Abstract

Alzheimer’s disease (AD), the leading cause of dementia, could potentially be mitigated through early detection and interventions. However, it remains challenging to assess subtle cognitive changes in the early AD continuum. Computational modeling is a promising approach to explain a generative process underlying subtle behavioral changes with a number of putative variables. Nonetheless, internal models of the patient remain underexplored in AD. Determining the states of an internal model between measurable pathological states and behavioral phenotypes would advance explanations about the generative process in earlier disease stages beyond assessing behavior alone. Previously, Gershman et al., 2017b proposed the latent cause model, which provides a normative account of memory modification phenomena in Pavlovian fear conditioning. Here, we assumed the latent cause model as an internal model and estimated internal states defined by the model parameters being in conjunction with measurable behavioral phenotypes. The 6- and 12-month-old AppNL-G-F knock-in AD model mice and the age-matched control mice underwent memory modification learning, which consisted of classical fear conditioning, extinction, and reinstatement. The results showed that AppNL-G-F mice exhibited a lower extent of reinstatement of fear memory. Computational modeling revealed that the deficit in the AppNL-G-F mice would be due to their internal states being biased toward overgeneralization or overdifferentiation of their observations, and consequently, the competing memories were not retained. This deficit was replicated in another type of memory modification learning in the reversal Barnes maze task. Following reversal learning, AppNL-G-F mice, given spatial cues, failed to infer coexisting memories for two goal locations during the trial. We concluded that the altered internal states of AppNL-G-F mice illustrated their misclassification in the memory modification process. This novel approach highlights the potential of investigating internal states to precisely assess cognitive changes in early AD and multidimensionally evaluate how early interventions may work.

Introduction

Alzheimer’s disease (AD) is the leading cause of dementia, which severely disturbs daily lives in the aging population and causes a tremendous social burden (Nandi et al., 2022). Neuropathological hallmarks, including amyloid-β (Aβ) plaques and neurofibrillary tangles (NFT), define AD biologically, and advances in biomarkers have enabled early diagnosis (Jack et al., 2024; Jack et al., 2018). Abnormal biomarkers can appear years before symptoms arise, a stage referred to as preclinical AD (Sperling et al., 2011; Sperling et al., 2014). As the disease progresses, the cognitive symptom gets severe, and their degree defines mild cognitive impairment (MCI) and the onset of AD dementia. Cognitive decline has been reported in a wide range of domains, including memory, language, visuospatial function, and executive function, leading to behavioral change as early as a decade before dementia (Amieva et al., 2008; Knopman et al., 2021). The early stage of AD provides a time window to intervene in disease progression, yet there is an explanatory gap and inconclusive consensus on what particular behavioral phenotype can be directly linked to neuropathology in early AD. Given the present circumstance, the subtle and heterogeneous cognitive change before the onset of dementia poses a challenge to assess clinical outcomes with traditional measurement (Jutten et al., 2023).

To precisely assess clinical symptoms and effects of early intervention for AD pathology, determining universal behavioral phenotypes as well as understanding how such behaviors change from asymptomatic to symptomatic is needed. Memory impairment is the predominant first symptom of AD (Barnes et al., 2015). The symptoms are commonly identified as a deficit in recalling previously learned or recognized items (Grober et al., 2018). Previous studies suggested that the performance of prioritized recall, in which memories are recalled in order of assigned value, is a sensitive measure in the early stages of AD (for review, see Knowlton and Castel, 2022). It remains elusive how memory impairments may arise from biased information processing that could affect the encoding, maintaining, or retrieval process of memory function. Using genetic mouse models is a common approach to dissecting the effects of pathological changes on cognitive symptoms measured in behavioral tasks while controlling for potential confounding factors (Webster et al., 2014; Zhong et al., 2024). However, the symptoms at the early stage of AD are relatively mild in traditional measurements, and phenotypes may be inconsistent among studies even when using the same AD mouse model (Jankowsky and Zheng, 2017). As behavioral phenotypes in conjunction with brain pathology states may not be captured by current assessments robustly, it is crucial to seek more sensitive and comprehensive approaches.

Recently proposed computational models provide generative processes underlying observed behavior, potentially bridging the gap between behavioral phenotype and AD pathology. Indeed, such models not only replicated the memory task performance of AD patients in different disease stages (Lee et al., 2020a; Lee and Stark, 2023; Pooley et al., 2011) but also were valuable in detecting cognitive decline in preclinical AD patients (Bock et al., 2021; Vanderlip et al., 2024). However, previous approaches did not suppose an internal model of the world to predict the future from current observations given prior knowledge. Internal models with sufficient explanatory power can replicate various behavioral phenotypes in specific tasks through a common generative process. Estimating an internal model in the early stages of AD patients would elucidate how AD alters their internal states and thereby their behaviors along with disease progression, which is informative for precise diagnosis and assessment of early intervention effects. To our knowledge, only a few studies tried to estimate internal states in amnestic MCI and AD patients and reported that a certain retention rate underlying motor learning (Sutter et al., 2024), but not learning rate in associative learning (Wessa et al., 2016) differed from healthy controls. This circumstance demands us to investigate internal models illustrating not only learning but also its interaction with memory with higher explanatory power.

