Neural Correlates of Serial Dependence: Synaptic Short-term Plasticity Orchestrates Repulsion and Attraction
Authors: Xiuning Zhang
Xincheng Lu
Nihong Chen
Yuanyuan Mi
Venue: NeurIPS 2025 poster ()
Keywords: serial dependence
short-term plasticity
continuous attractor neural networks
sensitivity and stability
Primary area: neuroscience_and_cognitive_science

Abstract: Serial dependence reflects how recent sensory history shapes current perception, producing two opposing biases: repulsion, where perception is repelled from recent stimuli, and attraction, where perception is drawn toward them. Repulsion typically occurs at the sensory perception stage, while attraction arises at the post-perception stage. To uncover the neural basis of these effects, we developed a two-layer continuous attractor neural network model incorporating synaptic short-term plasticity (STP). The lower layer, dominated by synaptic depression, models sensory processing and drives repulsion due to sustained neurotransmitter depletion. The higher layer, dominated by synaptic facilitation, models post-perception processing and drives attraction by sustained high neurotransmitter release probability. Our model successfully explains the serial dependence phenomena observed in the visual orientation judgment experiments, highlighting STP as the critical mechanism, with its time constants defining the temporal windows of repulsion and attraction. Furthermore, the model provides a neural foundation for the Bayesian interpretation of serial dependence. This study advances our understanding of how the neural system leverages STP to balance sensitivity in sensory perception with stability in post-perceptual cognition.

Neural Correlates of Serial Dependence: Synaptic Short-term Plasticity Orchestrates Repulsion and Attraction
Xiuning Zhang' xiuning Sumningg.hanggbutoook..com
Xincheng Lu 1xxc24mmalss tsinghua.
Nihong Chen nihongch@m. scnu. edu. cn
Yuanyuan Mi!*
miyuanyuandtsinghua. edu,
Abstract
Serial dependence reflects how recent sensory history shapes current perception, producing two opposing biases: repulsion, where perception is repelled from recent stimuli, and attraction, where perception drawn toward them. Repulsion typically occurs at the sensory perception stage, while attraction arises at the post-pereeption stage. To uncover the neural basis of these effects, we developed two-layer continuous attractor neural network model incorporating synaptic short-term plas- ticity (STP). The lower layer, dominated by synaptic depression, models sensory processing and drives repulsion due sustained neurotransmitter depletion. The higher layer, dominated by synaptic facilitation, models post-perception processing and drives attraction by sustained high neurotransmitter release probability. Our model successfully explains the serial dependence phenomena observed in the visual orientation judgment experiments, highlighting STP the critical mech- anism, with its time constants defining the temporal windows of repulsion and attraction. Furthermore, the model provides neural foundation for the Bayesian interpretation of serial dependence. This study advancee our understanding of how the neural system leverages STP to balance sensitivity in sensory perception with stability in post-peree post-perceptual cognition.
Introduction
The visual world casts dynamic images on the retina. From moment to moment, internal and external noise fluctuates across changes in lighting, occlusion, and viewpoint in the environment. Yet perceive coherence and stability in the world. Serial dependence an intrinsic mechanism through which visual system exploits temporal correlations and contextual redundancies by merging similar stimuli that slightly change over time. The visual system harnesses this autocorrelation by inducing positive serial dependencies, drawing the current perception towards the recent history. Through continuous serial dependencies, cognition compensates for variability in sensory input, stabilizing what would otherwise be noisy and discontinuous experience of the world 2
In contrast to the positive serial dependence, negative dependence is widely documented. Examples of negative serial dependence well-known phenomena of visual adaptation and aftereffects (5 6). e.g., a vertical grating appears to tilt clockwise after exposure to counterclockwise orientations. Such
*Corresponding authors. Department Psychological and Cognitive Sciences, Tsinghua University, Beijing 100084, China. "Key Laboratory of Brain, Cognition and Education Sciences, Ministry of Education; School of Psychology. Center for Studies of Psychological Application; Guangdong Key Laboratory of Mental Health and Cognitive Science, Philosophy and Social Science Laboratory of Reading and Development in Children and Adolescents: South China Normal University, Guangzhou 510631, China.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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repulsive biases have been observed in sensory cortex, as classical behavioral probe for neural encoding visual features 7 g such as orientation 9 IO], motion [T]. and face viewpoint [[2].
Given the coexistence of attractive and repulsive biases, the issue has been raised about the stage at which the two types of serial dependence originate. There has been growing evidence suggesting that repulsion typically occurs in the sensory stage, while attraction appears in the post-perception stage 13 14
15 16 17.
This study investigates how the cascade of neural processes is calibrated to the history of sensory and decisional events in neural networks, leveraging the unique characteristics of short-term synaptic plasticity (STP) [24] [5 26 27 28 29I, wherein synaptic efficacy varies dynamically with presynaptic activity. Two competing effects exist: short-term facilitation (STF) and short-term depression (STD). Previous studies have demonstrated that STP can regulate neural information processing
effectively [30 [1 32 For instance, STD can reduce output correlation by inhibiting high-frequency
inputs, thereby reducing the autocorrelation of temporal sequences (33; STF can facilitate the maintenance of input information by strengthening neuronal connections, thereby promoting the integration of temporal sequences (29]. Postsynaptic neurons receiving STD-dominated or STF- dominated synaptic inputs exhibit low-pass high-pass filtering responses, respectively, achieving diversified processing of temporal sequences (34). We hypothesize that STP underpins the neural basis of serial dependence, orchestrating its dynamic perceptual effects.
In this work, we develop a two-layer network model incorporating STP to elucidate the underlying mechanisms for both the attractive and repulsive effects in serial dependence. Specifically, to model the visual orientation judgment experiment, we adopt continuous attractor neural networks (CANNs) for each layer [35 36) The lower layer, characterized by STDD-dominance, models sensory processing, which produces repulsion via sustained neurotransmitter depletion. The higher layer, characterized by STF-dominance, models post-perception processing, which produces attraction via sustained high neurotransmitter release probability. Our model successfully explains the serial dependence phenomena observed in experiments. revealing that the STP time constants determine the temporal windows of repulsion and attraction. Additionally, our model provides a neural mechanistic explanation of the Bayesian interpretation of serial dependence.
Related Works Contemporary models of serial dependence employ efficient encoding and 18
Bayesian decoding to explain perceptual biases [13 prior stimuli recalibrate neural sensitivity, reshaping the probability distribution of the current stimu- lus to induce repulsive bias. In the decoding phase, Bayesian inference integrates sensory likelihood with prior, yielding the posterior perception and producing attractive or repulsive biases toward prior stimuli. However, the neural basis of this dual process lacks biological validation, and the underlying circuitry dynamics remain largely unexplored. Moreover, existing models fail to capture the temporal dynamies of serial dependence, such as bias reduction with longer inter-stimulus intervals (ISI). Bridging the Bayesian framework with a mechanistic neural model remains a challenge. Recent neuroimaging advances have spurred exploration of the neural computations underlying serial depen- dence. Some studies attribute attraction to short-term facilitation (STF) or slow excitatory NMDA currents in higher cortical regions, with enhanced synaptic efficacy or neuronal activity 22 23 However, these neural dynamic models cannot explain the repulsion effect and the dynamic balance between attraction and repulsion observed in experiments.
15
19
20
21.. In the encoding phase,
2 The Network Model
To unveil the neural mechanism underlying serial dependence, we developed a two-layer neural network with hetero-synaptic STP. Specifically, to model visual orientation processing, we adopted a continuous attractor neural network (CANN) for each layer (Fig. [A]. CANNS are a canonical model for neural information representation [37 38 39, which effectively mimies the encoding of
continuous features in local circuits, such as visual orientation [40 41 and spatial location 42 43
44. In the brain, stimulus information propagates from lower to higher cortical areas, establishing hierarchical processing from sensory perception to post-perceptual cognition. STP (Fig. B is
a fundamental neurophysiological property that dynamically modulates synaptic efficacy based on presynaptic firing history 45 46). manifesting either STF or STD. Flectrophysiological studies
suggest potential distinct regional specialization: sensory cortex exhibit STD-dominance [4 48
49 50], while high-level cortex such as prefrontal cortex (PFC) exhibit STF-dominance
24 53

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Therefore, the lower layer models STD-dominated processing in the visual cortex (e.g., VI), while the higher layer models STF-dominated processing high-level cortex (e.g., PFC).
Response
1.0
High level
(STF)
(Hz)
35
Low level (STD)
20
time (8)
1.0
TAME TIEDD
(H2)
05
Stimulus
time (s)
000
Figure 1: two-layer CANN with heterosynaptic STP. (A) Schematic of the network model. The hierarchical two-layer architecture mimics STD-dominated processing in the visual cortex and STF- dominated processing in the higher post-percepture cortex. Excitatory neurons within each layer aligned in mne-dimensional ring according to their preferred orientation 6, subject to global inhibition (gray solid circle). Intra-layer and inter-layer neurons are connected with color-scaled lines that denote synaptic connectivity strength. (B) An STDD-dominatdd network displays adaptive synaptic efficacy that sustains at low levels. During stimulation (shaded period), neural activity (r) increases the neurotransmitter release probability (u) while depleting the available neurotransmitter concentration (x)). Following stimulus offset, and x recover to baselines. (C) An STF-dominated network retains elevated synaptic efficacy (large value of u) for prolonged time.
In each layer of the CANN, neurons are aligned on a one-dimensional ring according to their preferred visual orientations 0 (-T/2, + (Fig. A). Denote h
(0M, () the synaptic current to neurons
at 0m at time t, where M = {L, H indexes the lower (L) or higher (H) layer. and TM (fas , t) the corresponding firing rate. The neuronal dynamics are described as:
8h (0r.t) TI.
(1,,0 +
(1)
+ Lene 1) + (r,,,
H (0H,()
= -hn (0 t) + + Jun (0 B'r) un (f t) xn (f' t) rn (6' t) dl'n
TH
0t
+ f JHL (0H, 81,) (6z d0', + (HE((OH,t))
where TM, with M = { HY. denotes the time constant of neurons in the lower or higher layer, respectively. p the neuronal density. (6 t) denotes background Gaussian white noises of zero mean and unit variance, and μMM the noise strength. The firing rate of neurons is calculated by, TM (MM,0, = (0M: 1)/
kMPl 122 (O'r. ()dd' ]. with the parameter kas controlling the divi- sive normalization strength [39]. We set the neuronal connections in the same layer between layers to be JKAs(0x () = = (VVTTakk exp [-(Ox 0/r)² /2aak with K, M E {L, H),, where Jh denotes the maximum strengths for intra-layer connections JH and inter-layer connections (J9r)) and αжм controls neuronal interaction range. Importantly, JиM depends only the difference (0 -0'))) which is manuslatio-invaiiaaa in the feature space, crucial property enabling a CANN to maintain a continuum of attractors to represent a continuous feature [39 51 52).
STP modulates the synaptic efficiency between neurons, which is characterized by two variables, the neurotransmitter release probability u and the available neurotransmitter resource x. When presynaptic neuron fires, the calcium accumulation at its axon terminal triggers two competing processes: 1) STF, due to the increase of neurotransmitter release probability u and STD, due to depletion of æ. The instantaneous synaptic efficacy is ua. The dynamics of STP are given by:
Juss (0 uM (0M, t) T
+ UMM (1 -u (0M. (BM. t), M = L,
(3)
Øt d (0M, x (0M,1) uas (0m t) (OMr (OM (), M I,,
Øt
where the time constants Ty and Ta determine how quickly u and x recover to baselines, respectively. Since larger Ty implies that remains at high-level after neuronal response for a longer time,
3

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corresponds to the STF effect; while a larger FT implies that z remains at low-level for longer time, it corresponds to the STD effect. Experimental data show that sensory cortices like V1 are STD-dominated, i.e., Ta >> Tf 47 while higher cortical regions such as PFC are STF-dominated, i.e., Tf > Td 24(3)) We set STP parameters in the lower and higher layers of our model accordingly (Fig. B-C), and the time constants also match the timescales of working memory (2 31.
3 STP Induces Repulsion and Attraction in a Single-Layer CANN
Before studying the performance of the two-layer network, we first explore how STP induces serial-dependent biases a single-layer CANN.
To compare the network performance with experimental data, we adopted the post-cueing adjustment
56 57, where participants viewed two sequentially presented visual stimuli S₁ and Sy, whose orientations 0f and 8 are randomly sampled in the range of (-T/2, / x/2] in each trial. After a delay period. participants reported the memorized orientation, denoted as od giving the cuing signal (Fig. 2 D top). External visual stimuli and the cueing signal are presented the lower layer, denoted as [e,( with ext E {sti, cue), which are expressed (ex t), with Otext controlling the signal strength, Gex the signal width (inversely related to the precision), and Mext the noise strength. In the retrieval phase, we modeled the cueing signal as a weak and ambiguous copy of the corresponding stimulus signal by setting the parameters aleue < Osti: Qeue > Asti and Heue Mst (32), with detailed noise settings Appendix A. We manipulated the variables, including the inter-stimulus interval (ISI, Aisi) and the inter-trial interval (ITI, A/m), and measured the adjustment error of the model, which given by Error
paradigm (Fig. 2 [54
55
as (o, Clext exp (0,, 0en)² ((a))/((aea))
0g 02. and compared it to the stimulus orientation difference AS = 0f 02.
B
repulsive C
m22
S1
ISS
$2
Delay
Cue
10
Eroor (*)
m2
0.5-
time (s)
0
0
-00
4$
60
D
82
Cue
attractive
(Hz))
8
Error (*)
-122
82
0'
time (s)
8 0
-00
-60
-30
4$
0
(")
60
90
Figure 2: Serial dependence in single-layer CANN with STP. (A-C) Repulsion effect induced by STD-dominance. (D-F) Attraction effect induced by STF-dominance. (A, D) Schematic illustration of the temporal dynamics of neural responses r, the available neurotransmitter resource x, and the neurotransmitter release probability in single-layer CANN with STD drD-nnmmn (A) or STF- dominance (D). Two stimuli S₁ and S2 with respective orientations 0f -30 and 05 0 are presented sequentially. A cueing signal is presented after the delay period to trigger the retrieval of 52. (Top) The red line marks the decoded stimulus orientation. (Bottom) The red lines during stimulus/delay periods denote stimulus orientations in current trial. The recall-period red line indicates the recalled orientation of the second stimulus. (B, E) Illustration of the repulsive and attractive biases. In the STD-dominated case (B), the retrieved neural response (0s, blue curve) is repelled away from the earlier presented stimulus (0f). In the STF-domidated case (E), the retrieved neural response is attracted toward Of. These biased effects exist in both the neural response (top) and in the neurotransmitter concentration (bottom). Gray and dotted curves represent simulation and fitting results, respectively. (C. F) Adjustment error (Error 0 05) a function of the difference between two stimuli (AS = 0f 0:) under different ISI conditions. It displays negative correlations (repulsion) in the STD-dominated case (C) and positive correlations (attraction) in the don-nnnid case. The shaded area represents standard error across simulation runs. For more details, see Appendix A.

