Experiment 1 assessed the prediction of the Cochran and Cisler, 2019 latent state model that gradual extinction results in less spontaneous recovery than standard extinction. Simulations (Figure 2B and C) confirmed this prediction. To assess this prediction, all rats received fear conditioning, consisting of four pairings of a tone CS and foot shock US (0.8 mA × 0.5 s). They were then allocated randomly to two extinction conditions. Rats in the first condition (standard extinction) received CS alone presentations each day across three days, while those in the second condition (gradual extinction) continued to receive pairings of the CS and shock US across these days. The duration of the shock remained at 0.5 s, but, critically, the intensity of the shock was reduced from one day to the next: from 0.4 mA on day one, to 0.2 mA on day two and, finally to 0.1 mA on day three. Rats in both conditions then received CS alone presentations across two further days. Finally, two weeks later, rats in both conditions were tested for spontaneous recovery of fear responses (freezing) to the extinguished CS (see Figure 2A for design).

Here and in subsequent experiments, results are reported for the data of interest; specifically, the levels of freezing elicited by the CS in the final session of extinction and the tests for spontaneous recovery and/or reinstatement. Figures and statistics for freezing levels across conditioning and extinction are included in Appendix 1.

Figure 2D shows mean freezing (±standard error of the mean [SEM]) across the final session of extinction and the spontaneous recovery test. During the final session of extinction, rats in both conditions displayed a moderate level of freezing, and there was no significant difference between the two groups ${\displaystyle (F<1).}$ By contrast, in the spontaneous recovery test, rats in Group Gradual froze significantly less than those in Group Extinction (${\displaystyle F_{1,13}=5.040,p=0.043,d=1.158,95\mathrm{\%}CI[0.044,2.280]}$), suggesting that gradual extinction had produced more robust extinction learning than standard extinction. This accords with the simulations of the Cochran and Cisler, 2019 latent state model which holds that rats which received gradual extinction encoded their conditioning and extinction experiences into a single state, while rats which received standard extinction encoded their conditioning and extinction into separate states.

Experiment 2 had two aims. The first was to replicate the results of the previous experiment by again using the spontaneous recovery test to compare the long-term effectiveness of gradual extinction relative to standard extinction. We additionally included a control group to provide some indication of the level of spontaneously recovered responding among rats exposed to gradual or standard extinction. The second aim was to assess the generality of the results from Experiment 1 by using a reinstatement manipulation to restore responding to the extinguished tone CS. Reinstatement typically consists of re-exposing rats to the US (shock) prior to testing of the CS alone. According to latent state models, the occurrence of the US after standard extinction is taken to imply that the conditioning state is again active, hence conditioned responses return. The hypothesis to be tested is that, among rats trained in the gradual extinction protocol, the occurrence of the shock is less likely to reinstate responding to the extinguished tone because the conditioning and extinction experiences occupy the same state: hence, they cannot be easily disambiguated.

The design is shown in Figure 2E. Three groups of rats received pairings of the tone CS and a 0.8 mA × 0.5 s foot shock US followed by extinction. For rats in Group Gradual, the intensity of the shock US paired with the CS was progressively reduced across the first three days of the extinction stage, and this was followed by a fourth day on which the CS was presented alone. For rats in Group Extinction, the extinction stage involved four days of CS alone exposure. Finally, rats in Group Home remained in their home cage across the first three days of this stage, before receiving a session of CS alone presentations on the fourth day. Two weeks later, all rats were tested for spontaneous recovery of extinguished responses, and the following day, for their reinstatement after a 0.5 mA × 0.5 s shock alone presentation.

Figure 2F shows mean freezing (±SEM) elicited by the CS across the final session of extinction (left), the spontaneous recovery test (middle), and the reinstatement test (right). In the final session of extinction, rats in Group Home froze significantly more to the CS than those in Groups Gradual and Extinction (${\displaystyle F_{1,21}=7.237,p=0.014,d=1.171,95\mathrm{\%}CI[-2.065,-0.264]}$). There was no significant difference in freezing between the latter two groups ${\displaystyle (F<0.1)}$ indicating that the gradual and standard extinction treatments were ultimately, equally effective in reducing conditioned fear responses.

