Contextual cues and transition statistics drive expression of competing motor memories

Summary

Learning multiple motor skills and expressing them appropriately in changing environments is challenging. While contextual cues help separate these memories, their interaction during retrieval remains unclear. We investigated how memory stability, recency, and transitional statistics of learning environments influence this process. Across six visuomotor adaptation experiments, participants learned opposing rotations linked to distinct cues under blocked or interleaved schedules and were tested in stable or dynamic environments. We found that contextual cues separated memories, but expression was biased toward stable memories after imbalanced training and toward recent ones when memory stability was equal. When training and testing statistics mismatch, cue-based retrieval failed, and behavior biases toward stability or recency. Conversely, high-entropy, interleaved training enabled appropriate, cue-based expression across testing conditions. These findings demonstrate that memory retrieval arises from arbitration between cues and learned transition priors, offering a unified framework that explains interference, recovery, and the benefits of variable practice.

Graphical abstract

Highlights

• •Motor memory retrieval relies on arbitration between cues and transition statistics
• •Stability and recency systematically bias motor memory expression
• •Mismatch in training and test environments might disrupt cue-dependent retrieval
• •High-entropy training enables flexible, cue-specific expression

Behavioral neuroscience; Statistical computing

Introduction

The brain’s ability to select and express the right action from a vast repertoire of learned behaviors is a cornerstone of adaptive behavior. Consider a tennis player preparing to return a serve, a chef switching between knives, or a musician adapting to different instruments. Years of practice hone distinct motor plans for each context, yet in the fleeting moment of action, the brain must swiftly suppress an anticipated response if the context shifts. This challenge of retrieving the correct memory amidst uncertainty extends beyond motor tasks to episodic, working, and language memory, highlighting a fundamental question in memory research: How does the brain retrieve the correct memory from a library of learned representations, particularly when contexts are ambiguous or rapidly changing?

This retrieval problem is pronounced when multiple memories compete for expression. Performance errors often stem not from forgotten skills but from expressing the wrong memory. In motor learning, studies of visuomotor adaptation reveal this distinction: when participants learn opposing perturbations (e.g., clockwise and counterclockwise rotations) in sequence, they exhibit anterograde interference, struggling to re-express the first skill after learning the second, despite intact initial learning.^1,2 These errors reflect retrieval failures, not acquisition deficits, underscoring the need for mechanisms that guide memory selection.

Traditional theories propose that contextual cues, such as specific postures, workspaces, or visual stimuli, solve this problem by tagging memories for later retrieval.³ For example, associating a motor skill with a unique cue enables rapid recall, as seen in savings, where re-encountering a perturbation elicits faster relearning.⁴ However, cues have limitations. Many are weak, ambiguous, or overlapping in real-world settings, and their effects are graded rather than absolute. For instance, varying premovement cues along a continuum results in a weighted blend of associated memories, consistent with Gaussian generalization.⁵ Moreover, retrieval can fail when cue-context relationships are disrupted, such as when blocked training with visual cues is followed by interleaved testing, leading to increased interference and impaired memory separation across domains.^6,7 These findings suggest that cues alone are insufficient for robust memory retrieval in dynamic environments.

We propose that the brain relies on transition statistics - learned expectations about how contexts evolve over time- as a fundamental mechanism for guiding memory retrieval across domains. Transition statistics encompass volatility (how frequently contexts change) and sequential regularities (which contexts follow others). For example, if a learner expects Context A to typically precede Context B, being in A primes anticipation of B, facilitating retrieval of the associated memory. In stable environments with rare switches, the brain persists with the current memory; in volatile settings with frequent changes, it remains flexible, ready to switch. This framework unifies memory organization across motor control, episodic, working, and language domains, offering a novel principle for adaptive behavior. While this principle is hypothesized to operate across multiple memory systems, here we test it directly in the domain of motor learning. Visuomotor adaptation provides a powerful experimental platform because the statistical structure of context transitions can be precisely controlled, and the resulting effects on memory expression can be measured with high resolution. The findings from this controlled setting can then inform theoretical accounts of how transition statistics might shape memory retrieval in other domains.

