{"paper_id":"7acde2ad-435d-4aa5-a36d-02ba9019aed3","body_text":"Cell-type-specific synaptic scaling mechanisms differentially\ncontribute to associative learning\nFabio Veneto1,∗, Ayc ¸a Kepc ¸e1,2,∗, Yue Kris Wu1,3,#, Julijana Gjorgjieva1,#\n1School of Life Sciences, Technical University of Munich, Freising, Germany;\n2Elite Master Program in Neuroengineering, Technical University of Munich, Munich, Germany\n3Zuckerman Mind Brain Behavior Institute, Columbia University, New Y ork, USA\n∗ These authors contributed equally to this work.\n# Co-senior and co-corresponding authors\nEmail: yw4297@columbia.edu; gjorgjieva@tum.de.\nAbstract\nExcitatory synaptic scaling regulates network dynamics by proportionally adjusting excitatory synap-\ntic strengths after sensory perturbations. During associative learning, blocking excitatory scaling in\nconditioned taste aversion paradigms prolongs generalized aversive responses and delays mem-\nory specificity. Recent evidence also implicates inhibitory synaptic scaling in the regulation of\nnetwork dynamics. Specifically, parvalbumin (PV)-expressing inhibitory neurons, targeting periso-\nmatic regions of excitatory (E) pyramidal neurons, and somatostatin (SST)-expressing neurons,\ntargeting distal dendrites, exhibit distinct scaling responses. This leaves open the question of how\ncomplex plasticity mechanisms regulate recurrent excitatory-inhibitory circuit dynamics in asso-\nciative learning. Using computational approaches, we demonstrate that Hebbian plasticity drives\nmemory generalization to novel stimuli not presented during conditioning. Following conditioning,\ndiverse synaptic scaling mechanisms progressively induce memory specificity, which can be reg-\nulated by top-down inputs. Our results reveal that, in the absence of excitatory scaling, PV-to-E\nscaling can effectively compensate and rescue memory specificity, highlighting the presence of\ndegenerate mechanisms in the brain. Notably, in the process of establishing memory specificity,\nexcitatory scaling and PV-to-E scaling function synergistically, while concurrently opposing SST -\nto-E scaling. The synergistic and antagonistic plasticity mechanisms are orchestrated to shape\nthe temporal evolution of memory representations, from generalized to precise.\nIntroduction\nSynaptic scaling is considered a crucial homeostatic synaptic plasticity mechanism that adjusts\nthe strength of all incoming synapses to a neuron to stabilize network dynamics in response to\nsensory perturbations (Turrigiano et al., 1998; Turrigiano, 2008; Pozo and Goda, 2010; Tetzlaff\n1\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\net al., 2011; Wu et al., 2020; Wen and Turrigiano, 2024). Typically studied for synapses between\nexcitatory neurons, this process either downscales or upscales the synapses to compensate for\nhyperactive or hypoactive activity, respectively (Turrigiano et al., 1998; Kim et al., 2012; Keck et al.,\n2013; Torrado Pacheco et al., 2021). Unlike Hebbian plasticity, which can occur from seconds to\nminutes, synaptic scaling operates on a much slower timescale, unfolding over hours to days (Tur-\nrigiano et al., 1998; Ibata et al., 2008; Watt, 2010; Keck et al., 2017). Beyond the homeostatic\nrole of excitatory synaptic scaling in compensating for sensory perturbations, recent studies have\nrevealed the importance of excitatory synaptic scaling in associative learning (Wu et al., 2021).\nIn a classical conditioned taste aversion (CTA) paradigm (Figure 1A), by pairing an aversive un-\nconditioned stimulus (US) with a conditioned stimulus (CS), mice learned the association between\nthe CS and aversion immediately after the conditioning. Four hours after conditioning, mice dis-\nplayed generalized aversion to a novel test stimulus (TS), a tastant absent during the condition-\ning. When tested after 24h and 48h with the TS, the generalized aversive behavior diminished,\nand mice exhibited aversion exclusively to the CS, reflecting the formation of memory specificity.\nBlocking excitatory synaptic scaling significantly prolonged the generalized aversive behavioral\nresponse, with mice continuing to exhibit aversion to TS even 24 hours post-conditioning (Figure\n1A). Nonetheless, after blocking excitatory synaptic scaling, mice developed memory specificity\nafter 48h post-conditioning, suggesting that other mechanisms may complementarily achieve the\nspecific refinement of memory representations.\nIn addition to excitatory synaptic scaling, inhibitory synaptic scaling has also been found to regu-\nlate network dynamics in response to sensory perturbations (Kilman et al., 2002; Swanwick et al.,\n2006; Prestigio et al., 2021). Notably, the scaling of inhibitory synapses is target-dependent (Pres-\ntigio et al., 2021), whereby hyperactivity in excitatory pyramidal neurons (E) induces upscaling\nof inhibitory synapses at perisomatic regions of excitatory neurons while unexpectedly down-\nscaling of inhibitory synapses at dendritic regions. These connectivity preferences have been\nrelated to molecularly distinct interneuron subtypes (Tremblay et al., 2016) (Figure 1B). For in-\nstance, parvalbumin (PV)-expressing inhibitory neurons primarily innervate perisomatic regions,\nwhereas somatostatin (SST)-expressing inhibitory neurons predominantly target distal dendritic\nregions (Lazarus and Huang, 2011; Hioki et al., 2013; Dorsett et al., 2021). Y et, how these in-\nhibitory synaptic scaling mechanisms interact with the well-established excitatory synaptic scaling\nduring associative learning remains elusive.\nHere, combining analytical calculations and numerical simulations, we demonstrate that rapid Heb-\nbian plasticity drives memory generalization to novel test stimuli that are absent during condition-\ning. Following conditioning, we find that different forms of synaptic scaling regulate neural dynam-\nics, progressively inducing memory specificity over time. Our findings highlight the critical role of\ndifferent forms of synaptic scaling in achieving precise memory representations and propose a role\nfor top-down inputs in modulating associate learning. When excitatory scaling is absent, memory\n2\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nA\nConditioning\nCS US\nTesting\nTS\n4h / 24h / 48h\nC\nE1\nP1\nS1 S2\nE2\nP2\nCS\nCS\nUS\nE1\nP1\nS1 S2\nE2\nP2\nTS\nTS\nConditioning Post-Conditioning and testing\nThree-factor Hebbian plasticity\nSynaptic scaling, set-point regulation\nActive\nmechanisms\nChanges induced by hyperactivity\nB\nE\ndendritic\ninhibition\nsomatic\ninhibition\nE\ndendritic\ninhibition\nsomatic\ninhibition\nBefore After\nExperimental results\nBlocking\nE-to-E scaling\nControl\n4h 24h 48hTesting\nCS: conditioned stimulus\nUS: unconditioned stimulus\nTS: test stimulus\nE: excitatory\nP: PV\nS: SST\n: Memory generalization\n: Memory specificity\nFig. 1. Experimental paradigm and computational framework for associative learning. A. Conditioned taste aversion\n(CTA) paradigm applied in Wu et al. (2021). Conditioning is induced by pairing an aversive unconditioned stimulus (US)\nwith a conditioned stimulus (CS) (left). Memory generalization and specificity are evaluated by measuring the mouse’s\naversive behavioral response to a novel test stimulus (TS) at either 4h, 24h, or 48h (left). Mice exhibit an aversive\nbehavioral response to TS at 4h but not at 24h and 48h, indicating a switching from memory generalization to memory\nspecificity (right). When blocking excitatory scaling, memory generalization persists at 24h but diminishes by 48h (right).\nB. Target-specific inhibitory synaptic scaling reported in Prestigio et al. (2021). Hyperactivity in postsynaptic excitatory\nneurons induces a downscaling of dendritic inhibition while upscaling somatic inhibition.C. Schematic of network model\nwith two subnetworks. Each subnetwork consists of one excitatory, one PV and one SST population. Different subnet-\nworks are tuned to different stimuli corresponding to different tastants in the conditioned taste aversion experiments.