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3.1 STD-dominance induces repulsion in a single-layer CANN
We first demonstrated that a single-layer CANN with STD-dominance induces serial-dependent repulsion. In each trial, stimuli S₁ and S2 activate neurons sequentially in the form of bump-shaped activities centered at 0j and 02 respectively (Fig. 2 top), which deplete synaptic resources of active neurons (Fig. 2 A bottom) and reduce their synaptic efficacy. The neurotransmitter concentration ((),t) depleted by S1 and S2 forms a double-troughe distribution with minima at 0j and f2 (red curves in Fig. A bottom). The late presentation of S2 implies the late recovery of corresponding neurotransmitters, resulting in (05;, t) < 20) t) (gray curve in Fig. 23. bottom). Due to the time constants Fι > Tf. neurotransmitter concentration remains at low levels during the maintenance period, and they can be mathematically expressed as, 20, = 1 (t) exp [- 0t) /2a²] (t) exp [-(0- 0:)²/20 /2a²], validated by our numerical simulation (dotted gray curve in Fig. 2B. Appendix C; the variation of u(f,t) t) and u(f, f))x(f, t) over time, see Appendix D). When the retrieval cue for S2 is presented, the network generates a response bump (blue curve in Fig. [3, top) centered at 0g (decoded via population vector from neural activity, Appendix A). Notably, before presenting the retrieval cue, the double-trough distribution of x<00 1) is lower on the side of 0g closer to of resulting in weaker synaptic connections in this region. This creates asymmetric neuron interactions, pushing the network response f2 away from f7, manifesting the repulsion effect (Fig. 2
We conducted 20 simulation runs (100 trials each, cue = 2 as examples), modeling behaviors of different participants (Appendix A). Analysis using Derivative of Gaussian function (DoG, G(x)) = ve(x/o) AbuG exp(-x² / with ADoG denoting the curve's amplitude, Fig. FCg re- vealed a negative correlation between the stimulus similarity AS and the adjustment error Error sample t-test against zero on the sum of error: ((19)= = 197.36, p .001). Stimuli with higher similarity (smaller AS) generate stronger repulsion (larger (0g - 02l) We found that the amplitude AD& 2.229"and the repulsion effect peaks AS = 31.71% in agreement with the V1 repulsion observed in psychophysical experiments 15 16 17.. To test generality, we re-ran the one-layer model by randomly cueing S or S2 in interleaved trials. The results showed that the adjustment error curve aligns with that in Fig. 2F, with a magnitude of -3551 (I(19) = (68.57.p p < .001, Appendix E).
By manipulating ISI, we further investigated the regulation of STD the repulsion effect, and found that: when A4st < Ta. decreasing A increases the repulsion effect (all t(19) > 43.18, p << .001). Conversely, if neurotransmitters are sufficiently recovered, the repulsion is reduced significantly.
3.2 STF-dominance induces attraction in single-layer CANN
We continued to explore how STF affects serial dependent biases in a single-layer CANN. As shown in Fig. DD two sequentially presented stimuli S₁ and S2 trigger neural activity bumps centered at 0j and 85. respectively, causing the increase of neurotransmitter release probability of active neurons, and so do the interactions between them. Since the neural activity bumps caused by two stimuli are superimposed, creating a bimodal distribution of u(0, t) peaked at 0j and 05. The latter- presented S2 induces slower decay of the corresponding neurotransmitter release probabilities, resulting in u(05, 1) > u(ff,1) f). Since the time constant of STP Ty >> Ta. the neurotransmitter release probabilities remain at high levels during the maintenance period, which can be mathematically expressed as u(0,t) t)- = (t) exp [- - / + (t) exp (( 05)² /332/2aa], validated by numerical simulation (dotted gray curve in Fig. - bottom, Appendix C; the variations of a<0., t) and u(8, t)z(0, t) over time see Appendix D). During the retrieval phase (cue = 2 examples), the neurotransmitter release probabilities near 65 on the side closer to 6f have larger values than those on the side away from 0g. causing stronger neuronal interactions in this region. Consequently, this shifts the network response center 03 triggered by the cucing signal towards 0% manifesting the attraction effect (Fig. 2 top). We found that the adjustment error (Error) correlates positively with the stimulus similarity (1(19) 122.92, p < .001), with a DoG amplitude ADoG = 1.48%, peaking at AS = 24.52"(Fig 2 which is in agreement with the attraction effect observed in PFC and other higher cortical areas 17 60 [6]. When randomly cueing S₁ Sz, the adjustment error curve aligns with that in Fig. 2 with a magnitude of 1.68 (t(19)= = 96.77, p < ,001, Appendix E).
By varying ISI (Fig. F),, we found that the attraction effect (ADar) increases as A/is decreases, under the condition A4ss < Ty (all 1(19)= 85.63, p < .001). Conversely, when neurotransmitter release probabilities decay to the baseline, the attraction effect is reduced significantly.
5

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4 STP Orchestrates Repulsion and Attraction in a Two-layer Network
4.1 Reproducing perceptual biases in a visual orientation judgment task
Using the post-cueing paradigm, we further demonstrated that heterosynaptic STP in two layers of the model induces repulsive and attractive effects, respectively. We carried out 20 runs, each containing 100 consecutive trials. Let us consider the (n + 1)th trial (Fig. A two visual stimuli S with orientation 0. 0. for i = 1, 2, are presented to the lower layer of the network sequentially, which trigger neuronal responses in the bump-shape centered at 0T,M-= (M = H), respectively, in each layer. We implemented a recall paradigm, in which a randomly selected stimulus serves as the recall cue (Stwe cue = {1, 2}) and triggers a retrieved bump activity centered at (d.n++1 We then eue,
calculated the adjustment errors (Error = gd.n+t1 0gin+t) for cued stimuli and their relationship to both the orientation difference in the current (ASwitthi Gunnnte orientation difference cued in the preceding trial (A.Sbetween 0'e
g0 within-trial) and the
0u between-trial).
Within-trial repulsion. According to the study in Sec. 3.1, in the lower-layer CANN with STD- dominance (modeling information processing in VI), ge.t
cue. in any nth trial exhibits the repulsion effect from other within -rial stimuli, as shown by the orange curve in Fig. 33 (bottom). This effect arises due to the spatially asymmetric distribution of available neurotransmiterss (x (0z, t)) caused by STD (gray curve). Notably, while disturbances in Z (0z, t) from previous trial stimuli (S persist, their influence negligible because 7 < 2Trial (Tiiia is the trial duration), and that 05-"-1 and 0d are uniformly distributed around 0% making the cumulative effect statistically insignificant during the nihh trial delay. The repulsively shifted neuronal responses in the lower layer are transmitted the higher layer via feedforward connections (black curve in Fig. 3 top). Different from the lower layer, because of STF-dominance, the high layer has enhanced neurotransmitter release probabilities ( t) in the region around the current trial stimuli (gray curve in Fig. BB top). This enhanced synaptic efficacy selectively amplifies feedforward inputs centered at 0d.m cue.LL These repulsively shifted inputs from the low layer make the triggered neural response the high layer exhibit repulsion (orange curve in Fig. 3 top).
Between-trial attraction. After two visual stimuli in the 11th trial are presented, neurotransmitter release probabilities u (0H, t) in the higher layer exhibit a three- peak distribution, peaking at 61:n+11 05.=t1 and |I (Appendix C). Since uz (0n, t) decays slowly in the high-layer, it maintains at a relatively high level during the delay period of the nth trial, and the neuronal activity induced by the retrieval cue in the high-layer further facilitates the neurotransmitter release probabilities around gd.
0
cuc.H (Fig. A bottom), resulting in an amplitude hierarchy during the delay period in the (n + 1)th
trial: Aque. (L) >> A A!/2m++1 (1) (gray curve in Fig. 3C top). This dynamic characteristic causes the gd.n neural activity induced by the recall cue in the (n 1)th trial to shift toward sue. manifesting the attraction effect (orange curve in Fig. 3C top).
Statistical analysis shows that the model's ' adjustment error (Error cue.H 0 negatively correlates with the within-trial stimulus similarity (ASwinin), peaking at 38.13% (Auc = -..11 1(19) = 12.62. p < .001; Fig. 3D, blue curve); whereas, the network's adjustment error positively correlates with the hetieen-trial stimulus similarity (AShheween), peaking at 17.83"( ADeG 1.18%,
1(19) = 7.94, p < .001; Fig. 3. red curve). Notably, these two opposite effects are consistent with the repulsive and attractive biases observed in post-cue behavioral and neurophysiological experiments (58 59 61). and their magnitudes are comparable to the strength of classical serial dependence effects reported in the literature (c.g., ADoG = 1.17%[14), ADoG 1.32 [20]. ADoG 1559 To account for potential readout bias due to asymmetric neural responses, we decoded high-layer activity using multiple methods (population vector method, center-of-mass, maximum likelihood, and peak decoding, Appendix F). All approaches yielded consistent results, confirming robust within-trial repulsion and between-tri trial attraction.
Psychophysical experiments also indicate that reporting the cued stimulus in the previous trial significantly affects the current between-trial attraction. By applying a partial no-report paradigm (see Appendix B), we found that when no report is required the previous trial, the current target less attracted to the previous one, and the within-trin trial repulsion effect increases slightly (between:

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Aboc = 0.14", t(19) p .802; within: ADeG 1.29", t(19) 9.21, p .001; Fig. 3E). consistent with the psychophysical experimental data [ 62]. Based this, our model further predicts that compared actual visual stimulus values (i.e., ASS hetween f 0 the retrieved stimulus contributes more to the eetween-trial attractive effect (ADoc = 1.28 t(19) = 8.9, p 001; Fig. F3..
which is consistent with the psychophysical experimental data (20]. Thus, the between-trial attraction
effect stems more from the memory representation difference (i.c., A Aberween = 6d. 0
cuc.H
within trial
trial
trial n+1
repulsive
within trial
between trial
Cue
(Hzz)
repulsive
m2
1.0
LaoL
0
02
C between trial
attractive
m12
(Hz)
40
04
repulsive
0
6 Amm Cauhh
diest
.122
0.0
12
time (s)
0
8
8
cue.1
D
within
within between trial
48
1.5
between trial
1.5
1.8
4R
Error (*)
Error (*)
Error
1.5
-1.
-1.5
-60
(*)
4 (*)
Figure 3: Serial dependence in the two-layer CANN model. (A) Temporal dynamics of the model variables. Two stimuli presented sequentially evoke neural responses. Post-delay, the network retrieves S1 or $2 based on the task cue. Plots (top to bottom): lower-layer firing rate, lower-layer available neurotransmitter resource, higher-layer firing rate, and higher-layer neurotransmitter release probability. After stimulus offset, rr. (0,) and I'H (0r) return to baseline; xr, (0r.) and un (0nr))) persist, affecting decoding within and across trials. (B) Within-trial repulsion
two-layer model. Low-layer decoded signal (02,7 orange curve) is biased away from the non-target (0" due to the asymmetric neurotransmitter concentration profile (gray). This propagates to the higher layer, where spatial asymmetry in ur (On, .) (gray) shifts the response bump, causing repulsion. (C) Between-trial attraction the two-layer model. Lower-layer signal propagates to the higher layer, where u (0H²) I) asymmetry (gray, top) in (n+1)th trial shifts the response bump (orange curve, top) toward gd.m causing attraction. All variables normalized. (D) Within-trial repulsion and between-trial attraction. Retrieval eтror (angular difference between higher-layer readout and cued stimulus) plotted against the difference between the prior and current stimuli. (E) Within Within-triall and between -eriee biases without cueing in the prior trial. (F) Within aithin-trial and between- triil biases plotted against the difference between the prior stimulus (or its report) and the current stimulus. For more details, see Appendix B.
4.2 The neural basis of Bayesian interpretation of serial dependence
Contemporary models in the field explaining repulsion and attraction in serial dependence often
adopt the Bayesian inference framework, such as the gain model [ and two-process model [13 20 These models consider the whole process involving two stages (Fig. A]): 1) sensory encoding, in which orientation-sslectivee neurons in the sensory cortex encode stimuli in the form of tuning

