Spatial correspondences of Audiovisual Stimuli on Double Flash Illusion Perception and its Cognitive Modeling

1 Spatial correspondences of Audiovisual Stimuli on Double Flash Illusion 2 Perception and its Cognitive Modeling 3 4 Yabo Zheng1, Lihan Chen1,2,3* 5 1 School of Psychological and Cognitive Sciences and Beijing Key Laboratory of 6 Behavior and Mental Health, Peking University 7 2 National Engineering Laboratory for Big Data Analysis and Applications, Peking 8 University, Beijing 100871, China 9 3 Key Laboratory of Machine Perception (Ministry of Education), Peking University, 10 Beijing 100871, China 11 12 Author Note: 13 We declare no conflict of interest in this research. Data,analysis and modeling scripts 14 are available at: https://github.com/AbelZheng/SiFI-Spatial-Characteristics.git 15 Financial Support: STI2030-Major Project (2021ZD0202600) and Natural Science 16 Foundation of China (T2192932) to L.C. 17 *Correspondence author email: [email protected] 18 19 20 21 22 23 24 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 25 Abstract: Perceptual processing integrates information from multiple sensory 26 modalities to form a coherent representation of the environment. A classic example of 27 such is the Sound-Induced Flash Illusion (SIFI), where the perceived number of visual 28 flashes is altered by conflicting auditory stimuli. While the SIFI is a well-established 29 phenomenon of multisensory integration, the influence of physical spatial 30 characteristics—specifically stimulus eccentricity and spatial congruence—on 31 integration levels remains debated.To address this gap, this study used the SIFI 32 paradigm to investigate the effect of visual stimulus spatial location and the spatial 33 congruence between auditory and visual stimuli on audiovisual integration. In 34 Experiments 1 and 2, we found that when spatial attention was controlled via cueing, 35 unimodal visual performance remained consistent across locations. However, the 36 susceptibility to SIFI increased progressively from the central to the peripheral visual 37 field, exhibiting a spatial pattern of Gaussian distribution. Bayesian modeling further 38 supported this by showing that this spatial modulation was driven by an increase in 39 the integration weight assigned audiovisual representations in the periphery, rather 40 than changes in sensory uncertainty alone. Conversely, Experiment 3 demonstrated 41 that the spatial congruence of audiovisual stimuli did not affect the SIFI or alter the 42 integration processing. These findings refine our current understanding of the spatial 43 modulation upon audiovisual integration. By incorporating the visual system's spatial 44 properties into a Bayesian framework, we provide a computational explanation for the 45 eccentricity-dependent nature of multisensory integration. 46 Keywords: Audiovisual integration, Sound-induced flash illusion, spatial modulation, 47 Bayesian modeling 48 49 50 51 52 53 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 54 1.Introduction 55 The environment in which we live is rich with information spanning multiple sensory 56 modalities. To facilitate efficient interaction with this environment, the brain 57 adaptively perceives its surroundings by integrating multisensory information (Bauer 58 et al., 2020). Multisensory integration (MSI) is the process by which an observer 59 combines information originating from different sensory channels into a coherent and 60 unified perceptual experience (Stein & Stanford, 2008). This cross-modal integration 61 enhances an observer's perceptual efficiency and precision, leading to benefits such as 62 reduced reaction times (Pomper et al., 2014) , heightened stimulus salience (Driver & 63 Noesselt, 2008), and improved information decoding (Zion Golumbic et al., 2013). 64 Multisensory integration (MSI) is significantly modulated by visual eccentricity, 65 operating through a complex interplay of spatial and temporal rules where behavioral 66 enhancement, such as faster reaction times and increased detection accuracy, is most 67 robust when stimuli are spatiotemporally congruent (Bruns et al., 2024; Cuppini et al., 68 2025; Garcia et al., 2017; Porada et al., 2026; Recanzone, 2009). When informational 69 inputs from different sensory modalities conflict, the brain may erroneously integrate 70 mismatched stimuli into a unified percept, resulting in cross-sensory perceptual 71 interference (Sterzer et al., 2009; Wang et al., 2013).As visual eccentricity increases, 72 the auditory localization bias—known as the ventriloquist effect—progressively 73 decreases, a phenomenon consistently observed in both neurocomputational models 74 and empirical data (Cuppini et al., 2025). Other phenomena, such as bistable perception, 75 serve as quantifiable behavioral indicators of an individual’s multisensory processing 76 capacity and their tendency to integrate information (Hirst et al., 2020). A paradigmatic 77 example of this domain is the Sound-Induced Flash Illusion (SIFI), where the high 78 temporal resolution of the auditory channel distorts visual perception (Shams et al., 79 2002). This illusion typically manifests as “fission”, where a single flash paired with 80 multiple beeps is perceived as multiple flashes (Keil, 2020; Keil & Senkowski, 2018), 81 or “fusion”, where multiple flashes paired with fewer beeps are perceived as a single 82 flash (McGovern et al., 2014). The susceptibility to these illusions is governed by the 83 principle of temporal proximity; stimuli are generally integrated only when they fall 84 within a specific “temporal window of integration” (TWI) (Hirst et al., 2020; Lewald .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 85 & Guski, 2003; Stein et al., 2014; Stein & Meredith, 1993). Furthermore, this 86 integration process is highly plastic, modulated by factors such as aging (DeLoss et al., 87 2013), increased cognitive load (Michail & Keil, 2018) and top-down manipulations of 88 perceptual expectations (Wang et al., 2019), all of which can significantly widen or 89 narrow the temporal scale of multisensory integration. 90 91 Theoretical frameworks for multisensory integration have evolved from the directed 92 attention hypothesis, which emphasizes attentional resource allocation (Welch et al., 93 1986) but struggles to explain the automatic nature of cross-modal influences 94 (Odegaard et al., 2016), to the modality appropriateness theory, which posits that 95 sensory dominance is determined by a modality’s precision for a given task 96 (Andersen et al., 2004; Hirst et al., 2020; McGovern et al., 2016). 97 These cognitive models are complemented by computational approaches, such as 98 maximum likelihood estimation and Bayesian causal inference, which suggest the 99 brain performs optimal perceptual inferences by weighting sensory reliability and 100 assessing common signal sources (Ernst & Bulthoff, 2004; Shams & Beierholm, 101 2010). Physiologically, these processes are supported by neural oscillation 102 synchronization, where cross-modal communication occurs through phase reset or 103 neural entrainment (Bauer et al., 2021; Fries, 2015; Lakatos et al., 2019; Senkowski & 104 Engel, 2024; Thorne & Debener, 2014). Despite these advancements, significant 105 debate remains regarding the role of spatial characteristics in the Sound-Induced Flash 106 Illusion (SIFI). While neuroimaging suggests enhanced auditory-visual connectivity 107 in the peripheral visual field (Eckert et al., 2008; Ghazanfar & Schroeder, 2006; 108 Rockland & Ojima, 2003), behavioral evidence for this “eccentricity effect” is 109 inconsistent: several studies report increased SIFI susceptibility in the periphery 110 (Chen et al., 2017; Shams et al., 2002; Tremblay et al., 2007) , yet others find no such 111 spatial influence (Gavin et al., 2022), particularly at eccentricities yet to be fully 112 explored in humans (Falchier et al., 2002). Furthermore, the interaction between 113 spatial proximity (Stein et al., 2014) and inverse effectiveness (Holmes, 2009) 114 remains unresolved, as empirical results vary on whether spatial disparity modulates 115 or has no effect on illusion perception (Aller et al., 2015; Innes-Brown & Crewther, 116 2009). .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 117 118 Therefore, the impact of stimulus spatial characteristics on the SIFI remains a pivotal 119 yet unresolved area of research. Two critical questions persist: whether visual stimuli 120 at different locations share a uniform susceptibility to auditory integration, and 121 whether spatial inconsistency diminishes integration levels. While maintaining spatial 122 stability is fundamental to navigating a multisensory environment (Kording et al., 123 2007), research on auditory spatial cues in SIFI remains sparse due to the auditory 124 channel's lower spatial resolution compared to vision (Kumpik et al., 2014). 125 Furthermore, evidence regarding the interaction between spatial and temporal 126 characteristics is inconsistent. While most studies suggest an “eccentricity effect”, 127 some studies found no such influence (Gavin et al., 2022; Shulman et al., 1985). 128 Previous paradigms often presented stimuli at randomized locations without spatial 129 cues. Since visual processing efficiency peaks near the central fovea, these studies 130 may have overlooked the influence of unimodal uncertainty and attentional bias on 131 the integration process. Therefore, controlling for spatial attention is essential to 132 isolating the true effect of eccentricity. 