In this study, we assumed the latent cause model as an internal model explaining the memory modification process to solve a problem such that a novel observation should be classified into previously acquired memory or novel memory (Gershman et al., 2017b). We hypothesized that the internal state of the latent cause model is altered along with disease progression from the preclinical stage of AD. To test this, we used the AppNL-G-F knock-in AD mouse model (Saito et al., 2014). This model of mice carries the Swedish KM670/671 NL, Iberian I716F, and Arctic E693G mutations on the gene of amyloid-β precursor protein (APP) and displays Aβ plaque accumulation and neuroinflammation across age, reproducing neuropathological change in preclinical AD without artifacts caused by APP overexpression (Saito et al., 2014; Sasaguri et al., 2017). In this study, the 6- and 12-month-old AppNL-G-F knock-in mice and the age-matched control mice were engaged in a memory modification task consisting of Pavlovian fear conditioning, extinction, and reinstatement. Internal states across trials were estimated for each mouse, simultaneously with determining a set of model parameters such that the simulated behavior under the latent cause model given the parameters fits enough to the observed behavior. Because we found a deficit in the AppNL-G-F mice as overgeneralization or overdifferentiation of their observations into certain memories indicated by parameters in the latent cause model, we further confirmed whether this deficit could be replicated in another kind of memory modification task, the reversal Barnes maze paradigm. In the latent cause framework, we discussed how the internal states in the AppNL-G-F mice diverged from those in the control mice during the memory modification process.

Results

The latent cause model, an internal model, explains memory modification processes in the classical fear conditioning paradigm

The latent cause model proposed by Gershman et al., 2010 is an internal model such that an agent infers a latent cause as a source of the co-occurrence of events in the environment. It was later adapted to model the memory modification process, a problem to infer previously acquired latent causes or a novel latent cause for every observation in the Pavlovian fear conditioning paradigm in rodents and humans (Gershman et al., 2017b). In the latent cause model, an agent learning an association between a conditioned stimulus (CS) and an unconditioned stimulus (US) has an internal model such that stimuli x (i.e., d-dimensional vector involving the CS or context) and outcome r (i.e., US) at time t are generated at an associative strength w (i.e., d-dimensional vector) from k-th latent cause ztk of total K latent causes by a likelihood p(x|ztk) and p(r|ztk), respectively (Figure 1A). p(x|ztk) and p(r|ztk) follow Gaussian distributions in which each mean is calculated from previous observations, while each variance (σx2 and σr2) was a priori defined as a hyperparameter. Since latent causes are unobservable, the agent given an observation infers which latent cause is likely to generate current observation by Bayes’ rule. The prior of z follows the Chinese restaurant process, that is

P(zt=k|z1:t−1)∝{∑t′<tK(τ(t)−τ(t′))I[zt′=k]if k≤K (i.e., k is an old cause),αotherwise (i.e., k is a new cause).

Prior of ztk refers to the frequency that zk was inferred so far, where I[⋅]=1 if its argument is true; otherwise, 0. This prior is biased by a temporal kernel , as an analogy of the power law of the forgetting curve,

K(τ(t)−τ(t′))=(τ(t)−τ(t′))−g,

to exponentially decay the probability that zk inferred at previous trial t’ is inferred again at current trial t by a temporal scaling factor g if the time interval between trial t’ and t increases. A new latent cause is inferred at a probability governed by the concentration parameter α. Higher α or lower likelihood of the current observation biases the agent to infer a new latent cause given an observation (i.e. differentiation) rather than to infer an old one (i.e., generalization) (Figure 1B). Although the latent cause model allows for having an infinite number of latent causes, agents with appropriate α and g favor to infer a smaller number of latent causes for observations instead of inferring a unique latent cause for every observation.

Internal state in the latent cause model in the Pavlovian fear conditioning, extinction, and reinstatement.