\nDuring conditioning, excitatory (E1) and PV (P1) populations in subnetwork 1 receive additional inputs corresponding to\na CS, while the US is present. During the test period, excitatory (E2) and PV (P2) populations in subnetwork 2 receive\nadditional inputs corresponding to a TS. Three-factor Hebbian plasticity operates during conditioning, whereas synaptic\nscaling and set point regulation mechanisms are active during both conditioning and post-conditioning phases.\nspecificity can be rescued by PV-to-E scaling, indicating the existence of degenerate mechanisms\nin the brain. We find that excitatory scaling and PV-to-E scaling work synergistically while counter-\nacting the effects of SST -to-E scaling. This intricate interplay between synergistic and antagonistic\nplasticity mechanisms drives the temporal evolution of memory specificity, facilitating a smooth\ntransition from generalized to specific memory representations.\n3\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nResults\nTo investigate how different plasticity mechanisms – rapid Hebbian and slower forms of synaptic\nscaling – interact with each other and give rise to memory specificity in associative learning, we\ndeveloped a rate-based recurrent network model consisting of two interconnected subnetworks.\nEach subnetwork includes one excitatory (E) population and two distinct inhibitory populations: PV\nand SST (see Methods, Figure 1C). We assume that different subnetworks are tuned to different\nstimuli corresponding to different tastants in the conditioned taste aversion experiments. Inspired\nby experimental studies indicating that PV inhibitory neurons primarily innervate perisomatic re-\ngions, while SST inhibitory neurons predominantly target distal dendritic regions, we modeled\nsomatic inhibition to the excitatory population as coming from the PV population and dendritic in-\nhibition as coming from the SST population (Figure 1C) (Lazarus and Huang, 2011; Pfeffer et al.,\n2013; Dorsett et al., 2021). The network connectivity was designed to incorporate previously re-\nported experimental features, including the absence of inhibitory connections from PV and SST\ninterneurons to SST interneurons (Pfeffer et al., 2013).\nThree-factor Hebbian plasticity strengthens excitatory-to-excitatory connections\nduring conditioning\nTo model the conditioning procedure in the conditioned taste aversion paradigm, the excitatory\n(E1) and PV (PV 1) populations in subnetwork 1 receive additional inputs to represent the condi-\ntioned stimulus (CS) (Figure 2A) (Ji et al., 2015). Inspired by experimental studies demonstrating\nthat reward or punishment plays a crucial role in learning (Pawlak, 2010; Gerstner et al., 2018),\nwe applied a three-factor Hebbian learning rule to update the E-to-E connection strength during\nconditioning:\nτhebb\ndwEi Ej\ndt = ηrEj(rEi − r bs\nEi ) i, j ∈ {1, 2} (1)\nη =\n\n\n\n1 in the presence of unconditioned stimulus\n0 otherwise\n(2)\nwhere τhebb is the time constant of Hebbian plasticity, rEi denotes the activity of the excitatory\npopulation in subnetwork i with the superscript ‘bs’ representing the baseline activity before con-\nditioning, i, j representing the indices of subnetworks. The presence of the aversive unconditioned\nstimulus (US) determines the third factor η and serves as a gate for Hebbian plasticity, enabling\nplasticity during the conditioning phase while disabling it elsewhere.\nDuring the simulation of conditioning, the CS leads to an increase in the excitatory activity in sub-\nnetwork 1 (rE1) (Figure 2B). Despite not being directly stimulated by the CS, the excitatory activity in\nsubnetwork 2 (rE2) also increases, albeit to a lesser extent, due to recurrent excitatory connections\nbetween E1 and E2 (Figure 2B). During conditioning, in the presence of the US, E-to-E connection\n4\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nA Conditioning\nE1\nP1\nS1\n S2\nE2\nP2\nCS\nCS\nUS\nB C\nFiring rate\n0.5\n1.0\n1.5\n2.0\n2.5\n5 10 15 20 25\nTime (s)\nrbs\nr , r E1 E2\nWeights\n0.4\n0.5\n0.6\n0.7\n5 10 15 20 25\nTime (s)\nw , w E1E1 E1E2\nw , w E2E2 E2E1\n0 0\nConditioning Conditioning\nFig. 2. Hebbian plasticity enhances excitatory activity and strengthens E-to-E connections during conditioning. A. Net-\nwork schematic of the conditioning phase. During conditioning, E and PV populations of subnetwork 1 receive additional\ninputs that correspond to the conditioned stimulus. During this phase, the unconditioned stimulus is present, modulat-\ning Hebbian plasticity. B. Activity of excitatory population in subnetwork 1 (r E1) and subnetwork 2 (rE2). Conditioning is\napplied during the interval from 5 to 20s by increasing the inputs to E and PV populations in subnetwork 1. The dashed\nline represents the baseline activity level measured before conditioning. C. Excitatory to excitatory connection strength\nduring conditioning. Different connections are indicated by the differently colored lines.\nstrengths increase through Hebbian plasticity, with the strongest enhancement observed in the\nconnection strength within the excitatory population of subnetwork 1 (wE1E1) (Figure 2C).\nMemory undergoes transient generalization caused by Hebbian plasticity before\ngradually achieving specificity\nTogether with Hebbian plasticity acting on excitatory-to-excitatory synapses during conditioning,\nwe incorporated synaptic scaling at the connections from E to E synapses, i.e., excitatory scaling.\nThis is consistent with experimental findings that hyperactivity (hypoactivity) of excitatory neurons\nleads to downscaling (upscaling) of E-to-E synapses. Synaptic scaling adjusts synaptic weights to\nmaintain stable activity levels, preventing activity from becoming excessively low or high (Turrigiano\net al., 1998; Kim et al., 2012; Keck et al., 2013; Torrado Pacheco et al., 2021). This process\nis generally considered to be multiplicative and independent of presynaptic activity (Turrigiano,\n2008). Following previous computational studies (Van Rossum et al., 2000), we modeled the\nchange of connection strength from the excitatory population in subnetwork j to the excitatory\npopulation in subnetwork i via synaptic scaling as follows:\nτ EE\nss\ndwEi Ej\ndt = (1 − rEi\nθEi\n)wEi Ej. (3)\nHere, τss represents the time constant of synaptic scaling for individual type of connections, θEi\ndenotes the target firing rate or the set point of the excitatory population in the subnetwork i.\nTo investigate how different inhibitory synaptic scaling, discovered experimentally to excitatory\ndendrites and somas (Prestigio et al., 2021), collectively affect associative learning, we imple-\nmented synaptic scaling from PV-to-E and SST -to-E synapses. In line with the observed decrease\nin somatic inhibition induced by the hyperactivity of postsynaptic excitatory neurons (Prestigio\n5\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\net al., 2021), PV-to-E synapses are scaled by:\nτ EP\nss\ndwEi Pj\ndt = −(1 − rEi\nθEi\n)wEi Pj. (4)\nSimilarly, consistent with the observed increase in dendritic inhibition resulting from the hyperac-\ntivity of postsynaptic excitatory neurons (Prestigio et al., 2021), SST -to-E synapses are scaled\nby:\nτ ES\nss\ndwEi Sj\ndt = (1 − rEi\nθEi\n)wEi Sj. (5)\nThe set points of the two excitatory populations were allowed to change (Leman et al., 2025),\nto reflect distinct dynamics and activity levels that emerge due to direct stimulation of one popu-\nlation during the conditioning phase. In particular, the set points were jointly determined by the\ncorresponding activity and the set point regulator β according to the following dynamics:\nτθ\ndθEi\ndt = (−θEi + rEi) + (−θEi + βEi) (6)\nwhere τθ is the time constant governing the plasticity of the set points. The set point regulator β\ncan be considered a form of a global homeostatic mechanism that uniformly regulates the activity\nof the entire network and is dynamically updated according to:\nτβ\ndβEi\ndt = −βEi + rEi (7)\nβEi → βEi − k at t cond onset (8)\nwhere τβ denotes the time constant governing the plasticity of the set point regulator and k is a\nfree parameter that determines the magnitude of the abrupt decrease in the set point regulator β\nof excitatory populations in both subnetworks at the onset of conditioning t cond onset. Conditioning\nraises the excitatory activity rE, thereby increasing both the set point θ and the set point regulator\nβ. In contrast, this sudden reduction in β counteracts the increases induced by conditioning and\nfunctions as a homeostatic mechanism to globally regulate the overall activity level.