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curves, i..,, r(0k) = a exp [8 cos(0 - 0x)) - I]. with 0₁ denoting the orientation preference and a, B controlling the amplitude and width the tuning curve, respectively. 2) decision integration, which higher cortical areas estimate stimuli through weighted integration, i.e., 0 = Eo. ((,.) with Wk representing the decision weight. Although differing in regulatory strategies, both the gain and two-process models posit that the brain modulates these two processes during sequential information processing. In particular, the two-process model assumes that: 1) at the sensory encoding stage, neurons undergo adaptive sensitivity regulation, reducing tuning curve amplitudes near previous stimuli 0 (black curves in Fig. A modifying a based on (0x - -0)),, which effectively alters the likelihood function in Bayesian inference; 2) the decision stage. higher cortical areas develop weight biases toward previous stimuli (green curves in Fig. 44. modifying wy based on (0,- 8))), equivalent to changing the prior distribution in Bayesian inference. These dual operations shift the posterior distribution, producing repulsion in sensory perception and attraction in post-perception, but the neural basis of these operations is unknown. Also, the existing models have not explained the dynamic characteristics of serial dependence, such as the temporal decay of serial-dependent effects, the within-trial repulsion and between-trial attraction.
Our two-layer CANN model with hetero-STP provides a neural basis for the Bayesian interpretation of serial dependence, specifically, 1) negative regulation at sensory encoding: neurons responding to the presented orientation O will experience resource depletion after activation (Fig. 4 bottom, black curve, equation Appendix C). This reduces neuronal synaptic efficacy and affects the feedforward transmission to the higher layer, analogous to the modulation of the likelihood function in the Bayesian framework. It drives the repulsion effect 2) positive regulation at the decision stage: neurons in the higher layer responding to the previous stimulus have enhanced neurotransmitter release probabilities
have analyzed (Fig. 4 bottom, blue curves).
the cueing orientation (Fig- 4B green curve, Appendix C). This creates biased strong neuronal connections in the network toward the stimulus history, analogous the modulation of the prior in the Bayesian framework. When a new stimulus arrives (the likelihood information), the high-layer CANN whose connections are implicitly modulated by the stimulus history (the prior) effectively carries out the history-dependent computation (the posterior).
B
attractive (between trial) repulsive (within trial)
attractive
posterior
read-out weight @
population response
attractive
prior
likelihood
dm
repulsive
repulsive
0
8"
8
8 0
Figure 4: An STP-based Bayesian interpretation of serial dependence. (A) Schematic of Bayesian interpretation. Orientation stimuli (black curves) generate neural population responses (blue curves, likelihood), integrated by readout weights (green distributions) to produce the posterior decision. Adaptation induces repulsive effects; recent stimulus history amplifies decisional weights, eliciting attractive effects. (B) STP correlations of Bayesian inference. Bottom: neurons in the lower layer respond the prior cued signal and current stimuli, inducing neurotransmitter depletion (gray curve). Recent stimuli evoke stronger repulsion, resulting in a net repulsive bias in the population response (blue curve). Middle: Lower-layer response (blue curve, likelihood) propagates to the higher-layer network; neurotransmitter release probability (green curve, prior) biases toward the cued target. Top: Higher-layer population response (blue curve) displays repulsive bias from the stimulus from the same trial and attractive bias toward the prior cued target.

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Model Prediction
Within-trial repulsion effects reflect neural network sensitivity to rapid changes, while between-tridl attraction effects demonstrate stability in long-term processing. In our model, these are due to the fact that STD reduces neurotransmitters, while STF increases neurotransmitter release probabilities. STP, with its time constants positioned between rapid neural encoding (hundreds of milliseconds) and experiential learning (seconds), serves the suitable neural correlate of adaptive cognitive functions, including motor control, speech recognition, and working memory. In our two-layer network, heterogeneous STP regulates the different information processing in two layers, specifically, the lower layer employs STD for information separation, while the higher layer employs STF for information integration. This area-specific STP regulation provides way for the neural system to balance information separation and integration, where the STP time constants determine the time boundaries for information separation and integration in temporal sequence processing.
To verify our hypothesis on the role of STP, we used the post-cueing paradigm to study the serial dependence effects by manipulating ISI and ITI time windows accordingly. We conducted 20 runs (100 trials each) for various parameter conditions. The relationship between the judgment error and the stimulus difference was fitted using DoG curve, with amplitude (ADag) derived from this fitting (hollow circles in Fig. 5 We have two key observations: (i) When ISI within a trial is shorter than the lower layer's STD time constant (ra), the network shows significant repulsion effect in judgment error (Os: t(19) = 8.66, << .001), with its strength inversely proportional to ISI. When ISI exceeds Td. repulsion transitions attraction (5s: ((19) 4.32. p << 01;; 10s: ((19) 5,42, p p< .001). Thus, the STD time constant determines the time window of repulsion, as illustrated in Fig. SAA (ii) When ITI is shorter than the higher layer's STF time constant Ty, the network exhibits significant attraction effect in judgment сπтог (all t(19) > 4.84, p .001), with its strength inversely proportional ITI. As ITI exceeds Ty. the attraction effect weakens substantially and becomes negligible when ITI is sufficiently long (both p >> .05). Thus, the STF time constant determines the time window of attraction, shown in Fig. 3
The cross-talk between two layers in our model is at the neural activity level, which generates different serial dependence biases. The bottom-up repulsion competes with the STF-maintained prior information (attractive bias), yielding the observed behavioral pattern-attracton within trials and repulsion between trials. This cross-layer competition exhibits time dependency: psychophysical evidence indicates that the attractive effect is strengthened with longer delays [1], reflecting faster decay STD-driven repulsion versus STF-sustained attraction. Our model (Fig. (5) captures this time-dependent interaction, where the short timescale of STD leads to a faster decay of repulsion. while STF in the higher layer maintains the attractive bias over longer duration.
(between trial)
Poo (within trial)
2-
10
ISI (s)
(s)
Figure 5: Model predictions temporal windows of information segregation and integration. (A) The adjustment error (amplitude of the DoG) reveals within-trin -trial repulsion, which gradually decreases and reverses to attraction the ISI increases. which decreases as the ITTI increases. *; < .05; #*; p < .01; ***; .001.
(B) The adjustment error reveals between-trial attraction,
6 Discussion
This study proposes a hierarchical computational strategy for the neural system in dynamic sequential processing, where the STP time constants critically determine the temporal windows and boundaries for information segregation and integration. By incorporating region-specific STP heterogeneity, our continuous attractor neural networks advance the synaptic theory of working memory (29). which

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posits that presynaptic neurotransmittes serve as dynamic buffer-loadedd refreshed, and read out by spiking activity enable both activity-based based and activity-silent memory representations. In VI, STID-dominated plasticity induces transient repulsive effect via neurotransmitter depletion, driving stimulus-specific suppression, in reminiscence of the classical visual adaptation effect [88] 63
64 65]. In contrast, STF-dominance in PFC sustains synaptic efficacy via calcium accumulation, thereby generating attractor dynamics that support temporal integration for working memory and decision-making [29] 66 67]. Specifically, the time constants of STD and STF dictate the temporal windows for segregation and integration, respectively, providing testable metrics for future research.
The current model resolves the apparently conflicting effects of serial dependence within a unified framework. Serial dependence, initially described as the attraction of current perception to recent stimuli, has been extended to reveal a dissociation between repulsive effects at the perceptual stage and attractive effects at underlying these bidirectional biases have been widely debated, with dual-process models proposing an efficient-coding account the sensory cortex and a decisional-iner inertia account in higher-order regions [1 15 20 21]. The repulsive effect reflects an optimization strategy in sensory systems [19], where STD-mediated local inhibition maximizes sensitivity to stimulus changes [69]. Conversely, the attractive effect relies STF-driven synaptic enhancement preserving historical information to enhance decoding efficiency in statistically regular environments. The order of STD and STF is erucial for the model performance. A reversed configuration lower STF- layer and higher STD-dominated sayer-yieliee exclusively attractive biases. Both within-trial (amplitude: 1.79%; 1(19)=6.79, p<.001) and between-trial effects (amplitude: 3: (19)=19.62. p<0011; Appendix G) showed significant attraction. Reversing this order (STF-dominance first) causes initial signal smoothing due to facilitation. Consequently, even though the downstream STD layer attempts to extract differential features, the loss of sensitivity to input variation cannot be recovered, resulting in failure to achieve the intended synergy between sensitivity and stability. Sensitivity analyses confirmed that the key repulsion and attraction effects were robust to parameter variations: changing the absolute values of Fa and Ty (while maintaining Ta > Ty. Appendix H) introducing 110% random perturbations to STP parameters (Appendix I) produced only minor amplitude changes. This indicates that the results depend on the relative rather than absolute timescales, demonstrating strong model robustness.
stages 14
15 16
60
61]- The neural mechanisms
Limitations and Future Works Our model elucidates how STP underlies Bayesian computation in biological networks. Bayesian models, such as dual-process frameworks [13 [5] 20 21, have long been used to explain serial dependence but often lack biological substrates and fail to account for temporal dynamics. In contrast, the two-layer CANN model with hetero-STP offers a biologically grounded implementation: the likelihood function maps STD-modulated sensory representations, the prior corresponds to STF-sustained memory traces, and their interaction yields the posterior. Unlike the conventional Bayesian models, which posit priors are shaped by long-term environmental modulations
statistics [19]. the Bayesian theory of serial dependence considers of likelihood function and prior in short timescale, and our model provides potential neural mechanism to support this view. Since the Bayesian view of serial dependence has been recognized in the field, we hope that linking our model to this view will strengthen our understanding of the neural mechanism of serial dependence. The theoretical and mathematical foundations of this mapping require further analysis. Our model accounts for most documented serial dependence phenomena and their associated neural mechanisms, yet a few experimentally observed patterns require further investigation. For example, long-timescale repulsive effects (>50 s) suggest sensory cortex mechanisms beyond current STP timescales. Implementing long-term negative feedback mechanisms in sensory cortices may explain this. In addition, future work could incorporate feedback projections to simulate top-down modulation, accounting for attractive effects observed in the sensory cortex (70). Integrating PFC cognitive control theories could clucidate the role of higher- level attention in information processing [7]] 722. These advances will deepen our understanding of the balance between information integration and segregation, opening up new avenues in brain- inspired computing.
apperience-dependee
10

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Acknowledgements
This work was supported by the National Science and Technology Innovation 2030 Major Pro- gram (No. 2021ZD0203700 202 2021ZD020370. Y.Y. Mi; No. 2021ZD0203600, N.H. Chen; No. 2021ZD0204103 H. Luo), NSFC 31930053, grant from Research Center for Brain Cognition and Human Development, Guangdong, China (No. 2024B0303390003,, and Science Fund for Creative Research Groups of the National Natural Science Foundation of China (T242 1004). We are deeply grateful to Prof. Huan Luo and Dr. Huihui Zhang for their generous advice and insightful discussions throughout the course of this study. Their constructive feedback and encouragement have been invaluable in shaping the ideas and refining the presentation of this work.
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Appendix
A Model Details
Single-layer CANN and two-layer CANN. The neural dynamics in single-layer CANN are described as:
ah(0,,) t)) + J(0, yu((' t)x((', t)r((' t)do' + Tai(0,t) (656(0,t) (5)
Øt
The calculation of u(O, t). t), r(0,t) was identical to the two-layer CANN in Sec. 2 The time constants for short-term depression (ra) and short-term facilitation (Ty) were set for the STD- dominated CANN and the STF-dominated CANN models, respectively.
We considered heterogeneity in intra-layer and inter-layer neuronal connections across different participants by including noise: JKM (0x, 0/rs))) JKM M (0x, al μrE5), with K, M {L, H & denotes white Gaussian noise of zero mean and unit variance and μ.j. the noise strength. We included noise in the neuronal connections of the single-layer CANN similarly, Model parameters are shown Tab. [
Population vector method. We decoded orientation value from neural activity across CANN layers using the population vector method, expressed as:
8d J [((((0,0) d)
(6)
J (r(0,, 1))d0
where (r(0,))) the averaged firing rate neurons during the cueing period.
B Experimental Paradigm and Statistical Methods
Post-cueing paradigm. Each trial consists of a first stimulus (S1) lasting 200 ms, an inter-stimulus interval (ISI) lasting 1000 ms, a second stimulus (S²) lasting 200 ms, a delay period of 3400 ms, retrieval cue (S;, = 1,2) lasting 500 ms, and an inter-trial interval (ITI) of 1000 ms. In the single-layer CANN, S2 was recalled during the cue phase to examine the influence of S1 on S2 within a trial. Simulations were performed for a single trial. In the two-layer CANN, the effects within and between trials were examined by recalling Si or S2 during the cue phase a randomized order across 100 consecutive trials. Simulations were conducted with 20 participants, each with various neuronal synaptic connection strengths as in Appendix A. For each participant, 100 trials were conducted.
Stimulus orientation settings. Orientations were selected from a uniform distribution over [-90%, 90%) with step size of 1 AS refers the angular difference between the previous stimulus and the current stimulus. To ensure an equal probability of its occurrence, AS and A were randomly generated with equal probability over [-90", 90%]. Take the first trial in the two-layer CANN as an example, ded was selected from uniform distribution over [-90%, 90%) randomly, then 6%.1 and 2 were calculated:
@%,1
g=:1
Swithin
(7)
uncuee
cuc
ge.1
Shewween
(8)
Subsequent stimuli were generated in the same way. For the nth trial, 0 of the current trial and g= of the subsequent trial were calculated according to the following formulas:
68.1
A S within
(9)
05,a+1
6
AS between
(10)
cuc
8 and gn m were assigned to S₁ or S2 randomly, meanwhile, the cue index in S was determined.
Behavioral readout. In single-layer CANN, external signals are input into the network, and the output is read from the same network using the population vector method. In two-layer CANN, external signals are input into the lower layer, and the output is read from the higher layer.
22