In the test for spontaneous recovery two weeks later, rats in Group Home again froze significantly more to the CS than those in Groups Extinction and Gradual (${\displaystyle F_{1,21}=22.113,p<0.001,d=1.886,95\mathrm{\%}CI[-2.937,-1.136]}$), indicating that fear responses only partially recovered in the latter groups. Despite the numerical difference, Group’s Gradual and Extinction did not significantly differ from each other in this test ${\displaystyle (F<3).}$ The lack of statistical significance is likely due to low levels of spontaneous recovery in these groups, masking any differences between them. This is supported by the finding that both Group Extinction and Group Gradual displayed a decrease in freezing from the final extinction session to the spontaneous recovery test, perhaps due to the treatments having failed to completely extinguish responding.

In the reinstatement test, CS freezing was significantly higher in Group Home compared to Groups Extinction and Gradual (${\displaystyle F_{1,21}=5.702,p=0.026,d=1.003,95\mathrm{\%}CI\left[-1.934,-0.133\right]}$) and, importantly, in Group Extinction compared to Group Gradual (${\displaystyle F_{1,21}=5.178,p=0.033,d=0.63,95\mathrm{\%}CI\left[0.098,2.178\right]}$). Thus, the reinstatement test revealed more effective extinction learning in Groups Gradual and Extinction than in Group Home and, importantly, more effective learning in Group Gradual than Group extinction.

Experiment 1 demonstrated that a gradual extinction protocol produced less spontaneous recovery than standard extinction and Experiment 2 showed the same pattern for reinstatement. According to the Cochran and Cisler, 2019 model, the effectiveness of gradual extinction is due to the series of small prediction errors, created via the progressive reduction in US intensity from that used to condition the CS to the final CS alone presentations. However, the designs of the previous experiments confounded the progressive reductions in shock intensity with exposure to lower-intensity shocks. It is possible that simply receiving lower-intensity shocks following conditioning, regardless of their order, is sufficient to produce the pattern of results observed thus far. If this were to be the case, then presenting the same number and intensity of CS-shock pairings, but in a scrambled order, would produce the same robustness of extinction as the progressive reduction in shock intensities. However, the Cochran-Cisler model predicts that the prediction errors produced by the scrambled CS-shock pairings would, like standard extinction, produce state-splitting, and thus, would not produce the same robustness of extinction. Simulations confirmed this prediction (Figure 3B and C).

Figure 3

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Experiment 3 tested this prediction (see Figure 3A for design). There were three groups. The gradual and standard extinction groups differed from the previous experiments only in that the initial three days of the extinction stage was followed by six daily sessions of CS alone presentations (as opposed to the two and one days of CS alone presentations used in Experiments 1 and 2). The six additional days of extinction were included to ensure that conditioned freezing was more fully extinguished than in the previous experiments. The third group (Scrambled) continued to receive CS-shock pairings across the initial three days of the extinction stage. The number of pairings and intensities of the shocks were identical to those received by the gradual group but the order in which the intensity of the shock changed was scrambled rather than progressively reducing as in the gradual group. Specifically, trials on which the CS was paired with the 0.4, 0.2, or 0.1 mA shock were delivered in a pseudo-random order within each session, (e.g. a 0.4 mA pairing followed by a 0.1 mA and then a 0.2 mA, etc.). This scrambled group then received six sessions of CS alone presentations as described for the other two groups. Two weeks later, all groups were tested for spontaneous recovery of freezing to the CS, and this was followed by a final test for reinstatement of freezing following shock re-exposure.

