{"paper_id":"0d0c56a2-9b46-4fb5-aa69-181bdc0056ea","body_text":"1 Spatial correspondences of Audiovisual Stimuli on Double Flash Illusion \n2 Perception and its Cognitive Modeling\n3\n4 Yabo Zheng1, Lihan Chen1,2,3*\n5 1 School of Psychological and Cognitive Sciences and Beijing Key Laboratory of \n6 Behavior and Mental Health, Peking University \n7 2 National Engineering Laboratory for Big Data Analysis and Applications, Peking \n8 University, Beijing 100871, China\n9 3 Key Laboratory of Machine Perception (Ministry of Education), Peking University, \n10 Beijing 100871, China\n11\n12 Author Note:\n13 We declare no conflict of interest in this research. Data,analysis and modeling scripts \n14 are available at: https://github.com/AbelZheng/SiFI-Spatial-Characteristics.git\n15 Financial Support: STI2030-Major Project (2021ZD0202600) and Natural Science \n16 Foundation of China (T2192932) to L.C.       \n17 *Correspondence author email: CLH@pku.edu.cn  \n18\n19\n20\n21\n22\n23\n24\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n25 Abstract: Perceptual processing integrates information from multiple sensory \n26 modalities to form a coherent representation of the environment. A classic example of \n27 such is the Sound-Induced Flash Illusion (SIFI), where the perceived number of visual \n28 flashes is altered by conflicting auditory stimuli. While the SIFI is a well-established \n29 phenomenon of multisensory integration, the influence of physical spatial \n30 characteristics—specifically stimulus eccentricity and spatial congruence—on \n31 integration levels remains debated.To address this gap, this study used the SIFI \n32 paradigm to investigate the effect of visual stimulus spatial location and the spatial \n33 congruence between auditory and visual stimuli on audiovisual integration. In \n34 Experiments 1 and 2, we found that when spatial attention was controlled via cueing, \n35 unimodal visual performance remained consistent across locations. However, the \n36 susceptibility to SIFI increased progressively from the central to the peripheral visual \n37 field, exhibiting a spatial pattern of Gaussian distribution. Bayesian modeling further \n38 supported this by showing that this spatial modulation was driven by an increase in \n39 the integration weight assigned audiovisual representations in the periphery, rather \n40 than changes in sensory uncertainty alone. Conversely, Experiment 3 demonstrated \n41 that the spatial congruence of audiovisual stimuli did not affect the SIFI or alter the \n42 integration processing. These findings refine our current understanding of the spatial \n43 modulation upon audiovisual integration. By incorporating the visual system's spatial \n44 properties into a Bayesian framework, we provide a computational explanation for the \n45 eccentricity-dependent nature of multisensory integration.\n46 Keywords: Audiovisual integration, Sound-induced flash illusion, spatial modulation, \n47 Bayesian modeling \n48  \n49\n50\n51\n52\n53\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n54 1.Introduction\n55 The environment in which we live is rich with information spanning multiple sensory \n56 modalities. To facilitate efficient interaction with this environment, the brain \n57 adaptively perceives its surroundings by integrating multisensory information (Bauer \n58 et al., 2020). Multisensory integration (MSI) is the process by which an observer \n59 combines information originating from different sensory channels into a coherent and \n60 unified perceptual experience (Stein & Stanford, 2008). This cross-modal integration \n61 enhances an observer's perceptual efficiency and precision, leading to benefits such as \n62 reduced reaction times (Pomper et al., 2014) , heightened stimulus salience (Driver & \n63 Noesselt, 2008), and improved information decoding (Zion Golumbic et al., 2013). \n64 Multisensory integration (MSI) is significantly modulated by visual eccentricity, \n65 operating through a complex interplay of spatial and temporal rules where behavioral \n66 enhancement, such as faster reaction times and increased detection accuracy, is most \n67 robust when stimuli are spatiotemporally congruent (Bruns et al., 2024; Cuppini et al., \n68 2025; Garcia et al., 2017; Porada et al., 2026; Recanzone, 2009). When informational \n69 inputs from different sensory modalities conflict, the brain may erroneously integrate \n70 mismatched stimuli into a unified percept, resulting in cross-sensory perceptual \n71 interference (Sterzer et al., 2009; Wang et al., 2013).As visual eccentricity increases, \n72 the auditory localization bias—known as the ventriloquist effect—progressively \n73 decreases, a phenomenon consistently observed in both neurocomputational models \n74 and empirical data (Cuppini et al., 2025). Other phenomena, such as bistable perception, \n75 serve as quantifiable behavioral indicators of an individual’s multisensory processing \n76 capacity and their tendency to integrate information (Hirst et al., 2020). A paradigmatic \n77 example of this domain is the Sound-Induced Flash Illusion (SIFI), where the high \n78 temporal resolution of the auditory channel distorts visual perception (Shams et al., \n79 2002). This illusion typically manifests as “fission”, where a single flash paired with \n80 multiple beeps is perceived as multiple flashes (Keil, 2020; Keil & Senkowski, 2018), \n81 or “fusion”, where multiple flashes paired with fewer beeps are perceived as a single \n82 flash (McGovern et al., 2014). The susceptibility to these illusions is governed by the \n83 principle of temporal proximity; stimuli are generally integrated only when they fall \n84 within a specific “temporal window of integration” (TWI) (Hirst et al., 2020; Lewald \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n85 & Guski, 2003; Stein et al., 2014; Stein & Meredith, 1993). Furthermore, this \n86 integration process is highly plastic, modulated by factors such as aging (DeLoss et al., \n87 2013), increased cognitive load (Michail & Keil, 2018) and top-down manipulations of \n88 perceptual expectations (Wang et al., 2019), all of which can significantly widen or \n89 narrow the temporal scale of multisensory integration.  \n90  \n91 Theoretical frameworks for multisensory integration have evolved from the directed \n92 attention hypothesis, which emphasizes attentional resource allocation (Welch et al., \n93 1986) but struggles to explain the automatic nature of cross-modal influences \n94 (Odegaard et al., 2016), to the modality appropriateness theory, which posits that \n95 sensory dominance is determined by a modality’s precision for a given task \n96 (Andersen et al., 2004; Hirst et al., 2020; McGovern et al., 2016). \n97 These cognitive models are complemented by computational approaches, such as \n98 maximum likelihood estimation and Bayesian causal inference, which suggest the \n99 brain performs optimal perceptual inferences by weighting sensory reliability and \n100 assessing common signal sources (Ernst & Bulthoff, 2004; Shams & Beierholm, \n101 2010). Physiologically, these processes are supported by neural oscillation \n102 synchronization, where cross-modal communication occurs through phase reset or \n103 neural entrainment (Bauer et al., 2021; Fries, 2015; Lakatos et al., 2019; Senkowski & \n104 Engel, 2024; Thorne & Debener, 2014). Despite these advancements, significant \n105 debate remains regarding the role of spatial characteristics in the Sound-Induced Flash \n106 Illusion (SIFI). While neuroimaging suggests enhanced auditory-visual connectivity \n107 in the peripheral visual field (Eckert et al., 2008; Ghazanfar & Schroeder, 2006; \n108 Rockland & Ojima, 2003), behavioral evidence for this “eccentricity effect” is \n109 inconsistent: several studies report increased SIFI susceptibility in the periphery \n110 (Chen et al., 2017; Shams et al., 2002; Tremblay et al., 2007) , yet others find no such \n111 spatial influence (Gavin et al., 2022), particularly at eccentricities yet to be fully \n112 explored in humans (Falchier et al., 2002). Furthermore, the interaction between \n113 spatial proximity (Stein et al., 2014) and inverse effectiveness (Holmes, 2009) \n114 remains unresolved, as empirical results vary on whether spatial disparity modulates \n115 or has no effect on illusion perception (Aller et al., 2015; Innes-Brown & Crewther, \n116 2009). \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n117\n118 Therefore, the impact of stimulus spatial characteristics on the SIFI remains a pivotal \n119 yet unresolved area of research. Two critical questions persist: whether visual stimuli \n120 at different locations share a uniform susceptibility to auditory integration, and \n121 whether spatial inconsistency diminishes integration levels. While maintaining spatial \n122 stability is fundamental to navigating a multisensory environment (Kording et al., \n123 2007), research on auditory spatial cues in SIFI remains sparse due to the auditory \n124 channel's lower spatial resolution compared to vision (Kumpik et al., 2014). \n125 Furthermore, evidence regarding the interaction between spatial and temporal \n126 characteristics is inconsistent. While most studies suggest an “eccentricity effect”, \n127 some studies found no such influence (Gavin et al., 2022; Shulman et al., 1985). \n128 Previous paradigms often presented stimuli at randomized locations without spatial \n129 cues. Since visual processing efficiency peaks near the central fovea, these studies \n130 may have overlooked the influence of unimodal uncertainty and attentional bias on \n131 the integration process. Therefore, controlling for spatial attention is essential to \n132 isolating the true effect of eccentricity.