\nTo evaluate memory specificity after conditioning, we presented a test stimulus (TS) to the network\nby providing excitatory inputs to the E and PV populations in subnetwork 2 at three distinct test time\npoints (4h, 24h, and 48h), and measured the activity of the excitatory population in subnetwork 1,\ndenoted by r test\nE1\n(Figure 3A). This activity is compared to a reference activity,r ref\nE1\n, obtained by sim-\nulating the network under identical initial conditions but without applying conditioning (Figure S1A).\nWe observed that r test\nE1\nexceeds r ref\nE1\nduring TS presentation at 4h (Figure 3B), whereas, at 24h and\n48h, r test\nE1\nis smaller than r ref\nE1\n(Figure 3B). These results suggest that, following conditioning, the\nmemory initially generalizes to test stimuli but eventually becomes specific over time.\n6\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nFEC\nBA Testing at 4h Testing at 24h Testing at 48hTesting\nE1\nP1\nS1\n S2\nE2\nP2\nTS\nTS\nD\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\nrref\nr   , r   E1 E2\nTime (h)\nWeights\n4 24 480.0\n0.9\n1.8\n w     , w       E1E1 E2E2\nw     , w       E1P1 E2P2\nw     , w       E1S1 E2S2\n0.5\n1.0\n1.5\n2.0\n2.5Firing rate\n15 seconds4h\nTime (s)\nFiring rate\n0.5\n1.0\n1.5\n2.0\n2.5\n15 seconds24h\nrref\nr   , r   E1 E2\nTime (s)\n0.5\n1.0\n1.5\n2.0\n2.5Firing rate\n15 seconds48h\nTime (s)\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point θ\nrbs\nθ   ,θ     E1 E2\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point regulator β\nrbs\nβ   ,β     E1 E2\nFig. 3. Memory gradually transitions from generalization to specificity. A. Network schematic of the testing phase.\nAfter conditioning, E (E2) and PV (P2) populations of subnetwork 2 receive additional inputs that correspond to the test\nstimulus. The unconditioned stimulus is not presented during this phase. B. Responses of excitatory populations in\nsubnetwork 1 and subnetwork 2 when presenting a test stimulus for 15s (gray) at 4h (left), 24h (middle) and 48h (right).\nThe black horizontal lines indicate the reference activity (r ref ), measured by the excitatory population in subnetwork 1\nin response to a test stimulus under identical initial weights conditions but without plasticity. Here, a moderate value of\nk = 0.25 is applied. C. Different connection strengths (E-to-E, PV-to-E and SST -to-E) after conditioning.D. Evolution of\nset points regulators of excitatory population in subnetwork 1 (βE1) and subnetwork 2 (βE2) after conditioning up to 48h.\nThe gray horizontal dashed line represents the baseline activity level measured before conditioning. E. Same as D but\nfor set point θ. F. Activity of excitatory population in subnetwork 1 (rE1) and subnetwork 2 (rE2) after conditioning.\nAlthough synaptic scaling is active throughout the entire simulation, including the conditioning\nphase, its slow time constant renders changes in the E-to-E connection strength during condi-\ntioning negligible. Following conditioning, the weights evolve solely due to the different forms of\nsynaptic scaling, undergoing significant changes over time: E-to-E weights decrease, PV-to-E\nweights increase, and SST -to-E weights decrease (Figure 3C). Following the abrupt decrease at\nthe onset of conditioning, the set point regulators gradually rise over time, driven by increased\nexcitatory activity in the early post-conditioning period (Figure 3D). Due to the set point regulators\nbeing lower than the baseline activity, the set points, decreased throughout the post-conditioning\nperiod, eventually stabilizing at a new steady state lower than the initial set points (Figure 3E).\nConsequently, following conditioning, the excitatory activity, along with PV and SST activity, grad-\nually decreases over time and converges towards the new set points (Figure 3F). Our results\nindicate that synaptic scaling gradually reshapes network connectivity after conditioning, driving a\nprogressive reduction in excitatory, PV, and SST activity (Figure S2) as the system stabilizes to a\nnew equilibrium.\n7\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nCharacterization of the temporal evolution of memory representations\nTo characterize how memory representations dynamically evolve over time, we aimed to describe\nthe network’s response to the test stimulus following conditioning in the model. To that end, we\nintroduced a procedure consisting of two phases for calculating the weights in the network during\nand post-conditioning, followed by the testing phase where we defined a ”Generalization Index” to\nmeasure the degree of memory specificity or generalization (Figure 4A).\nDuring conditioning (Phase 1), the excitatory firing rate can be well approximated by an exponential\nfunction (see Methods), capturing the simulated activity dynamics (Figure S3). We derived the\nevolution of E-to-E synaptic weights during this phase from solving the dynamics of the three-factor\nHebbian learning rule, producing values that closely match those observed in simulations (Figure\nS3). Given that synaptic scaling operates on a substantially longer timescale than the duration\nof conditioning, its effects are negligible in this phase. After conditioning (Phase 2), excitatory\nfiring rates can also be well described by an exponential function allowing us to compute the set\npoint regulator β. Subsequently, we derived the set point θ from the obtained β. This allows us to\naccurately determine the synaptic weight evolution during post-conditioning (Figure S4).\nTo quantify the degree of memory specificity or generalization, we defined a new measure, called\nthe Generalization Index (GI):\nGI =\nr test\nE1\n− r ref\nE1\nr ref\nE1\n. (9)\nThe GI quantifies the relative change in the excitatory population activity of subnetwork 1 between\nthe test and the previously defined reference conditions. A positive GI (e.g. r test\nE1\n> r ref\nE1\n) suggests\nthat a memory has been generalized, a negative GI (e.g. r test\nE1\n≤ r ref\nE1\n) indicates that a memory is\nspecific. The magnitude of GI reflects the strength of memory specificity or generalization. Ap-\nplying the above procedure, we found that the GI gradually transitions from positive to negative\n(Figure 4B). This transition suggests that, following conditioning, the memory initially generalizes\nto test stimuli but gradually becomes specific over time. Taken together, our procedure provides\na quantitative characterization of the temporal dynamics underlying evolving memory representa-\ntions, revealing how these representations are progressively reshaped over time.