133 This study aims to resolve these discrepancies by systematically investigating the 134 spatial dimensions of audiovisual integration. The first aim of this research examines 135 the effect of visual eccentricity on integration capacity: Experiment 1 extends the 136 parameter range beyond the conventional 10° threshold to map the peripheral visual 137 field more comprehensively, while Experiment 2 utilizes a wider spatial range 138 combined with Bayesian cognitive modeling to characterize the underlying 139 computational mechanisms. The second aim, Experiment 3, explores the role of 140 audiovisual (in)consistency by comparing the effects of ipsilateral, contralateral, and 141 binaural auditory stimuli on illusion perception. By synthesizing behavioral data with 142 computational modeling, this study seeks to delineate how the spatial properties of the 143 visual system and multisensory processing converge into a coherent cognitive 144 mechanism. 145 146 2. Experiments .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 147 2.1 Experiment 1: Investigating the Effect of Visual Stimulus Spatial Eccentricity 148 on Audiovisual Integration 149 This computer-based experiment was designed to replicate the sound-induced flash 150 illusion (SIFI) and, concurrently, explore whether stimuli presented in the central, 151 near-peripheral, and far-peripheral visual fields exhibit differential susceptibility to 152 audiovisual integration. Specifically, we compared the susceptibility of the SIFI 153 across visual stimulus eccentricities of 0°, 7°, and 21°. 154 For the conditions most likely to induce the SIFI—the 1 Flash 2 Beeps (1F2B) and 2 155 Flashes 1 Beep (2F1B) conditions—six different levels of Stimulus Onset 156 Asynchrony (SOA) were established: -120 ms, -70 ms, -30 ms, +30 ms, +70 ms, and 157 +120 ms. As illustrated in Figure 1, the sign of the SOA represents the relative 158 temporal order: a negative sign indicates the unimodal stimulus (e.g., flash in 1F2B) 159 preceded the audiovisual pair, while a positive sign indicates it followed. This 160 experiment also served as a preliminary study for parameter refinement during the 161 research process. 162 Based on previous research on visual stimulus spatial eccentricity and corresponding 163 neuroanatomical evidence (Chen et al., 2017; Falchier et al., 2002; Gavin et al., 2022; 164 Shams et al., 2002; Tremblay et al., 2007), the following hypotheses were formulated: 165 First, the SIFI phenomenon, particularly the fission illusion (where the number of 166 auditory stimuli exceeds the number of flashes), would be reliably replicated across 167 the participant sample, leading to a significant decrease in the correct perception rate. 168 Second, stimuli presented at different spatial locations would exhibit different levels 169 of audiovisual integration; specifically, the 7°and 0°eccentricities (within 170 approximately 10°) would show no significant difference, while the more peripheral 171 21°eccentricity would be more susceptible to the illusion, consequently yielding a 172 lower reported accuracy rate from participants. 173 Participants 174 Fifteen university students were recruited. Following preliminary parameter 175 adjustments and accuracy-based screening, nine valid participants (5 female; mean .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 176 age = 20.44, SD = 1.01) were included in the final analysis. All participants reported 177 normal or corrected-to-normal vision and hearing, were naïve to the purpose of the 178 experiment, and were right-handed. Each participant received a monetary 179 compensation of ¥80 upon completion. All participants provided written informed 180 consent prior to the experiment and received compensation upon completion. The 181 study protocol (with approved No.# 2021-10-18) was approved by the Academic 182 Affairs Committee of the School of Psychological and Cognitive Sciences at Peking 183 University. The above protocol was also applied to the following Experiments 2 and 184 3. 185 Apparatus and Stimuli 186 Experiments were conducted in a dimly lit, sound-attenuated laboratory. Visual 187 stimuli were presented on a 27-inch monitor (1920 × 1080 resolution, 144 Hz refresh 188 rate) positioned 60 cm from the participant. The visual target was a white disk (1° 189 radius), and the spatial cue was a white square frame (2° side length). Auditory 190 stimuli (10 ms pure tone, 3000 Hz) were presented via headphones using a sound card 191 with a 96 kHz sampling rate. The experiment was implemented via PsychToolbox-3 192 (Brainard, 1997; Kleiner M et al., 2007; Pelli, 1997). 193 Experimental Design 194 The experiment employed a within-subjects design based on the classic SIFI 195 paradigm. The independent variables were stimulus onset asynchrony (SOA, six 196 levels: ±30, ±70, ±120 ms) and visual eccentricity (five levels: -21°, -7°, 0°, 197 7°, 21°). The dependent variables were response accuracy (proportion of correct 198 flash reports) and reaction time (RT). 199 Experimental Procedure 200 A strict training protocol ensured task comprehension. Participants completed practice 201 trials with feedback and proceeded to the main experiment only after achieving >90% 202 accuracy. To prevent fatigue, breaks were mandated every 40 trials. As shown in 203 Figure 1, each trial began with a fixation cross (1000 ms), followed by a spatial cue 204 (white frame, 500 ms) appearing at one of the five locations to distinctively guide .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 205 spatial attention. After a 500 ms gap, the target flash (33 ms) appeared at the cued 206 location. In audiovisual trials, 10 ms beeps (3500 Hz) accompanied the flashes. A red 207 fixation would appear to prompt participants to report the perceived number of flashes 208 via keypress (“Z” or “M”, counterbalanced) within 3 seconds. 209 210 211 212 Figure 1. Experimental procedure . Left: task flow of each trial. Visual stimuli are 213 presented at a specific location, while auditory stimuli are delivered binaurally 214 through headphones. Top Right: A schematic showing all possible stimulus locations, 215 example stimuli, and their relative size relationships. In each trial, the cue and the disk 216 (flash) appear at only one specific location. Bottom Right: The temporal sequencesfor 217 a 1F2B (1 Flash, 2 Beeps) trial. This demonstrates the temporal relationship between 218 stimuli under positive and negative SOA. One pair of audiovisual stimuli is always 219 synchronized to begin simultaneously. 220 221 Across all trials, excluding the attention check trials (which involved the cue frame 222 but no flash), participants viewed 1 or 2 flashes, accompanied by 0, 1, or 2 auditory 223 stimuli, leading to the 9 combination conditions detailed in Table 1. The core 224 conditions of interest for investigating the SIFI were 1F2B and 2F1B (where F 225 denotes the number of flashes and B denotes the number of beeps), which required the 226 manipulation of the Stimulus Onset Asynchrony (SOA). Specifically, the 1F2B and .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 227 2F1B conditions consisted of 12 trials for each combination of the 5 eccentricity 228 levels and 6 SOA levels, totaling 720 trials, which constituted 65% of the total 229 experiment. 230 Table 1. Experiment 1: Trial Distribution Number of auditory stimuli 0 1 2 Sum 0 50 15 15 80 1 50 100 360 510 Number of flashes 2 50 360 100 510 231 232 233 The formal experiment comprised a total of 1100 trials, requiring approximately 80 234 minutes to complete. Participants were instructed to take a minimum one-minute rest 235 after every 50 trials before pressing a key to continue. 236 Data Analysis 237 The collected response data from all participants were aggregated, and the correct 238 response rates for various conditions were calculated. A repeated-measures Analysis 239 of Variance (ANOVA) was employed for comparisons across levels. It is important to 240 note that the experimental design intentionally oversampled the 1F2B and 2F1B 241 conditions by including more SOA levels, leading to an inherently unbalanced trial 242 distribution. 243 To ensure a more precise analysis of this data, fully gather evidence supporting all 244 observable effects, and mitigate potential biases arising from the asymmetry between 245 the null and alternative hypotheses (Dienes, 2014), the Bayes Factor analysis method 246 was additionally utilized via JASP software(JASP, 2023). For all Bayesian ANOVAs, 247 the default JASP settings were applied, with the prior r scales for fixed effects, .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 248 random effects, and covariates set to 0.5, 1 and 0.354, respectively. The interpretation 249 of Bayes Factor values followed the guidelines of Dienes (2014): values greater than 250 3 represent strong evidence for the alternative hypothesis (𝐻1); values between 1 and 251 3 indicate anecdotal support for H1; values between 0.3 and 1 suggest anecdotal 252 support for the null hypothesis (𝐻0); and values less than 0.3 denote strong evidence 253 for 𝐻0. This approach quantified the relative likelihood of the data under both 𝐻0 254 and 𝐻1, effectively addressing issues related to the unbalanced design and testing 255 biases (Dienes, 2014). 256 The accuracy rates under different conditions are shown in Figure 2. A two-way 257 repeated-measures ANOVA was conducted on the accuracy rates, with Bonferroni 258 correction applied for post-hoc tests. Both the auditory stimulus and the audiovisual 259 interaction passed Mauchly's test of sphericity (auditory stimulus: χ² = 2.269, p = 260 0.322; interaction: χ² = 3.361, p = 0.186). 261 262 Figure 2. Violin Plots of Participant Report Accuracy Across Conditions in 263 Experiment 1. The width of the violin plot represents the probability density 264 distribution of the data. Each individual dot represents the data point of a single 265 participant under the corresponding condition. The horizontal lines within the violin 266 plots indicate the upper quartile, median, and lower quartile of the data, respectively. 267 * denotes p<.05, ** denotes p<.01, *** denotes p<.001. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 268 The ANOVA results revealed a significant main effect of the number of flashes on 269 participants' response accuracy, F(1,8) = 14.067, 𝑝 = 0.006, 𝜂2 p = 0.637, 𝐵𝐹10 270 = 8.012. Participants' accuracy in perceiving two flashes was significantly higher, 271 |MD| = 0.047, p = 0.006, BF₁₀ = 55.529. The number of auditory stimuli also had a 272 significant effect on response accuracy, F(2,16) = 11.421, p < 0.001, 𝜂2 p = 0.588, 273 BF₁₀ = 3.704. Under the condition of one auditory stimulus, participants' response 274 accuracy was significantly higher than with two stimuli (|MD| = 0.040, p < 0.001, 275 BF₁₀ = 21.489) and with no auditory interference (|MD| = 0.024, p = 0.038, BF₁₀ = 276 8.012). 277 The interaction between the two factors was also significant, F(2,16) = 6.083, p = 278 0.011, 𝜂2 p= 0.432, BF₁₀ = 93.434. Simple main effects analysis was conducted, 279 focusing on whether the number of auditory stimuli had different effects under each 280 flash condition. When there was one flash, the simple main effect of sound stimuli 281 was significant, F(2,16) = 20.792, p < 0.001, BF₁₀ = 83.776. The difference between 282 0B and 1B was not significant, |MD| = 0.027, p = 1.000, BF₁₀ = 0.900. However, 283 accuracy under 0B was significantly higher than under 2B, |MD| = 0.050, p = 0.024, 284 BF₁₀ = 1.985. Accuracy under 1B was also significantly higher than under 2B, |MD| 285 = 0.076, p < 0.001, BF₁₀ = 111.291. This indicates a clear flash fission illusion: when 286 the number of sound stimuli exceeded the actual number of flashes, participants' 287 subjective reports of the number of flashes also increased. 288 When there were two flashes, the number of auditory stimuli had no significant effect 289 on accuracy, F(2,16) = 1.712, p = 0.212, BF₁₀ = 0.928. Under two flashes, 290 participants' reported accuracy was high across different numbers of auditory stimuli, 291 and no significant flash fusion illusion was observed. 292 Focusing further on participants’ accuracy when a single flash was presented at 293 different eccentricities, we conducted a two-way repeated-measures ANOVA with 294 factors of eccentricity and number of auditory stimuli. The interaction between 295 eccentricity and auditory number violated sphericity (χ²₃₅ = 100.573, p < 0.001), so 296 degrees of freedom were adjusted with the Greenhouse–Geisser correction. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 297 As shown in Figure 3, the main effect of spatial eccentricity was significant, F(4,32)= 298 9.342, p < 0.001, 𝜂2 p = 0.539, BF₁₀ = 85.524. Accuracy at 21° in both hemifields was 299 lower than in central vision (left 21°: |MD| = 0.055, p = 0.004, BF₁₀ = 170.112; right 300 21°: |MD| = 0.070, p < 0.001, BF₁₀ = 489.405). In addition, accuracy differed 301 between 7° and 21° in both hemifields (left: |MD| = 0.045, p = 0.028, BF₁₀ = 9.183; 302 right: |MD| = 0.049, p = 0.013, BF₁₀ = 10.061), whereas performance at 7° did not 303 differ from central vision. The main effect of auditory-stimulus number was also 304 significant, F(2,16) = 10.622, p = 0.001, 𝜂2 p = 0.570, BF₁₀ = 29.283. The 305 eccentricity × auditory-number interaction was not significant after correction, 306 F(3.504,28.035) = 1.583, p = 0.211, 𝜂2 p = 0.165, BF₁₀ = 0.882. 307 308 Figure 3. Response accuracy across conditions for trials with a single flash in 309 Experiment 1. Different colored lines represent different numbers of auditory stimuli. 310 Error bars indicate one standard error (SE). * denotes p<.05, ** denotes p <.01, *** 311 denotes p <.001. 312 313 Simple-main-effect analyses examined whether the eccentricity profile was equivalent 314 across auditory conditions. Without auditory distractors, eccentricity had no 315 significant impact on accuracy, F(4,32) = 1.332, p = 0.280, BF₁₀ = 0.330. In contrast, 316 when one or two auditory stimuli were presented, eccentricity strongly modulated 317 accuracy (1B: F(4,32)= 8.630, p < 0.001, BF₁₀ = 623.599; 2B: F(4,32)= 10.217, p < .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 318 0.001, BF₁₀ = 1 093.603). Thus, no reliable eccentricity effect emerged in the 319 unimodal visual task, whereas introducing auditory stimuli in a cross-modal setting 320 revealed marked performance differences between peripheral and peri-foveal 321 locations. 322 Prior analyses confirmed the presence of sound-induced flash illusions and showed 323 that the spatial position of visual stimuli modulates audiovisual integration. 324 Temporal alignment is also critical, as the inter-stimulus interval systematically 325 shapes susceptibility to the SIFI. We therefore investigated whether the impact of 326 spatial eccentricity varies across temporal contexts—specifically, whether a space– 327 time interaction exists. 328 Figure 4 illustrates performance in fission-illusion trials (F1B2) as a function of SOA 329 and eccentricity. 330 331 332 Figure 4. Response accuracy in the fission illusion condition (1F2B) across different 333 SOAs. Different colored lines represent the various spatial locations of the visual 334 stimuli. Error bars indicate one standard error (SE). * denotes p <.05, ** denotes p 335 <.01, *** denotes p <.001 336 A two-way repeated-measures ANOVA (eccentricity × SOA) revealed significant 337 main effects of both eccentricity, F(4,32) = 10.217, p< 0.001, 𝜂2 p = 0.561, BF₁₀ = .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 338 17.954, replicating earlier findings, and SOA, F(5,40) = 8.078, p< 0.001, ηp² = 0.502, 339 BF₁₀ = 182.648. Contrary to the expectation that shorter SOAs should promote 340 stronger integration, accuracy at |SOA| = 30 ms was significantly higher than at |SOA| 341 = 70 ms (p< 0.01), with no other pairwise SOA comparisons reaching significance. 342 Additionally, a significant eccentricity × SOA interaction emerged, F(20,160) = 343 2.233, p = 0.003, 𝜂2 p = 0.218, BF₁₀ = 67.643. 344 Simple-main-effect analyses revealed that eccentricity reliably influenced 345 performance exclusively within the SOA = –70 ms and +70 ms windows (–70 ms: 346 F(4,32) = 5.372, p = 0.002, BF₁₀ = 42.601; +70 ms: F(4,32) = 4.368, p = 0.006, BF₁₀ 347 = 10.316). These are precisely the SOAs that maximized illusion susceptibility. Thus, 348 when auditory and visual signals are temporally discrepant yet still integrated, the 349 spatial location of the visual event determines the strength of that integration. At 350 SOAs that are too brief or too prolonged—conditions in which observers appear 351 largely immune to auditory influence—the modulatory effect of spatial position 352 disappears. 353 Discussion 354 We successfully replicated the fission illusion (Shams et al., 2002) and extended the 355 findings to the spatial domain. Our results demonstrate that while SIFI susceptibility 356 is stable within the central 10°, it significantly increases in the far periphery (21°). 357 Importantly, by using pre-cues to equate spatial attention, we ruled out the possibility 358 that this effect stems from reduced peripheral attention or visual acuity. 359 These findings partially align with earlier work showing stronger SIFI at peripheral 360 locations (Chen et al., 2017; Shams et al., 2002; Tremblay et al., 2007). First, 361 previous studies sampled only ≤ 10° eccentricity and reported marginal or null 362 differences; we likewise found no change between 0° and 7°, consistent with Gavin et 363 al. (2022). Second, by extending the spatial span to 21°, we reveal a steep increase in 364 illusion susceptibility, while unimodal visual sensitivity remains unchanged. 365 Audiovisual integration therefore exhibits a distinctive spatial signature, suggesting 366 that visual input from different spatial locations deploy different integration strategies 367 or weighting schemes. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 368 Our results deviate from the assumption that decreasing SOAs monotonically increase 369 illusion strength. At ±30 ms, accuracy was significantly high—exceeding baseline 370 levels—suggesting facilitation over fission. This suggests that when auditory stimuli 371 are too close in time, they may be perceptually fused or fall within a single cycle of 372 neural oscillation, failing to trigger the “two-beep” induced fission (Fiebelkorn & 373 Kastner, 2019). 374 375 Taken together, the results broaden the known spatial landscape of the SIFI. But we 376 still cannot adjudicate between two mechanistic accounts: (a) greater visual 377 uncertainty in the periphery biases the brain’s optimal estimate toward the auditory 378 count (Shams & Beierholm, 2010), and (b) stronger direct connectivity between 379 auditory cortex and the peripheral representation of early visual cortex (Eckert et al., 380 2008) gives auditory input heavier weight. To further disentangle whether this spatial 381 effect arises from sensory uncertainty or integration weights, Experiment 2 will 382 expand the eccentricity range and employ Bayesian modeling. 383 2.2 Experiment 2: Extended Spatial-Eccentricity for SIFI with Hierarchical 384 Bayesian Modelling 385 Building on the previous findings, we exploited a 360° acoustic arena to sample 386 observer performance in the SIFI paradigm at five eccentricities (0°, 15°, 30°, 45°, 387 60°; 15° steps). Using hierarchical Bayesian modelling anchored in the classical 388 causal-inference framework (Shams et al., 2006; Shams & Beierholm, 2010), we 389 compared two families of models: (1) a “visual-uncertainty” family that assumes 390 fixed AVI weights but allows visual likelihood variance to increase with eccentricity, 391 and (2) an “AV-weight” family that keeps likelihood variance constant while letting 392 the prior weight assigned to the common-cause hypothesis vary with retinal location. 393 At the behavioral level, we predict that across the 0–60° eccentricity range, visual 394 accuracy will decline and reports will become increasingly biased by the number of 395 auditory beeps, while performance on unimodal (flash-only) and congruent 396 audiovisual trials remains invariant. Computationally, if the uncertainty model family 397 provides a superior fit, it would favor the classic view that audiovisual integration 398 (AVI) computations are spatially identical, with performance deficits driven solely by .