---

Table 1: Model Parameters
Parameter
Meaning
Value
General Network Parameters
N
Number of neurons
100
T
Time constant of synaptic current
0.01 s
JJ
Neuronal interaction noise strength
0.01
Parameters for STD-dominated single-layer CANN (Fig. 2A-C)
J
Maximum synaptic connection strength
0.13
Range of neuronal interaction
0.5
k
Global inhibition strength Background noise strength Time constant of x Time constant of u Increment of u produced by a spike
0.0018
1bb
0.5
3
Tf
0.3
Uo
0.5
Parameters for STF-dominated single-layer CANN (Fig. 2D-F)
J
Maximum synaptic connection strength
0.09
Range of neuronal interaction
0.15
k
Global inhibition strength Background noise strength Time constant of x:
0,0095
H4
0.5
0)3
Tf
Time constant of u
5 $
Uo
Increment of produced by a spike
0.2
Parameters for two-layer network (Fig. 3)
J..
Max synaptic connection strength (low-to-low)
0.13
ag
Range of neuronal interaction (low-Ievel)
0.5
k
Global inhibition strength (low-level)
0,0018
pr
Background noise strength (low-level)
0.5
T
Time constant of x (low-level)
3
Tf
Time constant of u (low-level)
0.3
UL
Increment of produced by spike (low-level)
0.5
JAL
Max synaptic connection strength (low-to-high)
0.02
agL
Range of neuronal interaction (low-to-high)
0.15
Jhn
Max synaptic strength (high-to-high)
0.09
ag
Range of neuronal interaction (high-level)
0.15
ku
Global inhibition strength (high-level)
0.0095
pg
Background noise strength (high-level)
0.5
T
Time constant of x (high-level)
0.3
H
Time constant of u (high-level)
5
UH
Increment of produced by a spike (high-level)
0.2
External Input
Oaii
Strength of external stimulus Spatial scale of external stimulus Noise strength of external stimulus
20
asti
0.3
Astii
0.5
Ogque
Strength of external cue
2.5
Gque
Spatial scale of external cue Noise strength of external cue
0.4
Heue
Adjustment error. For each trial, we measured the adjustment error as the angular distance between the cued stimulus angle and the decoded response angle.
Error
0d
0
(LI)
23

---

Serial bias analysis. Serial bias was calculated as the averaged adjustment error using a 30 sliding window, as function of within-trial and between-trial angular differences. In Fig. 3p, E:
A within
(12)
berween
0%
0
(13)
que
In Fig. 3R we further analyzed the average error as a function of the memory representation angular difference:
A Reetween
@d.r cue
6s.n+1 n+1
(14)
cue
DoG curve. To measure the amplitude of serial dependence, we fit the error plot with the first derivative of Gaussian curve (DoG) G(x) ve(x/o) exp(-x² /202). where ADoc is the amplitude of the curve peak, a is the curve width.
Partial no-report paradigm. To test whether serial dependence occurs without prior reported stimulus, the cue was absent in 40% of the trials. Trials following those without a report were used to analyze serial biases.
Computer resources. We used Python 3.1 and Brainpy 2.6.0. 0o..ppos20244011 for simulations, All experiments were conducted on consumer-grade desktop computer (AMD Ryzen 9 9950X, 32GB DDR5 RAM) with hour-scale runtimes.
C Numerical Simulation of u and x
The fitting of æ curve in an STD-dominated single-layer CANN. In an STD-dominated single-layer CANN, ø is fitted by the following equation:
x00, 1)
(t) exp -0 22 (t) (00-00//22)
(15)
set 0 30% , 0: 0 as the initial guess value. The amplitudes (t) and (t) decayed from the early delay period (Fig. SIA) to the late delay period (Fig. SI We calculated these parameters from the time point after S2 disappeared (to 1.5 s) to the time point before the cue period (te = 4.8 s), shown as dots in Fig. STC,, and found that they decayed exponentially with time constant Ta (curve in Fig. SSCC), described
For example, in Fig. B
1 (t) A (40) exp [- (t (n)/ 1,2
(16)
where (to) 0.46, 43(to) 0.68.
The above analysis is applicable to other combinations of Of and 02. Table The fitting parameters of curve
t (s)
0f (9)
0j (9)
A1
A2
a
2.0
-32.72
6.13
0.39
0.57
0.31
4.5
-32.72
6.13
0.17
0.25
0.31
The fitting of u curve in an STF-dominated single-layer CANN. In an STF-dominated single-layer CANN, the u curve was fitted by the following equation:
u(0, () (1) exp [-(0 (0 01)2 / A1)(1) exp [-(0 02)3/2n²]
(17)
In Fig. 2E, we fixed 0f -0 and 05 = 0". The amplitude parameters ( and (1) decayed from the early delay period (Fig. SID) to the late delay period (Fig. STE). We calculated these parameters from the time point after Sy disappeared (to = 1.5 s) to the time point before the cue period (t, 4.8 s), shown dots in Fig. SII, and found that they decayed exponentially with the time constant Ty (curve in Fig. STF), described as:
(t) = (to) exp [- ( - to)/T/) 1.2
(18)
where Ab(4)) = 0.09, Ag = 0.12.
The above analysis is applicable to other combinations of 0 and 02.
24

---

A
x (t = 2)
B
x (t 4.5 s)
A
0.5
0.5
0.5
0.0
-T/2
m/2
-T7/2
6
2
time (s)
D
2t)
u (t= 4.5
0.1
0.1
0.1
0
0
0.0
0.0
-T1/2
11/2
-T1/2
0
m/2
6
2
time (s)
Figure S1: The fitting of x and curves in a single-layer CANN. (A-C) a in an STD-dominated single-layer CANN. (D-F) in STF-dominated single-layer CANN. (A, D) Simulation (gray
curve) and fitting results (dotted curve) in the early delay period (t 2.0 s). (B, E) Simulation (gray
curve) and fitting results (dotted curve) the late delay period 4.5 s). (C, F) Exponential decay during the delay period. Dots represent the simulation results, and curves represent the exponential fitting results.
Table 3:
The fitting parameters u curve
(s)
0f (9)
0g (9)
A
A²
a
2.0
-30.00
0.00
0.08
0.11
0.31
4.5
-30.00
0.00
0.05
0.07
0.31
The fitting of æy and uy curve in two-layer CANN. In two-layer CANN, the æy curve in the (n 1)th trial was fitted by the following equation:
(lL,t) = 1 exp (02 -0-- (2mmt1//2200 (t) exp -(0 00 /
A (1) (I) exp [-(0,. - -0000 )2/ /2a
(19)
In Fig. 4B, we set 6t = 20", gh+1 = -00. and 07. = 0% as the initial guess values. The
amplitude parameters AqUC (t), (1) and (2) decayed from the early delay period (Fig. A
to the late delay period (Fig. 3). We calculated the fitted parameters from the time point after
S sm++1 disappeared (4o = 7.8 s) to the time point before the cue period (te = 11.1 s), shown as dots in Fig. S2C, and found that they decayed exponentially with time constant of ra (curve in Fig. S2
which can also be described as:
(t) (to) exp (- to) to)/Ta) 1, cue
(20)
where (tu) = 0.23, (to) 0.44. (to) 0.68.
The above analysis is applicable to other combinations of 6% 0-+ and 0g+1 Table 4: The fitting parameters of æ curve
8 g (9)
g (9)
A
A
42
Qg
8.3
39.13
-35.41
3.26
0.19
0.37
0.57
0.33
10.8
39.13
-35.41
3.26
0.08
0.16
0.25
0.33
25

---

curve in the (n + 1)th trial can be fit by the following equation:
(OH. A (t) exp
- (0 0 //02
+ (t) exp -(0 12 / /20
A (t) exp
-(01s fdhm H )2/22)20 /20
(21)
In Fig.3 3C and Fig. 43, we fixed 0 = 20" 0 -30", and 02 = 0% A (1) and (1)
decayed from the early delay period (Fig. (2 to the late delay period (Fig. $2 We calculated
these parameters from the time point after S2 disappeared (to 7.8 s) to the time point before the
cue period (te = 11.1 s), shown as dots in Fig. S2F. and found that they decayed exponentially with
the time constant Ty (curve in Fig. S2F), which can also be described as:
(t) = (t)) exp [- to)/ 2,
(22)
where (to) = 0.22, A (to) = 0.14, A7 = 0.08.
The above analysis is applicable to other combinations of The 0f+1 and 0g+1
Table 5: The fitting parameters of и curve
t (s)
P (?)
0g (?)
0
A
A
4
au
8.3
20.00
-30.00
0.00
0.20
0.12
0.07
0.31
10.8
20.00
-30.00
0.00
0.31
0.08
0.04
0.31
A
x =t= 8.3 s)
B
X
(t 10.8 s)
8 knnt
8 s/m1
dun
1.0
CURH
1.0
CUs
A. 1int
A 2.
0.6
0.5
0.5
0.3
0.0
-T/2
T1/2
-T1/2
0
T1/2
8
time (s)
Ug (t= 8.3 s)
E
u, (t= 10.8 s)
0.4
0
gunei
dun
Ouo
0.41
0
amii
Knet
CURH
A
Al. 1.0
A nm
0.2
0.2
0.2
0.1
0.0
0.0
-1/2
0
T1/2
-T/22
T1/2
1,
time (s)
10
Figure S2: The fitting of or and uy curves in two-layer CANN. (A-C) æz, in an STD--ommnated low layer. (D-F) un in an STF-dominated high layer.
D Dynamics of STP Variables
In Fig. 2A, we illustrated only the dynamics of the available neurotransmitter x(0,t) t) to emphasize that, under the STD-dominated condition (ra > Ty), the slow recovery of x(0, is the main factor producing the repulsive effect. Here, the release probability u(0, t) rapidly decays to zero after stimulus presentation and contributes minimally ( A3A top). Upon presentation of the retrieval signal, the instantaneous synaptic efficacy u(0, (f, f) shows an asymmetric distribution the side near the previous stimulus S₁ is weaker (Fig. A, bottom), resulting in repulsion.
In Fig. 2D, we illustrated only the dynamics of the release probability u(0, (0))) to highlight facilitation accumulation under the STF-dominated condition (7Ş > Ta). Here, 2000, I) rapidly recovers to baseline and contributes minimally (Fig. 53 top). Upon retrieval, the synaptic efficacy u(0, ()x I) is enhanced near S (Fig. S3B, bottom), producing attractive bias.
26

---

A
Delay Cue
Delay
102
0.9
0.3
7/
-03
-02
time
time
Figure S3: Dynamics of STP components in one-layer networks. (A) STD-dominated condition
(Ta > Tf). Top: release probability u(O. t) rapidly decays. Bottom: synaptic efficacy u(e, t)x((6 t) weaker near S1. (B) STF-dominated condition (Ty > Ta). Top: available neurotransmitter a(0,, t) rapidly recovers. Bottom: synaptic efficacy u(8, t) (f, t) is enhanced near S₁.
E Control Analysis on the Recalled Stimulus in the Single-layer CANN
In the one-layer model (Fig. 2). only the second stimulus (S₂) was cued to examine the influence of the preceding one (S1) on the subsequent one (S2) based on the definition of serial dependence. To confirm that this choice does not qualitatively affect the model behavior, we conducted additional control experiments in which the one-layer model was re-run with random cucing of either S₁ or S₃ in interleaved trials.
The results showed that under STD-dominance, the model consistently exhibited significant repulsive bias (ADeG -3511; ((19) = 168.52 57. < .001, Fig. S4/)) identical in sign and statistical significance to the repulsion reported in Fig. 2C. Under STF-dominance, the model consistently exhibited a significant attractive bias (ADeG T.68%; ((19) = 96.97, < .001, Fig- S43), identical to the attraction reported in Fig. FF..2F. These findings demonstrate that the choice of the recalled stimulus (Si or S2) does not alter the qualitative pattern of serial dependence, confirming the robustness of our main conclusions.
A
B
2
E)ror())
Error(9)
0-
-2
-1
-4
-2
-90
-60
-30
30
60
90
-90
-60
30
AS(")
AS(")
Figure $4: Control analysis of the recalled stimulus in the one-layer model. (A) STD-dominated single-layer CANN re-run with randomly cued SI or S2 in interleaved trials. The adjustment error curve showed a significant repulsive bias. (B) STF-dominated single-layer CANN re-run with randomly cued SI S2 in interleaved trials. The adjustment error curve showed significant attractive bias.
F Readout Rules
In main analyses, decoded orientation from neural activity via population vector method (PVM, Appendix A). To evaluate potential readout bias from asymmetrical responses, we reanalyzed Fig. 3D using three other methods:
Center-of-Mass (COM). The center-of-mass (COM) decoding computes the circular mean of the population activity, implemented explicitly center-of-mass estimator on the
27