\n133 This study aims to resolve these discrepancies by systematically investigating the \n134 spatial dimensions of audiovisual integration. The first aim of this research examines \n135 the effect of visual eccentricity on integration capacity: Experiment 1 extends the \n136 parameter range beyond the conventional 10° threshold to map the peripheral visual \n137 field more comprehensively, while Experiment 2 utilizes a wider spatial range \n138 combined with Bayesian cognitive modeling to characterize the underlying \n139 computational mechanisms. The second aim, Experiment 3, explores the role of \n140 audiovisual (in)consistency by comparing the effects of ipsilateral, contralateral, and \n141 binaural auditory stimuli on illusion perception. By synthesizing behavioral data with \n142 computational modeling, this study seeks to delineate how the spatial properties of the \n143 visual system and multisensory processing converge into a coherent cognitive \n144 mechanism. \n145\n146 2. Experiments\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n147 2.1 Experiment 1: Investigating the Effect of Visual Stimulus Spatial Eccentricity \n148 on Audiovisual Integration \n149 This computer-based experiment was designed to replicate the sound-induced flash \n150 illusion (SIFI) and, concurrently, explore whether stimuli presented in the central, \n151 near-peripheral, and far-peripheral visual fields exhibit differential susceptibility to \n152 audiovisual integration. Specifically, we compared the susceptibility of the SIFI \n153 across visual stimulus eccentricities of 0°, 7°, and 21°.\n154 For the conditions most likely to induce the SIFI—the 1 Flash 2 Beeps (1F2B) and 2 \n155 Flashes 1 Beep (2F1B) conditions—six different levels of Stimulus Onset \n156 Asynchrony (SOA) were established: -120 ms, -70 ms, -30 ms, +30 ms, +70 ms, and \n157 +120 ms. As illustrated in Figure 1, the sign of the SOA represents the relative \n158 temporal order: a negative sign indicates the unimodal stimulus (e.g., flash in 1F2B) \n159 preceded the audiovisual pair, while a positive sign indicates it followed. This \n160 experiment also served as a preliminary study for parameter refinement during the \n161 research process.\n162 Based on previous research on visual stimulus spatial eccentricity and corresponding \n163 neuroanatomical evidence (Chen et al., 2017; Falchier et al., 2002; Gavin et al., 2022; \n164 Shams et al., 2002; Tremblay et al., 2007), the following hypotheses were formulated: \n165 First, the SIFI phenomenon, particularly the fission illusion (where the number of \n166 auditory stimuli exceeds the number of flashes), would be reliably replicated across \n167 the participant sample, leading to a significant decrease in the correct perception rate. \n168 Second, stimuli presented at different spatial locations would exhibit different levels \n169 of audiovisual integration; specifically, the 7°and 0°eccentricities (within \n170 approximately 10°) would show no significant difference, while the more peripheral  \n171 21°eccentricity would be more susceptible to the illusion, consequently yielding a \n172 lower reported accuracy rate from participants. \n173 Participants\n174 Fifteen university students were recruited. Following preliminary parameter \n175 adjustments and accuracy-based screening, nine valid participants (5 female; mean \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n176 age = 20.44, SD = 1.01) were included in the final analysis. All participants reported \n177 normal or corrected-to-normal vision and hearing, were naïve to the purpose of the \n178 experiment, and were right-handed. Each participant received a monetary \n179 compensation of ¥80 upon completion. All participants provided written informed \n180 consent prior to the experiment and received compensation upon completion. The \n181 study protocol (with approved No.# 2021-10-18) was approved by the Academic \n182 Affairs Committee of the School of Psychological and Cognitive Sciences at Peking \n183 University. The above protocol was also applied to the following Experiments 2 and \n184 3. \n185 Apparatus and Stimuli\n186 Experiments were conducted in a dimly lit, sound-attenuated laboratory. Visual \n187 stimuli were presented on a 27-inch monitor (1920 × 1080 resolution, 144 Hz refresh \n188 rate) positioned 60 cm from the participant. The visual target was a white disk (1° \n189 radius), and the spatial cue was a white square frame (2° side length). Auditory \n190 stimuli (10 ms pure tone, 3000 Hz) were presented via headphones using a sound card \n191 with a 96 kHz sampling rate. The experiment was implemented via PsychToolbox-3 \n192 (Brainard, 1997; Kleiner M et al., 2007; Pelli, 1997).\n193 Experimental Design\n194 The experiment employed a within-subjects design based on the classic SIFI \n195 paradigm. The independent variables were stimulus onset asynchrony (SOA, six \n196 levels: ±30, ±70, ±120 ms) and visual eccentricity (five levels: -21°, -7°, 0°, \n197 7°, 21°). The dependent variables were response accuracy (proportion of correct \n198 flash reports) and reaction time (RT).\n199 Experimental Procedure\n200 A strict training protocol ensured task comprehension. Participants completed practice \n201 trials with feedback and proceeded to the main experiment only after achieving >90% \n202 accuracy. To prevent fatigue, breaks were mandated every 40 trials. As shown in \n203 Figure 1, each trial began with a fixation cross (1000 ms), followed by a spatial cue \n204 (white frame, 500 ms) appearing at one of the five locations to distinctively guide \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n205 spatial attention. After a 500 ms gap, the target flash (33 ms) appeared at the cued \n206 location. In audiovisual trials, 10 ms beeps (3500 Hz) accompanied the flashes. A red \n207 fixation would appear to prompt participants to report the perceived number of flashes \n208 via keypress (“Z” or “M”, counterbalanced) within 3 seconds.\n209\n210\n211\n212 Figure 1. Experimental procedure . Left: task flow of each trial. Visual stimuli are \n213 presented at a specific location, while auditory stimuli are delivered binaurally \n214 through headphones. Top Right: A schematic showing all possible stimulus locations, \n215 example stimuli, and their relative size relationships. In each trial, the cue and the disk \n216 (flash) appear at only one specific location. Bottom Right: The temporal sequencesfor \n217 a 1F2B (1 Flash, 2 Beeps) trial. This demonstrates the temporal relationship between \n218 stimuli under positive and negative SOA. One pair of audiovisual stimuli is always \n219 synchronized to begin simultaneously. \n220\n221 Across all trials, excluding the attention check trials (which involved the cue frame \n222 but no flash), participants viewed 1 or 2 flashes, accompanied by 0, 1, or 2 auditory \n223 stimuli, leading to the 9 combination conditions detailed in Table 1. The core \n224 conditions of interest for investigating the SIFI were 1F2B and 2F1B (where F \n225 denotes the number of flashes and B denotes the number of beeps), which required the \n226 manipulation of the Stimulus Onset Asynchrony (SOA). Specifically, the 1F2B and \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n227 2F1B conditions consisted of 12 trials for each combination of the 5 eccentricity \n228 levels and 6 SOA levels, totaling 720 trials, which constituted 65% of the total \n229 experiment.\n230 Table 1.  Experiment 1: Trial Distribution\nNumber of auditory stimuli\n0 1 2 Sum\n0 50 15 15 80\n1 50 100 360 510\nNumber of\nflashes\n2 50 360 100 510\n231\n232  \n233 The formal experiment comprised a total of 1100 trials, requiring approximately 80 \n234 minutes to complete. Participants were instructed to take a minimum one-minute rest \n235 after every 50 trials before pressing a key to continue.  \n236 Data Analysis\n237 The collected response data from all participants were aggregated, and the correct \n238 response rates for various conditions were calculated. A repeated-measures Analysis \n239 of Variance (ANOVA) was employed for comparisons across levels. It is important to \n240 note that the experimental design intentionally oversampled the 1F2B and 2F1B \n241 conditions by including more SOA levels, leading to an inherently unbalanced trial \n242 distribution.\n243 To ensure a more precise analysis of this data, fully gather evidence supporting all \n244 observable effects, and mitigate potential biases arising from the asymmetry between \n245 the null and alternative hypotheses (Dienes, 2014), the Bayes Factor analysis method \n246 was additionally utilized via JASP software(JASP, 2023). For all Bayesian ANOVAs, \n247 the default JASP settings were applied, with the prior r scales for fixed effects, \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n248 random effects, and covariates set to 0.5, 1 and 0.354, respectively. The interpretation \n249 of Bayes Factor values followed the guidelines of Dienes (2014): values greater than \n250 3 represent strong evidence for the alternative hypothesis (𝐻1); values between 1 and \n251 3 indicate anecdotal support for H1; values between 0.3 and 1 suggest anecdotal \n252 support for the null hypothesis (𝐻0); and values less than 0.3 denote strong evidence \n253 for 𝐻0. This approach quantified the relative likelihood of the data under both 𝐻0 \n254 and 𝐻1, effectively addressing issues related to the unbalanced design and testing \n255 biases (Dienes, 2014). \n256 The accuracy rates under different conditions are shown in Figure 2. A two-way \n257 repeated-measures ANOVA was conducted on the accuracy rates, with Bonferroni \n258 correction applied for post-hoc tests. Both the auditory stimulus and the audiovisual \n259 interaction passed Mauchly's test of sphericity (auditory stimulus: χ² = 2.269, p = \n260 0.322; interaction: χ² = 3.361, p = 0.186). \n261\n262 Figure 2. Violin Plots of Participant Report Accuracy Across Conditions in \n263 Experiment 1. The width of the violin plot represents the probability density \n264 distribution of the data. Each individual dot represents the data point of a single \n265 participant under the corresponding condition. The horizontal lines within the violin \n266 plots indicate the upper quartile, median, and lower quartile of the data, respectively. \n267 * denotes p<.05, ** denotes p<.01, *** denotes p<.001. \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n268 The ANOVA results revealed a significant main effect of the number of flashes on \n269 participants' response accuracy,  F(1,8) = 14.067, 𝑝 = 0.006, 𝜂2\np = 0.637, 𝐵𝐹10\n270 = 8.012. Participants' accuracy in perceiving two flashes was