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 399 increased peripheral visual noise; however, a superior fit for the AV-weight family 400 would align with neuroanatomical evidence (Eckert et al., 2008; Falchier et al., 2002; 401 Rockland & Ojima, 2003), suggesting that different retinotopic loci possess intrinsic 402 susceptibilities to auditory influence, modeled as location-specific prior weights 403 within a Bayesian causal-inference framework. 404 Participants 405 Thirteen undergraduate students took part in the experiment. After applying an 406 accuracy criterion, data from eleven participants (six female) were retained. 407 Participants’ ages were ranged from 19 to 22 years (M = 20.27, SD = 1.01). All 408 participants had normal hearing and normal or corrected-to-normal vision, were right- 409 handed, and had no prior experience with similar experiments. Each participant 410 received 80 RMB in cash after the session. 411 Apparatus and stimuli 412 The experiment was conducted in a single, well-ventilated laboratory under dim 413 ambient lighting. As shown in Figure 5 (left), participants performed the computer- 414 based task on a 1.4-m-radius curved “audio-screen” display (resolution 1920 × 1080, 415 refresh rate 60 Hz). Sounds were delivered via a sound card sampled at 44.1 kHz and 416 presented through closed-back monitor headphones worn throughout the experiment. 417 Visual stimuli were white, Gaussian-ramped disks (Figure 5, right) chosen to 418 minimise sharp-edge after-effects (Stiles et al., 2020). A white square frame (4° × 4°) 419 served as the location cue. With the viewing distance fixed at 1.4 m by a chin-rest, the 420 disk subtended 2° of visual angle. Auditory stimuli were 10-ms pure tones at 2000 421 Hz. Participants responded using three keyboard keys (“Z”, “?/” and spacebar) while 422 maintaining a stable head position. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 423 424 Figure 5. Experimental Scene and Stimulus Examples for Experiment 2. Left: An 425 illustration of the laboratory setting. The screen displays all possible locations for 426 stimulus presentation; however, during an actual trial, the flash appears at only one 427 specific location. Right: The gradient disk stimuli used in Experiments 2 and 3, which 428 feature logarithmic decay along the axial direction. 429 Design and Procedure 430 As in Experiment 1, flashes were delivered at different spatial locations while the 431 number of accompanying beeps varied. The critical independent variable was visual 432 eccentricity, with nine levels: −60°, −45°, −30°, −15°, 0°, 15°, 30°, 45°, and 60°. 433 Because we focused on spatial rather than temporal properties of audiovisual 434 integration, SOA was not factorially manipulated; instead, only two SOAs—40 ms 435 (“short”) and 70 ms (“long”)—were used for the single-channel continuation stimuli 436 in both fission (more beeps than flashes) and fusion (more flashes than beeps) blocks. 437 Whenever both modalities were stimulated, the first audiovisual pair was always 438 presented simultaneously; subsequent unimodal stimuli followed at the designated 439 SOA. 440 The stimulus set was expanded (0-3 flashes; 0-2 beeps) to increase difficulty and 441 discourage response bias. Three-flash trials were used as a quality control measure, 442 with a 50% accuracy threshold for participant exclusion. As shown in Table 2, the 443 primary fission and fusion conditions consisted of 12 trials per SOA and eccentricity 444 level. These were embedded within a total of 1,150 trials. To manage fatigue, 445 participants took mandatory breaks for at least one minute every 80 trials. Total 446 experimental duration was approximately 90 minutes. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 447 Table 2. Experiment 2: Trial Distribution Number of auditory stimuli 0 1 2 Sum 0 (No.of auditory stimuli is random) 43 1 90 135 216 441 2 90 216 135 441 Number of Flash 3 45 90 90 225 448 449 Procedure 450 The task closely followed Experiment 1. After stimulus offset, an “X” appeared at the 451 bottom of the screen to signal the response window; the deadline was shortened to 2.5 452 s and the inter-trial interval to 0.75 s to reduce overall duration. Participants pressed 453 “Z” or “?/” to report “1” or “2” flashes (key mapping counter-balanced across 454 subjects); the space-bar was used for trials containing three flashes. All other 455 procedural details were identical to Experiment 1. 456 Data analysis 457 Responses were pooled and the mean reported number of flashes calculated for each 458 condition. Repeated-measures ANOVAs were used for factorial comparisons. To 459 mitigate the imbalance in trial counts, Bayesian factors were again computed with 460 JASP (JASP Team, 2023). 461 Figure 6 shows the mean reported flashes. 462 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 463 464 Figure 6. Violin Plots of Participant Response Accuracy Across Conditions in 465 Experiment 2. The width of each violin plot represents the probability density 466 distribution of the data. Individual dots represent data points for each participant 467 within that specific condition. The horizontal lines within the violin plots denote the 468 upper quartile, median, and lower quartile of the data. * p<.05, ** p<.01, *** p<.001 469 470 A 2 (target flashes: 1 vs. 2) × 3 (auditory beeps: 0, 1, 2) within-subjects ANOVA 471 analysis revealed significant main effects of both flashes and beeps, with no 472 interaction between them. For flashes, participants reported significantly more flashes 473 when two were presented compared to one (F(1, 10) = 156.11, p < .001, ηp² = .940, 474 BF₁₀ = 1.24 × 10⁵), with a mean difference of 0.563 (p < .001, BF₁₀ = 2.20 × 10¹⁴). 475 For beeps, there was a significant main effect (F(2, 20) = 42.11, p < .001, ηp² = .808, 476 BF₁₀ = 2.41 × 10⁵), where two beeps increased flash reports relative to both zero 477 beeps (|MD| = 0.426, p < .001, BF₁₀ = 5.29 × 10⁶) and one beep (|MD| = 0.353, p 478 < .001, BF₁₀ = 5.33 × 10⁴). However, the interaction between flashes and beeps was 479 not significant (F(2, 20) = 0.83, p = .450, ηp² = .077, BF₁₀ = 0.321), indicating that 480 the effect of flashes was consistent across beep conditions. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 481 Bonferroni-corrected post-hoc tests (Figure 6) confirmed the fission illusion: for 1- 482 flash trials, 0B ≈ 1B (|MD| = 0.115, p = .946, BF₁₀ = 8.66), but 2B > 1B > 0B (all ps 483 < .001). For 2-flash trials, 2B again produced higher reports than 1B or 0B (|MD|s ≥ 484 0.367, ps < .001). No reliable fusion illusion was observed; instead, two beeps 485 generally increased flash reports, consistent with cross-modal summation. All 486 subsequent analyses therefore focus on 1-flash trials to characterise the spatial profile 487 of fission. 488 Focusing again on 1-flash trials, we submitted accuracy to a 2-way repeated-measures 489 ANOVA with factors Auditory Level (0B, 1B, 2B) and Eccentricity (−60° to +60° in 490 15° steps). Both factors passed Mauchly’s test (auditory: χ²₂ = 5.296, p = .071; 491 eccentricity: χ²₃₅ = 33.423, p = .663). 492 The results demonstrated significant main effects of auditory beeps and eccentricity, 493 as well as a significant interaction between them. For auditory level, the characteristic 494 fission pattern is dominant (F(2, 20) = 38.42, p < .001, ηp² = .367, BF₁₀ = 7.99 × 10⁴), 495 with two beeps eliciting more flash reports than both one beep and zero beeps (all ps 496 < .001), which did not differ significantly. Eccentricity also significantly affected 497 reports (F(8, 80) = 8.86, p < .001, ηp² = .112, BF₁₀ = 4.10 × 10⁴): central vision (0°) 498 yielded lower (more accurate) reports than every peripheral location (ps < .05), and 499 right 15° produced lower reports than right 45° (|MD| = 0.214, p = .006, BF₁₀ = 71.16 500 (Figure 7). Critically, the auditory × eccentricity interaction was significant (F(16, 501 160) = 3.17, p < .001, ηp² = .072, BF₁₀ = 1.43 × 10³). Simple-main-effect analyses 502 revealed that eccentricity had no effect in the unimodal visual condition (0B: F(8, 80) 503 = 1.52, p = .163, BF₁₀ = 0.37) and only a marginal effect in the congruent audiovisual 504 condition (1B: F(8, 80) = 1.96, p = .062, BF₁₀ = 0.999). However, in the conflict 505 condition (2B), a strong eccentricity effect was observed (F(8, 80) = 18.18, p < .001, 506 BF₁₀ = 5.39 × 10⁷), where reports approached the veridical count of one flash only in 507 central vision, while all peripheral locations showed significantly more reports of 508 flashes, indicating stronger fission illusions in the visual periphery. 509 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 510 511 Figure 7. Mean reported number of stimuli for single target-flash trials across 512 auditory conditions in Experiment 2. Different colored lines represent different 513 numbers of auditory stimuli. Error bars indicate one standard error of the mean 514 (SEM). * denotes p<.05, ** denotes p<.01, *** denotes p<.001. 515 516 Together with Experiment 1, these findings confirm that when attention is largely 517 equated across the visual field, unisensory visual perception is spatially flat, whereas 518 multisensory processing—especially under audiovisual conflict—is sharply 519 modulated by retinal eccentricity. 520 In the 1F2B condition, we used two SOAs: 40 ms and 70 ms. To test whether spatial 521 eccentricity interacts with temporal context, we compared performance across 522 eccentricity and SOA. Because the target was always one flash and the distractors 523 always two beeps, accuracy and reported count are perfectly inversely related, and 524 Figure 8 shows that accuracy follows an inverted Gaussian profile across space. We 525 therefore used hit-rate as the metric and assumed a Gaussian relationship between 526 eccentricity x and P(hit): .