---

unit circle:
8 cMM arg
Σ 1:ctl:
In our simulations, the COM and population vector method (PVM) yield identical estimates. This equivalence arises because the tuning curves are symmetric, densely and uniformly distributed across the stimulus space, and without truncation or nonlinearity. Under such conditions, both COM and PVM effectively perform linear weighted average of the population activity.
Maximum Likelihood (ML). We assume that each neuron's firing rate follows a Poisson distribution with a mean (0) given by its tuning curve. The most likely stimulus 0.L maximizes the log-
likelihood function:
0M. = arg max Σ (ri (: (0) log(ri!))
We evaluated the log- segllikel across all candidate 0 values and selected the one that yielded the maximum.
Peak Decoding (Peak). As a minimal heuristic, we also tested a peak decoder, which simply selects the preferred stimulus of the neuron with the highest firing rate:
Opaak Ost,
arg
All three methods produced consistent results with PVM, confirming robust within-trial repulsion (serial bias amplitudes/curve peak at: PVM: -0.90%/37.92 "2... Fig. BD: COM: -O.909/.9333 /3..99., Fig. SSA
ML: -0.97%/36.97 Fig. [SSB; Peak:
Fig. S5C) and between-trial attraction (PVM:
1.179/19.34% COM: 1.1 1.17%1..34; ML: 1.05% : Peak: I.93%/18.21 These results demonstrate
that the qualitative pattern of serial dependence is robust to the choice readout rule.
A
B
Wittin trail
Ve tin trai
Within 3ull
1.5
Setween-tra trai
1.5
Sotwaen trii
1.5-
Briweon HK!!
Enront)
Error(")
Errart")
0.0
-60
-30
0
90
-30
30
60
90
AS(())
A5("))
AS(")
Figure S5: Comparison of different readout rules for decoding perceptual decisions. (A) Center-of-
mass (COM) decoding. (B) Maximum likelihood (ML) decoding. (C) Peak decoding.
G Importance of the Order Between STD and STF Layers
To examine the importance of the order of short-term depression (STD) and short-term facilitation (STF) in the model architecture, conducted control simulations with reversed synaptic configura- tions. A network with lower STF-dominated layer (T = 5, Ta 0.3) and higher STD-dominated layer (Ta Ty 0.3) exhibited exclusively attractive serial biases. Both within-trial effects and between-trial effects showed robust attraction (Fig. S6). confirming that the functional synergy between sensitivity and stability critically depends on the correct sequential order of STD and STF layers.
H Parameter Sensitivity Analysis
To evaluate the robustness of the model with respect to the choice of short-term plasticity (STP) parameters, we conducted a series sensitivity analyses. The time constants for STD-doninated and STF-dominated synapses were selected based on previous physiological studies 47 48 53 50
As these parameters are critical for shaping the network dynamics, we varied their absolute values while preserving their dominance relationship (i.c., Ta Ty for STD, and Ty > Ta for STF).
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Figure S6: Effect of reversing STD/STF order serial dependence bias. Both within-trial and between-trial bias curves showed exclusively attractive effects.
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Figure S7: Sensitivity of serial dependence effects to short-term plasticity (STP) parameters. (A) Robustness of STD-dominated synapses in producing repulsive bias. All parameter sets showed significant repulsion effects. (B) Robustness of STF-dominated synapses in producing attractive bias. All parameter sets showed significant attraction effects. (C-D) Robustness of serial dependence in two-layer networks. In both cases, within trial repulsion and between- trial attraction remained significant, differing only in effect magnitude.
Robustness of STD dominance in inducing repulsion effects. For the STD-dominated condition (Fig. 2C), maintained > Ty and compared two sets of parameters (r₃ 0. Ta = 3 vs. Tf = 0.3, Ta = 4). In both cases, the model exhibited statistically significant repulsion effect .001), with only the magnitude of repulsion varying (-2.29 in Fig. 2C,
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Robustness of STF dominance in inducing attraction effects. For the STF-dominated condition
(Fig. 2h, we maintained ,y >> тa and compared two sets of parameters (ry = Ta 0.1 vs. Tf 4, = 0.3). In both cases, the model exhibited a statistically significant attraction effect (both ((19) > 85.12, p < .001), with only the magnitude of attraction varying (1.48 in Fig. 2 1.56 and
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Robustness of parameters in two-layer networks. Using the same ISI and ITI parameters in Fig. BD, we adjusted the absolute values of Ta and Ty the low and high layers while preserving their relative relationships (r > T/ and o > +.). Serial dependence effects were computed for two parameter sets (T = 2, J = in Fig. S7 = 4, of = 6 in Fig. S7D). The results showed that within-trial repulsion and between-trial attraction effects remained statistically significant (within-trial: both t(19) > 5.52, p < .001; between-trial. both ((19) > 3.48,
.01), with only their magnitudes varying (within-trial -0.34 and 1.44;; between-trial: 0.73 and 1.169).
Our results demonstrated that, although changes in absolute values of Ta and 7, modulate the strength of sequence-dependent effects, their relative relationship (i.e., whether STD or STF dominance) that determines the qualitative nature of repulsion and attraction.
I Effect of Synaptic Heterogeneity on Model Performance
To explore how the heterogeneity of STP affects model performance, we re-ran the model with an inter-stimulus interval (ISI) of and applied =10% random perturbations STP parameters (Ta and Tf) of all synapses. Under STDDdommnance, the adjustment error curve (variant STD, Fig. (S8A) aligned with that in Fig. 2 (uniform STD, Fig. [S8JA. Results showed minimal amplitude change (from 2.29 to -2288% and minimal DoG peak shift (from 31.71% to 31.78%). ) Under STF-dominance, the adjustment error curve (variant STF, Fig. (8B) also closely matched that in Fig. FF (uniform STF, Fig. S8B). Results showed stable attraction amplitude (1.48%) and minimal DoG peak shift (from 24.49* to 24.41%). These results indicate that moderate heterogeneity in STP has a negligible impact on the qualitative pattern of serial dependence.
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Figure S8: Effect of synaptic heterogeneity on model performance. (A) STD-dommnated single-layer CANN re-run with uniform or variant Tą. (B) STF-dominated single-layer CANN re-run with uniform or variant Ty-
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Reviews:
[{"review_id": "jg8RPL4vDE", "reviewer": "Reviewer_kncR", "summary": "The authors propose a model endowed with short-term synaptic plasticity to address “serial dependence”. Specifically, the authors aim to reconcile “repulsive” effects (when the current percept is pushed away from a recent sensory input) and “attractive” effects (the percept is drawn toward recent history) within a unified framework. They perform experiments to understand both within-trial and across-trial behavior in their model. Finally, they also provide a loose analogy to Bayesian viewpoints on serial dependence.", "questions": "Please refer to my review above.", "limitations": "N/A", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "This paper presents a concise and incremental contribution to the literature on short-term synaptic plasticity in neural network models. They tackle an interesting question – serial dependence. I do believe that this would be a useful addition to the literature. However, I’m concerned that the current manuscript appears preliminary and requires substantial revision before it is ready for publication. I’ve detailed some of the concerns/comments below.\n\nI like the start of the introduction. It sets up a clear phenomenon. However, the flow is interrupted by the “related works” section before returning to the introduction. My suggestion to the authors is to have a dedicated “Contributions” subsection at the end of the intro (and before the related works section). This will allow them to complete stating the question, their approach, and what they bring to the table.\n\nFigure 2 needs significant improvement, particularly in terms of captioning and legends.\n\n- I don’t understand what the red horizontal lines are in A, D\n\n- I’m guessing that the different saturated lines in C, F are different ISIs? I had initially thought this was the length of the delay period but it was mentioned otherwise somewhere else in the text. What do the shaded lines represent? Are these standard errors across runs?\nWhy are the authors showing $x$ in A and $u$ in B? This wasn't very clear at first. Why not show both $x$ and $u$ for both the panels? Or $x \\times u$\n\nOverall, the magnitude of the effects reported in Fig. 2 appears very marginal. This is not a compelling demonstration. Did the authors perform any statistical tests to support their findings? Also, is the magnitude of effects reported in prior psychophysics literature consistent with what’s being described here (i.e., a maximum of ~2 degrees either way)? This seems very important to clarify.\n\nAdditionally, my understanding is that even this effect completely relies on the choice of $\\tau$s. I would like to see some kind of sensitivity analysis to understand how robust any of these effects are. It’s possible that the authors chose the values for these time constants based on biological (not modeling) literature. If so, that would also be additionally useful to clarify.\n\nOne suggestion to sort of bypass this comment about hyperparameter choices is that the $\\tau$s can be learnable and the model is trained (with gradient descent) to report the perceived orientation. For example: Fig. 4 in Linsley et al. ICLR 2020. Recurrent Neural Circuits For Contour Detection. This is not exactly the same kind of thing the authors are going for, but I’m mentioning this as a motivating example.\n\nIt also seems to me that it’s important to show negative ISIs. The authors mention that “without loss of generality,” they always cue the second stimulus, but it is not clear to me why this is in principle the same as cueing the first one. In one case, the memory of the stimulus seems way more important. Can the authors clarify?\n\nThe parallels to the Bayesian framework, though interesting, are very vague and unclear to me. Are the authors arguing that, depending on the magnitude of instantaneous noise, the network’s readout is non-deterministic? I didn’t find any experiments systematically testing the effect of noise in this context.\n\nL147 “modeling behaviors of different participants”. What does this mean?\n\nSome grammatical errors that I could spot. Please do a thorough proofread.\nL122 “cuing”\nFig. 2 Caption “The detailed simulations, see Appendix A”\nL153 “manupilating”", "was_revised": true, "final_justification": "Interesting modeling effort. Incrementally extends a large body of work in short-term synaptic plasticity, but nonetheless relevant to the NeurIPS community.", "rebuttal": "Thanks for the valuable comments. We sincerely appreciate the detailed and constructive suggestions. Below, we provide a point-by-point response to each of the questions.\n\n1.\tAccording to your suggestion, revised manuscript adds 'Contributions' subsection to Introduction end and moves 'Related Works' post-Introduction.\n\n2.\tThanks for pointing out the unclear descriptions in Fig.2. We will clarify them in the revised manuscript.\n\n(1)\tIn Fig.2A,D (top), the red line marks the decoded stimulus orientation. In the bottom panel, the red lines during stimulus/delay periods denote stimulus orientations in current trial (i.e., $\\theta_1^s=-30\\degree, \\theta_2^s=0\\degree$). The recall-period red line indicates the recalled orientation of the second stimulus ($\\theta_2^d$).\n\n(2)\tYes, Fig. 2C, F demonstrate adjustment errors under different ISI conditions. The shaded area represents standard error across simulation runs.\n\n(3)\tIn Fig.2A, we choosing to only illustrate the dynamics of the available neurotransmitter $x$ is to highlight that in the STD-dominated condition ($\\tau_d \\gg \\tau_f$), the slow dynamics of $x$ leads to the repulsion effect; while the neurotransmitter release probability $u$ rapidly returns to the baseline and has little contribution. We have the same consideration for only illustrating the dynamics of $u$ in Fig.2D. The reason for we not illustrating the dynamics of $x \\times u$ is that it confounds the dynamics of $x$ and $u$ in the STD- or STF-dominated condition. But, as concerned by the reviewer, we will add illustrations of the dynamics of $u$, $x$, and $x \\times u$ in Appendix in the revised manuscript.\n\n3.\tThanks for raising this important question. Please note that a serial bias of \\~2 degree is commonly observed in psychophysical experiments (Fritsche et al., Current Biology, 2017; Pascucci et al., PLOS Biology, 2019; Czoschke et al., British Journal of Psychology, 2019; Fischer et al., Nat Commun, 2020; Moon et al., Psychonomic Bulletin & Review, 2023). Our model performances are highly consistent with psychophysical experimental observations, which include two parts (Fig.3D-F): 1) in the post-cueing task, our model produces the serial bias amplitudes agreeing with the experimental data (\\~2 degree); 2) in our model, the judgement error curve against the difference between the prior and current stimuli also agrees well with the experimental data. \n\nAs concerned by the reviewer, we performed statistical tests on all relevant model performances, which are all statistically significant. We will include these results in the revised manuscript. As an example, here we present the statistical tests for Fig.2C,F. Specifically, we conducted one-sample t tests and cluster-based permutation tests. One-sample t test revealed significant repulsion effect induced by STD-dominance in all ISI conditions (all t(19) > 43.18, p < .001; Fig. 2C) and significant attraction effect induced by STF-dominance in all conditions (all t(19) > 85.63, p < .001; Fig. 2F). These effects were confirmed by using a cluster-based permutation test, showing a significant cluster (p < .001) when $\\Delta S$ was between 1° and 88°. \n\n4.\tThanks for raising this important issue. Indeed, our choice of time constants $\\tau$s for STD-dominance and STF-dominance is based on the biological data (see e.g, Abbot et al., Science, 1997; Chung et al. Neuron, 2002; Yu et al., Neuron, 2022; Wang et al., Nat. Neurosci., 2006). But as pointed out by the reviewer, since these parameters are so critical, it is worth analyzing the sensitivity of model on their values, which at least justifies why the biological system adapts to this parameter regime. We therefore conducted the sensitivity analyses. For example, for the STD-dominance condition (Fig.2C), we varied the absolute values of $\\tau_d$ and $\\tau_f$ while keeping $\\tau_d \\gg \\tau_f$ holds ($\\tau_f$=0.1, $\\tau_d$=3 vs. $\\tau_f$=0.3, $\\tau_d$=4), we observed the same statistically significant repulsion effect (both t(19) > 213.97, p < .001), with only its magnitude varying (original: -2.29°; new experiments: -1.34° and -3.61°). We also analyzed the sensitivity of the attraction effect on time constants $\\tau$s in both single- and two-layer networks, found that the STP parameter variations do not alter the model performance. We will report these results in the revised manuscript.