\nThe global homeostatic mechanism adjusts the set points and the strength of mem-\nory specificity\nThe global homeostatic mechanism in our model (Eq. 8), governed by the parameterk, influences\nthe set point regulators and thus the new set points. For a small k, in the absence of the global\nhomeostatic mechanism, the set points θ slightly increase throughout the post-conditioning pe-\nriod and stabilize at a new steady state moderately above the baseline activity (i.e., the initial set\npoints) (Figure 5A). Following conditioning, excitatory activity decreases and approaches the new\n8\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nA B\nDuring Conditioning\n(Phase 1)\nPost-Conditioning\n(Phase 2) Testing\nCalculate β\nCalculate θ\nFit Rates \nin Phase 2\nCalculate Weights \nin Phase 1\nFit Rates \nin Phase 1\nCalculate Weights \nin Phase 2\nCalculate Rates \nwith test stimulus\nCalculate \nGeneralization \nIndex\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\n numerics\nanalytics\nFig. 4. A procedure to assess the evolution of memory representations. A. Workflow chart for calculating the Gen-\neralization Index (GI) (Eq. 9), see main text. B. Evolution of the GI after conditioning. Numerical results (solid line)\nrepresent GI measurements taken hourly post-conditioning, while analytical results are derived from continuous GI cal-\nculations using the procedure described in Figure 4A. The GI shifts from positive to negative, indicating the transition\nfrom memory generalization to memory specificity.\nset points (Figure 5B). The GI remains positive throughout the post-conditioning period consistent\nwith memory generalization (Figure 5C). In contrast, increasing the influence of the global home-\nostatic mechanism (large k), suppresses the set points θ and excitatory activity (Figure 5D, E).\nIn this case, the GI shifts from positive to negative throughout the post-conditioning period (Fig-\nure 5F) and reaches a lower value compared to the immediate k condition (Figure 3C), indicating\nenhanced memory specificity. Taken together, these results suggest that the global homeostatic\nmechanism significantly influences the set points and regulates the degree of memory specificity.\nTop-down inputs regulate memory specificity\nIn addition to bottom-up inputs driven by sensory stimuli, primary sensory cortical areas also re-\nceive abundant top-down inputs from higher-order regions which influence neuronal processing\nin local recurrent circuits (Johnson and Burkhalter, 1997; Garrett et al., 2014). To investigate\nhow top-down inputs influence associative learning, we applied an additional input to SST popu-\nlations (a common target of top-down inputs) during conditioning (Batista-Brito et al., 2018; Shen\net al., 2022). When introducing an inhibitory top-down input to both SST populations (Figure 6A),\nwe found that inhibition of SST interneurons disinhibits excitatory neurons, leading to a drastic\nincrease in the firing rates of both subnetworks during conditioning (Figure 6B). However, after\n9\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nk = 0\nk = 0.5\nA B C\nD E F\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point regulator β\nrbs\nβ   ,β     E1 E2\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point θ\nrbs\nθ   ,θ     E1 E2\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point θ\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point regulatorβ\nrbs\nβ   ,β     E1 E2\nrbs\nθ   ,θ     E1 E2\nrbs\nr   , r   E1 E2\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\nnumerics\nanalytics\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\n numerics\nanalytics\nFig. 5. The global homeostatic mechanism regulates the emergence of memory specificity. A. Evolution of set point θ\n(left) and set point regulator β (right) in subnetwork 1 and subnetwork 2 after conditioning up to 48h for k = 0, corre-\nsponding to the absence of the global homeostatic mechanism. The gray horizontal dashed line represents the baseline\nactivity level measured before conditioning. B. Evolution of excitatory firing rate in subnetwork 1 and subnetwork 2 after\nconditioning up to 48h for k = 0. C. Evolution of the GI after conditioning. For k = 0, GI remains positive after condition-\ning. A positive GI indicates memory generalization, whereas a negative GI represents memory specificity. D - F. Same\nas (A - C) but for k = 0.5. The GI transitions from positive to negative after 4h after conditioning.\nconditioning, excitatory activity rapidly declines (Figure 6C). Furthermore, due to the large initial\nchange in firing rates, the synaptic weights undergo substantial modification (Figure 6D). The GI\ntransitions from positive to negative earlier in the post-conditioning period than in the absence of\ninhibitory top-down input, indicating a faster emergence of memory specificity (Figure 6E). In con-\ntrast, when applying excitatory top-down input to both SST populations in the same amount during\nconditioning (Figure 6F), the excitatory firing rate of subnetwork 1 slightly increases, while subnet-\nwork 2 decreases (Figure 6G). After conditioning, both subnetworks’ excitatory activity gradually\ndecline below baseline levels (Figure 6H). Although the firing rates at 48h show negligible differ-\nences compared to the case with inhibitory top-down inputs, the changes in synaptic weights are\nsignificantly smaller (Figure 6I), leading to a marked difference in the GI (Figure 6J).\nThese findings suggest that top-down inhibition of SST would transiently enhance excitatory activ-\nity but paradoxically accelerate memory specificity, whereas top-down excitation of SST confines\nthe degree of increase in excitatory activity and delays the refinement of memory representations.\n10\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nB\nF G\nH I J\nDuring Conditioning\nE1\nP1\nS1\n S2\nE2\nP2\nCS\nCS\nUS\nExc. top-down input Exc. top-down input\nA During Conditioning\nInh. top-down input\nE1\nP1\nS1\n S2\nE2\nP2\nCS\nCS\nUS\nInh. top-down input\nFiring rate\n0.5\n1.5\n2.5\n3.5\n4.5\nrbs\nr   , r   E1 E2\n5 10 15 20 25\nTime (s)\n0\nTime (h)\nFiring rate\n4 24 480.5\n1.5\n2.5\n3.5\n4.5\nrbs\nr   , r   E1 E2\n0\nFiring rate\n0.5\n1.5\n2.5\n3.5\n4.5\n5 10 15 20 25\nTime (s)\nrbs\nr   , r   E1 E2\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\nE\nTime (h)\nWeights\n4 24 480.0\n0.9\n1.8\n w     , w       E1E1 E2E2\nw     , w       E1P1 E2P2\nw     , w       E1S1 E2S2\nC D\nTime (h)\nFiring rate\n4 24 480.5\n1.5\n2.5\n3.5\n4.5\nrbs\nr   , r   E1 E2\nTime (h)\nWeights\n4 24 480.0\n0.9\n1.8\n w     , w       E1E1 E2E2\nw     , w       E1P1 E2P2\nw     , w       E1S1 E2S2\nFig. 6. Top-down inputs influence memory specificity. A. Network schematic of the conditioning phase in the presence\nof inhibitory top-down inputs. During conditioning, the E and PV populations of subnetwork 1 receive additional inputs\nthat correspond to the conditioned stimulus, while the SST population of both subnetworks 1 and 2 receives additional\ninhibitory top-down inputs. B. Activity of excitatory population in subnetwork 1 (r E1) and subnetwork 2 (r E2) during\nconditioning in the presence of inhibitory top-down inputs. Conditioning is marked by the gray interval from 5 to 20s.\nThe gray horizontal dashed line represents the baseline activity level measured before conditioning. C. Activity of\nexcitatory population in subnetwork 1 (r E1) and subnetwork 2 (r E2) after conditioning in the presence of inhibitory top-\ndown inputs. D. Different connection strengths (E-to-E, PV-to-E and SST -to-E) after conditioning. E. Evolution of\nthe Generalization Index (GI) after conditioning in the presence of inhibitory top-down inputs. A positive GI indicates\nmemory generalization, whereas a negative GI represents memory specificity.F - J.Same as (A - E) but in the presence\nof excitatory top-down inputs.