significantly higher, \n271 |MD| = 0.047, p = 0.006, BF₁₀ = 55.529. The number of auditory stimuli also had a \n272 significant effect on response accuracy,  F(2,16) = 11.421, p < 0.001, 𝜂2\np = 0.588, \n273 BF₁₀ = 3.704. Under the condition of one auditory stimulus, participants' response \n274 accuracy was significantly higher than with two stimuli (|MD| = 0.040, p < 0.001, \n275 BF₁₀ = 21.489) and with no auditory interference (|MD| = 0.024, p = 0.038, BF₁₀ = \n276 8.012). \n277 The interaction between the two factors was also significant,  F(2,16) = 6.083, p = \n278 0.011, 𝜂2\np= 0.432, BF₁₀ = 93.434. Simple main effects analysis was conducted, \n279 focusing on whether the number of auditory stimuli had different effects under each \n280 flash condition. When there was one flash, the simple main effect of sound stimuli \n281 was significant,  F(2,16) = 20.792, p < 0.001, BF₁₀  = 83.776. The difference between \n282 0B and 1B was not significant, |MD| = 0.027, p = 1.000, BF₁₀ = 0.900. However, \n283 accuracy under 0B was significantly higher than under 2B, |MD| = 0.050, p = 0.024, \n284 BF₁₀ = 1.985. Accuracy under 1B was also significantly higher than under 2B, |MD| \n285 = 0.076, p < 0.001, BF₁₀ = 111.291. This indicates a clear flash fission illusion: when \n286 the number of sound stimuli exceeded the actual number of flashes, participants' \n287 subjective reports of the number of flashes also increased. \n288 When there were two flashes, the number of auditory stimuli had no significant effect \n289 on accuracy,  F(2,16) = 1.712, p = 0.212, BF₁₀  = 0.928. Under two flashes, \n290 participants' reported accuracy was high across different numbers of auditory stimuli, \n291 and no significant flash fusion illusion was observed.\n292 Focusing further on participants’ accuracy when a single flash was presented at \n293 different eccentricities, we conducted a two-way repeated-measures ANOVA with \n294 factors of eccentricity and number of auditory stimuli. The interaction between \n295 eccentricity and auditory number violated sphericity (χ²₃₅ = 100.573, p < 0.001), so \n296 degrees of freedom were adjusted with the Greenhouse–Geisser correction. \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n297 As shown in Figure 3, the main effect of spatial eccentricity was significant, F(4,32)= \n298 9.342, p < 0.001, 𝜂2\np = 0.539, BF₁₀  = 85.524. Accuracy at 21° in both hemifields was \n299 lower than in central vision (left 21°: |MD| = 0.055, p = 0.004, BF₁₀ = 170.112; right \n300 21°: |MD| = 0.070, p < 0.001, BF₁₀ = 489.405). In addition, accuracy differed \n301 between 7° and 21° in both hemifields (left: |MD| = 0.045, p = 0.028, BF₁₀ = 9.183; \n302 right: |MD| = 0.049, p = 0.013, BF₁₀ = 10.061), whereas performance at 7° did not \n303 differ from central vision. The main effect of auditory-stimulus number was also \n304 significant, F(2,16) = 10.622, p = 0.001, 𝜂2\np = 0.570, BF₁₀  = 29.283. The \n305 eccentricity × auditory-number interaction was not significant after correction, \n306 F(3.504,28.035) = 1.583, p = 0.211, 𝜂2\np = 0.165, BF₁₀  = 0.882.  \n307\n308 Figure 3. Response accuracy across conditions for trials with a single flash in \n309 Experiment 1. Different colored lines represent different numbers of auditory stimuli. \n310 Error bars indicate one standard error (SE). * denotes p<.05, ** denotes p <.01, *** \n311 denotes p <.001.\n312\n313 Simple-main-effect analyses examined whether the eccentricity profile was equivalent \n314 across auditory conditions. Without auditory distractors, eccentricity had no \n315 significant impact on accuracy, F(4,32) = 1.332, p = 0.280, BF₁₀  = 0.330. In contrast, \n316 when one or two auditory stimuli were presented, eccentricity strongly modulated \n317 accuracy (1B: F(4,32)= 8.630, p < 0.001, BF₁₀ = 623.599; 2B: F(4,32)= 10.217, p < \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n318 0.001, BF₁₀ = 1 093.603). Thus, no reliable eccentricity effect emerged in the \n319 unimodal visual task, whereas introducing auditory stimuli in a cross-modal setting \n320 revealed marked performance differences between peripheral and peri-foveal \n321 locations.\n322 Prior analyses confirmed the presence of sound-induced flash illusions and showed \n323 that the spatial position of visual stimuli modulates audiovisual integration. \n324 Temporal alignment is also critical, as the inter-stimulus interval systematically \n325 shapes susceptibility to the SIFI. We therefore investigated whether the impact of \n326 spatial eccentricity varies across temporal contexts—specifically, whether a space–\n327 time interaction exists. \n328 Figure 4 illustrates performance in fission-illusion trials (F1B2) as a function of SOA \n329 and eccentricity.  \n330\n331\n332 Figure 4. Response accuracy in the fission illusion condition (1F2B) across different \n333 SOAs. Different colored lines represent the various spatial locations of the visual \n334 stimuli. Error bars indicate one standard error (SE). * denotes p <.05, ** denotes p \n335 <.01, *** denotes p <.001 \n336 A two-way repeated-measures ANOVA (eccentricity × SOA) revealed significant \n337 main effects of both eccentricity, F(4,32) = 10.217, p< 0.001, 𝜂2\np = 0.561, BF₁₀  = \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n338 17.954, replicating earlier findings, and SOA, F(5,40) = 8.078, p< 0.001, ηp² = 0.502, \n339 BF₁₀ = 182.648. Contrary to the expectation that shorter SOAs should promote \n340 stronger integration, accuracy at |SOA| = 30 ms was significantly higher than at |SOA| \n341 = 70 ms (p< 0.01), with no other pairwise SOA comparisons reaching significance. \n342 Additionally, a significant eccentricity × SOA interaction emerged, F(20,160) = \n343 2.233, p = 0.003, 𝜂2\np = 0.218, BF₁₀  = 67.643.\n344 Simple-main-effect analyses revealed that eccentricity reliably influenced \n345 performance exclusively within the SOA = –70 ms and +70 ms windows (–70 ms: \n346 F(4,32) = 5.372, p = 0.002, BF₁₀  = 42.601; +70 ms: F(4,32) = 4.368, p = 0.006, BF₁₀  \n347 = 10.316). These are precisely the SOAs that maximized illusion susceptibility. Thus, \n348 when auditory and visual signals are temporally discrepant yet still integrated, the \n349 spatial location of the visual event determines the strength of that integration. At \n350 SOAs that are too brief or too prolonged—conditions in which observers appear \n351 largely immune to auditory influence—the modulatory effect of spatial position \n352 disappears.\n353 Discussion  \n354 We successfully replicated the fission illusion (Shams et al., 2002) and extended the \n355 findings to the spatial domain. Our results demonstrate that while SIFI susceptibility \n356 is stable within the central 10°, it significantly increases in the far periphery (21°). \n357 Importantly, by using pre-cues to equate spatial attention, we ruled out the possibility \n358 that this effect stems from reduced peripheral attention or visual acuity. \n359 These findings partially align with earlier work showing stronger SIFI at peripheral \n360 locations (Chen et al., 2017; Shams et al., 2002; Tremblay et al., 2007). First, \n361 previous studies sampled only ≤ 10° eccentricity and reported marginal or null \n362 differences; we likewise found no change between 0° and 7°, consistent with Gavin et \n363 al. (2022). Second, by extending the spatial span to 21°, we reveal a steep increase in \n364 illusion susceptibility, while unimodal visual sensitivity remains unchanged. \n365 Audiovisual integration therefore exhibits a distinctive spatial signature, suggesting \n366 that visual input from different spatial locations deploy different integration strategies \n367 or weighting schemes. \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n368 Our results deviate from the assumption that decreasing SOAs monotonically increase \n369 illusion strength. At ±30 ms, accuracy was significantly high—exceeding baseline \n370 levels—suggesting facilitation over fission. This suggests that when auditory stimuli \n371 are too close in time, they may be perceptually fused or fall within a single cycle of \n372 neural oscillation, failing to trigger the “two-beep” induced fission (Fiebelkorn & \n373 Kastner, 2019).\n374\n375 Taken together, the results broaden the known spatial landscape of the SIFI. But we \n376 still cannot adjudicate between two mechanistic accounts: (a) greater visual \n377 uncertainty in the periphery biases the brain’s optimal estimate toward the auditory \n378 count (Shams & Beierholm, 2010), and (b) stronger direct connectivity between \n379 auditory cortex and the peripheral representation of early visual cortex (Eckert et al., \n380 2008) gives auditory input heavier weight. To further disentangle whether this spatial \n381 effect arises from sensory uncertainty or integration weights, Experiment 2 will \n382 expand the eccentricity range and employ Bayesian modeling. \n383 2.2 Experiment 2: Extended Spatial-Eccentricity for SIFI with Hierarchical \n384 Bayesian Modelling \n385 Building on the previous findings, we exploited a 360° acoustic arena to sample \n386 observer performance in the SIFI paradigm at five eccentricities (0°, 15°, 30°, 45°, \n387 60°; 15° steps). Using hierarchical Bayesian modelling anchored in the classical \n388 causal-inference framework (Shams et al., 2006; Shams & Beierholm, 2010), we \n389 compared two families of models: (1) a “visual-uncertainty” family that assumes \n390 fixed AVI weights but allows visual likelihood variance to increase with eccentricity, \n391 and (2) an “AV-weight” family that keeps likelihood variance constant while letting \n392 the prior weight assigned to the common-cause hypothesis vary with retinal location.