(A) Schematic diagram of latent cause framework in a simple Pavlovian fear conditioning paradigm. An experimental mouse observes a tone, a context, and an electrical shock, which are set down in a parallelogram. Among the stimuli, the tone is designed as the conditioned stimulus (CS), and the electrical shock is designed as the unconditioned stimulus (US) with additional consideration of context effect. The mouse has an internal model such that a latent cause z generates the observation where the tone and the context induce the shock at an associative weight wcs and wcontext, respectively. The latent cause is a latent variable represented by a white square. The posterior probability of z is represented by a black arrow from z to the observation. The stimuli (i.e., tone, context, and shock) are observed variables represented in shaded circles, and the associative weight w is represented by a black arrow between the two. Since latent causes are unobservable, the mouse infers which latent cause is more likely from posterior distribution over latent causes given the observation following Bayes’ rule. (B) Schematic diagram of internal state posited in the latent cause model demonstrating the memory modification process in the fear conditioning paradigm. The mouse has acquired zA through two observations of the CS accompanied by the US in the same context. Now, the mouse observes the tone alone, then infers a new latent cause zB generating the CS and context without US as wcs and wcontext equal to 0. The internal state at the time consists of zA with largely decreased posterior probability and thereby slightly decreased wcs and wcontext, in addition to zB. The mouse in this panel is likely to differentiate the current observation from zA, as it assigns a higher probability for zB. The posterior probability of zA and zB is represented by the relative size of their diagram. If the mouse generalizes zA to the current observation without inferring zB, it would largely decrease wcs and wcontext of zA to minimize prediction error. (C) Observed and simulated conditioned response (CR) during reinstatement in fear conditioning. In the acquisition phase, a CS was accompanied by a US, inducing associative fear memory in the animal, as it exhibits a higher CR to the CS. In the extinction phase, the CS was presented without the US, inducing extinction memory with decreased CR. After an unsignaled shock without the preceding CS, the CR increases again, and this is called reinstatement. The observed CR was sampled from a 2-month-old male wild-type C57BL/6J mouse (magenta line plot with square markers), where the vertical and horizontal axis indicate CR and cumulative trial, respectively. The latent cause model parameters were estimated so as to minimize the prediction error between the observed and the simulated CR given the parameter (gray line with square markers). The estimated parameter value: 𝛼 = 2.4, g = 0.316, η = 0.64, max. no. of iteration = 9, w0 = –0.006, σr2 = 4.50, σx2 = 4.39, θ = 0.03, λ = 0.02, K = 6. Trials with red, blue, and yellow backgrounds correspond to the acquisition, extinction, and unsignaled shock, where the first and second extinction consists of 19 and 10 trials, respectively (see Materials and methods). Three trials with white backgrounds are tests 1, 2, and 3 to evaluate if conditioning, extinction, and reinstatement are established. The vertical dashed lines separate the phases. (D) The evolution of the posterior probability and (E) the associative weight of each latent cause across the reinstatement experiment, where wcs (top panel) and wcontext (bottom panel) were computed. (D, E) Each latent cause is indicated by a unique subscript number and color, wcs, and wcontext. The latent causes acquired during the acquisition phase and their associative weight are termed zA and wA, respectively. Meanwhile, latent causes acquired during the extinction phase and their associative weight are termed zB and wB, respectively.

According to the latent cause model, the agent solves two computational problems during Pavlovian fear conditioning learning. One is to compute the posterior probability of each latent cause given its associative weight between stimuli x and shock r with a history of observations, and the other is to compute the associative weight of each latent cause given its posterior. Both computations are achieved through the expectation-maximization (EM) algorithm, as the former and the latter computation correspond to E-step and M-step, respectively. In the E-step, the posterior of each latent cause is computed from its prior and the likelihood of current observation given the latent cause following Bayes’ rule, consequently determining the most likely latent cause at the current trial as the one with the maximal posterior, then moves to the M-step. In the M-step, the agent predicts shock by a linear combination of stimuli and associative weight in each latent cause. The weight is updated based on the Rescorla-Wagner rule (Rescorla and Wagner, 1972) to minimize the prediction error between observed and predicted shock. The amount of the weight change depends on learning rate η and prediction error, which is biased by the posterior probability of the latent causes. The amount of weight change will be smaller even in larger prediction errors if the latent cause is unlikely. The agent estimates weights for all latent causes and then returns to E-step. This procedure is iterated a preset number of times, and thereby, the posterior probability over latent causes and their associative weights are determined. Finally, the agent concludes the expected shock in the current trial by a linear combination of observed stimuli and an expectation of weight, which is weighted by the posterior distribution over latent causes. The conditioned response (CR) for the expected shock is determined as an integral of Gaussian distribution (mean is the expected shock, variance is λ) above threshold θ, where λ and θ are hyperparameters. Thus, these parameters of the latent cause model determine an internal state of the agent leading to particular behavioral outcomes given an observation.