\n\n5.\tThanks for raising this question. We tend to believe that time constants $\\tau$s are invariant when the brain is performing a cognitive task, since it is hard for the neural system to change all neurons’ $\\tau$s rapidly. If there exists task-dependent serial dependence effect, we tend to believe this is due to some modulating factors (such as neuromodulators). Nevertheless, it is interesting to train a recurrent neural network with learnable $\\tau$s and a properly designed loss function to explore serial dependence effects, and if the trained network does not exhibit the association between biases and STP-dominance as proposed in this work, it will further strengthen our model.\n\n6.\tThank you for raising this issue. We apologize for the confusion in our descriptions. Actually, except in the one-layer model where we cued the second stimulus only (Fig.2), we always cued both stimuli in the two-layer model. Specifically, in the two-layer model experiments (Fig. 3–5), we employed a recall paradigm where either S1 or S2 was randomly cued in each trial, as described on L183 in the manuscript. Based on this paradigm, we computed the within/between-trial serial dependence effects, and our results are consistent with experimental findings. In the one-layer model (Fig. 2), we did cue the 2nd stimulus only. To address your concern – whether cueing S2 was the same as cueing S1, we conducted additional analyses. We re-run the one-layer model by randomly cueing S1 or S2 in interleaved trials. The results show that in STD-dominance, the adjustment error curve aligns with that in Fig.2C, with a magnitude of -3.51° (t(19) = 168.57, p < .001); and in STF-dominance, the adjustment error curve aligns with that in Fig. 2F, with a magnitude of 1.68° (t(19) = 96.97, p < .001). These results indicate that the choice of recalled stimulus (S1 or S2) does not affect our conclusion.\t\n\nWe will clarify the above confusion in the revised manuscript and add the new analysis results.\n\n7.\tThanks for raising this important issue. The serial dependence effect is indeed not deterministic but a statistical phenomenon over many trials. However, here we linking our model to the Bayesian framework is for another purpose, that is, we want to show that our model provides a potential neural mechanism for the widely recognized Bayesian interpretation of serial dependence in the field (Pascucci et al., Plos Biology, 2019). Let us explain this in more detail.\n\nThe Bayesian framework for serial dependence consists of two stages:\n\n(1)\tSensory Encoding Stage: The Bayesian framework posits that, after exposure to the previous stimulus ($\\theta_n$, Fig. 4A bottom), neurons preferring stimuli near $\\theta_n$ undergo adaptation, manifested as reduced responses to new inputs. This alters the likelihood function in the Bayesian framework and generates the repulsion effect in sensory perception. \n\nIn the first layer of our model, due to STD-dominance, the available neurotransmitter $x$ decays after the presence of the first stimulus, and the distribution of $x$ values across the neuron population is non-uniform (black curve in Fig. 4B bottom), with more active neurons having smaller $x$. When the second stimulus is presented, this non-uniform distribution of $x$ across the neuron population induces alternated responses compared to that to the first stimulus, which can be regarded as the likelihood function is changed in the Bayesian framework. \n\n(2)\tPost-Perception Decision Stage: The Bayesian framework posits that higher cortical areas develop weight bias toward the prior stimulus ($\\theta_n$, Fig. 4A top), modifying the prior distribution and inducing the attraction effect. \n\nIn the second layer of our model, due to STF-dominance, the neurotransmitter release probability $u$ (green curve, Fig. 4B middle) increases at the location of the previous stimulus ($\\theta_{cue}^{d,n}$), which facilitates neuronal responses at the previous stimulus location, as if the prior distribution of stimulus is changed in the Bayesian framework.  \n\n   In summary, our model provides a qualitative interpretation of the Bayesian framework for serial dependence, and we hope this link helps us to better understand the neural mechanism of serial dependence.\n\n8.\tThanks for raising this question. In our model, we used each run with slightly different model parameters to represent the behavior of each simulated individual, with 20 runs representing the behavioral data of 20 participants. Specifically, to model the variability between participants, we incorporated noises into the synaptic connections within and between layers ($J_{LL}, J_{HH}, J_{HL}$ in Eqs.1-2), and these noises were independently sampled in each run, leading to slightly different network responses (see Appendix, lines 22–24). Furthermore, to model the trial-to-trial variability within-participant, we incorporated noises into the input signal across 100 trials within each run. The above two types of noises simulate, respectively, the inter-individual and intra-individual variabilities in experiments.\n\n9.\tThanks for pointing out grammar errors. We will thoroughly proofread the revised manuscript.\n\nFinally, we thank the reviewer for carefully reviewing our manuscript and providing many constructive suggestions, which are highly valuable to improve our work, and we commit to incorporating the corrections and new analyses into the final version of the paper. We hope our replies have addressed all concerns of the reviewer, and if not, please feel free to discuss with us."}, {"review_id": "BmgPlLMwco", "reviewer": "Reviewer_kFr8", "summary": "This paper proposes a two-layer continuous attractor neural network model incorporating synaptic short-term plasticity to elucidate the neural mechanisms underlying repulsive and attractive effect in serial dependence during perception. The lower sensory-processing layer mediates repulsion through neurotransmitter depletion, which drives short-term depression (STD). Conversely, the higher post-perceptionl layer mediates attraction via sustained neurotransmitter release probability, which drives short-term facilitation (STF). The model successfully replicates serial dependence phenomena observed in visual orientation tasks and identifies STP time constants as critical determinants of repulsion/attraction timescales. Furthermore, it offers a biologically implementation for Bayesian interpretations of serial dependence, linking STD to likelihood modulation and STF to prior integration.", "questions": "Q1. How does the repulsion induced by STD cross talk with attraction induced by STF between two layers? Does the neurotransmitter depletion influence the accumulation of calcium in upper layer? Are there biological evidences?\nQ2.Figure 4 shows the relation with Baysian framework, do we have some mathematical equivalence between two frameworks?\nQ3.Figure 5 shows that repulsion or attraction depends on the comparison between time constant $\\tau_d,\\tau_f$ and ISI/ITI. Are these time constants task dependent? For example, in other perceptual task such as face detection or color discrimination?\nQ4.How to distinct the results from STF or top-down cognitive control on the attraction effect?\nQ5.Can we extend this model to sequential sound detection further multisensory situation? If so, what should be changed on the model setup?", "limitations": "1. STP is uniform in each layer in the model, which is not the case biologically. Author should discuss this simplification on the results.\n2.The model ignore the topdown feedback, thus the model can not discuss the effect of attention or working memory on the repulsion or attraction effect, and the goal-oriented bias can not be explained in the present model.\n3. There is two-layer continuous attract model on multi sensory integration and Bayesian integration by Wenhao Zhang, the present model should clearly point out the progress of the present model.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Quality：\nStrength: 1)The set up of two-layer CANN model is consistent with biological evidence that sensory areas(e.g. V1) often exhibits short term depression while  higher order cortex area(e.g PFC) exhibits short term facilitation.\n2) The paper systematically implements the temporal-spatial pattern of repulsion and attraction effect by adjust the parameters such as ISI/ITI and $\\Delta$S, which are consistent with classic psychological experiments.\n3) The paper connects the STP to the Bayesian framework, STD to likelihood while STP to prior distribution. \nWeakness:\n1）\tThe paper needs to screening the effects of parameters one the repulsion and attraction in perception and analyze the robustness of parameters such as $\\tau_d$ and $\\tau_f$.\n2）\tThe paper did not compare their neural activity with experimental observations such fMRI or electrophysiological recording data.\n\nStgrength:\n1)The logic flow is fluent, starting from the effect of stp in single layer network to reciprocal interaction between two layer and lastly to the Bayesian framework.\n2) Figures in the paper can intuitively demonstrate the temporal-spatial dynamics of the network, especially, the prediction of ISI on the transition from repulsion to attraction along with change of ISI in figure 5 \nWeakness:\nSome details of the implementation should be clarified such as the noise term during the simulation.\nThe biological basis or the reasons to choose some specific value of parameters also should be clarified such $\\tau_d$ $\\tau_f$ in lower and higher layer of the model.\nProvide some explanation or proof on the continuous attractor guaranteed by rotate-transfer invariant.\n\nSignificance:\nStrength:\nUnified the explanation of repulsion and attraction effect using one single model endowed with STP and bridges the gap between Bayesian computation and neural implementation.\nProvide some testable experiments, such as ISI on the transition from repulsion to attraction.\nWeakness: Lack of the feedback influence from higher order cortex perform attention and decision.\n\nOriginality:\n\nStrength:\n\nClearly proposed that $\\tau_d$ and $\\tau_f$ as the temporal indication of information integration and separation, which is original.\nThe paper provide a biological explanation of likelihood and prior in Bayesian computation in neural system.\n\nWeakness:\nAuthors did not notice the importance of the labor division of STD and STF  in a hierarchical information processing during the  perception.", "was_revised": false, "final_justification": "", "rebuttal": "Thanks for your valuable comments and constructive suggestions. Below are our point-by-point responses to your questions.\n\n**Weakness:**\n\n1. Quality:\n\nThanks for raising this important question. \n\n(1) Our choice of time constants $\\tau_d$ and $\\tau_f$ for STD-dominance in sensory cortex and STF-dominance in higher cortex was motivated by the experimental data. To address the concern of the reviewer, we have conducted simulations assessing the robustness of STD/STF dominance in inducing the repulsion/attraction effect. The results showed that while absolute $\\tau_d$ and $\\tau_f$ values modulate the bias amplitude, it is their relative values determining whether the effect is repulsive or attractive. For instance, varying $\\tau_f$ and $\\tau_d$ absolute values while maintaining the relationship $\\tau_f \\gg \\tau_d$ (Fig. 2F: $\\tau_f$=5, $\\tau_d$=0.1; $\\tau_d$=4, $\\tau_d$=0.3) preserves statistically significant attraction (both t(19) > 85.12, p < .001), although its magnitude varies (from 1.48° in Fig.2F to 1.56° and 1.16°, respectively). Robustness analyses in single- and two-layer networks further confirm that STP parametric variations preserve our findings. These results will be reported in the revised manuscript.\n\n(2) Since our model was built at the neural circuit level, we could not compare neural activities in our model directly to experimental observations. Nevertheless, the performances of our model are consistent with experimental data. These include, for instances, 1) fMRI studies (Schwiedrzik et al., 2014; Sheehan et al., 2022) that show repulsive effects in early sensory cortex, while attraction is associated with higher visual-parietal-frontal networks; 2) EEG/MEG evidence of two-stage processing—sensory repulsion and prefrontal attraction (Luo et al., 2025). These findings align with the two-layer dynamics of our model: stimulus-specific repulsion via low-layer STD and predictive attraction via high-layer STF.\n\n2. Strength:\n\nThanks for the valuable comments and suggestions. \n\n(1) In our model, three sources of noises were considered: 1) External Input Noise: included in $I_{ext}(\\theta,t)$ (Gaussian white noise, $\\mu$: amplitude) during encoding/recall (Line 123); 2) Background Noise: Layer-specific $\\mu_{L/H}\\xi_b(\\theta_{L/H},t)$ in Eqs. 1–2; 3) Synaptic Weight Noise: included in $J_{LL}, J_{HH}, J_{HL}$ (Eqs. 1–2), which were fixed per run but resampled between different runs (each run modelling the behavior data of one participant, Appendix, line 22). Simulations used second-order Runge-Kutta (Eqs. 1–4). Together, these different types of noises account for the variability of within-participant behaviors across trials, and the variability of between-participant behaviors.\n\n(2) Our choice of $\\tau_f$ and $\\tau_d$ values is motivated by experimental data, which showed that STD-dominance in sensory cortex (Abbott et al., 1997; Chung et al., 2002; Yu et al., 2022) and STF-dominance in PFC (Wang et al., 2006).\n\n(3) Recently, there have been accumulated experimental evidence showing the existence of continuous attractor networks in neural systems. For example, using two-photon imaging on Drosophila's central brain, Kim et al. (Science, 2017) found that heading-direction neurons are aligned in a ring according to their preferred head-directions, forming a ring-like continuous attractor network. The bump of the continuous attractor network continuously shifts along the ring during rotation.\n\n3. Significance:\n\nThanks for the insightful comment. Indeed, the current model ignores the top-down feedback from attention/decision-making areas. Notably, even without explicit feedback, our hierarchical model successfully explains serial dependence through layer-specific synaptic plasticity: STD-driven repulsion in the lower circuit versus STF-driven attraction in the higher circuit. This dissociative mechanism may provide a baseline for general serial dependence, upon which attention further modulates the bias in a task-dependent manner. Nevertheless, we will expand discussion (L310–312) on the top-down modulation in shaping serial effects in the revised manuscript. There are experimental studies suggesting that attentional feedback can induce attractive biases even in early visual areas (John-Saaltink et al., 2016), highlighting a key direction for our future research.