\n393 At the behavioral level, we predict that across the 0–60° eccentricity range, visual \n394 accuracy will decline and reports will become increasingly biased by the number of \n395 auditory beeps, while performance on unimodal (flash-only) and congruent \n396 audiovisual trials remains invariant. Computationally, if the uncertainty model family \n397 provides a superior fit, it would favor the classic view that audiovisual integration \n398 (AVI) computations are spatially identical, with performance deficits driven solely by \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n399 increased peripheral visual noise; however, a superior fit for the AV-weight family \n400 would align with neuroanatomical evidence (Eckert et al., 2008; Falchier et al., 2002; \n401 Rockland & Ojima, 2003), suggesting that different retinotopic loci possess intrinsic \n402 susceptibilities to auditory influence, modeled as location-specific prior weights \n403 within a Bayesian causal-inference framework. \n404 Participants  \n405 Thirteen undergraduate students took part in the experiment. After applying an \n406 accuracy criterion, data from eleven participants (six female) were retained. \n407 Participants’ ages were ranged from 19 to 22 years (M = 20.27, SD = 1.01). All \n408 participants had normal hearing and normal or corrected-to-normal vision, were right-\n409 handed, and had no prior experience with similar experiments. Each participant \n410 received 80 RMB in cash after the session.\n411 Apparatus and stimuli  \n412 The experiment was conducted in a single, well-ventilated laboratory under dim \n413 ambient lighting. As shown in Figure 5 (left), participants performed the computer-\n414 based task on a 1.4-m-radius curved “audio-screen” display (resolution 1920 × 1080, \n415 refresh rate 60 Hz). Sounds were delivered via a sound card sampled at 44.1 kHz and \n416 presented through closed-back monitor headphones worn throughout the experiment. \n417 Visual stimuli were white, Gaussian-ramped disks (Figure 5, right) chosen to \n418 minimise sharp-edge after-effects (Stiles et al., 2020). A white square frame (4° × 4°) \n419 served as the location cue. With the viewing distance fixed at 1.4 m by a chin-rest, the \n420 disk subtended 2° of visual angle. Auditory stimuli were 10-ms pure tones at 2000 \n421 Hz. Participants responded using three keyboard keys (“Z”, “?/” and spacebar) while \n422 maintaining a stable head position.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n423\n424 Figure 5. Experimental Scene and Stimulus Examples for Experiment 2. Left: An \n425 illustration of the laboratory setting. The screen displays all possible locations for \n426 stimulus presentation; however, during an actual trial, the flash appears at only one \n427 specific location. Right: The gradient disk stimuli used in Experiments 2 and 3, which \n428 feature logarithmic decay along the axial direction. \n429 Design and Procedure  \n430 As in Experiment 1, flashes were delivered at different spatial locations while the \n431 number of accompanying beeps varied. The critical independent variable was visual \n432 eccentricity, with nine levels: −60°, −45°, −30°, −15°, 0°, 15°, 30°, 45°, and 60°. \n433 Because we focused on spatial rather than temporal properties of audiovisual \n434 integration, SOA was not factorially manipulated; instead, only two SOAs—40 ms \n435 (“short”) and 70 ms (“long”)—were used for the single-channel continuation stimuli \n436 in both fission (more beeps than flashes) and fusion (more flashes than beeps) blocks. \n437 Whenever both modalities were stimulated, the first audiovisual pair was always \n438 presented simultaneously; subsequent unimodal stimuli followed at the designated \n439 SOA. \n440 The stimulus set was expanded (0-3 flashes; 0-2 beeps) to increase difficulty and \n441 discourage response bias. Three-flash trials were used as a quality control measure, \n442 with a 50% accuracy threshold for participant exclusion. As shown in Table 2, the \n443 primary fission and fusion conditions consisted of 12 trials per SOA and eccentricity \n444 level. These were embedded within a total of 1,150 trials. To manage fatigue, \n445 participants took mandatory breaks for at least one minute every 80 trials. Total \n446 experimental duration was approximately 90 minutes.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n447 Table 2. Experiment 2: Trial Distribution \nNumber of auditory stimuli\n0 1 2 Sum\n0 (No.of auditory stimuli is random) 43\n1 90 135 216 441\n2 90 216 135 441\nNumber of \nFlash\n \n3 45 90 90 225\n448  \n449 Procedure  \n450 The task closely followed Experiment 1. After stimulus offset, an “X” appeared at the \n451 bottom of the screen to signal the response window; the deadline was shortened to 2.5 \n452 s and the inter-trial interval to 0.75 s to reduce overall duration. Participants pressed \n453 “Z” or “?/” to report “1” or “2” flashes (key mapping counter-balanced across \n454 subjects); the space-bar was used for trials containing three flashes. All other \n455 procedural details were identical to Experiment 1. \n456 Data analysis  \n457 Responses were pooled and the mean reported number of flashes calculated for each \n458 condition. Repeated-measures ANOVAs were used for factorial comparisons. To \n459 mitigate the imbalance in trial counts, Bayesian factors were again computed with \n460 JASP (JASP Team, 2023).\n461 Figure 6 shows the mean reported flashes. \n462\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n463\n464 Figure 6. Violin Plots of Participant Response Accuracy Across Conditions in \n465 Experiment 2. The width of each violin plot represents the probability density \n466 distribution of the data. Individual dots represent data points for each participant \n467 within that specific condition. The horizontal lines within the violin plots denote the \n468 upper quartile, median, and lower quartile of the data. * p<.05, ** p<.01, *** p<.001\n469\n470 A 2 (target flashes: 1 vs. 2) × 3 (auditory beeps: 0, 1, 2) within-subjects ANOVA \n471 analysis revealed significant main effects of both flashes and beeps, with no \n472 interaction between them. For flashes, participants reported significantly more flashes \n473 when two were presented compared to one (F(1, 10) = 156.11, p < .001, ηp² = .940, \n474 BF₁₀ = 1.24 × 10⁵), with a mean difference of 0.563 (p < .001, BF₁₀ = 2.20 × 10¹⁴). \n475 For beeps, there was a significant main effect (F(2, 20) = 42.11, p < .001, ηp² = .808, \n476 BF₁₀ = 2.41 × 10⁵), where two beeps increased flash reports relative to both zero \n477 beeps (|MD| = 0.426, p < .001, BF₁₀ = 5.29 × 10⁶) and one beep (|MD| = 0.353, p \n478 < .001, BF₁₀ = 5.33 × 10⁴). However, the interaction between flashes and beeps was \n479 not significant (F(2, 20) = 0.83, p = .450, ηp² = .077, BF₁₀ = 0.321), indicating that \n480 the effect of flashes was consistent across beep conditions.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n481 Bonferroni-corrected post-hoc tests (Figure 6) confirmed the fission illusion: for 1-\n482 flash trials, 0B ≈ 1B (|MD| = 0.115, p = .946, BF₁₀ = 8.66), but 2B > 1B > 0B (all ps \n483 < .001). For 2-flash trials, 2B again produced higher reports than 1B or 0B (|MD|s ≥ \n484 0.367, ps < .001). No reliable fusion illusion was observed; instead, two beeps \n485 generally increased flash reports, consistent with cross-modal summation. All \n486 subsequent analyses therefore focus on 1-flash trials to characterise the spatial profile \n487 of fission. \n488 Focusing again on 1-flash trials, we submitted accuracy to a 2-way repeated-measures \n489 ANOVA with factors Auditory Level (0B, 1B, 2B) and Eccentricity (−60° to +60° in \n490 15° steps). Both factors passed Mauchly’s test (auditory: χ²₂ = 5.296, p = .071; \n491 eccentricity: χ²₃₅ = 33.423, p = .663).\n492 The results demonstrated significant main effects of auditory beeps and eccentricity, \n493 as well as a significant interaction between them. For auditory level, the characteristic \n494 fission pattern is dominant (F(2, 20) = 38.42, p < .001, ηp² = .367, BF₁₀ = 7.99 × 10⁴), \n495 with two beeps eliciting more flash reports than both one beep and zero beeps (all ps \n496 < .001), which did not differ significantly. Eccentricity also significantly affected \n497 reports (F(8, 80) = 8.86, p < .001, ηp² = .112, BF₁₀ = 4.10 × 10⁴): central vision (0°) \n498 yielded lower (more accurate) reports than every peripheral location (ps < .05), and \n499 right 15° produced lower reports than right 45° (|MD| = 0.214, p = .006, BF₁₀ = 71.16 \n500 (Figure 7). Critically, the auditory × eccentricity interaction was significant (F(16, \n501 160) = 3.17, p < .001, ηp² = .072, BF₁₀ = 1.43 × 10³). Simple-main-effect analyses \n502 revealed that eccentricity had no effect in the unimodal visual condition (0B: F(8, 80) \n503 = 1.52, p = .163, BF₁₀ = 0.37) and only a marginal effect in the congruent audiovisual \n504 condition (1B: F(8, 80) = 1.96, p = .062, BF₁₀ = 0.999). However, in the conflict \n505 condition (2B), a strong eccentricity effect was observed (F(8, 80) = 18.18, p < .001, \n506 BF₁₀ = 5.39 × 10⁷), where reports approached the veridical count of one flash only in \n507 central vision, while all peripheral locations showed significantly more reports of \n508 flashes, indicating stronger fission illusions in the visual periphery.\n509  \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n510\n511 Figure 7. Mean reported number of stimuli for single target-flash trials across \n512 auditory conditions in Experiment 2. Different colored lines represent different \n513 numbers of auditory stimuli. Error bars indicate one standard error of the mean \n514 (SEM). * denotes p<.05, ** denotes p<.01, *** denotes p<.001. \n515\n516 Together with Experiment 1, these findings confirm that when attention is largely \n517 equated across the visual field, unisensory visual perception is spatially flat, whereas \n518 multisensory processing—especially under audiovisual conflict—is sharply \n519 modulated by retinal eccentricity.