Figure 3D shows mean freezing (±SEM) across the final session of extinction (left), the spontaneous recovery test (middle), and the reinstatement test (right). In the final session of extinction and spontaneous recovery test, the level of freezing did not differ between the three groups ${\displaystyle (Fs<2)}$. Once again, the overall level of spontaneous recovery was very low which may have masked differences between the groups; the daily CS alone presentations across the additional six days may have over-extinguished the CS. By contrast, in the reinstatement test, the level of freezing to the CS was significantly lower in Group Gradual compared to Groups Extinction and Scrambled (${\displaystyle F_{1,19}=9.598,p=0.006,d=1.326,95\mathrm{\%}CI\left[0.460,2.378\right]}$). Freezing did not significantly differ in the latter two groups (${\displaystyle Fs<2}$). Thus, despite the lack of difference in the spontaneous recovery test, Group Gradual exhibited less reinstatement than Groups Extinction and Scrambled, replicating the result of Experiment 2 and, importantly, showing that exposure to the lower-intensity shocks in a pseudo-random or scrambled order is not sufficient to decrease fear restoration. Rather, the series of small prediction errors, created by progressively reducing shock intensities, is critical.

The previous experiments leave open the possibility that the gradual extinction effect is due to the devaluation of the US representation rather than any change in prediction error. That is, after conditioning, the subject presumably holds a representation of the CS and the shock US. Receiving the series of lower-intensity shocks following conditioning degrades the subject’s shock representation, such that the shock comes to be represented as very weak. Thus, recall of the CS-shock association in tests for spontaneous recovery (Experiment 1) or reinstatement (Experiments 2 and 3) elicits little fear. This explanation differs from that of the Cochran and Cisler, 2019 model in that degradation of the shock representation is not bound to the size of any prediction error. Rather, it implies that shifting immediately to a very low-intensity shock (0.1 mA) after conditioning with a high-intensity shock (0.8 mA) would be sufficient to protect against spontaneous recovery and/or reinstatement. By contrast, the Cochran-Cisler model predicts that shifting immediately to a very low-intensity shock (0.1 mA) would still produce a large prediction error, resulting in state-splitting and, thereby, susceptibility to fear restoration. Simulations in relation to this prediction are shown in Figure 3F and G.

Experiment 4 tested this prediction (see Figure 3E for design). There were four groups. The gradual and standard extinction groups differed from those in the previous experiments only in that the initial three days of the extinction stage was followed by three daily sessions of CS alone presentations. Three days were chosen as an intermediary between one and six, as we assumed that those amounts of extinction under-extinguished or over-extinguished the CS, respectively. The treatment of the remaining two groups differed from that of Groups Gradual and Extinction only in the initial three days of the extinction stage. One group (0.1 × 3) received pairings of the CS and the lowest intensity shock, 0.1 mA, on each of these days, matching the total amount of shocks administered to Group Gradual. The final group (0.1 × 1) received pairings of the CS and a 0.1 mA shock for only the first of these days, and CS alone presentations for the remaining two days. This group was included to test whether a single session of low-intensity shocks was sufficient to protect against fear restoration. After the final three days of the extinction stage, across which all groups received CS alone presentations, all groups were tested for spontaneous recovery of freezing to the CS. The interval to the spontaneous recovery test was increased to three weeks (from two weeks in the previous experiments) in an attempt to increase recovery of the extinguished CS. The following day, all groups received a shock-alone presentation and a test for reinstatement of extinguished freezing.

Figure 3H shows mean freezing (±SEM) across the final session of extinction (left), the spontaneous recovery test (middle), and the reinstatement test (right). In the final session of extinction, CS freezing levels did not significantly differ between the groups ${\displaystyle (Fs<2)}$. By contrast, in the spontaneous recovery test, the CS freezing in Group Gradual was significantly lower than the average level of freezing in the other three groups, (${\displaystyle F_{1,28}=5.171,p=0.031,d=0.977,95\mathrm{\%}CI\left[-1.765,-0.092\right]}$), which did not differ from each other ${\displaystyle (Fs<1)}$. In the reinstatement test, Group Gradual displayed numerically less CS freezing than the other three groups. However, this difference did not reach significance, and there were no differences among the other three groups.

Taken together, these results indicate that repeated exposure to the lowest intensity shock is not sufficient to protect against fear restoration in a test of spontaneous recovery. Rather, protection is only observed when the shock intensity decreases in a progressive and gradual manner before the shock is omitted altogether. The overall pattern of results was similar in the reinstatement test but did not reach significance due to variability within the groups. Nonetheless, it is clear that the results do not support an account of gradual extinction in terms of a devalued shock representation.