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 527 𝑃(𝐻𝑖𝑡) = 𝐴 ∗ 𝑒 ―(𝑥―𝜇)2 2𝜎2 528 Data for each SOA were fitted separately; the two SOAs were also collapsed to obtain 529 an average curve. Adjusted R² was computed for each model. Table 3 summarises the 530 parameters. In all cases, the Gaussian described the data well (adjusted R² > .94) and 531 the curves for 40 ms and 70 ms were almost superimposable. Thus, univariate 532 accuracy can be characterised by a central-peaked Gaussian that declines toward the 533 periphery. What remains unknown is whether this spatial gradient reflects auditory 534 interference or merely weaker unisensory vision in the periphery; the modelling 535 analyses that follow will address this question. 536 Table 3 Table of Gaussian Curve Fitting Parameters for Response Accuracy in 1F2B 537 Trials 538 Amplitude 𝐴 Mean 𝜇 Standard deviation 𝜎 Goodness of fit 𝑅2 SOA = 40 ms 0.682 -4.046 33.630 0.933 SOA = 70 ms 0.676 -1.414 33.748 0.903 Mean 0.678 -2.739 33.748 0.922 539 540 The hit-rates for the two SOA conditions, together with the collapsed data and their 541 fitted Gaussian curves, are plotted in Figure 8. Accuracy was virtually identical at 40 542 ms and 70 ms, with no discernible separation. A 9 (eccentricity) × 2 (SOA) repeated- 543 measures ANOVA confirmed a significant main effect of eccentricity, F(8, 80) = 544 18.18, p < .001, ηp² = .645, BF₁₀ = 1.73 × 10¹², replicating the previous analysis, but 545 neither a significant main effect of SOA, F(1, 10) = 0.14, p = .895, ηp² < .001, BF₁₀ = 546 0.24, nor a significant eccentricity × SOA interaction, F(8, 80) = 0.72, p= .671, ηp² 547 = .007, BF₁₀ = 0.09. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 548 549 Figure 8. Participant response accuracy across eccentricities in the 1F2B condition of 550 Experiment 2. Different colored lines represent various SOA conditions and the grand 551 average of the data; error bars indicate one standard error (SE). 552 553 Thus, within the two SOAs tested, audiovisual integration was unaffected by temporal 554 separation. Given we focuses on spatial rather than temporal characteristics, the 40- 555 ms and 70-ms data were pooled for all subsequent modelling analyses. 556 Bayesian modelling 557 The findings from Experiments 1 and 2 demonstrate that the spatial location of visual 558 stimuli significantly modulates SIFI perception, suggesting that different regions of 559 the visual field may utilize distinct audiovisual integration mechanisms. Integrating 560 modality reliability theory with the modeling framework established by Hirst et al. 561 (2020)(Hirst et al., 2020), we propose two hypotheses to account for this spatial 562 variation in multisensory capacity. 563 564 First, The Spatial Weighting Hypothesis. The direct cross-modal influence of auditory 565 stimulation may have a greater impact in the peripheral visual field, resulting in 566 greater informational weight being assigned to the auditory modality during the 567 integration process. Combined with responses that integrate auditory information, this 568 makes illusory perception more likely to occur. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 569 Second, the Visual Uncertainty Hypothesis: This account posits that the increase in 570 illusory percepts in the periphery is a direct consequence of reduced visual reliability. 571 As visual acuity declines with eccentricity, the uncertainty surrounding visual 572 numerosity perception increases. Within a Bayesian framework, the brain compensates 573 for this unreliable visual signal by relying more heavily on the relatively more precise 574 auditory information, leading to the perception of the sound-induced flash illusion. 575 To investigate which mechanism better supports the current findings, we implemented 576 Bayesian modeling to perform hierarchical inference about internal cognitive 577 processes (Van De Schoot et al., 2021). We used PyMC5, a Python library for 578 probabilistic programming that offers extensive choices of prior and posterior 579 distributions, for model construction and comparison, and implemented algorithms 580 such as Markov Chain Monte Carlo (MCMC) for posterior sampling (Abril-Pla et al., 581 2023). 582 Following the Bayesian ideal observer model (Shams & Beierholm, 2010), we model 583 perceived numerosity as a weighted combination of auditory and visual information. 584 Sensory inputs are treated as probability distributions; when signals originate from the 585 same source, their likelihoods are multiplied to create a joint audiovisual 586 representation. The observer then forms a final perceptual estimate by calculating the 587 precision-weighted average of the individual sensory channels and the integrated 588 likelihood. This approach ensures that the resulting percept is a reliable inference 589 based on the relative uncertainty of each modality. 590 Mathematically, this process can be described as follows: when an observer forms a 591 perceptual representation 𝑆𝑣 of visual information based on received audiovisual 592 sensory information x𝑣 and xa, the following occurs: 593 First, if the observer believes that visual and auditory stimuli originate from different 594 sources (C = 2, where C represents causal structure, i.e., the number of sources), and 595 can independently receive information from both modalities, the sensory information 596 received through each modality is, due to the presence of noise, essentially 597 represented as Gaussian distributions. The means 𝜇𝑣 and 𝜇𝑎 represent individual .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 598 subjective estimates, while standard deviations 𝜎v and 𝜎a represent the uncertainty 599 of unisensory information: 600 601 p x𝑣│𝐶 = 2 = 1 2𝜋 𝑒 ―(x𝑣―𝜇𝑣) 2𝜎2 𝑣 2 602 p 𝑥𝑎│𝐶 = 2 = 1 2𝜋 𝑒 ―(𝑥𝑎―𝜇a) 2𝜎2 𝑎 2 603 When an individual cannot completely separate auditory and visual stimuli in 604 perception, integration occurs. In this case, the observer believes that the audiovisual 605 stimuli originate from the same source (C = 1), and subsequently forms a unified 606 representational estimate of the audiovisual stimuli. Computationally, this audiovisual 607 representation xav is obtained by multiplying the likelihood functions of the 608 unisensory auditory and visual channels, and the result is also a Gaussian distribution: 609 p(𝑥𝑎𝑣|𝐶 = 1) ~ 𝑝(𝑥𝑣|𝐶 = 2) × p 𝑥𝑎│𝐶 = 2 610 p(𝑥𝑎𝑣|𝐶 = 1) = 1 2𝜋 𝑒 ―(𝑥𝑎𝑣―𝜇𝑎𝑣) 2𝜎2 𝑎𝑣 2 611 Here, both the mean 𝜇𝑎𝑣 and standard deviation 𝜎av of the audiovisual stimulus 612 estimate can be expressed in terms of the distribution parameters of the unisensory 613 stimuli: 614 615 𝜇𝑎𝑣 = 𝜇𝑣𝜎2 𝑣 + 𝜇𝑎𝜎2 𝑎 𝜎2 𝑣 + 𝜎2 𝑎 𝜎2 𝑎𝑣 = 𝜎2 𝑣𝜎2 𝑎 𝜎2 𝑣 + 𝜎2 𝑎 616 617 When making perceptual decisions, according to Bayes' formula, individuals will 618 form weighted averages of the unisensory inference 𝑆𝑣,𝐶=2 and the integrated .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 619 inference 𝑆𝑎𝑣, using the probabilities of same-source versus different-source 620 scenarios as weights, thereby generating the optimal inference for unisensory 621 information. 622 𝑆𝑣 = 𝑝 𝐶 = 1│𝑥𝑎,𝑥𝑣 𝑆𝑎𝑣 + 𝑝 𝐶 = 2│𝑥𝑎,𝑥𝑣 𝑆𝑣,𝐶=2 623 Using weight (w) to represent the probability of audiovisual integration occurring in 624 subjects, we obtain: 625 𝑆𝑣 = w 𝑆𝑎𝑣 + (1 ― 𝑤) 𝑆𝑣,𝐶=2 626 This hierarchical inference structure can be well characterized by Bayesian models, 627 and through manipulation of different parameters, we can investigate the source of 628 differences in subjects' audiovisual integration levels across various spatial 629 eccentricities. To explore the specific mechanisms underlying these spatial 630 distribution characteristics, we constructed five models as shown in Figure 9. The 631 models share these common variables: 𝑣 (visual information likelihood, representing 632 the observer's sensory estimate of visual information) and 𝑎 (auditory information 633 likelihood, representing the sensory estimate of auditory information), which are 634 sampled from two Gaussian distributions. Since this involves fitting the 1F2B 635 condition, sampling is performed from distributions with a mean of 1 and standard 636 deviation of 𝜎𝑣 and a mean of 2 and standard deviation of 𝜎𝑎, respectively. The 637 standard deviation parameters 𝜎𝑣 and 𝜎𝑎, which characterize the uncertainty of 638 unisensory information, are free parameters in the model that need to be fitted through 639 data sampling. Observers combine noisy audiovisual signals and their respective 640 uncertainties to form a unified stimulus representation, assuming the signals originate 641 from the same source (𝑎𝑣). Since the final weighted average is essentially a weighted 642 average of the means, only 𝜇𝑎𝑣 needs to be calculated during the sampling process. 643 Finally, the observer's estimate of visual perception is obtained through weighted 644 averaging of 𝜇𝑎𝑣 and their own sensory sample 𝑣 to produce the optimal estimate 645 (opt), where the weight 𝑤 is also a free parameter of the model. 646 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 647 648 Figure 9. Diagram of Five Bayesian Model Structures. Key elements of the structure 649 diagram: Nodes: Each ellipse represents a random variable or deterministic variable. 650 Nodes filled in gray typically represent observed data. Arrows: Arrows indicate 651 dependency relationships from one variable to another. Deterministic Nodes: Nodes 652 labeled “Deterministic” indicate that the variable is a deterministic function of its 653 parent variables, with values determined by the parent nodes. Shape: Numbers next to 654 nodes represent the shape of tensor variables. For example, 9×1 may represent a 655 vector containing 9 elements. Distribution: For each node that is sampled from a 656 distribution, the specific distribution is provided. For example, “Normal” indicates a 657 normal distribution, “Uniform” indicates a uniform distribution. The parameters of a 658 distribution may depend on other nodes. 