Reinstatement exemplifies the memory modification process and indeed is well explained by the latent cause model. Reinstatement occurs when agents who have learned and then extinguished an association between a CS and a US exhibit CR again after being exposed to the US alone following the extinction. The latent cause model explains the reinstatement of fear memory with the changes of agent’s internal state as follows. First, an agent repeatedly observed a CS accompanied with a US in a Pavlovian fear conditioning procedure (Figure 1C, ‘Acquisition’). Because these observations are novel for the agent, it inferred a set of latent causes zA (z1, z2, and z3 in Figure 1D) where the CS is associated with the US by associative weight wA (w1, w2, and w3 in Figure 1E) during the acquisition. Considering the effect of the context, w contains both wcs and wcontext (Figure 1E). After the acquisition, the agent inferred zA and then predicted the upcoming US, leading to increased CR when it observed the CS (Figure 1C, ‘Test 1’ after ‘Acquisition’). Second, the agent repeatedly observed the CS alone in an extinction procedure. Early in the extinction, the agent would infer zA and then exhibit higher CR to the CS, while the US was absent (Figure 1C, left ‘Extinction’). This state increases prediction error, then prompts the agent either to decrease wA toward 0 or to infer a novel set of latent causes zB where the CS is not accompanied with the US, that is, associative strength wB = 0 (Figure 1B); both processes are run in the mouse in Figure 1CDE. Note that the sets A and B were introduced arbitrarily for explanation here. Later in the extinction, zB rather than zA is inferred, leading to the decreased CR (Figure 1C, right ‘Extinction’ or ‘Test 2’). Third, when the agent observes the US alone after the extinction (Figure 1C, ‘Unsignaled shock’), the probability of zA or associative weight of some latent causes increases, hence it predicts the US and thereby the CR increases again, that is reinstatement (Figure 1C, ‘Reinstatement’ at ‘Test 3’); in the mouse in Figure 1CDE, the unsignaled shock increases not only the posterior probability of zA that has maintained higher wcs but also wcontext in w6 interpreted as a modification in the association between context and US in z6. Thus, it is rational to expect that certain parameters of the latent cause model are in conjunction with particular behaviors in the reinstatement paradigm (see Appendix 2 for the relationship between parameters, CR, and internal states). As demonstrated in Gershman and Hartley, 2015, the likelihood that α > 0 in human participants correlates with the degree of their spontaneous recovery, that is, a return of the CR after a long hiatus following an extinction procedure. Furthermore, a recent study has shown that the latent cause model explains maladaptive decision-making in post-traumatic stress disorder patients as a perseverated inference of previously acquired latent causes even under situations where they should infer novel latent causes (Norbury et al., 2022). By estimating such parameters from the behaviors of each experimental mouse, how the internal state of the AD group diverges from that of the control group could be determined.

AppNL-G-F mice showed unimpaired associative fear and extinction learning but a lower extent of reinstatement

To examine the age and AppNL-G-F knock-in effects on the reinstatement, all cohorts of control and homozygous AppNL-G-F mice were tested at the age of either 6 months or 12 months in the reinstatement paradigm based on auditory-cued fear conditioning (Figure 2A and Supplementary file 1a). According to previous studies, the AppNL-G-F mice displayed an age-dependent Aβ deposition from 4 months old and memory impairments could be detected at 6 months of age (Masuda et al., 2016; Saito et al., 2014; Sakakibara et al., 2018). The widespread of Aβ accumulation was confirmed in this study, and results were provided in Figure 2—figure supplement 1. Given that age affects the Aβ accumulation caused by AppNL-G-F knock-in, a one-way ANCOVA was used to evaluate the AppNL-G-F knock-in effects on behavioral measures controlling for age.

AppNL-G-F mice exhibited successful associative learning and extinction but a lower extent of reinstatement.

(A) Schematic diagram of reinstatement paradigm in this study. In the acquisition phase, the conditioned stimulus (CS) was accompanied with the unconditioned stimulus (US) three times. In the following phase, either the CS or the US was presented at certain times. The context was the same throughout the experiment. (B) Freezing rate during CS presentation across reinstatement paradigm. The markers and lines show the median freezing rate of each group in each trial. Red, blue, and yellow backgrounds represent acquisition, extinction, and unsignaled shock in (A). The dashed vertical line separates the extinction 1 and extinction 2 phases. Freezing rate during CS presentation in test 1 (C), test 2 (D), and test 3 (E). Discrimination index (DI) between test 2 and test 1 (F), between test 3 and test 2 (G), and between test 3 and test 1 (H) calculated from freezing rate during CS presentation. (C–E) The data are shown as median with interquartile range. *p < 0.05, **p < 0.01, and ***p < 0.001 by one-way ANCOVA with age as covariate; #p < 0.05, ##p < 0.01, and ###p < 0.001 by Student’s t-test comparing control and AppNL-G-F mice within the same age. Detailed statistical results are provided in Supplementary file 1b. (F–H) The dashed horizontal line indicates DI = 0.5, which means no discrimination between the two phases. †p < 0.05 by one-sample Student’s t-test, and the alternative hypothesis specifies that the mean differs from 0.5; *p < 0.05, **p < 0.01, and ***p < 0.001 by one-way ANCOVA with age as a covariate; #p < 0.05, ##p < 0.01, and ###p < 0.001 by Student’s t-test comparing control and AppNL-G-F mice within the same age. Detailed statistical results are provided in Supplementary file 1c and d. (B–H) Colors indicate different groups: orange represents 6-month-old control (n = 24), light blue represents 6-month-old AppNL-G-F mice (n = 25), pink represents 12-month-old control (n = 24), and dark blue represents 12-month-old AppNL-G-F mice (n = 25). Each black dot represents one animal.