Evidence for transition statistics spans multiple domains. In motor adaptation, learning rates adjust to environmental volatility: stable perturbations accelerate adaptation, while unpredictable switches slow it, consistent with Bayesian learners downweighing errors in high-volatility settings.⁸ Similarly, cues signaling context repetition enhance single-trial adaptation, while cues indicating change dampen it.^9,10,11 In skill acquisition and procedural memory, implicit sequence learning tasks, such as the serial and alternating serial response time tasks, show sensitivity to high-probability motor transitions even without conscious awareness.^12,13 In episodic memory, abrupt context shifts (event boundaries) segment experiences, reducing interference, while stable contexts promote integration.^14,15 In spatial memory, the hippocampus encodes probabilistic transition graphs between locations, enabling flexible route planning and also supports cognitive map formation.¹⁶ Infants leverage transitional probabilities to segment speech into words, detecting structure without explicit cues.^17,18 Bilingual individuals who frequently switch languages exhibit smaller switch costs, reflecting flexible retrieval shaped by transition experience.¹⁹ In the attention domain, probabilistic cueing and temporal expectation paradigms demonstrate that the allocation of attention is guided by the learned transition statistics of where and when events are likely to occur.^20,21 In perceptual decision-making, humans adapt cautiously in volatile environments, guided by inferred transition structures.²² In working memory, temporal clustering of items influences recall order, driven by learned transition probabilities.²³ These parallels suggest that transition statistics are a domain-general mechanism for organizing memory retrieval. The brain learns not just memory-cue associations but also the temporal structure of contexts, enabling a meta-learning process that optimizes retrieval across motor, episodic, and other memory systems.

Mechanistically, this process is formalized through Bayesian context-inference models, such as the contextual inference (COIN) model.^9,10,11 Context is a latent variable, and the brain maintains a probabilistic belief over possible contexts, updated via sensory cues, recent errors, and transition priors. Retrieval reflects a posterior distribution combining these factors, not just cue-driven selection. High volatility in the environment shifts expression toward recent memories, while stability favors more experienced ones. This process aligns with neural mechanisms where motor cortex populations simultaneously encode multiple action plans, weighted by context likelihood.²⁴ The principle of transition statistics extends to neural population codes, where dynamic factor combinations encode context-dependent memories.²⁵ It is important to note that the COIN model is one computational instantiation of this broader principle; other models, such as the contextual dual-rate state-space model, implement different assumptions (e.g., cue-gated learning without explicit transition inference). Our experiments are designed to test the core qualitative predictions of the arbitration framework, rather than to adjudicate between specific computational implementations. By manipulating training schedules (blocked vs. interleaved) and testing environments (stable vs. volatile), we can assess whether behavior reflects the integration of cue information with learned transition statistics.

To test this theory, we conducted six visuomotor adaptation experiments, manipulating cue presence, training order, stability, and transition entropy (Figure 1). Participants learned opposing motor mappings with distinct cues under blocked or interleaved schedules, then expressed them under varied cue and transition conditions. Our findings reveal how transition statistics shape memory expression, offering behavioral evidence for a domain-general framework with implications for neural mechanisms, skill learning, and rehabilitation.

Figure 1.

Experimental procedure and learning schedules

(A) Sketch of experimental setup used to present the start and targets.

(B) Trial structure and cue manipulation. Each trial began with the cursor in a start circle. After a delay, both a primary target (straight ahead) and a secondary target (30° right or left) appeared simultaneously. Participants first reached the primary target, then the secondary target. During the acquisition phase, a 30° visuomotor rotation was applied to the cursor during the primary reach only. The direction of the rotation was linked to the location of the secondary target: counter-clockwise rotation (Task A) when the secondary target was on the right (Cue A); clockwise rotation (Task B) when the secondary target was on the left (Cue B). The secondary target thus served as an explicit contextual cue predicting the upcoming perturbation. During the expression phase (error-clamp), the cursor was clamped to a straight trajectory (0° rotation) regardless of hand movement, allowing the measurement of the expressed memory without error feedback. Cues during expression could be A, B, or absent (No Cue). Red line: cursor trajectory; black line: hand path; hand symbol: instantaneous hand position; yellow dot: rotated cursor position.

(C–H) Training and testing schedules for all six experiments. Each panel shows the sequence of perturbations (Task A: −30°; Task B: +30°; expression Task N: 0°) and cue presentations across trials.

(C) Experiment 1a (memory stability bias). Learning: 160 trials of Task A with Cue A, followed by 20 trials of Task B with Cue B (blocked, high environmental stability). Expression: three independent groups received only Cue A, only Cue B, or No Cue throughout the error-clamp block. This design tests whether extensive practice on Task A (high memory stability) biases retrieval even when the cue signals Task B, which was practiced only briefly.

(D) Experiment 1b (recency bias). Learning: 160 trials of Task A with Cue A, followed by 160 trials of Task B with Cue B (blocked, high environmental stability; equal memory stability). Expression: same as Experiment 1a. This design tests whether, when memory stability is equated, retrieval is biased toward the more recently learned task.

(E) Experiment 2a (environmental stability mismatch, unequal memory stability). Learning: same as Experiment 1a (160 A, 20 B; blocked, high environmental stability). Expression: Cue A, Cue B, and no-cue trials presented in randomly interleaved order (low environmental stability). This creates a mismatch between the stable training environment and the volatile test environment, testing whether cue-based retrieval collapses when environmental statistics change.