\n520 In the 1F2B condition, we used two SOAs: 40 ms and 70 ms. To test whether spatial \n521 eccentricity interacts with temporal context, we compared performance across \n522 eccentricity and SOA. Because the target was always one flash and the distractors \n523 always two beeps, accuracy and reported count are perfectly inversely related, and \n524 Figure 8 shows that accuracy follows an inverted Gaussian profile across space. We \n525 therefore used hit-rate as the metric and assumed a Gaussian relationship between \n526 eccentricity x and P(hit): \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n527 𝑃(𝐻𝑖𝑡) = 𝐴 ∗  𝑒\n―(𝑥―𝜇)2\n2𝜎2\n528 Data for each SOA were fitted separately; the two SOAs were also collapsed to obtain \n529 an average curve. Adjusted R² was computed for each model. Table 3 summarises the \n530 parameters. In all cases, the Gaussian described the data well (adjusted R² > .94) and \n531 the curves for 40 ms and 70 ms were almost superimposable. Thus, univariate \n532 accuracy can be characterised by a central-peaked Gaussian that declines toward the \n533 periphery. What remains unknown is whether this spatial gradient reflects auditory \n534 interference or merely weaker unisensory vision in the periphery; the modelling \n535 analyses that follow will address this question. \n536 Table 3 Table of Gaussian Curve Fitting Parameters for Response Accuracy in 1F2B \n537 Trials\n538\nAmplitude 𝐴 Mean 𝜇\nStandard \ndeviation 𝜎\nGoodness of fit \n𝑅2\nSOA = 40 ms 0.682 -4.046 33.630 0.933\nSOA = 70 ms 0.676 -1.414 33.748 0.903\nMean 0.678 -2.739 33.748 0.922\n539\n540 The hit-rates for the two SOA conditions, together with the collapsed data and their \n541 fitted Gaussian curves, are plotted in Figure 8. Accuracy was virtually identical at 40 \n542 ms and 70 ms, with no discernible separation. A 9 (eccentricity) × 2 (SOA) repeated-\n543 measures ANOVA confirmed a significant main effect of eccentricity, F(8, 80) = \n544 18.18, p < .001, ηp² = .645, BF₁₀ = 1.73 × 10¹², replicating the previous analysis, but \n545 neither a significant main effect of SOA, F(1, 10) = 0.14, p = .895, ηp² < .001, BF₁₀ = \n546 0.24, nor a significant eccentricity × SOA interaction, F(8, 80) = 0.72, p= .671, ηp² \n547 = .007, BF₁₀ = 0.09.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n548\n549 Figure 8. Participant response accuracy across eccentricities in the 1F2B condition of \n550 Experiment 2. Different colored lines represent various SOA conditions and the grand \n551 average of the data; error bars indicate one standard error (SE). \n552\n553 Thus, within the two SOAs tested, audiovisual integration was unaffected by temporal \n554 separation. Given we focuses on spatial rather than temporal characteristics, the 40-\n555 ms and 70-ms data were pooled for all subsequent modelling analyses.\n556 Bayesian modelling \n557 The findings from Experiments 1 and 2 demonstrate that the spatial location of visual \n558 stimuli significantly modulates SIFI perception, suggesting that different regions of \n559 the visual field may utilize distinct audiovisual integration mechanisms. Integrating \n560 modality reliability theory with the modeling framework established by Hirst et al. \n561 (2020)(Hirst et al., 2020), we propose two hypotheses to account for this spatial \n562 variation in multisensory capacity. \n563\n564 First, The Spatial Weighting Hypothesis. The direct cross-modal influence of auditory \n565 stimulation may have a greater impact in the peripheral visual field, resulting in \n566 greater informational weight being assigned to the auditory modality during the \n567 integration process. Combined with responses that integrate auditory information, this \n568 makes illusory perception more likely to occur. \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n569 Second, the Visual Uncertainty Hypothesis: This account posits that the increase in \n570 illusory percepts in the periphery is a direct consequence of reduced visual reliability. \n571 As visual acuity declines with eccentricity, the uncertainty surrounding visual \n572 numerosity perception increases. Within a Bayesian framework, the brain compensates \n573 for this unreliable visual signal by relying more heavily on the relatively more precise \n574 auditory information, leading to the perception of the sound-induced flash illusion. \n575 To investigate which mechanism better supports the current findings, we implemented \n576 Bayesian modeling to perform hierarchical inference about internal cognitive \n577 processes (Van De Schoot et al., 2021). We used PyMC5, a Python library for \n578 probabilistic programming that offers extensive choices of prior and posterior \n579 distributions, for model construction and comparison, and implemented algorithms \n580 such as Markov Chain Monte Carlo (MCMC) for posterior sampling (Abril-Pla et al., \n581 2023). \n582 Following the Bayesian ideal observer model (Shams & Beierholm, 2010), we model \n583 perceived numerosity as a weighted combination of auditory and visual information. \n584 Sensory inputs are treated as probability distributions; when signals originate from the \n585 same source, their likelihoods are multiplied to create a joint audiovisual \n586 representation. The observer then forms a final perceptual estimate by calculating the \n587 precision-weighted average of the individual sensory channels and the integrated \n588 likelihood. This approach ensures that the resulting percept is a reliable inference \n589 based on the relative uncertainty of each modality. \n590 Mathematically, this process can be described as follows: when an observer forms a \n591 perceptual representation 𝑆𝑣 of visual information based on received audiovisual \n592 sensory information x𝑣 and xa, the following occurs: \n593 First, if the observer believes that visual and auditory stimuli originate from different \n594 sources (C = 2, where C represents causal structure, i.e., the number of sources), and \n595 can independently receive information from both modalities, the sensory information \n596 received through each modality is, due to the presence of noise, essentially \n597 represented as Gaussian distributions. The means 𝜇𝑣 and 𝜇𝑎 represent individual \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n598 subjective estimates, while standard deviations 𝜎v and 𝜎a represent the uncertainty \n599 of unisensory information:\n600              \n601 p x𝑣│𝐶 = 2 = 1\n2𝜋\n𝑒\n―(x𝑣―𝜇𝑣)\n2𝜎2\n𝑣\n2\n602 p 𝑥𝑎│𝐶 = 2 = 1\n2𝜋\n𝑒\n―(𝑥𝑎―𝜇a)\n2𝜎2\n𝑎\n2\n603 When an individual cannot completely separate auditory and visual stimuli in \n604 perception, integration occurs. In this case, the observer believes that the audiovisual \n605 stimuli originate from the same source (C = 1), and subsequently forms a unified \n606 representational estimate of the audiovisual stimuli. Computationally, this audiovisual \n607 representation xav is obtained by multiplying the likelihood functions of the \n608 unisensory auditory and visual channels, and the result is also a Gaussian distribution:\n609 p(𝑥𝑎𝑣|𝐶 = 1) ~ 𝑝(𝑥𝑣|𝐶 = 2) ×  p 𝑥𝑎│𝐶 = 2\n610 p(𝑥𝑎𝑣|𝐶 = 1) =  1\n2𝜋\n𝑒\n―(𝑥𝑎𝑣―𝜇𝑎𝑣)\n2𝜎2\n𝑎𝑣\n2\n611 Here, both the mean 𝜇𝑎𝑣 and standard deviation  𝜎av of the audiovisual stimulus \n612 estimate can be expressed in terms of the distribution parameters of the unisensory \n613 stimuli:\n614\n615\n𝜇𝑎𝑣 = 𝜇𝑣𝜎2\n𝑣 + 𝜇𝑎𝜎2\n𝑎\n𝜎2\n𝑣 + 𝜎2\n𝑎\n𝜎2\n𝑎𝑣 = 𝜎2\n𝑣𝜎2\n𝑎\n𝜎2\n𝑣 + 𝜎2\n𝑎\n616\n617 When making perceptual decisions, according to Bayes' formula, individuals will \n618 form weighted averages of the unisensory inference 𝑆𝑣,𝐶=2  and the integrated \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n619 inference 𝑆𝑎𝑣, using the probabilities of same-source versus different-source \n620 scenarios as weights, thereby generating the optimal inference for unisensory \n621 information.\n622 𝑆𝑣 = 𝑝 𝐶 = 1│𝑥𝑎,𝑥𝑣 𝑆𝑎𝑣 + 𝑝 𝐶 = 2│𝑥𝑎,𝑥𝑣 𝑆𝑣,𝐶=2\n623 Using weight (w) to represent the probability of audiovisual integration occurring in \n624 subjects, we obtain: \n625 𝑆𝑣 = w 𝑆𝑎𝑣 + (1 ― 𝑤) 𝑆𝑣,𝐶=2\n626 This hierarchical inference structure can be well characterized by Bayesian models, \n627 and through manipulation of different parameters, we can investigate the source of \n628 differences in subjects' audiovisual integration levels across various spatial \n629 eccentricities. To explore the specific mechanisms underlying these spatial \n630 distribution characteristics, we constructed five models as shown in Figure 9. The \n631 models share these common variables: 𝑣 (visual information likelihood, representing \n632 the observer's sensory estimate of visual information) and 𝑎 (auditory information \n633 likelihood, representing the sensory estimate of auditory information), which are \n634 sampled from two Gaussian distributions. Since this involves fitting the 1F2B \n635 condition, sampling is performed from distributions with a mean of 1 and standard \n636 deviation of 𝜎𝑣 and a mean of 2 and standard deviation of 𝜎𝑎, respectively. The \n637 standard deviation parameters 𝜎𝑣 and 𝜎𝑎, which characterize the uncertainty of \n638 unisensory information, are free parameters in the model that need to be fitted through \n639 data sampling. Observers combine noisy audiovisual signals and their respective \n640 uncertainties to form a unified stimulus representation, assuming the signals originate \n641 from the same source (𝑎𝑣). Since the final weighted average is essentially a weighted \n642 average of the means, only 𝜇𝑎𝑣 needs to be calculated during the sampling process. \n643 Finally, the observer's estimate of visual perception is obtained through weighted \n644 averaging of 𝜇𝑎𝑣 and their own sensory sample 𝑣 to produce the optimal estimate \n645 (opt), where the weight 𝑤 is also a free parameter of the model.\n646\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n647\n648 Figure 9. Diagram of Five Bayesian Model Structures. Key elements of the structure \n649 diagram: Nodes: Each ellipse represents a random variable or deterministic variable. \n650 Nodes filled in gray typically represent observed data. Arrows: Arrows indicate \n651 dependency relationships from one variable to another. Deterministic Nodes: Nodes \n652 labeled “Deterministic” indicate that the variable is a deterministic function of its \n653 parent variables, with values determined by the parent nodes. Shape: Numbers next to \n654 nodes represent the shape of tensor variables. For example, 9×1 may represent a \n655 vector containing 9 elements. Distribution: For each node that is sampled from a \n656 distribution, the specific distribution is provided. For example, “Normal” indicates a \n657 normal distribution, “Uniform” indicates a uniform distribution. The parameters of a \n658 distribution may depend on other nodes.