\n11\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nSynaptic scaling is essential for associative learning, with distinct contributions\nfrom specific cell types\nNext, we investigated the role of synaptic scaling in associative learning by blocking all synaptic\nscaling mechanisms. In the absence of synaptic scaling mechanisms, both firing rates and weights\nstay unchanged during the post-conditioning period (Figure 7A), r test\nE1\nexceeded r ref (Figure 7B),\nand the GI remains positive (Figure 7C), suggesting memory generalization. Together, these\nresults indicate that synaptic scaling is crucial for achieving memory specificity.\nBut to which extent do the different types of synaptic scaling affect associative learning? When\nselectively blocking E-to-E scaling (Figure 7D), we found that excitatory firing rates of both subnet-\nworks gradually converge to levels close to their baseline (Figure 7E). The GI shifts from positive\nto negative, albeit at a later time point compared to when all scaling mechanisms are present.\nThis indicates that the memory eventually becomes specific (Figure 7F), as shown experimentally\n(Wu et al., 2021). Blocking PV-to-E scaling (Figure 7G) elevates excitatory firing rates of both sub-\nnetworks constantly beyond their baseline levels (Figure 7H), resulting in a positive GI and hence\ngeneralized memories (Figure 7I). In contrast, when SST -to-E scaling is blocked (Figure 7J), the\nexcitatory firing rates of both subnetworks promptly decrease to levels below their baseline (Fig-\nure 7K). This results in the GI transitioning from positive to negative earlier in the post-conditioning\nperiod than with intact scaling mechanisms (Figure 7L), indicating a more rapid emergence of\nmemory specificity.\nTo assess the robustness of the observed results to parameter selection, we conducted numerous\nsimulations using different initial weight conditions (see Methods). We found that, in 93% of initial\nweight conditions, PV-to-E scaling is essential to achieve memory specificity, whereas blocking\nSST -to-E scaling always accelerates the transition to memory specificity (see Methods, Figure S5,\nS6). Together, these results suggest that E-to-E and PV-to-E scaling operate synergistically, while\nSST -to-E scaling acts antagonistically, to collectively regulate the timing of memory specificity.\n12\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nBlocking E-to-E scaling\nBlocking PV-to-E scaling\nBlocking SST-to-E scaling\nD\nG\nE\nH\nF\nI\nJ K L\nBlocking all scaling mechanisms\nA B C\nE1\nP1\nS1\n S2\nE2\nP2\nE1\nP1\nS1\n S2\nE2\nP2\nE1\nP1\nS1\n S2\nE2\nP2\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\n-30\n50\n0\nTime (h)\n4 24 48\nGeneralization Index-30\n0\n50\nE1\nP1\nS1\n S2\nE2\nP2\nBlocked\nFig. 7. Cell-type-specific synaptic scaling contributions to memory refinement in associative learning. A. Network\nschematic when blocking all scaling mechanisms (red connections). Cross-connections are also blocked accordingly.B.\nActivity of excitatory population in subnetwork 1 (rE1) and subnetwork 2 (rE2) after conditioning when blocking all scaling\nmechanisms. The gray horizontal dashed line represents the baseline activity level measured before conditioning.\nC. Evolution of the Generalization Index (GI) after conditioning when blocking all scaling mechanisms. A positive GI\nindicates memory generalization, whereas a negative GI represents memory specificity. D - F. Same as (A - C) but for\nblocking E-to-E scaling. G - I. Same as (A - C) but for blocking PV-to-E scaling. J - L. Same as (A - C) but for blocking\nSST -to-E scaling.\n13\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nDiscussion\nHere, we investigated how different plasticity mechanisms shape associative learning in recurrent\ncircuits comprising multiple interneuron types. Using analytical and computational approaches,\nwe demonstrated that brief conditioning induces memory generalization through Hebbian plas-\nticity. Following conditioning, different forms of synaptic scaling progressively establish memory\nspecificity over time. Specifically, E-to-E and PV-to-E scaling function synergistically, but counter-\nact SST -to-E scaling, to collectively govern the timing of memory refinement. Our findings reveal\nthe cell-type-specific contributions of synaptic scaling and propose a role for top-down modulation\nin regulating associative learning.\nOur study revealed several key insights into the mechanisms and consequences of associative\nlearning. We demonstrated that different forms of synaptic scaling – a relatively slow process –\nare crucial for establishing memory specificity. This finding aligns with experimental observations\nshowing that memory specificity emerges only several hours after conditioning (Wu et al., 2021).\nIn the context of conditioned taste aversion, over time, the gradual fading of memory generalization\nmay reduce food avoidance along with increasing hunger. Faster mechanisms, such as Hebbian\ninhibitory plasticity, could accelerate the elimination of food avoidance, but at the cost of a higher\nrisk of encountering aversive food. In contrast, slower mechanisms, like synaptic scaling, may be\nmore beneficial for animals to minimize risk while avoiding starvation. In addition to the gustatory\ncortex, similar associative learning paradigms have been applied in other sensory cortical regions.\nFor instance, by pairing specific sounds with a foot shock in the auditory cortex (Letzkus et al.,\n2011), by associating specific visual stimuli with rewards in the visual cortex (Pakan et al., 2018),\nby pairing specific odors with rewards in the olfactory cortex (Ottenheimer et al., 2023). Given\nthe ubiquity of the cortical circuit motifs we modeled (Tremblay et al., 2016), our findings have the\npotential to provide broad insights into associative learning across sensory cortical regions.\nGoing beyond capturing existing experimental data, our model proposes a critical role of top-down\ninfluences in associative learning. Our findings demonstrate that a global, unspecific top-down\nsignal, mediated by the unconditioned stimulus (e.g., punishment or reward), acts as a gate for the\nHebbian learning process. In addition to these global signals, more specific top-down inputs, such\nas those related to attention and that target particular cell types (Park et al., 2025), can profoundly\ninfluence neural activity. These specific inputs can flexibly shift different subnetworks either into a\nlong-term potentiation (LTP)-dominated or long-term depression (LTD)-dominated regime, thereby\nshaping associative learning and the timing of memory specificity emergence. Notably, while both\ntypes of inputs affect learning, global, unspecific top-down signals exert minimal influence on ac-\ntivity levels, whereas more specific, cell-type-targeted inputs affect learning by strongly modulating\nactivity. Our model thus highlights that distinct sources of top-down inputs can act in parallel, each\ncontributing to learning in mechanistically different ways.\n14\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nFurthermore, our computational model allowed us to test and identify the cell-type-specific con-\ntributions to associative learning. Specifically, E-to-E scaling and PV-to-E scaling operate syner-\ngistically while opposing SST -to-E scaling. Our findings indicate that disabling excitatory synaptic\nscaling while preserving all forms of inhibitory synaptic scaling achieves memory specificity within\n48 hours after conditioning. In contrast, disabling PV-to-E synaptic scaling while maintaining other\nscaling mechanisms prevents the establishment of memory specificity within the same period.\nThese results highlight a powerful role of different forms of inhibitory synaptic scaling in facilitating\nprecise associative learning.