\n\n\n4. Originality:\n\nThank you for recognizing the originality of our work.\nAs suggested by the reviewer, in the revised manuscript, we will highlight the importance of the division of STD and STF in hierarchical information processing. Indeed, our model is built upon this biological mechanism: the lower-level circuit is dominated by STD, which provides high sensitivity to input changes, allowing rapid adaptation to current stimuli and the suppression of redundant information. In contrast, the higher-level circuit is dominated by STF, which supports the maintenance of prior information to ensure representational stability, thereby giving rise to the attractive bias.\nThis hierarchical dissociation optimizes information processing by functionally decoupling the stability-sensitivity trade-off. Without such separation, STF dominance in early areas would cause excessive feature persistence, impairing subsequent stimulus processing. Similarly, STD dominance in higher areas would disrupt contextual integration. Thus, the layered STD/STF division not only constitutes our core mechanism but aligns with fundamental neural computation principles. We will expand on these optimization perspectives in the Discussion in the revised manuscript.\n\n\n**Questions:**\n\n1. Thanks for raising this question. \nThere is no synapse-level cross-talk between two layers. The cross-talk between two layers in our model is at the neural activity level, which generates different serial dependence biases. Firstly, STD induces repulsive bias in the lower layer. This bias propagates via static feedforward pathways (translation-invariant, non-STP; cf. Yang et al., eLife, 2024; Zhang et al., J. Neurosci., 2016) to the higher layer. Secondly, the bottom-up repulsion competes with the STF-maintained prior information (attractive bias), yielding the observed behavioral pattern—attraction within trials and repulsion between trials.\nThis cross-layer competition exhibits time-dependency: psychophysical evidence indicates the attractive effect is strengthened with longer delays (Fritsche et al., 2017), reflecting faster decay of STD-driven repulsion versus STF-sustained attraction. Our model (Fig. 5) captures this time-dependent interaction, where the short timescale of STD leads to a faster decay of repulsion, while STF in the higher layer maintains the attractive bias over longer duration. We will illustrate the dynamics of this crosstalk across layers in the revised manuscript.\n\n2. We only presented a qualitative link between our model and the Bayesian framework, and there is no formal mathematical equivalence. \n\n3. We tend to believe that time constants $\\tau$s are task-independent, since it is hard for the neural system to change these parameters rapidly in a task-dependent manner. If there are task-dependent serial dependence bias, we tend to believe this is due to some other modulating factors (such as neuromodulators).\n\n4. Thanks for raising this question. Our model shows that STF-dominance can generate attractive bias, while top-down control may have the similar effect. Since STP is such a general property of neural systems, we tend to believe that the STP-based mechanism is at least involved in serial dependence, with top-down control further modulating the bias flexibly. Anyway, further experimental data is needed to clarify this issue. \n\n5. Thanks for the interesting question. Our model can be extended to study sequential dependence in the auditory domain, as sound frequency is continuous, auditory cortex neurons exhibit frequency tuning, and the auditory system's topographic and hierarchical organization is preserved throughout the pathway (Wang et al., Annual Review of Neuroscience, 2018; Wang, Nature Neuroscience, 2007). These features align with our model structure.\n\n**Limitations:**\n\n1. Thanks for pointing out this limitation. \nActually, we have conducted some preliminary experiments to explore the heterogeneity of STP on the model performance. Specifically, in the STF-dominant network (Fig. 2F), fixing inter-stimulus interval at 1s, we applied ±10% random perturbations to STP parameters of all synapses. Results showed stable attraction amplitude (1.48°) and minimal DoG peak shift (from 24.49° to 24.41°), indicating negligible impact of moderate heterogeneity. Based on this observation, we tend to believe that both the within-trial repulsion (Figure 3D) and the between-trial attraction effect will be sustained under moderate parameter perturbations. In the revised manuscript, we will include these results in Appendix.\n\n2. We will discuss these limitations as pointed out by the reviewer in the revised manuscript. \n\n\n3. Thanks for the interesting question. Zhang’s paper studied multisensory integration by using two reciprocally coupled CANNs. Our model also studied information integration, in the form of attraction bias. It will be interesting to explore how the two models can be combined together. For instance, to include STP and sequential stimuli in Zhang’s model, we can explore how serial dependence interact with multisensory integration. \n\nFinally, we thank the reviewer for the insightful comments. Your suggestions are valuable in improving our work, and we are committed to incorporating the revisions and new analyses into the final version. We hope our responses have addressed all your concerns, and we would be happy to engage in further discussion if needed."}, {"review_id": "CZr8cx0BSO", "reviewer": "Reviewer_fkF9", "summary": "In psychophysics and behavioral science, there is by now a large literature documenting the biases in perceptual decision related to the stimulus history. This paper proposed a neural network model to explain these serial dependence effects. Their main model is a two-layer coupled continuous attractor network (CANN), with plasticity in the connectivity. The first layer of the network was assumed to exhibit synaptic depression (STD), while the second layer was assumed to exhibit synaptic facilitation (STF). The network was shown to generate both attractive biases and repulsive biases. Both types of biases have been reported in the previous experimental studies.", "questions": "How was perceptual decision modeled in the network? Different readout rules may lead to different results as the population activity profile may be asymmetric. It would be interesting to examine this question. \n\nWould it be possible to show some direct comparisons to example experimental results?\n\nAre there any patterns of biases reported in experiments that the current model can not explain? If the answer is yes, it would be useful to discuss these as well. \n\n\nSome more questions about the choice of the models:\n\n(i) Would it be possible for a single-layer network to explain both attraction/repulsion?\n\n(ii) Is the order the the STD and STF important? That is, would a model with STF in the first layer and STD in the second layer lead to different predictions than those shown in the paper?\n\n(iii) Is the attractor dynamics important in the model? If not, one may be able to derive a more general network mechanism.", "limitations": "The  limitations of the work were properly discussed.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 4, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\nOverall, this is a solid paper that makes an interesting contribution.\n\n- The paper is well written. Although the work is technical, it is relatively easy to follow. The logic of the paper is generally clear. \n\n- The literature on the serial biases in psychophysics is quite messy. Given that, it is particularly nice to see models attempting to unify these experimental findings into a unifying computational framework. \n\n- The proposed network model can simultaneously explain both attractive biases and repulsive biases. \n\n- The model generates direct predictions that can be tested in future experiments (Fig. 5).\n\n\n\nWeaknesses:\n\n- The dependence of the results on the choice of key model parameters (e.g., the time constants of STD/STF) was not discussed. Thus, the robustness of these findings remain unclear. \n\n- While qualitatively comparisons to the experimental results were provided in the paper, there was no direct comparison to the data. \n\n- Line 82-85 motivates the model by citing papers showing STD in sensory areas and LTP in high-level areas. I believe these experimental data are only suggestive. It remains largely unclear what happens regarding STD/STF when the brain is performing some tasks. Can the authors tone this statement down? [minor weakness]", "was_revised": true, "final_justification": "The rebutal addressed most of the concerns I had. The authors proposed several revisions that would make the paper stronger.  I increased the score for “quality” from 3 to 4. \n\nI will keep my overall rating, which is already an “accept”. I think this paper should be a nice contribution for NeurIPS.", "rebuttal": "Thank you for the positive, encouraging and valuable comments, and constructive questions. In the below, we would like to clarify your concerns one by one. \n\n**Weakness:**\n\n1.\tAbout the dependence of the results on the choice of key model parameters:\nThank you for raising this important issue. \nOur choice of time constants $\\tau$s for STD-dominance and STF-dominance is based on the biological data (see e.g., Abbot et al., Science, 1997; Chung et al., Neuron, 2002; Yu et al., Neuron, 2022; Wang et al., Nature Neuroscience, 2006). \nBut as pointed out by the reviewer, since these parameters are so critical, it is worth analyzing the robustness of our findings on their values. We therefore conducted the robustness analyses. For example, for the STD-dominance condition (Fig.2C), we varied the absolute values of $\\tau_d$ and $\\tau_f$ while keeping $\\tau_d \\gg \\tau_f$ holds ($\\tau_f$=0.1, $\\tau_d$=3 vs. $\\tau_f$=0.3, $\\tau_d$=4), and we observed the same statistically significant repulsion effect (both t(19) > 213.97, p < .001), with only its magnitude varying (original: -2.29°; new experiments: -1.34° and -3.61°). We also analyzed the robustness of attraction effect on time constants $\\tau_d$ and $\\tau_f$ in both single- and two-layer networks, and found that the STP parameter variations do not alter the model performance qualitatively. We will report these results in the revised manuscript.\n\n2.\tAbout the qualitative comparisons to the experimental results:\nThanks for raising this question. \nSince our model was built at the neural circuit level, we could not compare neural activities in our model directly to experimental observations. Nevertheless, the performances of our model are consistent with experimental data. These include, 1) our model quantitatively reproduces experimental serial bias amplitudes (\\~2°) for both within-trial repulsion and between-trial attraction [Fritsche et al., Curr. Biol. 2017; Cicchini et al. Proc. R. Soc. B 2018; Pascucci et al. PLOS Biol. 2019; Czoschke et al. Br. J. Psychol. 2019; Fischer et al. Nat. Commun. 2020; Moon et al. Psychon. Bull. Rev. 2023]. 2) the judgment error curve as a function of prior-current stimulus difference also closely matches the experimental data. Furthermore, 1) fMRI studies (Schwiedrzik et al., 2014; Sheehan et al., 2022) showed repulsion in early sensory cortices, while attraction involves higher visual-parietal-frontal networks; 2) Luo et al. (2025) presented EEG/MEG evidence of two-stage processing—sensory repulsion and prefrontal attraction. These findings align with the two-layer dynamics of our model: stimulus-specific repulsion via low-layer STD and predictive attraction via high-layer STF. We will add more discussion about these comparisons in the revised manuscript.\n\n3.\tWe appreciate the reviewer's comment. We agree that existing evidences only suggest that sensory cortices exhibit STD predominance and higher-level areas show STF predominance, but direct evidence on the task-dependent STD/STF dynamics remains unclear. We will moderate our statement accordingly in the revised manuscript. It is worth mentioning that previous studies noted that the STP timescale aligns with the working memory time window, providing neural substrate for information maintenance [Mongillo et al., Science 2008; Masse et al., Nat. Neurosci. 2019]. Here, our study extends this framework further by demonstrating that the regionally specialized STP critically underlies serial dependence in working memory.\n\n**Questions:**\n\n1.\tAbout the readout rule of perceptual decision:\nThanks for this insightful question. \nIn our model, perceptual decision was implemented by decoding high-layer network activity via population vector method (PVM). To evaluate potential readout bias from asymmetrical responses, we reanalyzed Fig.3D using three other methods: center-of-mass (COM), maximum likelihood (ML), and peak decoding (Peak). All methods confirm robust within-trial repulsion (serial bias amplitudes/curve peak at: PVM:−0.90°/37.92°; COM:−0.90°/37.92°; ML:−0.97°/36.97°; Peak:−0.61°/45.34°) and between-trial attraction (serial bias amplitudes: PVM:1.17°/19.34°; COM:1.17°/19.34°; ML:1.05°/19.86°; Peak:1.93°/18.21°), which are statistically significant across metrics. We will include these analyses extended to Figs. 2C, 2F, 3E, 3F, and 5 in the revised manuscript.\n\n2.\tYes, this has been addressed in our response to Question 2 above.\n\n3.\tThanks for raising this important issue. Our model accounts for most documented serial dependent phenomena and the associated neural mechanisms. We acknowledge that a few experimentally observed patterns require further investigation. Specifically: 1) Attractive biases in primary visual cortex (John-Saaltink et al., 2016) may involve top-down feedback reshaping sensory representations (discussed in Line 310). 2) Long-timescale repulsive effects (>50 s; Fritsche et al., 2020) suggest sensory cortex mechanisms beyond current STP timescales. Implementing long-term negative feedback mechanisms in sensory cortices may explain this. We will expand discussion on these unmodeled studies in the revised manuscript.\n\n4.\tAbout the possibility for a single-layer network to explain both attraction/repulsion: Thank you for this interesting question. A single-layer network cannot simultaneously account for both attraction and repulsion in sequential dependence due to the antagonistic nature of STD and STF. As Sec. 3 and Fig. 2 demonstrate, repulsion relies on STD-dominance, reducing neural responses and modeling sensory adaptation in primary cortical areas. Conversely, attraction depends on STF-dominance, enhancing responses and supporting information integration in higher-order regions. Since STD and STF modulate synaptic efficacy oppositely, it is not feasible for the same neural population to exhibit antagonistic effects within the same temporal window. Moreover, there is currently no empirical evidence supporting the coexistence of STD-dominant and STF-dominant synapses within the same local circuit. Therefore, explaining bidirectional behavioral effects (attraction and repulsion) necessitates a hierarchical, heterogeneous STP network structure.