longer foreperiods decreasing reaction times due to increased certainty of cue presentation (Mo & George, 1977; Näätänen, 1970; Niemi & Näätänen, 1981).

To control for a potential hazard rate and to emphasize the putative effect of a more global prior temporal prediction of action-effects, we implemented an"anti-hazard function". We thereby tested the hypothesis that the lack of sensory attenuation dependent on SOA in experiment 1 was due to complementary effects of action-effect predictability: the decreasing prior expectation of an action effect happening with increasing SOA, on the one hand, and an increasing hazard rate, on the other hand. If true, we would expect to see decreasing perceptual sensory attenuation and agency judgments with increasing SOAs when we homogenize hazard rate over the range of evaluated SOAs, as done in Experiment 2.

## 4.1. Procedure – Experiment 2

The design of the experiment was equal to experiment 1, besides the distributions of SOAs (see Fig. 1). In order to compensate for increasing hazard rates with increasing SOAs, SOAs were presented according to an inverse hazard function with SOAs ranging from 0 to 1378 ms (mean over all trials of the experiment: 522 ms) and smaller SOAs having a higher likelihood to occur.

To calculate the hazard rate, we first established 50 different SOAs, with a minimum of 0 s and a maximum of 1.5 s, by dividing this interval into 50 equally spaced time steps (i.e., SOAs):

$$SOA_i = (i - 1) \times \frac{1500}{(50 - 1)}; i = [1..50]$$

We then calculated the exponential probability density function:

$$expPDF(SOA) = \frac{\frac{1}{SOA} \exp(-\frac{SOA}{SOA})}{\sum_{i=1}^{50} \frac{1}{SOA} \exp(-\frac{SOA_i}{SOA})}$$

For each tone intensity, we presented 72 trials aligned to the expPDF, resulting in 360 trials in total as in experiment 1. The number of 72 trials is a consequence of the fact that for each of the 50 SOA levels only a discrete (integer) number of trials can be presented. To approximate the optimal distribution of trials with regard to the anti-hazard rate (i.e., to achieve a maximally flat hazard rate over a large range of SOAS), we started out with the approximately desired/affordable number of 70 trials per loudness condition and divided these 70 trials according to the 50 fractions of the expPDF. After rounding, the resulting numbers indicate the integer number of trials per SOA according to the expPDF, totaling 72 trials. Since infinitely long intervals are practically not feasible in an experiment the hazard rate increases steeply towards the longest SOAs used. Also, due to the necessary rounding of trial numbers, the hazard rate of tone occurrence is not fully homogeneous for lower SOAs but shows small steps (Fig. 1C). To arrive at a good level of homogeneity, trials with a large interval between keypress and tone (>0.95 s) and therefore HR > 7.14 % were excluded from the analysis. This cutoff was chosen as the heterogeneity of the hazard rate (as described above) led to small local peaks of HR of maximally 7.41 % at earlier SOAs. After exclusion of trials with a SOA > 0.95 s, the HR varied between 3.85 % and 7.41 % (mean = 5.25 %; SD = 0.96 %; Fig. 1C). As in experiment 1, trials were presented in 18 blocks of 20 trials with randomized SOAs per participant.

## 4.2. Analysis – Experiment 2

To examine the effect of SOA on sensory attenuation and to investigate a relationship with the sense of agency in a way equivalent to experiment 1, we first divided the sorted trials across all participants with the different SOAs into four intervals of equal trial numbers (see supplementary information – S2 for a more fine-grained time-resolved approach). These final intervals ranged for interval 1 from 0 to 122 ms, interval 2 from 122 to 306 ms, interval 3 from 306 to 551 ms, and interval 4 from 551 to 949 ms. The remaining analysis was identical to experiment 1. As in Experiment 1 agency judgements were extracted for each participant.

## 4.3. Results – Experiment 2

In experiment 2, as it was already the case in experiment 1, the difference in PSEs between different SOA conditions did not differ significantly from randomized data (minimal p-value: 0.36; Fig. 3; average goodness of fit (R²) for SOA1 = 0.99, SOA2 = 1, SOA3 = 1, SOA4 = 1). The Bayes factors indicated moderate evidence (BFs01 > 3) for the null hypothesis (no effect of SOA on PSE) over the alternative hypothesis (BF10 = 0.18; BF01 = 5.56).

