Extended Data Table 1 |. Comparison of the COIN model to other models.

Table shows which experimental phenomena (rows) can be explained by different single and multiple-context models (columns). Alphabetical superscripts index the key feature(s) missing from each model which are primarily responsible for their inability to explain a particular phenomenon. Note that we consider each model as described and implemented by its authors (although it might be possible to modify or extend these models to explain more features). Orange cross-ticks are for models that can partially explain a phenomenon.

	single-context models		multiple-context models
	dual-rate Smith et al. 1	memory of errors Herzfeld et al. 4	source of errors Berniker & Körding 16	winner-take-all Oh & Schweighofer 11	DP-KF Gershman et al. 12	MOSAIC Haruno et al. 26	COIN
spontaneous recovery	✔	✘ a	✘ b	✘ b	✘ c	✘ d	✔
evoked recovery	✘ e	✘ e	f	f	f	✘ d	✔
memory updating	✘ g	✘ g	✘ g	✘ h	✘ g,h	✔	✔
savings after full washout	✘ i	✔	✔	✔	✔	✔	✔
anterograde interference	✔	✘ a	✘ b	✘ b	✔	✘ j	✔
environmental consistency	✘ i	✔	✘ b	✘ b	✘ k	✔	✔
explicit/implicit learning	m	✘ l	✘ l	✘ l	✘ l	✘ l	✔

Spontaneous recovery, the gradual re-expression of P⁺ in the channel-trial phase (Fig. 2c), requires a single-context model to have multiple states that decay on different time scales or a multiple-context model that can change the expression of memories in a gradual manner based on the amount of experience with each context. Therefore, single-context models that have a single state^a, or multiple-context models that do not learn context transition probabilities^b or do not have state dynamics^d do not show spontaneous recovery. Models that learn transition probabilities but that do not represent uncertainty about the previous context^c (the ‘local’ approximation in DP-KF) can either include a self-transition bias or not. With a self-transition bias, the expression of memories changes in an abrupt manner (akin to evoked recovery) when, in the channel-trial phase, the belief about the previous context changes (e.g. from P⁻ to P⁺), and thus such models fail to explain the gradual nature of spontaneous recovery. Without a self-transition bias, the change in expression of memories is gradual based on updated context counts, but this occurs too slowly relative to the time scale on which the rise of spontaneous recovery occurs.

Evoked recovery, the rapid re-expression of the memory of P⁺ in the channel-trial phase (Fig. 2e) that does not simply decay exponentially to baseline (Extended Data Fig. 6e), requires a model to be able to switch between different memories based on state feedback. Therefore, single-context models^e that cannot switch between memories are unable to show the evoked recovery pattern seen in the data. Multiple-context models with memories that decay exponentially to zero in the absence of observations^f (as during channel trials) can only partially explain evoked recovery, showing the initial evocation but not the subsequent change in adaptation over the channel-trial phase. Models with no state decay^d cannot explain evoked recovery.

Memory updating requires a model to update memories in a graded fashion and to use sensory cues to compute these graded updates. Therefore, models that either have no concept of sensory cues^g or multiple-context models that only update the state of the most probable context in an all-or-none manner^h do not show graded memory updating.

Savings, faster learning during re-exposure compared to initial exposure, after full washout requires a single-context model to increase its learning rate or a multiple-context model to protect its memories from washout and/or learn context transition probabilities. Therefore, single-context models with fixed learning ratesⁱ do not show savings.

Anterograde interference, increasing exposure to P⁺ leads to slower subsequent adaptation to P⁻, requires a single-context model to learn on multiple time scales or a multiple-context model to learn transition probabilities that generalise across contexts. Therefore, single-context models with a single state^a, or multiple-context models that either do not learn transition probabilities^b or that learn local transition probabilities independently for each row of the transition probability matrix^j do not show anterograde interference.

Environmental consistency, the increase/decrease in single-trial learning for slowly/rapidly switching environments, requires a model to either adapt its learning rate or learn local transition probabilities based on context transition counts. Therefore, single-context models with fixed learning ratesⁱ or multiple-context models that either do not learn transition probabilities^b or that learn non-local transition probabilities based only on context counts^k do not show the effects of environmental consistency on single-trial learning.

Explicit and implicit learning, the decomposition of visuomotor learning into explicit and implicit components, requires a model to have elements that can be mapped onto these components. For most models, there is no clear way to map model elements onto these components^l. It has been suggested that the fast and slow processes of the dual-rate model correspond to the explicit and implicit components of learning, respectively. However, in a spontaneous recovery paradigm, this mapping only holds during initial exposure and fails to account for the time course of the implicit component during the counter-exposure and channel-trial phases^m (see Suppl. Inf.).