\n\n5.\tAbout the importance of STD and STF order: Thank you for raising this important question. The order of STD and STF is crucial for the model performance. This configuration allows the early STD layer to enhance sensitivity to subtle input differences by reducing responses to repeated stimuli, while the downstream STF layer integrates temporal information through response facilitation, thereby stabilizing perception. Reversing this order (STF-dominance first) causes initial signal smoothing due to facilitation. Consequently, even though the downstream STD layer attempts to extract differential features, the loss of sensitivity to input variation cannot be recovered, resulting in failure to achieve the intended synergy between sensitivity and stability. Following your suggestion, we simulated a reversed configuration—lower STF-dominated layer ($\\tau_f^L$= 5 s, $\\tau_d^L$ = 0.3 s) and higher STD-dominated layer ($\\tau_d^H$ = 3 s, $\\tau_f^H$ = 0.3 s)—yielded exclusively attractive biases. Both within-trial (amplitude: 1.79°; peaking at 26.79; t(19)=6.79, p<.001; cluster 1°-58°, p<.001) and between-trial effects (amplitude: 3.81°; peaking at 28.07°; t(19)=19.62, p<.001; cluster 1°-87°, p<.001) showed significant attraction.\n\n\n6.\tAbout the attractor dynamics: We thank the reviewer for raising this insightful question, which deepens our understanding of the role of attractor dynamics. Indeed, attractor dynamics plays a critical role in generating serial dependence effects, driving both within-trial repulsion and between-trial attraction. The stability of neuronal activity states ($r$) depends on synaptic state variables (neurotransmitter release probability $u$, available neurotransmitter resources $x$), with $r$ operating at a faster timescale than $u$ and $x$. Specifically, 1) within-trial repulsion: stimuli create local minima in $x$ state space (Fig. 2AB), suppressing responses to subsequent adjacent stimuli. This forms unstable attractors in $x$-state space, forcing $r$ away from the minima to produce repulsion; 2) between-trial attraction: prior stimuli induce peaks in $u$ state space (Fig. 2DE), enhancing responses to subsequent adjacent stimuli. This establishes stable attractors in $u$-state space, constraining $r$ near specific $u$ values to generate attraction. Notably, the stable attractor mechanism in $u$-state space aligns with Barbosa et al.'s findings (Nat Neurosci 2020) that working memory stores information via activity-silent states maintained by STF-dependent attractors. They reactivate during new trials, biasing ongoing processing.\n\nFinally, we thank the reviewer again for evaluating our manuscript carefully and providing many constructive suggestions, which are very helpful to improve our work. We will incorporate the recommended corrections and additional analyses into the final version of the paper. We hope our responses have addressed all your concerns, and we would be glad to engage in further discussion if needed."}, {"review_id": "g4aRfJVUT1", "reviewer": "Reviewer_rAyR", "summary": "In this study, the authors present a two-stage continuous attractor network model endowed with short term facilitation and depression, capable of explaining psychophysical results regarding the sequential dependence upon previous stimuli of perceptual judgments in task participants.", "questions": "Major concerns:\n\n1.\tIf the present model were really compatible with Bayesian accounts of sensory representation, shouldn’t its properties be in some way dependent on the statistics of the stimuli presented to the network? As it is, the short-term plasticity timescales and parameters are fixed by the modeler, whereas a serially dependent Bayesian prior over network activity states should theoretically be related to the timescale statistics of presented stimuli. Is there any room for dynamic adaptation of these parameters within the model, or any experimental evidence in favor of such a thing? As it stands, the present model seems to me to be a mechanistic alternative account for empirical data that is likely not compatible with Bayesian approaches; there ought to be experiments that could be used to disambiguate these two classes of model (or model modifications that could produce more synchrony), and a discussion of these points could be very beneficial for the community.\n\n2.\tRelatedly, does the present model make any testable predictions that could be used to validate it? Figure 5 seems to provide some traction on this question, but a more detailed discussion would be beneficial. In particular, how dependent are these results on the (as far as I can tell) arbitrarily selected timescales of STF and STD? More importantly, if this model were really underlying the psychophysical results observed, shouldn’t there be a near-exact relationship between the timescales of STF and STD in early sensory areas and PFC and the timescales of within-trial repulsion/ across-trial attraction?\n\nMinor concerns:\n\nLine 151: the \\Delta S change reported must be highly parameter-dependent, correct? The parameter-sensitivity of this result should be discussed (as well as its implications for testable model predictions as mentioned above).\n\nLine 226: citations need for the gain and two-process models.", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper is well-written and clear, with an appropriate amount of time spent constructing the two-stage model and analyzing its properties. The results are interpretable, intuitive, and thorough; the model is also reasonably well substantiated by a literature review and appears (as far as I can tell) original. I have some concerns about the authors’ attempt to relate their model to a Bayesian interpretation of serial dependence, explained below. While I do think that the model is quite well designed to explain the specific set of experimental results that the authors have selected, I have a hard time seeing how a model of this kind could be adapted to explain or provide predictions for neural responses or human reports in response to more complex, naturalistic stimuli, i.e. I view it as fundamentally a ‘toy’ model, that leaves little clue for how it could be extended to more complex situations.", "was_revised": true, "final_justification": "The authors did a good job addressing my concerns and proposing concrete modifications to their manuscript that will accordingly improve its quality. My initial assessment of the paper was 'Accept', and this remains my assessment.", "rebuttal": "Thank you for the valuable and constructive comments, and the recognition of the clarity, interpretability, and originality of our work. In the below, we would like to clarify your concerns one-by-one.\n\n**Weakness:**\n\n1.\tAbout the generality of the model  \n\nAs you noted, our model targets on explaining the serial dependence phenomena on simple physical features like visual orientation, which is a common strategy in the cognitive neuroscience field of using low-dimensional, well-controlled stimuli to isolate the core neural mechanisms. The simple features used in psychophysical experiments motivated us to build relatively simple network models. Nevertheless, we expect that this simple model gives us insight into the fundamental mechanism of serial dependence, that is, short-term synaptic plasticity, through distinct time constants for depression and facilitation, generating varying serial dependence biases.\n\nRecently, serial dependence experiments have been extended to include complex stimuli such as facial emotion, identity, and body size (e.g., Manassi et al., Journal of Vision, 2023), and similar bias phenomena have been observed. Considering that STP is a general property of neural systems and that STP can explain serial dependence with simple features, we strongly believe that the STP-based mechanism proposed in this work is also applicable to these complex features. However, to validate this, we need to first build much more complicated network models mimicking how the brain processes these complex features. Our present work can be regarded as the first step in demonstrating the feasibility of the STP-based mechanism for serial dependence, and in future work, we will extend the model to more complex situations.\n\n**Questions:**\n\nMajor concerns:\n\n1.\tAbout the link to Bayesian interpretation \n\nThanks for raising this important question. Please note that in serial dependence research, when people claim Bayesian interpretation, they do not refer to how sensory representation depends on the stimulus statistics over long time, but rather emphasize on how perception depends on the recent history of stimulus sequence, which falls into the time scale of STP. Specifically, the Bayesian theory of serial dependence consists of two stages of processing (Pascucci et al., Plos Biology, 2019).\n(1)\tSensory Encoding Stage: The Bayesian theory posits that, after exposure to the first stimulus ($\\theta_n$, Fig. 4A bottom), neurons preferring stimuli near $\\theta_n$ undergo adaptation, manifested as reduced responses to the second stimulus. This alters the likelihood function in the Bayesian framework and generates the repulsion effect in sensory perception. \nIn the first layer of our model, due to STD-dominance, the available neurotransmitter $x$ decays after the presence of the first stimulus, and the distribution of $x$ values across the neuron population is non-uniform (black curve in Fig. 4B bottom), with more active neurons having smaller values of $x$. When the second stimulus is presented, this non-uniform distribution of $x$ across the neuron population induces alternated responses compared to that to the first stimulus, which can be regarded as the likelihood function being changed in the Bayesian framework. \n\n(2)\tPost-Perception Decision Stage: The Bayesian theory posits that higher cortical areas develop weight bias toward the prior stimulus ($\\theta_n$, Fig. 4A top), modifying the prior distribution and inducing the attraction effect. \nIn the second layer of our model, due to STF, the neurotransmitter release probability $u$ (green curve, Fig. 4B middle) increases at the location of the previous stimulus ($\\theta_{cue}^{d,n}$), which facilitates neuronal responses at the previous stimulus location, as if the prior distribution of stimulus is changed in the Bayesian framework.\nIn summary, unlike the conventional Bayesian models, which posit priors are shaped by long-term environmental statistics (e.g., Wei et al., Nature Neuroscience, 2015), the Bayesian theory of serial dependence considers experience-dependent modulations of likelihood function and prior in short timescale, and our model provides a potential neural mechanism to support this view. Since the Bayesian view of serial dependence has been recognized in the field, we hope that linking our model to this view will strengthen our understanding of the neural mechanism of serial dependence. We will elaborate on this connection in the revised Discussion section.\n\n2.\tAbout model prediction\n\nYes, our model generates testable predictions and they can be validated. Specifically, our model proposes that $\\tau_d$ in sensory areas governs the within-trial repulsion-to-attraction transition, while $\\tau_f$ in high layers constrains the magnitude of across-trial attraction. These predictions address the reviewer's central query regarding hierarchical timescale dependencies. Please note that in our model, it is the relative relationship between $\\tau_d$ and $\\tau_f$, rather than their absolute values, that determines the serial dependence biases. The neuroscience data has shown that STF dominates in PFC while STD dominates in sensory cortex (STD: Abbot et al., Science, 1997; Chung et al., Neuron, 2002; Yu et al., Neuron, 2022; STF: Markram et al., Nature, 1996; Wang et al., Nature Neuroscience, 2006).\n\nAs concerned by the reviewer, we conducted extra experiments to analyze the model parameter dependence. The results show that the emergence of repulsive effect primarily depends on the relative relationship $\\tau_d \\gg \\tau_f$ in the lower-layer of the model, whereas the attractive effect relies on the $\\tau_f \\gg \\tau_d$ relationship in the upper-layer. The absolute values of $\\tau_d$ and $\\tau_f$ are not crucial, and they only modulate the amplitude of the bias effect when ISI/ITI are fixed. We will add discussions about this point in the revised manuscript.\n\nMinor concerns:\n\n1. Thanks for the question. $\\Delta S$ denotes the difference between the prior and current stimuli. In the classical serial dependence curves, both attractive and repulsive biases exhibit a peak around $\\Delta S$ of approximately 30°. In other words, the bias is strongest when the historical sensory information is about 20°–40° away from the current stimulus. \nRegarding the value of $\\Delta S$ generating the strongest bias, our study showed that it mildly depends on STP parameters. For instance, in the STD-dominance condition (Fig. 2C), when we varied the absolute values of $\\tau_d$ and $\\tau_f$ while keeping $\\tau_d \\gg \\tau_f$ holds ($\\tau_f$=0.1, $\\tau_d$=3 vs. $\\tau_f$=0.3, $\\tau_d$=2), we observed only minor shift in the peak repulsion angle (from 31.6° in Fig.2C to 28.5° and 32.9°, respectively). We also studied this sensitivity on STP time constants in both single- and two-layer networks, finding that the STP parameter variation does not alter the characteristic peak $\\Delta S$ value. We will report these results in the revised manuscript. \n\n2. Thanks for the suggestion. We will add citations for the gain model (Fischer et al., Nature Neuroscience, 2014) and two-process model (Schwiedrzik, Melloni et al., Cerebral Cortex, 2014; Pascucci et al., PLOS Biology, 2019) in the revised manuscript.\n\nFinally, we thank the reviewer for carefully reviewing our manuscript and providing many constructive suggestions, which are highly valuable to improve our work, and we commit to incorporating the corrections and new analyses into the final version of the paper. We hope our replies have addressed all concerns of the reviewer, and if not, please feel free to discuss with us."}]

Author rebuttal:

Meta-review: This paper studies our understanding of how the neural system leverages synaptic short-term plasticity to balance sensitivity in sensory perception with stability in post-perceptual cognition using a two-layer continuous attractor neural network. The reviewers found the paper well written on an important topic for the NeurIPS community. The rebuttal was engaging and addressed most of the reviewers’ concerns. All four reviewers unanimously recommended acceptance. Addressing the concerns raised in the reviews and including the rebuttal discussions in the final version will improve the paper quality.
Decision: Accept (poster)