According to the Cochran and Cisler, 2019 model, the size of the prediction error determines how new learning is encoded relative to what is already known. The results of the experiments conducted thus far are consistent with this model, but a feature of both the model’s explanation and the previous experiments is that all prediction errors have been generated by a change in the CS-US relationship. While the model permits contextual (e.g. spatio-temporal) information to be encoded concomitantly with the formation of the CS-US association, it predicts that only prediction errors relating to the CS-US association influence the process of state-splitting. The model also holds that a shift in context, whether it be a change in the physical environment or interpolating a delay between sessions (analogous to a change in the temporal context), means that the most recent active state is no longer most likely to be active (i.e. now all stored states are equally likely to be active). However, such shifts do not influence the process of state-splitting. That is, prediction error produced by a difference in contextual information does not influence whether new information is encoded into an existing or new state. Hence, the model predicts that the gradual extinction effect should survive a physical or temporal context shift: i.e., a physical or temporal context shift will not attenuate the effectiveness of gradual extinction in protecting against spontaneous recovery and/or reinstatement. Simulations confirmed these predictions (see Figure 4B, C, F and G).

Figure 4

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It is worth noting that, within a more general latent state framework (e.g. the models proposed by Redish et al., 2007; Gershman et al., 2017), prediction errors produced by context changes may well contribute to the process that determines the location of newly encoded information. In that case, the prediction error produced by combining a shift in shock intensity with a shift in physical context would be sufficient to cause state-splitting, resulting in the gradual extinction experience being encoded in a separate state. Thus, from this perspective, shifting the physical context between conditioning and extinction, should not only attenuate the effectiveness of gradual extinction: it should produce the opposite effect, resulting in higher levels of spontaneous recovery relative to the case where there had been no context shift.

Experiment 5 tested these differing predictions by combining gradual extinction with a shift in the physical context. Subjects received conditioning in either context A or context B (see Figure 4A for design). Next, rats in both groups received either standard or gradual extinction in context A. Finally, all rats were tested for spontaneous recovery in context A. Thus, all extinction and testing were conducted in the same context, rats only differed on their extinction treatment (gradual or standard) and conditioning context (A - ‘same’ context as extinction; B - ‘different’ context to that of extinction).

Figure 4D shows mean freezing (±SEM) across the final session of extinction (left) and the spontaneous recovery test (right). One rat from Group Gradual was removed from the analysis due to abnormally high freezing at the test (over 2 SDs when included in the average and 4 SDs when left out). Importantly, the inclusion/removal of this rat did not change the pattern of statistical difference between groups. In the final session of extinction, there was no significant difference in CS freezing between rats exposed to gradual or standard extinction (i.e. extinction type), no significant difference in CS freezing between rats extinguished in the same context as conditioning versus rats extinguished in a different context (i.e. conditioning location), and no significant interaction between these factors ${\displaystyle (Fs<1)}$. In the spontaneous recovery test, the level of CS freezing did not significantly differ in terms of extinction type or extinction location (Fs <2). However, there was a significant interaction between extinction type and extinction location (${\displaystyle F_{1,28}=5.827,p=0.025,d=1.260,95\mathrm{\%}CI[0.129,1.578]}$). From inspection of Figure 4D, the interaction was due to gradual extinction producing less spontaneous recovery than standard extinction when conditioning and extinction occurred in the same context; but more spontaneous recovery than standard extinction when conditioning and extinction occurred in different contexts. Thus, a shift in physical context between conditioning and extinction reversed the advantage of gradual extinction over standard extinction. The implication for latent state models is that combining the reduction in shock intensity with a change in context produced a prediction error sufficiently large to cause state-splitting. Thus, rats exposed to this combination (Group Gradual-Different) exhibited more freezing to the CS at the test than their standardly extinguished counterparts as the CS-shock experiences are likely to have been represented in multiple states of memory. More generally, these results support a view that physical context influences the process of state-splitting, which does not accord with the role afforded to context in the Cochran and Cisler, 2019 model.