In the acquisition phase of fear conditioning, the freezing rate gradually increased with the number of CS-US pairings (Figure 2B, leftmost red panel). In the test 1 phase, 24 hr after the acquisition, a significant genotype effect was observed in freezing rates during CS presentation [F(1,95) = 9.679, p = 0.002], where the AppNL-G-F mice showed a higher freezing rate than in the control (Figure 2C and Supplementary file 1b), indicating the associative fear memory was established in AppNL-G-F mice. As the increasing trials of CS alone presented, both groups showed a gradually decreased freezing rate in the extinction phase (Figure 2B, blue panel). In the test 2 phase, 24 hr after the last trial of the extinction, there was a significant age effect in freezing rates during CS presentation [F(1,95) = 4.698, p = 0.033], where 12-month-old mice showed a higher freezing rate than in the 6-month-old mice (Figure 2D and Supplementary file 1b). In the test 3 phase, 24 hr after given an unsignaled shock, mice showed an elevated freezing rate, and no significant genotype or age effect was detected (Figure 2B and E and Supplementary file 1b). To evaluate the effect of the context on the CR, we measured the preCS freezing rate during 1 min before the tone presentation (Figure 2—figure supplement 2). Generally, the preCS freezing rate was lower than CS freezing rate and gradually reduced but kept positive across trials after acquisition (Figure 2—figure supplement 2A and B), suggesting the context has a certain effect on CR. When we compared the preCS freezing rate (Figure 2—figure supplement 2E) and the CS freezing rate (Figure 2E) in test 3 within group by the paired samples t-tests, the CS freezing rate was significantly higher than the preCS freezing rate in all groups: 6-month-old control, t(23) = –6.344, p < 0.001, d = –1.295; 6-month-old AppNL-G-F, t(24) = –4.679, p < 0.001, d = –0.936; 12-month-old control, t(23) = –4.512, p < 0.001, d = –0.921; 12-month-old AppNL-G-F, t(24) = –2.408, p = 0.024, d = –0.482. Although the associative strength between the context and the US would be increased by the unsignaled shock, these results suggest that reinstatement was not solely explained by the CR for context, but also reactivation acquisition memory.

To evaluate the magnitude of how each mouse can discriminate between different phases, we calculated the discrimination index (DI) using freezing rates during the CS presentation. If the mouse shows the same freezing rate at the two test phases, the value of DI will be 0.5, while if the mouse shows a higher freezing rate in one phase compared to the other, DI will be far from 0.5. The results showed that the DIs between test 2 and test 1 were significantly lower than 0.5 in all groups (Figure 2F and Supplementary file 1c), indicating the successful establishment of extinction memory. The genotype effect was detected [F(1,95) = 5.013, p = 0.027] (Figure 2F and Supplementary file 1d), where AppNL-G-F mice showed lower values due to higher freezing in the test 1 phase. These results suggested that there was no markable fear and extinction learning deficit in AppNL-G-F mice at the behavioral level. The DIs between the test 3 and 2 phases in four groups were significantly higher than 0.5, indicating that the reinstatement was successfully induced after the unsignaled shock (Figure 2G and Supplementary file 1c). Six-month-old mice showed higher DIs, as a significant age effect was detected [F(1,95) = 7.480, p = 0.007] (Figure 2G and Supplementary file 1d). The DIs between the test 3 and 1 phases did not deviate from 0.5 for both 6- and 12-month-old control mice, suggesting that they displayed comparable freezing rates in tests 1 and 3 (Figure 2H and Supplementary file 1c). In contrast, the DIs between test 3 and 1 phases were significantly lower than 0.5 in 6-month-old AppNL-G-F mice [t(24) = –3.245, p = 0.003] and 12-month-old AppNL-G-F mice [t(24) = –6.165, p < 0.001] (Figure 2H and Supplementary file 1c). Moreover, a significant genotype effect was detected [F(1,95) = 15.393, p < 0.001] (Figure 2H and Supplementary file 1d), indicating AppNL-G-F mice exhibited a lower extent of reinstatement. Thus, these results suggest that mice retrieved fear memory in the test 1 phase and retrieved extinction memory in the test 2 phase, respectively. The fear memory and the extinction memory compete with each other: the US is present in the former, while it is absent in the latter. In the test 3 phase, after they observed the unsignaled shock, mice had to decide which memory was more relevant given the CS. The same level of freezing rate in tests 1 and 3 observed in control mice suggests that they could retain both fear and extinction memory and thereby infer the fear memory more preferentially. In contrast, AppNL-G-F mice displayed a lower freezing rate in test 3 compared to test 1, suggesting that they might still infer extinction memory even after the unsignaled shock or a completely new memory, while the initial fear memory might be suppressed or eliminated.