\n659 Model 1 serves as the baseline model, assuming neither individual differences in \n660 unisensory information nor differences across eccentricities. Consequently, each \n661 parameter yields only a single optimized value, with all factors considered constant. \n662 Model 2 is an individual differences model that, compared to the baseline, accounts \n663 for inter-subject variability in sampled sensory information by introducing shape \n664 parameters. This allows the model to independently sample v and a for each \n665 subject, modeling based on their own sensory information, but still without \n666 considering eccentricity effects. Model 3 is a weight model that introduces shape \n667 parameters for weight w, enabling separate sampling and estimation of integration \n668 weights for each eccentricity, resulting in different estimates across eccentricities. \n669 Model 4 is an uncertainty model that assigns shape parameters to  𝜎v, positing that \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n670 subjects exhibit different perceptual uncertainties for visual stimuli presented at \n671 different spatial locations, leading to eccentricity-dependent differences in subsequent \n672 integration. Model 5 is the integrated model, which combines features of the two \n673 previous eccentricity-based models. This most complex model aims to simultaneously \n674 capture the effects of eccentricity on both weight w and visual information \n675 uncertainty 𝜎v. \n676 Each of the five models was sampled using four parallel MCMC chains, with each \n677 chain drawing 2000 samples and discarding the first 1000 for tuning. For the \n678 integrated model, which has more parameters and thus requires more samples, each \n679 chain drew 4000 samples while discarding the first 2000. The sampling results \n680 showed adequate convergence for all parameters across models, with r ≤ 1.01, \n681 indicating that the data structure has been thoroughly explored and the models have \n682 been adequately fitted to the existing data. 𝑟 represents the potential scale reduction \n683 factor, which assesses MCMC sampling quality by examining the ratio of between-\n684 chain variance to within-chain variance to evaluate whether chains have converged to \n685 the same distribution; values close to 1 indicate good convergence, and all models in \n686 this experiment achieved stable convergence. \n687 To compare the performance of the five models, we employed Widely Applicable \n688 Information Criterion (WAIC) as the evaluation metric. This is a widely used model \n689 selection criterion in Bayesian statistics that identifies models fitting the data well \n690 without excessive complexity. Its calculation is based on the log pointwise predictive \n691 density (l𝑝𝑝𝑑) and the effective number of parameters (Wasserman, 2000). The \n692 specific formula is as follows:\n693\n694 𝑊𝐴𝐼𝐶 = ―2(𝑙𝑝𝑝𝑑 ― 𝑝𝑤𝐴𝐼𝐶)\n695\n696 where 𝑙𝑝𝑝𝑑 is the expected value of the log-likelihood function of the observed data \n697 over the posterior distribution of model parameters, representing goodness-of-fit; and \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n698 𝑝𝑤𝐴𝐼𝐶 represents the effective number of parameters, estimating model complexity. \n699 These two components separately assess model fit and complexity. WAIC seeks to \n700 balance these aspects to select the optimal model. The smallest WAIC value typically \n701 corresponds to the best model (Table 4). \n702 We calculated WAIC for the five models and plotted the comparison, shown in Figure \n703 10. The weight model performed best, substantially outperforming all other models, \n704 even surpassing the integrated model that considered both uncertainty and weight \n705 variations. Therefore, we can conclude that the eccentricity effect obtained in the \n706 current experiment operates by directly altering the information weight for integrated \n707 audiovisual same-source stimuli, making visual estimates in multisensory contexts \n708 more susceptible to interference from auditory information.\n709\n710 Table 4. Performance Metrics for Different Models\n711\nModels 𝑙𝑝𝑝𝑑 𝑆𝐸(𝑙𝑝𝑝𝑑) 𝑝𝑤𝐴𝐼𝐶 𝑊𝐴𝐼𝐶 Δ𝑊𝐴𝐼𝐶\nBaseline -30.36 6.17 1.54  63.80 65.94\nIndividual \ndifferences\n-19.97 6.55 11.00 61.94 64.08\nWeight 10.83 3.69 9.76 -2.14 \\\nUncertainty 4.01 3.43 14.07 20.12 22.26\nIntegrated 7.70 3.38 13.26 11.12 13.26\n712\n713 Table 5 shows the fit of the weight model on specific parameters. The key parameters \n714 in this model are 𝜎v，𝜎a, and the respective weights w for each of the 9 different \n715 eccentricities. The highest density interval (HDI) is used to represent the posterior \n716 distribution, encompassing the region of highest posterior density; here, the 3% and \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n717 97% percentiles are used as the lower and upper bounds. 𝑟  being close to 1 \n718 indicates that the chains have converged well; here, the model's estimates for each \n719 parameter are visible, demonstrating that model sampling has achieved stable \n720 convergence based on the existing data. \n721 Table 5: Posterior Parameter Distributions of the Weight Model\nParameters  M SD 3% HDI 97% HDI 𝑟\n𝜎𝑣 0.093 0.052 0.010 0.181 1.0\n𝜎𝑎 0.304 0.096 0.149 0.487 1.0\n𝑤( ― 60°) 0.830 0.096 0.672 1.000 1.0\n𝑤( ― 45°) 0.659 0.103 0.465 0.852 1.0\n𝑤( ― 30°) 0.391 0.091 0.223 0.566 1.0\n𝑤( ― 15°) 0.416 0.092 0.246 0.590 1.0\n𝑤(0°) 0.265 0.090 0.097 0.436 1.0\n𝑤(15°) 0.308 0.091 0.140 0.484 1.0\n𝑤(30°) 0.675 0.101 0.484 0.868 1.0\n𝑤(45°) 0.699 0.102 0.511 0.892 1.0\n𝑤(60°) 0.894 0.078 0.756 1.000 1.0\n722\n723 To further evaluate the model's predictive performance, the probability density \n724 distribution of the optimal estimate (opt) obtained at each eccentricity level is plotted \n725 in Figure 10. It can be observed that as eccentricity extends from central vision \n726 toward the periphery, the observer's estimate of the number of flashes also increases.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n727\n728 Figure 10. Model-predicted probability density distributions of reported counts. \n729 Colors indicate the posterior distributions for different spatial eccentricities. While the \n730 means shift across positions, the standard deviations of the distributions remain \n731 consistent across conditions. \n732\n733 Next, we quantitatively describe the mapping between the weighting model’s \n734 predicted results (opt) and spatial eccentricity. Assuming that incorrect responses in \n735 the 1F2B (1-flash, 2-beep) task consist of reporting two flashes, let 𝑝 denote the \n736 response accuracy. Thus, the mean reported number of flashes is N =  p +2 ×\n737 (1 ― 𝑝) = 2 ― 𝑝, or conversely, p =  2 ― N. In the behavioral data, we found that a \n738 Gaussian distribution effectively fits the spatial distribution of response accuracy. To \n739 validate the weighting model's descriptive power, we calculated a hypothetical \n740 accuracy (2 ― opt) and fitted a Gaussian curve to examine whether the model-\n741 generated posterior data exhibit spatial characteristics similar to the empirical \n742 accuracy distribution.\n743 As illustrated in Figure 11, the optimal estimates predicted by the model also follow a \n744 Gaussian relationship across space, R2 = 0.863, closely mirroring the overall \n745 distribution of the actual data. Due to occasional trials where participants reported \n746 three flashes (N>2), the actual 𝑝 is slightly lower than the theoretical 2−N. \n747 Consequently, the calculated  p distribution is slightly higher than the actual \n748 response accuracy; nonetheless, the high degree of similarity between the two \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n749 distributions confirms that the weighting model provides an optimal representation of \n750 the experimental data.\n751\n752\n753 Figure 11. Comparison of model-predicted and empirical accuracy across spatial \n754 eccentricities. Gray data points and lines represent the predicted accuracy p calculated \n755 from model-sampled opt. The green line (consistent with Figure 8) shows the \n756 Gaussian fit of the participants' empirical response data. Error bars denote ±1 standard \n757 error of the mean (SEM).\n758\n759 Discussion   \n760 Extending Experiment 1, the present experiment documented a robust eccentricity-\n761 dependent SIFI up to 60°: the farther into the periphery, the more flashes participants \n762 reported in 1F2B trials. Crucially, this spatial modulation emerged only when audition \n763 and vision conflicted; unimodal vision and congruent AV trials were flat across \n764 eccentricity. Curve-fitting showed that hit-rate follows a Gaussian profile centred on \n765 the fovea. Bayesian model comparison revealed that a weight model—where the prior \n766 probability of fusing AV signals increases with retinal eccentricity—outperformed an \n767 uncertainty model and a full model that varied both weight and visual noise. Thus, \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n768 stimuli located more peripherally are a priori more likely to be bound with concurrent \n769 sounds, supporting recent proposals that early sensory cortices exhibit space-specific \n770 cross-modal weighting (Eckert et al., 2008; Falchier et al., 2002; Rockland & Ojima, \n771 2003). \n772 Predictions generated by the weight model reproduced the empirical Gaussian spatial \n773 signature (R² = .86), confirming its explanatory power. In traditional causal-inference \n774 accounts, the fusion prior is usually treated as constant because stimulus location is \n775 fixed (Shams et al., 2005). Here, freeing the weight parameter captured the spatial \n776 prior: observers expect peripheral visual events to be auditory-causal, so auditory \n777 input dominates the final estimate. The failure of the uncertainty model aligns with \n778 the behavioural null-effect in unisensory flash trials: when attention is equated across \n779 locations, visual numerosity perception is spatially uniform, indicating that the visual \n780 system can compensate for lower peripheral acuity under unisensory conditions \n781 (Shulman et al., 1985).   \n782 Our findings converge with M/EEG studies identifying early-latency signatures of the \n783 flash illusion (47–120 ms) (Mishra et al., 2008; Shams et al., 2005) and fMRI \n784 evidence showing heightened recruitment of the superior temporal sulcus (STS) and \n785 superior colliculus (SC) during illusory trials (de Haas et al., 2012). Collectively, \n786 these data support the view that multisensory integration is not limited to high-level \n787 association cortices; rather, it is an early-stage process automatically modulated by \n788 the spatial receptive-field architecture of primary sensory areas.\n789  \n790 2.3  Experiment 3 – Impact of Spatial AV Congruency on SIFI  \n791 After establishing that visual eccentricity biases AV integration, we asked whether \n792 auditory spatial position matters. We simultaneously manipulated the location of \n793 flashes and beeps to compare integration when AV signals were spatially congruent \n794 versus incongruent. Because vision is the dominant modality in SIFI (Kumpik et al., \n795 2014), we expected a robust illusion under both arrangements with no additional \n796 penalty for spatial mismatch.   \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n797 Participants  \n798 Ten undergraduates (6 female, 60 %; age 19–22, M = 20.50, SD = 0.97) with normal \n799 hearing and normal/corrected vision participated. All were right-handed and naïve to \n800 the purpose. They received 50 RMB after a 40-min session.   \n801 Apparatus and Stimuli  \n802 Testing took place in the same dimly lit laboratory. Visual stimuli were presented on a \n803 27-in LCD (1920 × 1080, 120 Hz, 56 cm width) viewed at 60 cm. A white Gaussian-\n804 ramped disk (1° dia.) appeared 7° left or right of fixation; a 2° white square frame \n805 served as location cue. Auditory stimuli were 10-ms, 2000-Hz pure tones delivered \n806 via closed-back headphones at 44.1 kHz. Responses were made with “Z” and “?/” \n807 keys.   \n808 Design and Procedure   \n809 This experiment aimed to investigate the impact of audiovisual spatial congruency on \n810 multisensory integration. Visual stimuli were presented at one of two possible spatial \n811 locations (7° eccentricity in the visual field), consisting of one, two, or three flashes. \n812 The three-flash condition was included to prevent participants from adopting specific \n813 response strategies or developing a distinct response bias in their number judgments.\n814 Catch trials (attention checks) were implemented with no flash present; participants \n815 who committed more than five errors in these trials were to be excluded. Notably, all \n816 participants in this study committed four or fewer errors. Auditory stimuli consisted \n817 of zero to four beeps. Unlike previous experiments that utilized only binaural \n818 presentation, here we incorporated spatial cues for the auditory stimuli: beeps were \n819 presented either binaurally or monaurally (ipsilateral or contralateral to the visual \n820 stimulus).\n821 The trial distribution is detailed in Table 5. As with previous experiments, a higher \n822 number of trials were allocated to the critical 1F2B (1-flash, 2-beep) and 2F1B (2-\n823 flash, 1-beep) conditions to manipulate the interstimulus interval (ISI) and explore the \n824 temporal dynamics of integration. The ISI was set at 42 ms for flashes and 30 ms for \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n825 beeps (the latter corresponding to the 40 ms Stimulus Onset Asynchrony (SOA) used \n826 in Experiments 1 and 2). For the 1F2B and 2F1B conditions, four distinct temporal \n827 relationships were designed based on the stimulus sequence and interval length. \n828 Specifically, the “long interval” was three times the duration of the “short interval”. \n829 This variety in temporal combinations was designed to increase experimental \n830 diversity and facilitate a preliminary investigation into the combined effects of spatial \n831 congruency and temporal context on integration. Consequently, the number of 1F2B \n832 and 2F1B trials was four times that of other conditions. The experiment comprised \n833 684 trials in total, with mandatory breaks of at least one minute every 50 trials. The \n834 total duration was approximately 40 minutes.\n835\n836 Table 5. Trial distribution across conditions for Experiment 3.\n837\nNumber of auditory stimuli\n0 1 2 3 4 Sum\n0 6 18 18 18 18 78\n1 12 36 144 36 36 264\n2 12 144 36 36 36 264\nNumber \nof \nflashes\n3 6 18 18 18 18 78\n838 The procedure was largely consistent with those of Experiments 1 and 2. Each trial \n839 began with a white fixation cross presented at the center of a gray screen for 500 ms. \n840 Subsequently, a white square (2° in visual angle) appeared for 500 ms on either the \n841 left or right side to cue the spatial location of the upcoming target. After a 500 ms \n842 blank-screen interval, the audiovisual stimuli were presented.\n843 Following the stimulus presentation, the fixation cross turned red, serving as a \"go\" \n844 signal for the participant to respond. Once a response was made, the screen \n845 transitioned to a blank display. Participants reported seeing one or two flashes by \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n846 pressing the \"Z\" or \"/\" keys, which were counterbalanced across participants. In cases \n847 where three flashes were perceived, participants were instructed to press the spacebar. \n848 The maximum response window was 2.5 s. The inter-trial interval (ITI) was 0.75 s, \n849 with an additional random jitter incorporated to sufficiently sample various response \n850 states of the participants.  \n851 Data analysis   \n852 Similar to Experiment 2, all response data from this experiment were aggregated, and \n853 the mean reported numbers under various conditions were calculated. Comparisons \n854 across levels were conducted using repeated measures ANOVA, with additional \n855 Bayesian factor analysis performed in JASP (JASP Team, 2023). \n856 First, we examined whether a significant SIFI effect was observed by calculating the \n857 mean reported numbers for all participants under each auditory stimulus condition \n858 when visual stimuli were 1 and 2 flashes, with results shown in Figure 12. A two-way \n859 repeated measures ANOVA was conducted. Since the auditory stimulus number level \n860 failed Mauchly's test of sphericity, χ²(9) = 29.870, p < .001, Greenhouse-Geisser \n861 correction was applied. The data revealed a significant main effect of flash number on \n862 participants' reports, with reports under two flashes significantly higher than under \n863 one flash, F(1, 9) = 76.192, p < .001, ηp² = .894, BF₁₀ = 2615.170, mean difference \n864 |MD| = 0.544. The main effect of auditory stimulus number was also significant, \n865 F(1.4, 12.597) = 28.908, p < .001, ηp² = .894, BF₁₀ = 1.437 × 10⁸. The interaction \n866 between the two factors was significant as well, F(4, 36) = 2.647, p = .049, ηp² \n867 = .227, BF₁₀ = 1.419.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n868\n869 Figure 12. Violin plot of participants' reported numbers in Experiment 3. The width \n870 of the violin plot represents the density distribution of the data; each point represents \n871 the data of one participant under that condition. The horizontal lines inside the violin \n872 plot represent the upper quartile, median, and lower quartile of the data. * indicates p \n873 < .05, ** indicates p < .01, *** indicates p < .001.  \n874 Focusing specifically on the simple main effects of auditory stimuli under the two \n875 flash levels: When the target flash was 1 flash, the simple main effect of auditory \n876 number was significant, F(4, 36) = 19.461, p < .001, BF₁₀ = 1.560 × 10⁶. Specifically, \n877 no significant difference existed between 1B and 0B conditions, |MD| = 0.072, p = \n878 1.000, BF₁₀ = 0.586. However, with more than 1 auditory stimulus, participants' mean \n879 reported numbers were significantly higher than both the no-auditory-stimulus and \n880 audiovisual-congruent conditions, ps < .001, BF₁₀ > 1.5. When the target flash was 2 \n881 flashes, the simple main effect of auditory number was also significant, F(4, 36) = \n882 23.301, p < .001, BF₁₀ = 1.108 × 10⁷. Participants' reported numbers in the 1B \n883 condition were significantly lower than in other conditions, ps < .010, BF₁₀ > 25. \n884 That is, this experiment observed both significant flash fission illusion and flash \n885 fusion illusion: When auditory stimuli presented more stimuli than visual flashes, \n886 participants' reported numbers increased significantly, and when presented auditory \n887 stimuli were fewer than target flashes, participants' reported numbers were \n888 significantly lower than other conditions and unimodal perception without auditory \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n889 interference. Notably, although the three experiments so far have only found illusory \n890 interference during audiovisual incongruence without observing significant \n891 facilitation during consistent audiovisual information, in this experiment, the variance \n892 across all participants' data was notably smaller under the 1F1B condition, suggesting \n893 that congruent conditions may facilitate more efficient processing of visual \n894 information. \n895 To further examine the influence of spatial features of audiovisual stimuli on \n896 integrated perception, both fission and fusion illusions were observed in this \n897 experiment. However, the fission illusion phenomenon was more pronounced, with \n898 multiple conditions triggering fission perception. Therefore, the mean of participants' \n899 reports when the target flash was presented once was adopted as the comparison \n900 metric. \n901 To avoid potential influences from visual presentation field, a two-way ANOVA of \n902 spatial location and auditory stimulus number was first conducted. As shown in the \n903 left panel of Figure 13, the main effect of spatial field on participants' reported \n904 numbers was not significant; presenting stimuli in the left versus right visual fields \n905 had no effect on audiovisual integration, F(1, 9) = 0.056, p = .819, ηp² = .006, BF₁₀ = \n906 0.347. Therefore, when subsequently comparing audiovisual stimulus congruence, \n907 trials presented in the left and right visual fields were combined, focusing only on the \n908 relative spatial relationship between audiovisual stimuli. \n909 Participants' reported numbers were then compared when auditory stimuli were \n910 presented ipsilaterally, contralaterally, or bilaterally to the flash. ANOVA results \n911 showed that audiovisual stimulus congruence had no significant effect on participants' \n912 perceived numbers. Whether the sound was presented ipsilaterally, contralaterally, or \n913 bilaterally to the visual stimulus, participants reported similar numbers of flashes, F(2, \n914 18) = 0.494, p = .618, ηp² = .052, BF₁₀ = 0.170. \n915 Thus, it can be concluded that in audiovisual integration paradigms based on visual \n916 tasks such as the sound-induced flash illusion, the spatial location of auditory stimuli \n917 and the spatial relationship between auditory and visual stimuli have minimal \n918 influence on observers' perception.