659 Model 1 serves as the baseline model, assuming neither individual differences in 660 unisensory information nor differences across eccentricities. Consequently, each 661 parameter yields only a single optimized value, with all factors considered constant. 662 Model 2 is an individual differences model that, compared to the baseline, accounts 663 for inter-subject variability in sampled sensory information by introducing shape 664 parameters. This allows the model to independently sample v and a for each 665 subject, modeling based on their own sensory information, but still without 666 considering eccentricity effects. Model 3 is a weight model that introduces shape 667 parameters for weight w, enabling separate sampling and estimation of integration 668 weights for each eccentricity, resulting in different estimates across eccentricities. 669 Model 4 is an uncertainty model that assigns shape parameters to 𝜎v, positing that .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 670 subjects exhibit different perceptual uncertainties for visual stimuli presented at 671 different spatial locations, leading to eccentricity-dependent differences in subsequent 672 integration. Model 5 is the integrated model, which combines features of the two 673 previous eccentricity-based models. This most complex model aims to simultaneously 674 capture the effects of eccentricity on both weight w and visual information 675 uncertainty 𝜎v. 676 Each of the five models was sampled using four parallel MCMC chains, with each 677 chain drawing 2000 samples and discarding the first 1000 for tuning. For the 678 integrated model, which has more parameters and thus requires more samples, each 679 chain drew 4000 samples while discarding the first 2000. The sampling results 680 showed adequate convergence for all parameters across models, with r ≤ 1.01, 681 indicating that the data structure has been thoroughly explored and the models have 682 been adequately fitted to the existing data. 𝑟 represents the potential scale reduction 683 factor, which assesses MCMC sampling quality by examining the ratio of between- 684 chain variance to within-chain variance to evaluate whether chains have converged to 685 the same distribution; values close to 1 indicate good convergence, and all models in 686 this experiment achieved stable convergence. 687 To compare the performance of the five models, we employed Widely Applicable 688 Information Criterion (WAIC) as the evaluation metric. This is a widely used model 689 selection criterion in Bayesian statistics that identifies models fitting the data well 690 without excessive complexity. Its calculation is based on the log pointwise predictive 691 density (l𝑝𝑝𝑑) and the effective number of parameters (Wasserman, 2000). The 692 specific formula is as follows: 693 694 𝑊𝐴𝐼𝐶 = ―2(𝑙𝑝𝑝𝑑 ― 𝑝𝑤𝐴𝐼𝐶) 695 696 where 𝑙𝑝𝑝𝑑 is the expected value of the log-likelihood function of the observed data 697 over the posterior distribution of model parameters, representing goodness-of-fit; and .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 698 𝑝𝑤𝐴𝐼𝐶 represents the effective number of parameters, estimating model complexity. 699 These two components separately assess model fit and complexity. WAIC seeks to 700 balance these aspects to select the optimal model. The smallest WAIC value typically 701 corresponds to the best model (Table 4). 702 We calculated WAIC for the five models and plotted the comparison, shown in Figure 703 10. The weight model performed best, substantially outperforming all other models, 704 even surpassing the integrated model that considered both uncertainty and weight 705 variations. Therefore, we can conclude that the eccentricity effect obtained in the 706 current experiment operates by directly altering the information weight for integrated 707 audiovisual same-source stimuli, making visual estimates in multisensory contexts 708 more susceptible to interference from auditory information. 709 710 Table 4. Performance Metrics for Different Models 711 Models 𝑙𝑝𝑝𝑑 𝑆𝐸(𝑙𝑝𝑝𝑑) 𝑝𝑤𝐴𝐼𝐶 𝑊𝐴𝐼𝐶 Δ𝑊𝐴𝐼𝐶 Baseline -30.36 6.17 1.54 63.80 65.94 Individual differences -19.97 6.55 11.00 61.94 64.08 Weight 10.83 3.69 9.76 -2.14 \ Uncertainty 4.01 3.43 14.07 20.12 22.26 Integrated 7.70 3.38 13.26 11.12 13.26 712 713 Table 5 shows the fit of the weight model on specific parameters. The key parameters 714 in this model are 𝜎v，𝜎a, and the respective weights w for each of the 9 different 715 eccentricities. The highest density interval (HDI) is used to represent the posterior 716 distribution, encompassing the region of highest posterior density; here, the 3% and .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 717 97% percentiles are used as the lower and upper bounds. 𝑟 being close to 1 718 indicates that the chains have converged well; here, the model's estimates for each 719 parameter are visible, demonstrating that model sampling has achieved stable 720 convergence based on the existing data. 721 Table 5: Posterior Parameter Distributions of the Weight Model Parameters M SD 3% HDI 97% HDI 𝑟 𝜎𝑣 0.093 0.052 0.010 0.181 1.0 𝜎𝑎 0.304 0.096 0.149 0.487 1.0 𝑤( ― 60°) 0.830 0.096 0.672 1.000 1.0 𝑤( ― 45°) 0.659 0.103 0.465 0.852 1.0 𝑤( ― 30°) 0.391 0.091 0.223 0.566 1.0 𝑤( ― 15°) 0.416 0.092 0.246 0.590 1.0 𝑤(0°) 0.265 0.090 0.097 0.436 1.0 𝑤(15°) 0.308 0.091 0.140 0.484 1.0 𝑤(30°) 0.675 0.101 0.484 0.868 1.0 𝑤(45°) 0.699 0.102 0.511 0.892 1.0 𝑤(60°) 0.894 0.078 0.756 1.000 1.0 722 723 To further evaluate the model's predictive performance, the probability density 724 distribution of the optimal estimate (opt) obtained at each eccentricity level is plotted 725 in Figure 10. It can be observed that as eccentricity extends from central vision 726 toward the periphery, the observer's estimate of the number of flashes also increases. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 727 728 Figure 10. Model-predicted probability density distributions of reported counts. 729 Colors indicate the posterior distributions for different spatial eccentricities. While the 730 means shift across positions, the standard deviations of the distributions remain 731 consistent across conditions. 732 733 Next, we quantitatively describe the mapping between the weighting model’s 734 predicted results (opt) and spatial eccentricity. Assuming that incorrect responses in 735 the 1F2B (1-flash, 2-beep) task consist of reporting two flashes, let 𝑝 denote the 736 response accuracy. Thus, the mean reported number of flashes is N = p +2 × 737 (1 ― 𝑝) = 2 ― 𝑝, or conversely, p = 2 ― N. In the behavioral data, we found that a 738 Gaussian distribution effectively fits the spatial distribution of response accuracy. To 739 validate the weighting model's descriptive power, we calculated a hypothetical 740 accuracy (2 ― opt) and fitted a Gaussian curve to examine whether the model- 741 generated posterior data exhibit spatial characteristics similar to the empirical 742 accuracy distribution. 743 As illustrated in Figure 11, the optimal estimates predicted by the model also follow a 744 Gaussian relationship across space, R2 = 0.863, closely mirroring the overall 745 distribution of the actual data. Due to occasional trials where participants reported 746 three flashes (N>2), the actual 𝑝 is slightly lower than the theoretical 2−N. 747 Consequently, the calculated p distribution is slightly higher than the actual 748 response accuracy; nonetheless, the high degree of similarity between the two .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 749 distributions confirms that the weighting model provides an optimal representation of 750 the experimental data. 751 752 753 Figure 11. Comparison of model-predicted and empirical accuracy across spatial 754 eccentricities. Gray data points and lines represent the predicted accuracy p calculated 755 from model-sampled opt. The green line (consistent with Figure 8) shows the 756 Gaussian fit of the participants' empirical response data. Error bars denote ±1 standard 757 error of the mean (SEM). 758 759 Discussion 760 Extending Experiment 1, the present experiment documented a robust eccentricity- 761 dependent SIFI up to 60°: the farther into the periphery, the more flashes participants 762 reported in 1F2B trials. Crucially, this spatial modulation emerged only when audition 763 and vision conflicted; unimodal vision and congruent AV trials were flat across 764 eccentricity. Curve-fitting showed that hit-rate follows a Gaussian profile centred on 765 the fovea. Bayesian model comparison revealed that a weight model—where the prior 766 probability of fusing AV signals increases with retinal eccentricity—outperformed an 767 uncertainty model and a full model that varied both weight and visual noise. Thus, .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 768 stimuli located more peripherally are a priori more likely to be bound with concurrent 769 sounds, supporting recent proposals that early sensory cortices exhibit space-specific 770 cross-modal weighting (Eckert et al., 2008; Falchier et al., 2002; Rockland & Ojima, 771 2003). 772 Predictions generated by the weight model reproduced the empirical Gaussian spatial 773 signature (R² = .86), confirming its explanatory power. In traditional causal-inference 774 accounts, the fusion prior is usually treated as constant because stimulus location is 775 fixed (Shams et al., 2005). Here, freeing the weight parameter captured the spatial 776 prior: observers expect peripheral visual events to be auditory-causal, so auditory 777 input dominates the final estimate. The failure of the uncertainty model aligns with 778 the behavioural null-effect in unisensory flash trials: when attention is equated across 779 locations, visual numerosity perception is spatially uniform, indicating that the visual 780 system can compensate for lower peripheral acuity under unisensory conditions 781 (Shulman et al., 1985). 