The internal state underlying reinstatement simulated with the latent cause model differs between the ages and APP genotype

To seek the internal state of each mouse generating the behaviors in the reinstatement paradigm, we estimated the parameters of the latent cause model, minimizing prediction errors between the observed CR and simulated CR in the latent cause model given a set of parameters (see also Materials and methods). Figure 3 demonstrates the traces of observed CR, simulated CR, and the changes in the internal state in each group. We initially confirmed that the DIs in the simulated CRs in each group well replicated those in the observed CRs, except that the DI between test 3 and test 1 in the 6-month-old AppNL-G-F mice did not significantly deviate from 0.5 in simulated results (c.f. Figure 2F–H, Figure 3—figure supplement 1A–C). To check if the latent cause model has a certain bias to simulate CR in either group, we compared the residual (i.e., observed CR minus simulated CR) between groups. The fit was similar between control and AppNL-G-F mice groups in the test trials, except test 3 in the 12-month-old group (Figure 3—figure supplement 1D and E). In test 3, the residual was significantly higher in the 12-month-old control mice than AppNL-G-F mice, indicating the model underestimated the reinstatement in the control mice. These results suggest that the latent cause model fits our data with little systematic bias, such as an overestimation of CR for the control group in the reinstatement, supporting the validity of the comparisons in estimated parameters between groups.

The divergence of internal states between control and AppNL-G-F mice differed in age.

(A) Simulation of reinstatement in the 6-month-old control mice given a set of estimated parameters of the latent cause model. The estimated parameter value: 𝛼 = 2.4, g = 0.05, η = 0.42, max. no. of iteration = 2, w0 = 0.009, σr2 = 2.90, σx2 = 0.49, θ = 0.008, λ = 0.018, K = 10. (B) Simulation of reinstatement in 6-month-old AppNL-G-F mice. The estimated parameter value: 𝛼 = 1.1, g = 0.61, η = 0.51, max. no. of iteration = 2, w0 = 0.004, σr2 = 1.51, σx2 = 0.32, θ = 0.015, λ = 0.019, K = 30. (C) Simulation in 12-month-old control mice. The estimated parameter value: 𝛼 = 1.1, g = 0.92, η = 0.82, max. no. of iteration = 5, w0 = 0.009, σr2 = 1.88, σx2 = 0.51, θ = 0.010, λ = 0.017, K = 4. (D) Simulation in 12-month-old AppNL-G-F mice. The estimated parameter value for: 𝛼 = 1.0, g = 1.10, η = 0.04, max. no. of iteration = 2, w0 = 0.0025, σr2 = 1.51, σx2 = 0.18, θ = 0.011, λ = 0.011, K = 36. (A–D) The first row shows the trace of observed conditioned response (CR) and simulated CR. The observed CR is the median freezing rate during the conditioned stimulus (CS) presentation over the mice within each group; the observed CR of each group was divided by its maximum over all trials. The second row shows the posterior probability of each latent cause in each trial. The third and fourth rows show the associative weight of tone to shock (wcs) and that of context to shock (wcontext) in each trial. Each marker and color corresponds to a latent cause up to 5. Each latent cause is represented by the same color as that in the second row and contains wcs and wcontext. The vertical dashed lines indicate the boundaries of phases.

In the 6-month-old group, two latent causes (z1 and z2) were generated in the acquisition phase with increasing associative weight (rows 2–4 in Figure 3A and B). During the extinction phase, the same latent causes were inferred, and the corresponding associative weights declined, indicating the devaluation of previously acquired fear memory (rows 2–4 in Figure 3A and B). Notably, the wcs in w2 in control mice remained at a higher value compared to that in AppNL-G-F mice. At trial 35, given an unsignaled shock, wcontext in w1 was elevated in control mice (row 4 in Figure 3A), while both wcontext in w1 and w2 were elevated in AppNL-G-F mice (row 4 in Figure 3B). At trial 36 (test 3 phase), in control mice, higher values in wcontext in w1 and wcs in w2 contributed to increased CR (Figure 3A), whereas wcontext in w1 and w2 were the main components for reinstatement in AppNL-G-F mice (Figure 3B). This discrepancy suggests that the expectation of the US is different between 6-month-old control and AppNL-G-F mice.