\nTo preserve computational and analytical tractability, we made several simplifications. Biological\nneurons possess complex morphologies and exhibit a non-uniform distribution of ion channels\nand synaptic inputs across their dendritic trees (Jiang et al., 2015; Peng et al., 2021). Parvalbumin\n(PV) and somatostatin (SST) interneurons exhibit distinct targeting patterns on pyramidal neurons,\ninfluencing their computational properties. PV interneurons primarily innervate the perisomatic\nregion, including the soma and proximal dendrites, while, in contrast, SST interneurons target\ndistal dendrites (Dorsett et al., 2021; Schneider-Mizell et al., 2025). These dendritic nonlinearities\nand localized synaptic interactions play a crucial role in integrating synaptic inputs and shaping\nneuronal output (Poirazi et al., 2003; London and H¨ausser, 2005; Larkum et al., 2009), influencing\nnetwork dynamics and learning processes. Nevertheless, by using point neuron models combined\nwith the incorporation of known connectivity properties, our work provides valuable insight into how\ndifferent synaptic scaling mechanisms influence associative learning.\nIn our work, we primarily investigated various synaptic scaling mechanisms during associative\nlearning while excluding long-term inhibitory Hebbian plasticity. Although inhibitory synapses are\nknown to undergo modifications driven by Hebbian plasticity (Froemke et al., 2007; D’amour and\nFroemke, 2015; Hennequin et al., 2017; Lagzi et al., 2021; Schulz et al., 2021; Wu et al., 2022;\nMiehl and Gjorgjieva, 2022; Festa et al., 2024), experiments suggest that the timescale of long-\nterm inhibitory plasticity might be too rapid to explain the prolonged duration of memory general-\nization and the gradual emergence of memory specificity at 48 hours after blocking E-to-E scaling\n(Wu et al., 2021). Therefore, we postulate that this delayed emergence of memory specificity is\nlikely driven by slower processes, such as inhibitory synaptic scaling, as proposed in our study.\nIn addition, beyond the three cell types (E, PV, and SST) included in our model, several other\ninhibitory interneuron subtypes have been identified (Wilmes and Clopath, 2019; Hert ¨ag and\nSprekeler, 2020; Pardi et al., 2020; Canto-Bustos et al., 2022; Veit et al., 2023; Palmigiano et al.,\n2023; Hartung et al., 2024; Naumann et al., 2025). Among these, vasoactive intestinal peptide\n(VIP)-expressing interneurons are a prominent class often incorporated into canonical microcir-\ncuit motifs (Pfeffer et al., 2013; Waitzmann et al., 2024). VIP interneurons primarily inhibit SST\ncells and are known to receive top-down inputs, which can significantly impact recurrent network\ndynamics (Fu et al., 2014; Zhang et al., 2014; Dipoppa et al., 2018; Garrett et al., 2020; Bastos\n15\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\net al., 2023; Furutachi et al., 2024). Although VIP interneurons were not explicitly modeled in our\nstudy, by providing dedicated inputs to SST to emulate top-down modulation, our results suggest\na pivotal role of top-down modulation in shaping associative learning.\nTogether, our work offers new insights into how distinct plasticity mechanisms interact to shape\nassociative learning, highlights the significant impact of top-down influences and synaptic scaling,\nand reveals the cell-type-specific contributions to the establishment of precise memory represen-\ntations.\nMethods\nRate-based population model\nTo investigate the role of cell-type-specific synaptic scaling in associative learning, we constructed\na rate-based population model comprising two subnetworks. Each subnetwork includes one ex-\ncitatory, one PV, and one SST population. Different subnetworks are tuned to different stimuli\ncorresponding to different tastants in the conditioned taste aversion experiments. The dynamics\nof the network can be described as follows (Richter and Gjorgjieva, 2022):\nτ dr\ndt = −r + [W r + g − ρ]+ , (10)\nwhere τ is a diagonal matrix containing the time constants of firing rate dynamics for different pop-\nulations, r is a vector containing the firing rates of different populations,g is a vector containing the\ninputs to different populations, and ρ is a vector containing the rheobases of different populations,\n[]+ is a rectified function.\nr =\n\n\nrE1\nrP1\nrS1\nrE2\nrP2\nrS2\n\n\n, τ =\n\n\nτE1 0 0 0 0 0\n0 τP1 0 0 0 0\n0 0 τS1 0 0 0\n0 0 0 τE2 0 0\n0 0 0 0 τP2 0\n0 0 0 0 0 τS2\n\n\n, g =\n\n\ngE1\ngP1\ngS1\ngE2\ngP2\ngS2\n\n\n, ρ =\n\n\nρE1\nρP1\nρS1\nρE2\nρP2\nρS2\n\n\n.\nW is the connectivity matrix defined as follows:\nW =\n\n\nwE1E1 −wE1P1 −wE1S1 wE1E2 −wE1P2 −wE1S2\nwP1E1 −wP1P1 −wP1S1 wP1E2 −wP1P2 −wP1S2\nwS1E1 0 0 wS1E2 0 0\nwE2E1 −wE2P1 −wE2S1 wE2E2 −wE2P2 −wE2S2\nwP2E1 −wP2P1 −wP2S1 wP2E2 −wP2P2 −wP2S2\nwS2E1 0 0 wS2E2 0 0\n\n\n.\n16\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nTo model the conditioned taste aversion experimental paradigm, specifically, to simulate the con-\nditioned stimulus, additional inputs are provided to the excitatory (E 1) and PV (P1) populations in\nthe subnetwork 1 via increasing gE1 and gP1 by g∆E and g∆P, respectively. Similarly, to simulate\nthe test stimulus, additional inputs are applied to the excitatory (E2) and PV (P2) populations in the\nsubnetwork 2 via increasing gE2 and gP2 by g∆E and g∆P, respectively. Parameter values for two\nsubnetworks are the same unless mentioned otherwise.\nThree-factor Hebbian plasticity\nMotivated by experimental studies showing that reward or punishment plays a decisive role in\nlearning (Pawlak, 2010; Y agishita et al., 2014; He et al., 2015; Gerstner et al., 2018), we modeled\nHebbian plasticity using a three-factor learning rule as follows:\nτhebb\ndwEi Ej\ndt = ηrEj(rEi − r bs\nEi ),\nwhere τhebb is the time constant of Hebbian plasticity, r bs\nEi\nrepresents the baseline activity of the\nexcitatory population in subnetworki before conditioning, and i, j ∈ {1, 2}, representing the indices\nof subnetworks.\nThe third factor η is determined by the presence of the unconditioned aversive stimulus. More\nspecifically,\nη =\n\n\n\n1, in the presence of unconditioned stimulus,\n0, otherwise.\nThus, the third factor serves as a gate for Hebbian plasticity, enabling it during the conditioning\nphase while disabling it elsewhere.\nSynaptic scaling\nThe dynamics of the connection strength governed by synaptic scaling from the excitatory popu-\nlation in subnetwork j to the excitatory population in subnetwork i is given by (Van Rossum et al.,\n2000):\nτ EE\nss\ndwEi Ej\ndt = (1 − rEi\nθEi\n)wEi Ej.\nSimilarly, for PV-to-E synaptic scaling, we have:\nτ EP\nss\ndwEi Pj\ndt = −(1 − rEi\nθEi\n)wEi Pj.\nAnd for SST -to-E synaptic scaling, we have:\nτ ES\nss\ndwEi Sj\ndt = (1 − rEi\nθEi\n)wEi Sj.\n17\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nHere, τss represents the time constant of synaptic scaling for individual type of connections, θEi\ndenotes the target firing rate or the set point of the excitatory population in the subnetwork i.\nPlasticity of set points\nSet points of excitatory populations are subject to plastic changes, governed by the following\ndynamics:\nτθ\ndθEi\ndt = (−θEi + rEi) + (−θEi + βEi),\nwhere τθ is the time constant governing the plasticity of the set points. The set point θEi evolves\nbased on the current activity rEi and the set point regulator βEi. The set point regulator β is\ndynamically updated according to:\nτβ\ndβEi\ndt = −βEi + rEi,\nβEi → βEi − k at t cond onset,\nwhere τβ denotes the time constant governing the plasticity of the set point regulator and k is a\nfree parameter that determines the magnitude of the abrupt decrease in the set point regulator\nβ of excitatory populations in both subnetworks at the onset of conditioning. Conditioning raises\nthe activity rE, thereby increasing both the set point θ and the set point regulator β, in contrast,\nthis sudden reduction in β counteracts the increases induced by conditioning and functions as a\nhomeostatic mechanism to globally regulate the overall activity level (Kaleb et al., 2021).