(F) Experiment 2b (environmental stability mismatch, equal memory stability). Learning: same as Experiment 1b (160 A, 160 B; blocked). Expression: same interleaved cue presentation as Experiment 2a. This isolates the effect of environmental stability mismatch while controlling for differences in memory stability. (G) Experiment 3a (low environmental stability during learning and test). Learning: 320 trials of Task A and Task B randomly interleaved (low environmental stability; equal memory stability). Expression: Cue A, Cue B, and no-cue trials presented in randomly interleaved order (low environmental stability). This test determines whether learning under volatile conditions enables flexible, cue-driven retrieval even when the test environment remains unpredictable.

(H) Experiment 3b (low environmental stability during learning, high during test). Learning: same interleaved schedule as Experiment 3a (low environmental stability; equal memory stability). Expression: three independent groups received only Cue A, only Cue B, or No Cue throughout the error-clamp block (high environmental stability). This test determines whether the flexibility acquired through interleaved training persists when the test environment becomes predictable.

(I–K) Local transition probability (probability of switching contexts given the current context). These are objective properties of the experimental design, independent of any computational model.

(I) Blocked schedule with unequal practice (Experiments 1a, 2a).

(J) Blocked schedule with equal practice (Experiments 1b, 2b).

(K) Interleaved schedule (Experiments 3a, 3b).

Results

To test the hypothesis that internal models of context transitions guide memory retrieval, we conducted a series of visuomotor adaptation experiments. We independently manipulated two factors: the amount of practice on each task (to vary memory stability) and the statistical structure of transitions between tasks (to vary environmental stability). Our results indicate that the expression of learned motor memories is influenced by a combination of factors: the strength of memories acquired through extensive practice, the recency of experience, and the learned volatility of the environment. These findings suggest that retrieval involves an arbitration process integrating cue information with learned transition statistics.

Expression is contextual but biased by memory stability and recency

The first set of experiments examined whether contextual cues allow selective expression of motor memories and whether the stability or recency of prior experience modulates this expression. In Experiment 1a, participants first adapted to Task A (160 trials), followed by brief exposure to Task B (20 trials), each tagged with distinct contextual cues (Cue A for Task A, and Cue B for Task B). This training schedule has a low transitional probability of changing context and more stability in learning A than B. Learning was similar for task A (F_[2,33] = 2.68, p = 0.083) and Task B (F_[2,33] = 0.62, p = 0.541) across the three groups. In the subsequent error-clamp phase, participants were presented with one of the three contextual conditions: Cue A, Cue B, or No Cue (Figure 2A). Despite Task B being learned for a short duration, the expression was still context-dependent; participants generated distinct motor outputs based on the cue presented, indicating successful separation of memories. A one-way ANOVA confirmed a main effect of the Cue on the total expression (F_[2,33] = 5.589, p = 0.008, w² = 0.20, Effect size f = 0.58). Post-hoc tests revealed significant differences between Cue A (mean ± SE: 0.51±0.07) and both Cue B (mean ± SE: 0.05±0.10) (p_corrected=0.011) and No cue (mean ± SE: 0.06±0.06) (p_corrected=0.011), although Cue B and No cue were not significantly different (p_corrected=0.928). However, analysis of the early phase of expression (first five trials) showed that even Cue B (mean ± SE: −0.14±0.10) trials elicited stronger output than No Cue (mean ± SE: 0.16±0.08) (t₍₂₂₎ = −2.37, p=0.027, Cohen’s d = −0.97), revealing a short-lived contextual retrieval of Task B memory despite its instability. Since later clamp trials may become contaminated by the decay of memory traces and by collapsing beliefs about context identity, particularly in the absence of ongoing error signals, we focused our analyses on the early phase of expression (first five trials), where COIN is most likely to reflect prior learning and not subsequent re-averaging.

Figure 2.

Memory expression is guided by contextual cues but biased by the stability and recency of competing memories

(A) Experiment 1a design and behavioral results. Participants first learned Task A (30° counter-clockwise rotation paired with Cue A) for 160 trials, then Task B (30° clockwise rotation paired with Cue B) for 20 trials. During the subsequent error-clamp phase (Task N, no perturbation), three independent groups received only one cue type throughout: Cue A (blue), Cue B (yellow), or No Cue (red). Shaded areas represent ±1 SEM across participants (n=12 per group). Despite the brief training on Task B, participants expressed the memory appropriate to the presented cue, indicating successful context-memory binding. However, expression was asymmetric: Cue A trials elicited stronger Task A-like behavior than Cue B trials elicited Task B-like behavior, revealing a bias toward the more extensively practiced memory.