The transition of internal state in the 12-month-old group was similar to that in the 6-month-old group until the test 1 phase. Unlike the 6-month-old group, new latent causes (z3 and z4) were inferred during the extinction phase in the 12-month-old group (rows 2–4 in Figure 3C and D). At trial 35 given an unsignaled shock, the control mice inferred the latent causes z3 and z4 acquired in the extinction phase so that their weights wcontext in w3 and w4 were updated (row 4 in Figure 3C). In contrast, there was virtually no update of weights in AppNL-G-F mice (row 4 in Figure 3D). At trial 36 (test 3 phase), the elevated CR in control mice was attributed to a successful update of associative weight after the unsignaled shock (Figure 3C), whereas the CR in AppNL-G-F mice did not increase due to a redundant latent cause z5, which was newly inferred and reduced the posterior probability of latent causes having higher associative weight (Figure 3D).

The unsuccessful state inference at reinstatement was caused by misclassification in AppNL-G-F mice

Due to the different evolution of latent causes between ages (Figure 3), we separately discuss the contribution of differences in estimated parameters within the same age and their correlations with DI between test 3 (after unsignaled shock) and test 1 (after acquisition) (Figure 2H). We first investigated the individual internal state differences in the 12-month-old group, where the impairment was apparent at the behavioral level (Figure 2H). AppNL-G-F mice had significantly lower α (Mann-Whitney U = 100, p = 0.002) and lower σx2 (Mann-Whitney U = 88.5, p = 0.008) than control mice (Figure 4A). α and σx2 were significantly correlated each other (Figure 4—figure supplement 1). Both were also positively correlated with the DI (Figure 4B), and the trend was preserved after adjusting for the genotype effect (Figure 4—figure supplement 2). While the maximal number of inferable latent causes (K) was significantly higher in AppNL-G-F mice than in control mice (Supplementary file 1g), the total number of acquired latent causes was comparable between the groups (Ktotal in Supplementary file 1i). K was negatively correlated with α and σx2 (Figure 4—figure supplement 1).

Individual parameter estimation and internal state in the 12-month-old group.

(A) The estimated latent cause model parameter. (B) Correlation between discrimination index (DI) and estimated parameter values in the 12-month-old group. The count of latent causes initially inferred during the acquisition trials (C, left), extinction trials (i.e., test 1, extinction, test 2) (D, left), and trials after extinction (i.e., the unsignaled shock and test 3) (E, left), with the sum of posterior probabilities (C, D, E, right), and the sum of associative weights at test 3 in these latent causes (F, G, H). (A) Each black dot represents one animal. *p < 0.05, and **p < 0.01 by the Mann-Whitney U test. (B) The y-axis shows the DI between test 3 and test 1. Spearman’s correlation coefficient (ρ) was labeled with significance, where *p < 0.05 and ***p < 0.001. The blue line represents the linear regression model fit, and the shaded area indicates the confidence interval. Each dot represents one animal. (C–E) In the first column, the histogram of the number of latent causes (z) acquired in each phase is shown. The maximum number of latent causes that can be inferred is 3, 31, and 2 in panels C, D, and E. In the second column, the histogram of the sum of the posterior probabilities of the latent causes is shown. The horizontal axis indicates the proportion of the value in each group. (F–H). In the first and second columns, the sum of wcs and wcontext of latent causes are shown in the boxplot, respectively. Note that the initial value of associative weight could take non-zero values, though those were comparable between groups (Supplementary file 1g). Each black dot represents one animal. *p < 0.05, and **p < 0.01 by the Mann-Whitney U test comparing control and AppNL-G-F mice, and p-values greater than 0.1 were not labeled on the plot. (A–H) Pink represents 12-month-old control (n = 20), and dark blue represents 12-month-old AppNL-G-F mice (n = 18). Detailed statistical results are provided in Supplementary file 1g, h, and i.

We assume that the effect of K on the memory modification process together with α and σx2 could come to the surface in extremely artificial conditions, but not in natural conditions as in the empirical data (see Appendix 2—table 6). Statistical results for remaining parameters are shown in Supplementary file 1g and h. It should be noted that these estimated parameters and internal state might not be unique but one of the possible solutions.

We further characterized how the latent causes acquired in different phases contribute to the distinct internal states between control and AppNL-G-F mice. Lower α and lower σx2 would bias AppNL-G-F mice toward overgeneralization, as they favor inferring a small number of latent causes when facing the same cue. Indeed, the number of latent causes initially inferred at the acquisition phase was significantly lower in AppNL-G-F mice, where most of them inferred two latent causes, and more than half of the control mice inferred three latent causes (Figure 4C and Supplementary file 1i). Furthermore, when they initially observed the CS in the absence of the US in test 1, the posterior probabilities of acquisition latent causes in test 1 were significantly higher in the AppNL-G-F mice than in the control mice, leading to the higher CRs in test 1 in the simulation (Figure 4—figure supplement 3), consistent with the observed CR (Figure 2C).