782 Our findings converge with M/EEG studies identifying early-latency signatures of the 783 flash illusion (47–120 ms) (Mishra et al., 2008; Shams et al., 2005) and fMRI 784 evidence showing heightened recruitment of the superior temporal sulcus (STS) and 785 superior colliculus (SC) during illusory trials (de Haas et al., 2012). Collectively, 786 these data support the view that multisensory integration is not limited to high-level 787 association cortices; rather, it is an early-stage process automatically modulated by 788 the spatial receptive-field architecture of primary sensory areas. 789 790 2.3 Experiment 3 – Impact of Spatial AV Congruency on SIFI 791 After establishing that visual eccentricity biases AV integration, we asked whether 792 auditory spatial position matters. We simultaneously manipulated the location of 793 flashes and beeps to compare integration when AV signals were spatially congruent 794 versus incongruent. Because vision is the dominant modality in SIFI (Kumpik et al., 795 2014), we expected a robust illusion under both arrangements with no additional 796 penalty for spatial mismatch. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 797 Participants 798 Ten undergraduates (6 female, 60 %; age 19–22, M = 20.50, SD = 0.97) with normal 799 hearing and normal/corrected vision participated. All were right-handed and naïve to 800 the purpose. They received 50 RMB after a 40-min session. 801 Apparatus and Stimuli 802 Testing took place in the same dimly lit laboratory. Visual stimuli were presented on a 803 27-in LCD (1920 × 1080, 120 Hz, 56 cm width) viewed at 60 cm. A white Gaussian- 804 ramped disk (1° dia.) appeared 7° left or right of fixation; a 2° white square frame 805 served as location cue. Auditory stimuli were 10-ms, 2000-Hz pure tones delivered 806 via closed-back headphones at 44.1 kHz. Responses were made with “Z” and “?/” 807 keys. 808 Design and Procedure 809 This experiment aimed to investigate the impact of audiovisual spatial congruency on 810 multisensory integration. Visual stimuli were presented at one of two possible spatial 811 locations (7° eccentricity in the visual field), consisting of one, two, or three flashes. 812 The three-flash condition was included to prevent participants from adopting specific 813 response strategies or developing a distinct response bias in their number judgments. 814 Catch trials (attention checks) were implemented with no flash present; participants 815 who committed more than five errors in these trials were to be excluded. Notably, all 816 participants in this study committed four or fewer errors. Auditory stimuli consisted 817 of zero to four beeps. Unlike previous experiments that utilized only binaural 818 presentation, here we incorporated spatial cues for the auditory stimuli: beeps were 819 presented either binaurally or monaurally (ipsilateral or contralateral to the visual 820 stimulus). 821 The trial distribution is detailed in Table 5. As with previous experiments, a higher 822 number of trials were allocated to the critical 1F2B (1-flash, 2-beep) and 2F1B (2- 823 flash, 1-beep) conditions to manipulate the interstimulus interval (ISI) and explore the 824 temporal dynamics of integration. The ISI was set at 42 ms for flashes and 30 ms for .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 825 beeps (the latter corresponding to the 40 ms Stimulus Onset Asynchrony (SOA) used 826 in Experiments 1 and 2). For the 1F2B and 2F1B conditions, four distinct temporal 827 relationships were designed based on the stimulus sequence and interval length. 828 Specifically, the “long interval” was three times the duration of the “short interval”. 829 This variety in temporal combinations was designed to increase experimental 830 diversity and facilitate a preliminary investigation into the combined effects of spatial 831 congruency and temporal context on integration. Consequently, the number of 1F2B 832 and 2F1B trials was four times that of other conditions. The experiment comprised 833 684 trials in total, with mandatory breaks of at least one minute every 50 trials. The 834 total duration was approximately 40 minutes. 835 836 Table 5. Trial distribution across conditions for Experiment 3. 837 Number of auditory stimuli 0 1 2 3 4 Sum 0 6 18 18 18 18 78 1 12 36 144 36 36 264 2 12 144 36 36 36 264 Number of flashes 3 6 18 18 18 18 78 838 The procedure was largely consistent with those of Experiments 1 and 2. Each trial 839 began with a white fixation cross presented at the center of a gray screen for 500 ms. 840 Subsequently, a white square (2° in visual angle) appeared for 500 ms on either the 841 left or right side to cue the spatial location of the upcoming target. After a 500 ms 842 blank-screen interval, the audiovisual stimuli were presented. 843 Following the stimulus presentation, the fixation cross turned red, serving as a "go" 844 signal for the participant to respond. Once a response was made, the screen 845 transitioned to a blank display. Participants reported seeing one or two flashes by .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 846 pressing the "Z" or "/" keys, which were counterbalanced across participants. In cases 847 where three flashes were perceived, participants were instructed to press the spacebar. 848 The maximum response window was 2.5 s. The inter-trial interval (ITI) was 0.75 s, 849 with an additional random jitter incorporated to sufficiently sample various response 850 states of the participants. 851 Data analysis 852 Similar to Experiment 2, all response data from this experiment were aggregated, and 853 the mean reported numbers under various conditions were calculated. Comparisons 854 across levels were conducted using repeated measures ANOVA, with additional 855 Bayesian factor analysis performed in JASP (JASP Team, 2023). 856 First, we examined whether a significant SIFI effect was observed by calculating the 857 mean reported numbers for all participants under each auditory stimulus condition 858 when visual stimuli were 1 and 2 flashes, with results shown in Figure 12. A two-way 859 repeated measures ANOVA was conducted. Since the auditory stimulus number level 860 failed Mauchly's test of sphericity, χ²(9) = 29.870, p < .001, Greenhouse-Geisser 861 correction was applied. The data revealed a significant main effect of flash number on 862 participants' reports, with reports under two flashes significantly higher than under 863 one flash, F(1, 9) = 76.192, p < .001, ηp² = .894, BF₁₀ = 2615.170, mean difference 864 |MD| = 0.544. The main effect of auditory stimulus number was also significant, 865 F(1.4, 12.597) = 28.908, p < .001, ηp² = .894, BF₁₀ = 1.437 × 10⁸. The interaction 866 between the two factors was significant as well, F(4, 36) = 2.647, p = .049, ηp² 867 = .227, BF₁₀ = 1.419. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 868 869 Figure 12. Violin plot of participants' reported numbers in Experiment 3. The width 870 of the violin plot represents the density distribution of the data; each point represents 871 the data of one participant under that condition. The horizontal lines inside the violin 872 plot represent the upper quartile, median, and lower quartile of the data. * indicates p 873 < .05, ** indicates p < .01, *** indicates p < .001. 874 Focusing specifically on the simple main effects of auditory stimuli under the two 875 flash levels: When the target flash was 1 flash, the simple main effect of auditory 876 number was significant, F(4, 36) = 19.461, p < .001, BF₁₀ = 1.560 × 10⁶. Specifically, 877 no significant difference existed between 1B and 0B conditions, |MD| = 0.072, p = 878 1.000, BF₁₀ = 0.586. However, with more than 1 auditory stimulus, participants' mean 879 reported numbers were significantly higher than both the no-auditory-stimulus and 880 audiovisual-congruent conditions, ps 1.5. When the target flash was 2 881 flashes, the simple main effect of auditory number was also significant, F(4, 36) = 882 23.301, p < .001, BF₁₀ = 1.108 × 10⁷. Participants' reported numbers in the 1B 883 condition were significantly lower than in other conditions, ps 25. 884 That is, this experiment observed both significant flash fission illusion and flash 885 fusion illusion: When auditory stimuli presented more stimuli than visual flashes, 886 participants' reported numbers increased significantly, and when presented auditory 887 stimuli were fewer than target flashes, participants' reported numbers were 888 significantly lower than other conditions and unimodal perception without auditory .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 889 interference. Notably, although the three experiments so far have only found illusory 890 interference during audiovisual incongruence without observing significant 891 facilitation during consistent audiovisual information, in this experiment, the variance 892 across all participants' data was notably smaller under the 1F1B condition, suggesting 893 that congruent conditions may facilitate more efficient processing of visual 894 information. 895 To further examine the influence of spatial features of audiovisual stimuli on 896 integrated perception, both fission and fusion illusions were observed in this 897 experiment. However, the fission illusion phenomenon was more pronounced, with 898 multiple conditions triggering fission perception. Therefore, the mean of participants' 899 reports when the target flash was presented once was adopted as the comparison 900 metric. 901 To avoid potential influences from visual presentation field, a two-way ANOVA of 902 spatial location and auditory stimulus number was first conducted. As shown in the 903 left panel of Figure 13, the main effect of spatial field on participants' reported 904 numbers was not significant; presenting stimuli in the left versus right visual fields 905 had no effect on audiovisual integration, F(1, 9) = 0.056, p = .819, ηp² = .006, BF₁₀ = 906 0.347. Therefore, when subsequently comparing audiovisual stimulus congruence, 907 trials presented in the left and right visual fields were combined, focusing only on the 908 relative spatial relationship between audiovisual stimuli. 