The previous experiment showed that a shift in physical context reverses the effectiveness of gradual extinction. This is inconsistent with the Cochran and Cisler, 2019 model which holds that only prediction errors relating to the CS-shock relationship affect state-splitting. The aim of this experiment was to determine whether a shift in temporal context also influences the gradual extinction effect. A shift in temporal context was achieved by inserting a delay between conditioning and extinction. The Cochran-Cisler model predicts that, similar to a physical context shift, a temporal shift will reset latent state beliefs but not affect state-splitting. Nonetheless, a physical context shift reversed the effectiveness of gradual extinction; hence, a temporal shift may do the same (for simulations, see Figure 4F and G).

Experiment 6 tested this prediction (design in Figure 4E). Four groups of rats were conditioned to fear a tone CS across its pairings with 0.8 mA shock. Two groups were then subjected to gradual extinction while the remaining two groups received standard extinction. For one group in each of these pairs, the extinction stage commenced one day after conditioning; for the other group, the extinction stage commenced three weeks after conditioning. Importantly, the protocols were arranged so that all rats received extinction at the same time. After extinction, all rats were tested three weeks later for spontaneous recovery and reinstatement of freezing to the CS.

Figure 4H shows mean freezing (±SEM) across the final session of extinction (left), the spontaneous recovery test (middle), and the reinstatement test (right). In the final session of extinction, there was no significant difference in freezing to the CS between rats that received gradual versus standard extinction; no significant difference in freezing to the CS between rats that received extinction one or 21 days after conditioning, and no significant interaction between the factors of extinction type and extinction time ${\displaystyle (Fs<1)}$. In the spontaneous recovery test, there was no overall difference in CS freezing as a function of extinction type or extinction time ${\displaystyle (Fs<3)}$. However, there was a significant interaction between these two factors (${\displaystyle F_{1,28}=10.035,p=0.004,d=2.328,95\mathrm{\%}CI\left[0.396,1.844\right]}$), which was due to the fact that gradual extinction produced less spontaneous recovery than standard extinction when extinction commenced one day after conditioning, but more spontaneous recovery than standard extinction when extinction commenced three weeks after conditioning.

In the final reinstatement test, averaged across extinction time, there was no overall difference in CS freezing between rats that received either gradual versus standard extinction ${\displaystyle (F<1)}$. By contrast, averaged across extinction types, the level of CS freezing was greater among rats for which there was a delay between conditioning and extinction compared to those for which there was no delay (${\displaystyle F_{1,28}=6.270,p=0.01,d=0.902,95\mathrm{\%}CI\left[0.161,1.610\right]}$). From inspection of Figure 4H, this difference is likely due to high freezing in the Gradual-Delay group relative to both non-delay groups. This was confirmed by a significant interaction between the factors of extinction type and extinction time (${\displaystyle F_{1,28}=7.703,p=0.004,d=2.27,95\mathrm{\%}CI[0.257,1.705]}$), which was due to the same pattern of results observed in the spontaneous recovery test. Thus, a shift in temporal context, much like a shift in physical context, reversed the advantage of gradual extinction over standard extinction. This further supports the idea that contextual information contributes to the state-splitting process while not agreeing with the specific role for temporal context suggested by the Cochran-Cisler latent state model.

The six experiments presented here show that gradual extinction is more effective than standard extinction in protecting against spontaneous recovery and/or reinstatement. Two groups were represented in each of these experiments: Group Gradual and Group Extinction. Across the experiments, these groups differed with respect to the number of extinction sessions that followed the initial three days of extinction (where the groups received CS-US pairings of decreasing intensity or CS-alone presentations, respectively). Moreover, in Experiments 5 and 6 (physical and temporal context shift), the delay to spontaneous recovery testing was three weeks rather than two. Otherwise, the treatment of rats in Groups Gradual and Extinction was identical in each experiment.