In contrast, agency ratings were significantly modulated by SOA (F(3, 72) = 34.10, p < 0.001, η²p = 0.59; Greenhouse-Geisser corrected), with ratings varying significantly across all pairs of SOAs (maximal p = 0.003, Bonferroni corrected.) and ratings decreasing with longer SOAs (Fig. 2C), as was the case in experiment 1.

Several perceptual phenomena, e.g. attentional modulations, have been reported to vary periodically in time after the occurrence of transient events (Fiebelkorn et al., 2013; Köhler & Weisz, 2023; Landau & Fries, 2012). To rule out that we miss potentially existing
oscillating sensory attenuation as a function of SOA due to coarse temporal binning, we conducted an alternative analysis where we binned SOAs into 30 bins and computed spectral decompositions of PSE and agency ratings (supplementary information – S2). Most importantly, we observed no correlation between PSE and SOA ($p = 0.29$), while a significant negative correlation between agency ratings and SOA was evident ($p < 0.001$). We did observe a 7.5 Hz oscillation in the time course of loudness perception (corrected $p < 0.05$). The time course of agency ratings was not oscillating ($ps > 0.05$ for all frequency bins). This finding is in agreement with the theory of rhythmic attention and perception (e.g., Fiebelkorn et al., 2013). However, as oscillations appeared to be small and as there was no overall increase or decrease in PSEs as a function of SOA, we conclude that these oscillations do not systematically mask sensory attenuation.

## 5. Discussion

We investigated whether known phenomena of sensory attenuation from perceptual, tactile, and EEG studies on temporal action-effect prediction transfer to the auditory modality and if they relate to the sense of agency. We expected that they do transfer and, accordingly, that self-initiated tones are perceived less loudly when presented close in time to the action compared to with larger delays (Bays et al., 2005; Blakemore et al., 1999; Oestreich et al., 2016; Pinheiro et al., 2019; Van Elk et al., 2014). Different from our expectation, we did not observe significant differences in loudness perception (as represented in PSEs) as a function of the delay of auditory action effects. At the same time, agency judgments strongly decreased with increasing SOA in both of our experiments. The lack of a common modulation of both measures points to a dissociation of perceptual sensory attenuation and the sense of agency.

Our findings integrate into a growing body of literature questioning the postulated link between auditory action-effect prediction and sensory attenuation (Cao & Gross, 2015; Kiepe et al., 2024; Morillon et al., 2014; Myers et al., 2020; Reznik et al., 2021; Sato, 2008). In the auditory domain, studies investigating perceptual action-effect prediction have reported mixed results. Studies using a similar paradigm to ours found attenuated perception for self-initiated tones compared to passive stimulation (Sato, 2009; Weiss et al., 2011). In contrast, Cao & Gross (2015) reported a lack of significant differences between actively produced and passive tones. Sato (2008) showed attenuation for tones externally initiated in addition to attenuation for self-generation. Myers et al. (2020) applied a variation of the paradigm, introducing, amongst others, tone congruencies and alternating the order of standard and comparison tones. They found an enhancement in discrimination accuracy for self-initiated tones. Discrimination thresholds were lowest when self-generated tones occurred at the expected (congruent) frequency and highest for the self-generated unexpected (incongruent) frequency. In further experiments, they demonstrated that perceptual judgments were more accurate for active vs passive tones in congruent and incongruent trials, while absolute detection thresholds did not differ in congruent trials, but were higher in active trials for the unexpected frequency. Similarly, Kiepe et al. (2024) observed an enhanced perceptual processing, rather than attenuation, for self-initiated auditory effects. Their study, conducted in an online environment, involved comparing the loudness of two consecutive tones, similar to our experiment. In summary, some previous studies demonstrate that sensory attenuation may not be specific to self-generation of action-effects, but can be absent or even be reversed to an enhancement. This is consistent with the lack of attenuation (PSE) as a function of the latency of self-generated sounds in our data.