According to the latent cause model, lower σx2 would bias AppNL-G-F mice toward overdifferentiation unless the cue exactly matches to previously observed ones. In other words, they prefer to infer new potential causes when similar observations are presented instead of interpreting them generated from the same distribution. The likelihood of current stimuli given latent causes was calculated from a Gaussian distribution with the mean of stimulus values under the latent cause so far and fixed variance σx2. Repeated observation of the CS alone during the extinction would sufficiently increase the likelihood of stimuli given the latent causes inferred during the extinction in both AppNL-G-F and control mice. This attenuates the need to infer new latent causes and the number of latent causes acquired at the extinction phase was comparable between groups (Figure 4D and Supplementary file 1i). However, the CS was absent in the unsignaled shock and then presented again in test 3. These observations would decrease the likelihood of stimuli given past latent causes, and consequently increase the probability to infer the new latent causes. This volatility would be more obvious in AppNL-G-F mice with lower σx2. As a result, the number of latent causes acquired after the extinction (i.e., the unsignaled shock and test 3) as well as the sum of posterior probabilities of them were greater in AppNL-G-F mice than those in the control mice, despite that the mice received either the US or the CS alone that were the same with those they observed so far (Figure 4E and Supplementary file 1i).

Such internal states in AppNL-G-F mice would diverge the update of associative weight from those in the control mice after extinction (Figure 4F and G and Supplementary file 1i). Both AppNL-G-F and control mice would still infer the extinction latent causes at the unsignaled shock with higher posterior probabilities. Since the update of the associative weight of each latent cause is modulated by both prediction error and posterior probability of the latent cause, the associative weights in the extinction latent causes were increased by the unsignaled shock in the control mice (Figures 3C and 4G and Supplementary file 1i). In AppNL-G-F mice, however, they inferred new latent causes with low associative weight after the extinction (Figure 4E and H and Supplementary file 1i), which decreased the posterior probabilities of other latent causes and impeded update of their weight (Figures 3D and 4G). As the initial weight of new latent causes showed a trend toward significance that control mice showed a higher value (Supplementary file 1g), this would explain the significantly higher in wCS in extinction latent cause (Figure 4G). This distinct internal state, therefore, led to the lower CR and DI in test 3 in AppNL-G-F mice (Figure 2E and H). These results suggest that the α and σx2 would differentiate the internal state and thereby behavioral phenotypes between AppNL-G-F and control mice. In the Chinese restaurant process, the probability that a new latent cause is inferred decreases with trials, preventing that too many latent causes are inferred (Gershman and Blei, 2012). This could be one of the reasons why the overgeneralization by lower α was less effective than the overdifferentiation by lower σx2 in test 3 in AppNL-G-F mice.

As shown previously in Figure 2, Figure 2—figure supplement 1, Aβ aggregation has already widely spread in the brain of 6-month-old AppNL-G-F mice, but no clear behavioral impairments were detected by the conventional analysis. Similar to the 12-month-old group, we investigated the individual internal state differences in the 6-month-old group and tested whether the discrepancy in α and σx2 emerged earlier without behavioral impairment. We found that AppNL-G-F mice had significantly lower α (Mann-Whitney U = 38, p = 0.012), and it was significantly correlated with DI (Figure 5A and B and Supplementary file 1j, k). The σx2 was comparable between control and AppNL-G-F mice, but its significant correlation with DI was found (Figure 5A and B and Supplementary file 1j, k). Significant positive correlation between α and σx2 was also found in the 6-month-old group (Figure 5—figure supplement 1). Unlike in the 12-month-old group, the significant correlation between α and DI*,* as well as that between σx2 and DI was not preserved within subgroups (Figure 5—figure supplement 2), suggesting genotype would be confounder for α, σx2, and DI. The hyperparameter θ, a threshold to emit CR for stimulus inputs, was significantly higher in AppNL-G-F mice than in control mice. Since the λ was comparable between control and AppNL-G-F mice (Supplementary file 1j), the CR in AppNL-G-F mice could rapidly decrease with expected US during the extinction phase, even if their CR at the test 1 was higher than those in the control. The effect of higher θ was subtle when the expected US was far from its value, and therefore had little contribution to the DI between test 3 and test 1, which is in line with the correlation result in Supplementary file 1k. Statistical results for the remaining parameters are shown in Supplementary file 1j, k.

Individual parameter estimation and internal state in the 6-month-old group.

(A) The estimated parameters of the latent cause model. (B) Correlation between discrimination index (DI) and estimated parameter values in the 6-month-old group. The count of latent causes initially inferred during the acquisition trials (C, left), extinction trials (i.e., test 1, extinction, test 2) (D, left), and trials after extinction (i.e., the unsignaled shock and test 3) (E, left), with the sum of posterior probabilities (C, D, E, right), and th