The similarity of these two groups across experiments permitted an omnibus analysis comparing all rats that received either gradual or standard extinction. A single Group Gradual (i.e. all rats within Group Gradual in Experiments 1–6) and a single Group Extinction (i.e. all rats within Group Extinction in Experiments 1–6) were formed. An ANOVA assessed freezing levels across the final session of extinction and the spontaneous recovery test. Figure 5 shows that freezing levels were similar across the final session of extinction, but were higher for Group Extinction compared to Group Gradual across the spontaneous recovery test (${\displaystyle F_{1,92}=18.554,p<0.001,d=0.891,95\mathrm{\%}CI[0.479,1.298]}$).

Figure 5

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Averaged across experiments, rats that received gradual or standard extinction displayed similar levels of CS freezing at the final session of extinction, indicating both procedures produced an equivalent decrement in conditioned responding. However, gradually extinguished rats displayed less spontaneous recovery of CS freezing than standardly extinguished rats. Thus, the overall analysis further supports the prediction made by latent state models (e.g. Cochran and Cisler, 2019; Redish et al., 2007; Gershman et al., 2010; Gershman et al., 2017): specifically, that gradual extinction is more effective than standard extinction in protecting against spontaneous recovery, as it results in the encoding of conditioning and extinction into a single memory state.

Freezing was the measure of conditioned fear. Freezing was defined as the absence of all movements except those related to breathing (Fanselow, 1980). A time sampling procedure was used in which each rat was scored as freezing or not freezing every 2 s during the 30 s of each CS presentation and the 30 s immediately prior to each presentation. A percentage score was calculated for each rat, as the proportion of freezing observations to total observations. Freezing data were scored by the experimenter and an experienced observer who was blind to the experimental manipulations. The correlation between the two sets of scores was greater than 0.9 but any discrepancies were resolved in favor of the naïve observer.

Conditioning, extinction, and spontaneous recovery data were analyzed using a mixed-model ANOVA with a between the factor of Group and a within a factor of Day (for Extinction) or Trial (for Conditioning and Spontaneous Recovery). The type 1 error rate was controlled at α=0.05 which gave an F critical of 4.7 (df 1 and 13). Standardized 95% confidence intervals (CIs) were reported for significant results. Cohen’s d (0.8=large) and Partial Eta Squared (${\eta }_p^2)$ (0.14=large) were reported as a measure of effect size for between and within-factor results, respectively.

The data from conditioning, the common extinction session, the spontaneous recovery, and reinstatement tests were analyzed using a set of planned orthogonal contrasts (Hays, 1967). Data from the gradual extinction and extinction sessions (days 4–6) were analyzed using a mixed-model ANOVA with a between factor of Group and a within factor of Day. The type one error rate was controlled at α=0.05 which gave an F critical of 4.600 (df 1 and 14) for extinction training and 4.325 for all other stages (1 and 21 df). The first of the planned contrasts compared Groups Extinction and Gradual Extinction to Group Single Extinction to assess whether the treatments accorded the former groups had produced a greater long-term depressive effect on conditioned responding than the latter, i.e., the group just given the single extinction session. The second contrast compared Group Gradual Extinction to Group Extinction to assess whether the former exhibited less fear recovery on both tests than the latter, as had been found in the previous experiment for the spontaneous recovery test.

All data were analyzed using a set of planned orthogonal contrasts (Hays, 1967). The type one error rate was controlled at α=0.05 which gave an F critical of 4.325 (1 and 21 df) for all stages. The first contrast compared Group Gradual to Groups Extinction and Scrambled to assess whether the progressive reduction in shock intensity produced less fear restoration than extinction throughout or extinction preceded by the scrambled shock protocol. The second contrast compared Group Extinction against Group Scrambled to assess whether the reduction in shock intensity per se produced less fear restoration than standard extinction.

All data were analyzed using a set of planned orthogonal contrasts (Hays, 1967). The type one error rate was controlled at α=0.05 which gave an F critical of 4.196 for all stages (1 and 28 df).