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n919\n920\n921\n922 Figure 13. Participants' reported numbers under different conditions in Experiment 3. \n923 The left panel shows the reported number of flashes under different auditory stimulus \n924 numbers when visual stimuli were presented in the left or right visual field. The right \n925 panel combines stimuli from both visual fields, comparing reported numbers when \n926 auditory stimuli were presented ipsilaterally, contralaterally, and bilaterally to the \n927 visual target. * indicates p < .05, ** indicates p < .01, *** indicates p < .001. \n928\n929 Discussion\n930 This experiment focused on the spatial congruence of audiovisual stimuli and \n931 revealed that the perception of SIFI was not significantly influenced by the spatial \n932 relationship between the auditory and visual stimuli. Specifically, whether the visual \n933 stimulus was presented in the left or right visual field, and whether the auditory \n934 stimulus was presented ipsilaterally, contralaterally, or neutrally (binaurally) to the \n935 visual stimulus, no significant effect on participants' SIFI perception was observed. \n936 This finding suggests that spatial congruence of stimuli does not have a measurable \n937 effect on the level of audiovisual integration with SIFI.\n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n938 Notably, in addition to exhibiting the fission illusion—similar to the first two \n939 experiments—this experiment also demonstrated a pronounced fusion illusion when \n940 the number of auditory stimuli was fewer than the number of flashes. The main \n941 distinction between this experiment and Experiment 1 lies in the inclusion of \n942 additional stimulus conditions at the audiovisual level to mitigate potential systematic \n943 errors. When an individual’s prior perception regarding the overall possible number \n944 of audiovisual stimuli in the experiment changes, the level of audiovisual integration \n945 is subject to the influence of this perceptual expectation (Wang et al., 2019). This shift \n946 in expectation may account for the observed differences in participant performance, \n947 even under similar temporal and spatial conditions.\n948 In contrast to the findings of the first two experiments, the results of the current \n949 experiment provide greater support for a late-integration model of audiovisual \n950 processing. The observation that the SIFI effect under spatially incongruent \n951 (contralateral) conditions was similar to the effect under binaural presentation \n952 suggests that audiovisual integration may be mediated by higher-level brain regions \n953 involved in later-stage processing.  \n954 3 General Discussion\n955 This study exploited the robustness of the Sound-Induced Flash Illusion (SIFI) to \n956 investigate the effect of stimulus spatial characteristics on audiovisual integration \n957 capacity, successfully revealing the distribution pattern of how the level of \n958 audiovisual integration is influenced by stimulus spatial features, while replicating the \n959 SIFI originally discovered by Shams et al. (2002)(Shams et al., 2002).  \n960 In Experiment 1 and Experiment 2, we explored the influence of visual stimulus \n961 spatial location on observers' perception during audiovisual integration. The results \n962 indicated that, after controlling for matched attentional resource allocation across \n963 spatial locations, unimodal visual perception did not change with the spatial location \n964 of the stimulus. However, a clear difference in audiovisual bimodal processing was \n965 found between spatial locations: stimuli presented in the peripheral visual field \n966 (beyond 15°) were more significantly interfered with by auditory information, and the \n967 susceptibility to audiovisual integration increased towards the periphery, a spatial \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n968 distribution that can be approximated by a Gaussian curve. With modeling, we found \n969 that the unimodal information uncertainty in the peripheral visual field did not, in fact, \n970 change. Instead, the effect was driven by a mechanism that directly enhanced the \n971 influence of auditory information by altering the weighting ratio of audiovisual \n972 information during processing. In Experiment 3, we attempted to simultaneously \n973 manipulate the spatial location of both visual and auditory stimuli to explore whether \n974 their spatial congruence would affect the probability of integration. The results \n975 showed that SIFI remained stable across various spatial relationships between \n976 audiovisual stimuli; even when a potential interhemispheric integration (with \n977 contralateral layout of audiovisual stimuli) of sensory information was required, \n978 participants' perceptual performance was virtually identical to conditions with \n979 ipsilateral or binaural auditory stimulus presentation. With three experiments, we \n980 comprehensively explored the spatial characteristics of audiovisual integration from \n981 two aspects: the spatial location of visual information and the spatial relationship \n982 between audiovisual stimuli. \n983\n984 This work addresses existing gaps in the literature by expanding the range of spatial \n985 eccentricity to a broad 60° across both hemifields while strictly controlling for \n986 attentional consistency. These refinements provide a more robust resolution to \n987 previously disputed questions regarding spatial modulation of the SIFI. Furthermore, \n988 by integrating Bayesian modeling with Causal Inference theory, we characterize the \n989 underlying mechanisms from a computational perspective. Our analysis suggests that \n990 different retinotopic locations possess intrinsic differences in their responsiveness to \n991 audiovisual stimuli, which directly modulates the informational weighting during \n992 perceptual inference. This indicates that cross-modal influence is shaped by stimulus \n993 location in a relatively automatic, bottom-up manner (Keil & Senkowski, 2018). \n994\n995 There remain certain limitations in the current experiments. For instance, the \n996 imbalance in trial design—the deliberate inclusion of more audiovisual conflict trials \n997 (1F2B or 2F1B)—could raise concerns about the validity of the conclusions. Such an \n998 overall design might lead participants to form a certain expectation regarding the \n999 corresponding combinations, e.g., higher accuracy for perceiving two flashes when \n.CC-BY 4.0 International licenseperpetuity. It is made available under a \npreprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in \nThe copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint \n\n1000 one auditory stimulus is presented. Previous studies have shown that such perceptual \n1001 expectation can influence the probability of SIFI (Wang et al., 2019).\n1002 To minimize the impact of trial imbalance, we informed participants that all stimulus \n1003 combinations were possible and utilized Bayes Factor analysis (Dienes, 2014) to \n1004 robustly compare hypotheses across unequal sample sizes. Because the trial \n1005 distribution was uniform across all eccentricities, our primary spatial comparisons \n1006 remain valid. Furthermore, the robust illusions observed contradict the notion that \n1007 trial frequency awareness suppressed cross-modal influence (Wang et al., 2019). The \n1008 design strategically maximized sampling of illusory trials while variable SOAs \n1009 prevented practice effects. Future research should employ neuroimaging to localize \n1010 these effects in unimodal sensory cortices and incorporate eye-tracking to control for \n1011 microsaccades and bottom-up attentional capture. \n1012 In summary, this study provides a comprehensive characterization of the spatial \n1013 constraints governing audiovisual integration. Behaviorally, we refined previous \n1014 explorations by demonstrating that SIFI susceptibility is significantly modulated \n1015 across a broad 60°range of visual eccentricity. Conversely, our investigation into \n1016 spatial incongruence revealed that the relative position of auditory stimuli does not \n1017 significantly influence integration, highlighting the dominance of visual eccentricity \n1018 in shaping these percepts. At the modeling level, a Gaussian distribution successfully \n1019 quantified perceptual performance across the visual field, providing a robust \n1020 mathematical description of these spatial variations. Furthermore, Bayesian \n1021 computational modeling localized the eccentricity effect to a fundamental shift in the \n1022 allocation of sensory weights: visual stimuli in the far periphery possess a higher \n1023 probability of being integrated with auditory information compared to those at \n1024 fixation. By systematically manipulating spatial characteristics within the flash \n1025 illusion paradigm, this research deepens our understanding of the mechanisms \n1026 underlying multisensory processing. These findings offer a critical empirical \n1027 framework for the selection of stimulus locations in future multisensory research and \n1028 contribute to a more nuanced model of how the brain resolves audiovisual \n1029 information across the visual field.\n1030\n.CC-BY 4.0 International licenseperpetuity. 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