\nAnalytical procedure\nTo thoroughly characterize the temporal evolution of memory specificity and generalization –\nspecifically, how the network responds to the test stimulus following conditioning – we introduced\na procedure to determine how set point regulators, set points, weights, and rates during condi-\ntioning and after conditioning evolve dynamically. In this procedure (Figure 4A), we defined two\nphases, and assumed that the firing rates of excitatory populations during conditioning (Phase\n1) and after conditioning (Phase 2) in the absence of the test stimulus, which are experimentally\nmeasurable, are known. First, we formulate the time-variant firing rate of the excitatory population\nin the subnetwork i during conditioning (Phase 1) as an exponential function as follows:\nˆr (1)\nEi\n= a(1)\ni e(−b(1)\ni t) + c(1)\ni , (11)\nwhere a1\ni , b1\ni , and c1\ni are coefficients obtained by fitting the parameterized functions to the excita-\ntory firing rates of the subnetworki during conditioning in the simulation. Superscripts ‘(1)’ indicate\nPhase 1 corresponding to the conditioning period.\n18\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nBy solving the three-factor Hebbian learning equation (Eq. 1), we can obtain ˆ w(1)\nEi Ej\nduring condi-\ntioning as:\nˆw (1)\nEi Ej\n= f (1)\nwEi Ej\n(t) + C(1), (12)\nwhere\nf (1)\nwEi Ej\n(t) = η\nτHebb\n\"\na(1)\ni a(1)\nj\nb(1)\ni + b(1)\nj\ne(b(1)\ni +b(1)\nj )t +\na(1)\nj c(1)\ni − a(1)\nj rbs\nb(1)\nj\neb(1)\nj t +\na(1)\ni c(1)\nj\nb(1)\ni\neb(1)\ni t + (c(1)\ni c(1)\nj − c(1)\nj rbs)t\n#\n, (13)\nC(1) = wEi Ej (0) − η\nτHebb\n\"\na(1)\ni a(1)\nj\nb(1)\ni + b(1)\nj\n+\na(1)\nj c(1)\ni − a(1)\nj rbs\nb(1)\nj\n+\na(1)\ni c(1)\nj\nb(1)\ni\n#\n, (14)\nwhere wEi Ej(0) is the initial value before conditioning. Note that here we disregarded the effects of\nsynaptic scaling on the weights during conditioning due to its relatively slow timescale compared\nto the duration of the conditioning.\nWe then approximate the excitatory firing rates after conditioning (Phase 2) in a similar way:\nˆr (2)\nEi\n= a(2)\ni e(−b(2)\ni t) + c(2)\ni . (15)\nGiven k, which represents the magnitude of the abrupt decrease in the set point regulator β, the\nset point regulator ˆβ after conditioning can be determined analytically as follows:\nˆβ(2)\nEi\n= (rbs − k − a(2)\ni\n1 − b(2)\ni τβ\n− c(2)\ni )e\n− t\nτβ + a(2)\ni\n1 − b(2)\ni\ne−b(2)\ni t + c(2)\ni . (16)\nUsing the ˆβ from the above equation, the set points of excitatory populations ˆθ after conditioning\ncan be calculated as follows:\nˆθ(2)\nEi\n= L(2)\nEi\ne\n− 2\nτβ\nt\n+ M(2)\nEi\ne−b(2)\ni t + N(2)\nEi\ne\n− t\nτβ + c(2)\ni , (17)\nwith\nL(2)\nEi\n= rbs −\na(2)\ni +\na(2)\ni\n1−b(2)\ni τβ\n2 − τθb(2)\ni\n−\nrbs − k −\na(2)\ni\n1−b(2)\ni τβ\n− c(2)\ni\n2 − τθ\nτβ\n− c(2)\ni , (18)\nM(2)\nEi\n=\na(2)\ni +\na(2)\ni\n1−b(2)\ni τβ\n2 − τθb(2)\ni\n, (19)\nN(2)\nEi\n=\nrbs − k −\na(2)\ni\n1−b(2)\ni τβ\n− c(2)\ni\n2 − τθ\nτβ\n. (20)\n19\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nUsing the above obtained ˆθ, the weights after conditioning can be computed as follows:\nˆw(2)\nEi Ej\n= w init\nEi Ej e\nR t\n0 fi(x)dx, (21)\nˆw(2)\nEi Pj\n= −w init\nEi Pj e\nR t\n0 fi(x)dx, (22)\nˆw(2)\nEi Sj\n= w init\nEi Sj e\nR t\n0 fi(x)dx, (23)\nwith\nfi(x) = 1\nτss\n(1 − a(2)\ni e−b(2)\ni x + c(2)\ni\nL(2)\nEi\ne\n− 2\nτβ\nt\n+ M(2)\nEi\ne−b(2)\ni t + N(2)\nEi\ne\n− t\nτβ + c(2)\ni\n), (24)\nwhere w init\nEi Ej\n, w init\nEi Pj\n, and w init\nEi Sj\ndenote the weights right after conditioning from the excitatory, PV and\nSST population in the subnetwork j to the excitatory population in the subnetwork i. We obtain\nw init\nEi Ej\nfrom Eq. 12. In contrast, w init\nEi Pj\nand w init\nEi Sj\nare identical to their initial values wEi Pj(0) and\nwEi Pj(0), respectively, as they remain unchanged during conditioning.\nFrom the above-obtained weights, assuming all populations exhibit non-zero firing rates, the steady-\nstate firing rate for any given input at any given time after conditioning can be calculated as follows:\nr = (I − W)−1(g − ρ). (25)\nBy substituting the inputs from the test stimulus condition into the above equation, we can deter-\nmine the responses to the test stimulus over time, providing a comprehensive description of the\nevolution of memory specificity and generalization.\nSensitivity analysis\nTo assess the robustness of our results to parameter selection, we conducted grid simulations\nacross the model’s parameter space by changing each parameter from 0.01 to 1.01 with incre-\nments of 0.1. We further constrained the parameters for the cross-connections to be smaller than\nthose for within connections, resulting in a total of 72728 simulations. To ensure computational\nfeasibility, we performed these simulations and evaluated memory specificity in models with vary-\ning initial conditions of either plastic or static weights. We only focused on models that meet two\nexperimental conditions: (1) a transition from memory generalization to memory specificity oc-\ncurs between 4h and 24h, and (2) when E-to-E scaling is blocked, this transition occurs between\n24h and 48h. Models that meet these criteria are labeled as respecting ’experimentally-matched\nconditions’ (in total 828 out of 58087 in Figure S5, 258 out of 14641 in Figure S6). Using these se-\nlected models, we evaluated whether the role of cell-specific synaptic scaling mechanisms aligns\nwith the instance presented in the Results Section (Figure 7) by blocking either PV-to-E or SST -\nto-E scaling. If blocking PV-to-E scaling diminishes memory specificity and blocking SST -to-E\n20\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nscaling accelerates the transition from memory generalization to memory specificity in these se-\nlected models, we labeled them as ‘aligned conditions’ (Figure S5, S6). We found that 96% of\nthe selected models (1041 out of 1086) exhibit the same cell-type-specific contributions as in the\npresented example (Figure 7), suggesting that our results are robust to parameter selection.\nNumerical simulation\nSimulations were performed in Python with Numba (Lam et al., 2015). Differential equations were\nimplemented by Euler method with a timestep of 0.1 milliseconds. All simulation parameters are\nlisted in Table S1.\nData Availability\nThe simulation code is publicly available at https://github.com/comp-neural-circuits/cell-type-specific-\nsynaptic-scaling.\nContributions\nY .K.W. and J.G. designed research; F .V. and A.K. performed the numerical simulations; F .V. and\nY .K.W. performed the analytic calculations; F .V., A.K., Y .K.W., and J.G. wrote the paper.\nAcknowledgments\nWe thank Gina Turrigiano and Chi-Hong Wu as well as members of the Computation in Neural\nCircuits Group for helpful discussions. This work was funded by the European Research Council\n(Grant Agreement No. 804824 to J.G.) and by the DFG in the Collaborative Research Centre\n1080 (to J.G.). A.K. was also supported by TUM and the Elite Network of Bavaria. Y .K.W. was\nalso supported by the Add-on Fellowship of the Joachim Herz Foundation.\nReferences\nBastos G, Holmes JT, Ross JM, Rader AM, Gallimore CG, Wargo JA, et al. 