A possible explanation could be that sensory attenuation depends on absolute stimulus intensity. Studies on auditory action-effect prediction that tested perceptual sensitivity in detection tasks for near-threshold auditory stimuli instead of mid-level sound intensities suggest dependencies. Enhanced auditory sensitivity towards near-threshold self-generated tones was observed (Reznik et al., 2014, 2015). Similarly, Paraskevoudi & SanMiguel (2021) showed that even though the difference between self-generated versus passive stimuli did not affect detection thresholds in a 2-AFC sound detection task or discrimination sensitivity (JND) in the discrimination task, still a significant interaction between self-generation and intensity on the perceptual bias (i.e., PSE) in the discrimination task was found: Self-generated tones at a suprathreshold level were perceived as softer compared to externally-trigger tones, while self-generated tones at near-threshold intensities were perceived as louder compared to externally-generated tones. A dependency of sensory attenuation from absolute stimulus intensity would further underline that sensory attenuation does not primarily align with self-generation. Based on the findings by Reznik (2014, 2015) and Paraskevoudi & SanMiguel (2021), missing sensory attenuation or enhancement in our experiment should not be caused by an interaction with tone intensity, as tones were presented above the detection threshold.

Also in the tactile domain both reduced (Asimakidou et al., 2022; Bays et al., 2005; Kilteni et al., 2019; Kilteni & Ehrsson, 2022) and enhanced (Thomas et al., 2022, but see Job & Kilteni, 2023) perception of self- vs externally produced effects were reported, with recent literature challenging classical motor theory (Press et al., 2020, 2023; Thomas et al., 2022). However, sensory attenuation appears to be sensitive to the specific sensory modality involved, making direct comparisons between modalities difficult. Previous research underlines the distinction between the tactile and auditory modalities, revealing that temporal prediction is associated with decreased detection performance in the tactile modality while enhancing performance in the auditory modality (Kusnir et al., 2020). These findings indicate that the processes underlying sensory prediction are modality-dependent.

In our experiment, instead of comparing active vs passive trials, we investigated the effect of temporal predictability. Temporal action-effect prediction in audition is more broadly studied in the field of EEG where earlier and larger attenuation of event-related potential responses for effects directly after the action and later and/or less attenuation with increasing delay have been described (Oestreich et al., 2016; Pinheiro et al., 2019a; Van Elk et al., 2014). To our knowledge, little research has been conducted to test the perceptual effects in the auditory domain.

The few studies investigating the effect of temporal action-effect prediction on perception showed ambiguous results, especially when comparing different sensory modalities. In the visual domain, a study by Desantis et al. (2014) studied visual action-effect prediction before action onset until shortly after, using an identification task. Participants exhibited increased instead of decreased
sensitivity closely around the time of action (–220 to 280 ms). In contrast, in the tactile domain, several studies report sensory attenuation as a function of action-effect latency (e.g. Bays et al., 2005, 2006; Blakemore et al., 1999; Kilteni et al., 2019, 2021, 2023; Kilteni & Ehrsson, 2024; Knoetsch & Zimmermann, 2021). For instance, Bays et al. (2005) indicated a reduced perception of taps' force around the action. At a SOA of 300 ms, no attenuation was observed anymore. Blakemore (1999) found that ticklishness ratings increased with increasing delay (significant from 0 ms to 200 ms delay), also suggesting a limited time window of attenuation around the time of action. In contrast to the results from the tactile domain, our results reveal that auditory action-effects may not necessarily be perceptually modulated depending on the temporal distance to the action.

Yet, temporal prediction may be composed of different forms of prediction. A rather global prediction, i.e., a prior (Lange, 2013; Press et al., 2020; Thomas et al., 2022), would most likely lead to an attenuation around the action. Further, the task-specific probability distribution of action-effects may modulate prediction (Lange, 2013; Press et al., 2020; Thomas et al., 2022). This probability consists of the absolute probability of a specific effect and the conditional probability (hazard rate). In experiment 1, in which the absolute probability of SOA is kept equal between all conditions, it may be that enhanced conditional probability of occurrence for latter SOAs leads to a disappearance of the attenuation effect for earlier SOAs. However, other studies that also presented delay trials randomly within blocks, using tactile (Bays et al., 2005; Blakemore, Frith, & Wolpert, 1999) and EEG paradigms (Pinheiro et al., 2019; Van Elk et al., 2014), reported attenuation even without controlling for a potential hazard rate. Further, experiment 2 corroborates the findings of experiment 1, while taking the potential hazard rate into account, showing as well no attenuation effect between different SOAs. Potentially, also the average SOA influences the formation of temporal prediction. However, findings from studies in the tactile modality and EEG studies do not support this hypothesis (Bays et al., 2005; Pinheiro et al., 2019).