909 Participants' reported numbers were then compared when auditory stimuli were 910 presented ipsilaterally, contralaterally, or bilaterally to the flash. ANOVA results 911 showed that audiovisual stimulus congruence had no significant effect on participants' 912 perceived numbers. Whether the sound was presented ipsilaterally, contralaterally, or 913 bilaterally to the visual stimulus, participants reported similar numbers of flashes, F(2, 914 18) = 0.494, p = .618, ηp² = .052, BF₁₀ = 0.170. 915 Thus, it can be concluded that in audiovisual integration paradigms based on visual 916 tasks such as the sound-induced flash illusion, the spatial location of auditory stimuli 917 and the spatial relationship between auditory and visual stimuli have minimal 918 influence on observers' perception. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 919 920 921 922 Figure 13. Participants' reported numbers under different conditions in Experiment 3. 923 The left panel shows the reported number of flashes under different auditory stimulus 924 numbers when visual stimuli were presented in the left or right visual field. The right 925 panel combines stimuli from both visual fields, comparing reported numbers when 926 auditory stimuli were presented ipsilaterally, contralaterally, and bilaterally to the 927 visual target. * indicates p < .05, ** indicates p < .01, *** indicates p < .001. 928 929 Discussion 930 This experiment focused on the spatial congruence of audiovisual stimuli and 931 revealed that the perception of SIFI was not significantly influenced by the spatial 932 relationship between the auditory and visual stimuli. Specifically, whether the visual 933 stimulus was presented in the left or right visual field, and whether the auditory 934 stimulus was presented ipsilaterally, contralaterally, or neutrally (binaurally) to the 935 visual stimulus, no significant effect on participants' SIFI perception was observed. 936 This finding suggests that spatial congruence of stimuli does not have a measurable 937 effect on the level of audiovisual integration with SIFI. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 938 Notably, in addition to exhibiting the fission illusion—similar to the first two 939 experiments—this experiment also demonstrated a pronounced fusion illusion when 940 the number of auditory stimuli was fewer than the number of flashes. The main 941 distinction between this experiment and Experiment 1 lies in the inclusion of 942 additional stimulus conditions at the audiovisual level to mitigate potential systematic 943 errors. When an individual’s prior perception regarding the overall possible number 944 of audiovisual stimuli in the experiment changes, the level of audiovisual integration 945 is subject to the influence of this perceptual expectation (Wang et al., 2019). This shift 946 in expectation may account for the observed differences in participant performance, 947 even under similar temporal and spatial conditions. 948 In contrast to the findings of the first two experiments, the results of the current 949 experiment provide greater support for a late-integration model of audiovisual 950 processing. The observation that the SIFI effect under spatially incongruent 951 (contralateral) conditions was similar to the effect under binaural presentation 952 suggests that audiovisual integration may be mediated by higher-level brain regions 953 involved in later-stage processing. 954 3 General Discussion 955 This study exploited the robustness of the Sound-Induced Flash Illusion (SIFI) to 956 investigate the effect of stimulus spatial characteristics on audiovisual integration 957 capacity, successfully revealing the distribution pattern of how the level of 958 audiovisual integration is influenced by stimulus spatial features, while replicating the 959 SIFI originally discovered by Shams et al. (2002)(Shams et al., 2002). 960 In Experiment 1 and Experiment 2, we explored the influence of visual stimulus 961 spatial location on observers' perception during audiovisual integration. The results 962 indicated that, after controlling for matched attentional resource allocation across 963 spatial locations, unimodal visual perception did not change with the spatial location 964 of the stimulus. However, a clear difference in audiovisual bimodal processing was 965 found between spatial locations: stimuli presented in the peripheral visual field 966 (beyond 15°) were more significantly interfered with by auditory information, and the 967 susceptibility to audiovisual integration increased towards the periphery, a spatial .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 968 distribution that can be approximated by a Gaussian curve. With modeling, we found 969 that the unimodal information uncertainty in the peripheral visual field did not, in fact, 970 change. Instead, the effect was driven by a mechanism that directly enhanced the 971 influence of auditory information by altering the weighting ratio of audiovisual 972 information during processing. In Experiment 3, we attempted to simultaneously 973 manipulate the spatial location of both visual and auditory stimuli to explore whether 974 their spatial congruence would affect the probability of integration. The results 975 showed that SIFI remained stable across various spatial relationships between 976 audiovisual stimuli; even when a potential interhemispheric integration (with 977 contralateral layout of audiovisual stimuli) of sensory information was required, 978 participants' perceptual performance was virtually identical to conditions with 979 ipsilateral or binaural auditory stimulus presentation. With three experiments, we 980 comprehensively explored the spatial characteristics of audiovisual integration from 981 two aspects: the spatial location of visual information and the spatial relationship 982 between audiovisual stimuli. 983 984 This work addresses existing gaps in the literature by expanding the range of spatial 985 eccentricity to a broad 60° across both hemifields while strictly controlling for 986 attentional consistency. These refinements provide a more robust resolution to 987 previously disputed questions regarding spatial modulation of the SIFI. Furthermore, 988 by integrating Bayesian modeling with Causal Inference theory, we characterize the 989 underlying mechanisms from a computational perspective. Our analysis suggests that 990 different retinotopic locations possess intrinsic differences in their responsiveness to 991 audiovisual stimuli, which directly modulates the informational weighting during 992 perceptual inference. This indicates that cross-modal influence is shaped by stimulus 993 location in a relatively automatic, bottom-up manner (Keil & Senkowski, 2018). 994 995 There remain certain limitations in the current experiments. For instance, the 996 imbalance in trial design—the deliberate inclusion of more audiovisual conflict trials 997 (1F2B or 2F1B)—could raise concerns about the validity of the conclusions. Such an 998 overall design might lead participants to form a certain expectation regarding the 999 corresponding combinations, e.g., higher accuracy for perceiving two flashes when .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted February 19, 2026. ; https://doi.org/10.64898/2026.02.19.706740doi: bioRxiv preprint 1000 one auditory stimulus is presented. Previous studies have shown that such perceptual 1001 expectation can influence the probability of SIFI (Wang et al., 2019). 1002 To minimize the impact of trial imbalance, we informed participants that all stimulus 1003 combinations were possible and utilized Bayes Factor analysis (Dienes, 2014) to 1004 robustly compare hypotheses across unequal sample sizes. Because the trial 1005 distribution was uniform across all eccentricities, our primary spatial comparisons 1006 remain valid. Furthermore, the robust illusions observed contradict the notion that 1007 trial frequency awareness suppressed cross-modal influence (Wang et al., 2019). The 1008 design strategically maximized sampling of illusory trials while variable SOAs 1009 prevented practice effects. Future research should employ neuroimaging to localize 1010 these effects in unimodal sensory cortices and incorporate eye-tracking to control for 1011 microsaccades and bottom-up attentional capture. 1012 In summary, this study provides a comprehensive characterization of the spatial 1013 constraints governing audiovisual integration. Behaviorally, we refined previous 1014 explorations by demonstrating that SIFI susceptibility is significantly modulated 1015 across a broad 60°range of visual eccentricity. Conversely, our investigation into 1016 spatial incongruence revealed that the relative position of auditory stimuli does not 1017 significantly influence integration, highlighting the dominance of visual eccentricity 1018 in shaping these percepts. At the modeling level, a Gaussian distribution successfully 1019 quantified perceptual performance across the visual field, providing a robust 1020 mathematical description of these spatial variations. Furthermore, Bayesian 1021 computational modeling localized the eccentricity effect to a fundamental shift in the 1022 allocation of sensory weights: visual stimuli in the far periphery possess a higher 1023 probability of being integrated with auditory information compared to those at 1024 fixation. By systematically manipulating spatial characteristics within the flash 1025 illusion paradigm, this research deepens our understanding of the mechanisms 1026 underlying multisensory processing. These findings offer a critical empirical 1027 framework for the selection of stimulus locations in future multisensory research and 1028 contribute to a more nuanced model of how the brain resolves audiovisual 1029 information across the visual field. 1030 .CC-BY 4.0 International licenseperpetuity. 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