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It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nSupplementary Material\nTable S1: Model Parameters\nNetwork dynamics and network connectivity\nSymbol Value Unit Description\nτE 20 ms time constant of E rate dynamics\nτP 5 ms time constant of PV rate dynamics\nτS 10 ms time constant of SST rate dynamics\nWEEii 0.51 a.u. connection strength from E to E within subnetworks\nWEEij 0.51 a.u. connection strength from E to E across subnetworks\nWEPii 0.91 a.u. connection strength from PV to E within subnetworks\nWEPij 0.41 a.u. connection strength from PV to E across subnetworks\nWESii 0.51 a.u. connection strength from SST to E within subnetworks\nWESij 0.31 a.u. connection strength from SST to E across subnetworks\nWPEii 0.3 a.u. connection strength from E to PV within subnetworks\nWPEij 0.1 a.u. connection strength from E to PV across subnetworks\nWPPii 0.2 a.u. connection strength from PV to PV within subnetworks\nWPPij 0.1 a.u. connection strength from PV to PV across subnetworks\nWPSii 0.3 a.u. connection strength from SST to PV within subnetworks\nWPSij 0.1 a.u. connection strength from SST to PV across subnetworks\nWSEii 0.4 a.u. connection strength from E to SST within subnetworks\nWSEij 0.1 a.u. connection strength from E to SST across subnetworks\nρ 1.5 a.u. rheobase current for E, PV, and SST\nPlasticity mechanisms\nτhebb 4 min time constant of three-factor Hebbian learning\nτθ 24 h time constant of target activity dynamics\nτβ 28 h time constant of target activity regulator dynamics\nτss 8 h time constant of synaptic scaling dynamics\nk 0.25 a.u. amplitude of the decrease in target activity regulator\nInputs\ngE 4.5 a.u. background input to E\ngP 3.2 a.u. background input to PV\ngS 3 a.u. background input to SST\ng∆E 1 a.u. additional input to E\ng∆P 0.5 a.u. additional input to P\ng∆S 0.5 (−0.5) a.u. additional top-down excitatory (inhibitory) input to SST\n28\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\n1.0\n1.5\n2.0\n2.5Firing rate\n5 10 15 20 25\nTime (s)\n0\nrref\nrref\nr   , r   E1 E2\nA B\nE\n1\nP\n1\nS\n1\nS\n2\nE\n2\nP\n2\nTS\nTS\nFig. S1. Definition of reference activity. A. Network schematic when applying a conditioned stimulus to subnetwork\n2 in the absence of unconditioned stimulus. B. The reference activity r ref is determined by measuring the excitatory\npopulation activity of subnetwork 1 in response to the test stimulus in the absence of plasticity. The test stimulus is\napplied during the period marked in gray, and modeled by providing additional inputs to the excitatory and PV population\nof subnetwork 2.\nA B\nr S1\nr S2\nTime (h)\nFiring rate\n4 24 482.0\n2.2\n2.4\n2.6\nTime (h)\nFiring rate\n4 24 481.0\n1.1\n1.2\n r P1\nr P2\nFig. S2. Inhibitory population activity post-conditioning. A. Activity of PV population in subnetwork 1 (r P1) and subnet-\nwork 2 (rP2) after conditioning. B. Same as A but for SST population.\nBA\nTime (s)\nWeights\n205 15 100.4\n0.7\n0.5\n0.6\nw     , w       E1E1 E2E2\nw     , w       E1E2 E1E2\nw     , w       E1E1 E2E2\nw     , w       E1E2 E1E2\nFiring rate\n205 15 100.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r  E1 E2\nr   , r  E1 E2\nTime (s)\nFig. S3. Comparisons between numerical simulations and analytical calculations during conditioning in Phase 1. A.\nSimulated excitatory activity of subnetwork 1 ( rE1, same as in Figure 2) and subnetwork 2 (r E2, same as in Figure 2)\nduring conditioning, and fitted excitatory activity of subnetwork 1 ( ˆrE1) and subnetwork 2 ( ˆrE2) during conditioning. The\nhorizontal dashed line represents the baseline activity level measured before conditioning.B. Numerical simulated exci-\ntatory weight evolution (same as in Figure 2) during conditioning, and analytical calculated excitatory weights evolution\nduring conditioning.\n29\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nCBA\nD\nTime (h)\nFiring rate\n4 24 480.5\n1.0\n1.5\n2.0\n2.5\nrbs\nr   , r   E1 E2\nr   , r   E1 E2\nTime (h)\n4 24 480.5\n1.0\n1.5Set-point regulator β\nrbs\nβ   ,β     E1 E2\nβ   ,β     E1 E2\nTime (h)\nWeights\n4 24 480.4\n0.5\n0.6\n0.7\n w     , w       E1E1 E2E2\nw     , w       E1E2 E1E2\nw     , w       E1E1 E2E2\nw     , w       E1E2 E1E2\nTime (h)\nWeights\n4 24 480.4\n0.6\n0.8\n1.0\n1.2\nw     , w       E1P1 E2P2\nw     , w       E1P2 E1P2\nw     , w       E1P1 E2P2\nw     , w       E1P2 E1P2\nTime (h)\nWeights\n4 24 480.2\n0.3\n0.4\n0.5\n0.6\n w     , w       E1S1 E2S2\nw     , w       E1S2 E1S2\nw     , w       E1S1 E2S2\nw     , w       E1S2 E1S2\n4 24 480.5\n1.0\n1.5Set-point θ\nrbs\nθ   ,θ     E1 E2\nθ   ,θ     E1 E2\nTime (h)\nFig. S4. Comparisons between numerical simulations and analytical calculations post-conditioning in Phase 2. A.\nSimulated excitatory activity of subnetwork 1 ( rE1, same as in Figure 3) and subnetwork 2 (r E2, same as in Figure 3)\nafter conditioning, and fitted excitatory activity of subnetwork 1 ( ˆrE1) and subnetwork 2 ( ˆrE2) after conditioning. The\nhorizontal dashed line represents the baseline activity level measured before conditioning. B. Same as A but for set\npoint regulators after conditioning. C. Same as B but for set points after conditioning. D. (Left) Numerical simulated\nexcitatory weight evolution (same as in Figure 3) after conditioning, and analytical calculated excitatory weights evolution\nafter conditioning. (Middle, Right) Same as Left but for PV-to-E and SST -to-E weights respectively.\n30\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nwEiPi\nwEiPi\nwEiPjwEiSiwEiSjwEiEiwEiEj\nwEiPj wEiSi\nwEiSj wEiEi\nwEiEj\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\n0.0 0.5 1.00.0\n0.5\n1.0\n0.0 0.5 1.0\n 0.0 0.5 1.0\n 0.0 0.5 1.0\n 0.0 0.5 1.0\n 0.0 0.5 1.0\nExperimentally-matched \nconditions\nAligned \nconditions\nFig. S5. Pairwise density plots of plastic weight parameter distributions for experimentally matched models and aligned\nmodels. Experimentally matched models are defined as those in which the transition from memory generalization to\nspecificity occurs between 4h and 24h when all scaling mechanisms are active and shifts to between 24h and 48h\nwhen E-to-E scaling is blocked. Aligned models are a subset of experimentally matched models, characterized by a\ndiminished memory specificity when PV-to-E scaling is blocked and an accelerated transition when SST -to-E scaling\nis blocked. The x- and y-axes represent specific plastic connection weights. The substantial overlap between the two\ndistributions suggests that cell-type-specific contributions to associative learning demonstrated in Figure 7 are robust\nto parameter selection. Here, 98% of the experimentally matched models (811 out of 828) are aligned models.\n31\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint \n\nwPiEiwPiPiwPiSiwSiEi\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\n0.0\n0.5\n1.0\nwPiEi\nwPiPi wPiSi\nwSiEi\n0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0\nExperimentally-matched \nconditions\nAligned \nconditions\nFig. S6. Pairwise density plots of static weight parameter distributions for experimentally matched models and aligned\nmodels. Experimentally matched models are defined as those in which the transition from memory generalization to\nspecificity occurs between 4h and 24h when all scaling mechanisms are active and shifts to between 24h and 48h\nwhen E-to-E scaling is blocked. Aligned models are a subset of experimentally matched models, characterized by a\ndiminished memory specificity when PV-to-E scaling is blocked and an accelerated transition when SST -to-E scaling\nis blocked. The x- and y-axes represent specific static connection weights. The substantial overlap between the two\ndistributions suggests that cell-type-specific contributions to associative learning demonstrated in Figure 7 are robust\nto parameter selection. Here, 89% of the experimentally matched models (230 out of 258) are aligned models.\n32\n.CC-BY 4.0 International licenseavailable under a \nwas not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprint (whichthis version posted May 14, 2025. ; https://doi.org/10.1101/2025.05.14.654005doi: bioRxiv preprint","source_license":"CC-BY-4.0","license_restricted":false}