A possible reason for the absence of an observable attenuation effect at either SOA could be the non-zero predictability of the comparison tone, i.e., the fact that both tones could in principle be attenuated. Such double-attenuation could mask the effect if attenuation is similarly strong for both tones. We consider this an unlikely explanation for our finding, since the first tone should have been more predictable than the second tone. In our experiment, SOAs varied randomly from trial to trial. While this reduced the predictability of a specific SOA within a trial to a minimum, the finite range of possible SOAs across trials still allowed for a substantial level of predictability of the first tone, with different hazard rates in Experiments 1 and 2. Also, as mentioned above, a general, task-independent prediction of action effects, independent of task-specific SOA anticipation, can be expected (Lange, 2013; Press et al., 2020; Thomas et al., 2022). Both effects should lead to a prediction-associated attenuation around the time of the action, as suggested by EEG results (Pinheiro et al., 2019; Van Elk et al., 2014) and corresponding findings in the tactile modality (Bays et al., 2005; Blakemore et al., 1999). By contrast, the comparison tone, instead, should have been less predictable than the standard tone due to the overall much longer and also randomized interval after the standard tone (1200 – 1600 ms). Even shorter delays of the comparison tone have been shown to result in attenuation of the standard tone in previous research (Weiss et al., 2011).

Additionally, research on visual sensorimotor prediction has revealed that predictions can exhibit both temporal specificity and generality. For instance, Christensen et al. (2011) observed visuospatial enhancement of predicted outcomes with fine spatiotemporal tuning. Conversely, Yon and Press (Yon & Press, 2018) found that motor prediction could enhance the intensity of visual outcomes regardless of an immediate or delayed response. Building upon the evidence presented here, these findings underline the necessity for further research to investigate the impact of temporal action-effect prediction on sensory perception.

Moreover, our control analysis with the data of the second experiment showed that, although small oscillations may have been present in the time course of loudness ratings, oscillations in loudness perception (Köhler & Weisz, 2023) did not systematically mask a potential effect of sensory attenuation because there was no overall correlation between PSEs and SOA.

Our current and other recent findings question the link between action-effect prediction and sensory attenuation. Sensory attenuation does not seem to occur automatically and universally with voluntary actions. This also sheds doubt on the suggested relationship between sensory attenuation and the sense of agency (Press et al., 2023) and, hence, for sensory attenuation as an implicit measure of agency. Since we observed a decreasing sense of agency over SOA without corresponding sensory attenuation, a direct link between sensory attenuation, particularly in auditory loudness perception, and sense of agency cannot be confirmed. Comparing an active versus a passive condition, but otherwise using a similar task, Dewey and Knoblich (Dewey & Knoblich, 2014) also failed to find a correlation between perceptual sensory attenuation in the auditory domain and explicitly reported agency.

In conclusion, we have presented evidence here that perceptual auditory attenuation is not modulated by different latencies of self-initiated action effects. Therefore, findings from studies in the tactile modality and EEG cannot be directly extended to the perception of auditory stimulus intensity (Bays et al., 2005; Blakemore et al., 1999; Oestreich et al., 2016; Pinheiro et al., 2019; Van Elk et al., 2014). Combined with a growing body of literature reporting no sensory attenuation or an enhancement of predicted action effects, sensory attenuation as a necessary correlate of action-effect prediction and as an implicit measure of agency may have to be reconsidered.

CRediT authorship contribution statement

**Elisabeth Lindner**: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Tobias Schober**: Writing – review & editing, Writing – original draft, Visualization, Formal analysis. **Andrea Desantis**: Writing – review & editing, Writing – original draft, Supervision, Resources, Formal analysis, Conceptualization. **Alexander Gail**: Writing – review & editing, Writing – original draft, Supervision, Funding acquisition, Conceptualization.
# Declaration of generative AI and AI-assisted technologies in the writing process

During the preparation of this work, the authors used ChatGPT in order to improve language and readability. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

# Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

# Acknowledgments

We are grateful to Arezoo Pooresmaeili and her group at the European Neuroscience Institute in Göttingen for providing the facility, equipment and support during the course of the experiments. We also extend our thanks to Marcus Jeschke for his support with the artificial ear. Additionally, we thank Lena Radach and Judith Kunze for data collection and Jaime Cadena-Valencia for helpful advice and discussion. This work was supported by the German Research Foundation (DFG) Collaborative Research Consortium CRC-1528 "Cognition of Interaction" and grant TR 447/2-1, and by Agence Nationale de la Recherche, research funding ANR JCJC, project number ANR-18-CE10-0001.

# Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.concog.2025.103837.

# Data availability

Data will be made available on request.

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