The first contrast compared Group Gradual extinction against the remaining three groups to assess whether the progressive reduction in shock intensity produced less fear restoration than regular extinction or the low shock intensity manipulations. The second contrast compared Groups 0.1 × 3 and 0.1 against Group Standard Extinction to assess whether receiving the lower-intensity shocks produced less fear restoration than extinction. The final contrast compared Group 0.1 × 3 against Group 0.1 to assess whether receiving the low-intensity shocks for a single day differed in its fear restoration consequences than three such days.

All data were analyzed using a 2 × 2 mixed-model ANOVA with between factors of context and type of extinction. A within factor of trial for conditioning and testing and of day for extinction was included. The type one error rate was controlled at α=0.05 which gave an F critical of 4.196 for all stages (1 and 28 df).

All data were analyzed using a 2x2 mixed-model ANOVA with between factors of delay and type of extinction. A within factor of trial for conditioning and testing, and of day for extinction was included. The type one error rate was controlled at α=0.05 which gave an F critical of 4.196 for all stages (1 and 28 df).

Appendix 2—figure 1 displays trial-by-trial data from the spontaneous recovery and reinstatement tests (where appropriate) from Experiments 1–4 and Appendix 2—figure 2 displays the same data from Experiments 5 and 6. Please note that the source data files for all experiments conducted in this study are available via the Open Science Framework repository: https://osf.io/5D9Q3/.

Appendix 2—figure 1

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Appendix 2—figure 2

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The model conceptualizes context shifts (i.e. shifting the physical and/or temporal context) as a resetting of an agent’s beliefs in latent states. That is, when the context is shifted, beliefs are reset to be uniform, such that all known latent states are equally likely to be active (i.e. the degree of belief in a single state is 1 /L [L=total number of latent states]). This removes the agent’s bias to believing the state active on the most recent trial is likely to be active again. Critically, context shifts do not affect the state-splitting process. Only prediction errors relating to the CS-US relationship are able to determine whether a new state is inferred to be active or not. Thus, despite a context shift resetting current beliefs about active latent states, the model predicts that combining gradual extinction with a shift in context (physical or temporal shift) will not attenuate the gradual extinction effect. Appendix 3—figure 2C, D display simulations of gradual extinction with a physical context shift; and Appendix 3—figure 2E, F display simulations of gradual extinction with a temporal context shift.

A context shift is instantiated in the model as resetting beliefs to 1 /L for a physical context shift (L=number of latent states). For a temporal shift, as the chosen time interval grows, the beliefs approach 1 /L. The chosen interval for the simulations was t=200, effectively fully resetting beliefs to 1 /L. The context shift (temporal and physical) occurred between conditioning and extinction, the simulations remained identical to the gradual extinction simulation otherwise.

The pattern of associative strength was identical to the gradual extinction simulation, as the context shift had no impact on whether a new state was inferred. Thus, as there is only a single state at the spontaneous recovery stage, associative strength did not recover. Thus, the model predicts that the robust learning produced by gradual extinction is not affected by a physical or temporal context shift. However, the results of Experiments 5 and 6 contradict this prediction as they show that a context shift (physical or temporal) attenuates the effectiveness of gradual extinction. Therefore, an expanded role for context would be a worthwhile addition to Cochran and Cisler, 2019 latent state model.

Appendix 3—figure 1

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Appendix 3—figure 2

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The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

This work was supported by an Australian Government Research Training Fellowship to NGWK, an Australian Research Council (ARC) Discovery Early Career Researcher Award to JCL (DE210100292), an ARC Discovery Grant to RFW (DP2201036501) and an ARC Future Fellowship to NMH (FT190100697).

This study was performed in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals by the National Health and Medical Research Council of Australia. All of the animals were handled according to approved institutional Animal Care and Ethics Committee (ACEC) protocols of the University of New South Wales. The protocol was approved by the UNSW ACEC (Permit Number: 21-132B).

1. Preprint posted: January 16, 2024
2. Sent for peer review: January 16, 2024
3. Reviewed Preprint version 1: March 12, 2024
4. Reviewed Preprint version 2: June 28, 2024
5. Version of Record published: July 19, 2024

You can cite all versions using the DOI https://doi.org/10.7554/eLife.95849. This DOI represents all versions, and will always resolve to the latest one.

© 2024, Kennedy et al.

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