(B and C) Model simulations with default parameters. To illustrate how existing computational frameworks might account for these patterns, we simulated (B) the COIN model (Heald et al., 2021) and (C) the contextual dual-rate model (Lee & Schweighofer, 2009) using default parameters from the original publications. Both simulations show qualitatively distinct expression patterns across cues, but the bias patterns differ from those in the behavioral data (see panel e). Simulations are shown for qualitative comparison only; parameters were not fitted to the present data.

(D) Early expression (first five error-clamp trials) for Experiment 1a. Bar plots show mean motor output normalized to each participant’s pre-clamp baseline. Experimental data (left) show stronger expression for Cue A than Cue B, confirming the bias toward the extensively practiced memory. COIN and dual-rate simulations (right) show qualitatively similar cue-specific expression, though the bias direction differs.

(E) Expression bias in Experiment 1a. Bias was computed as the difference in normalized expression between Cue A and Cue B trials (positive values = bias toward Task A). Behavioral data show a clear positive bias, reflecting the advantage of extensive practice. In contrast, both model simulations with default parameters produced a negative bias when examined over the same early trials.

(F) Experiment 1b design and behavioral results. Participants learned both Task A and Task B for 160 trials each (equal practice). During the error-clamp phase, three independent groups received Cue A (blue), Cue B (yellow), or No Cue (red) throughout. Participants again expressed cue-appropriate memories, but now the expression was biased toward the more recently learned Task B.

(G and H) Model simulations for Experiment 1b. (G) The COIN model and (H) the dual-rate model simulations with default parameters. The COIN simulation exhibits a recency bias, while the dual-rate simulation shows symmetric expression across cues.

(I) Early expression for Experiment 1b. Behavioral data (left) show stronger expression for Cue B than Cue A, confirming the recency bias. COIN simulation (right, purple) qualitatively captures this pattern, while the dual-rate simulation (right, green) shows minimal bias.

(J) Expression bias in Experiment 1b. Behavioral data show a strong negative bias, indicating a preference for the recently learned Task B. The COIN simulation with default parameters qualitatively reproduces this recency bias, whereas the dual-rate simulation shows near-zero bias. Data are represented as mean ± SEM.

Importantly, expression was not symmetric across contexts (Figure 2D). Cue A’s motor output was stronger than Cue B’s, suggesting a bias toward the more stable Task A memory. This stability-driven bias was consistent across all cue conditions, even when No Cue was presented, where expression drifted toward Task A. Our bias analysis also captured this asymmetry (Figure 2E, early bias = 0.57). To illustrate how existing computational frameworks might account for these patterns, we simulated the COIN model (using default parameters from Heald et al., 2021) and the contextual dual-rate model (using parameters from Lee & Schweighofer, 2009).^9,26 Both models produced patterns that qualitatively resembled some aspects of the observed behavior (Figures 2B and 2C). The COIN simulation exhibited an overall bias toward the more practiced memory, reflecting the probabilistic weighting of context stability during inference. The dual-rate simulation produced cue-specific expression because each cue gates its own slow process, with Cue A expressing the well-trained Task A memory and Cue B retrieving the briefly trained Task B memory. The No Cue condition in the dual-rate model expressed the baseline slow state, yielding minimal output. However, both dual-rate and COIN models showed a qualitatively negative bias (toward Task B) during the early part of the expression phase (Figure 2E).

In Experiment 1b, the design was identical to 1a, except Task B was now trained for 160 trials, making both Tasks A and B equally stable. This schedule was designed to test the role of recency when both memories are stable, and context has a low transition probability. The learning was similar in all three groups (context A, context B, and no context) for both task A (F_[2,33] = 1.05, p = 0.363) and Task B (F_[2,33] = 0.11, p = 0.897). Participants again expressed context-specific behavior during the clamp phase (Figure 2F), with a significant main effect of Cue (F_[2,33] = 20.72, p < 0.001, w² = 0.52, Effect size f = 1.13). Post-hoc tests revealed significant differences between Cue A (mean ± SE: 0.15±0.10) and both Cue B (mean ± SE: −0.56±0.05) (p_corrected < 0.001) and No Cue (mean ± SE: −0.20±0.07) (p_corrected = 0.003). Expression in Cue B was also significantly different from No Cue (p_corrected = 0.003). However, unlike 1a, the expression bias was reversed; motor output was stronger for Cue B than for Cue A or No Cue, demonstrating a clear recency bias favoring the more recently learned Task B memory (Figure 2J). We also observed a bias toward the more recent memory B across the three groups (bias = −0.56). While now, the expression of memory A with Cue A was lesser than expression in Experiment 1a (t₍₂₂₎ = 2.87, p_corrected = 0.016, 95%CI: [3.01 18.6], Cohen’s d = 1.17), expression of memory B with Cue B was way higher as compared to the same expression condition in Experiment 1a (t₍₂₂₎ = 3.84, p_corrected <0.008, 95%CI: [5.85 19.6], Cohen’s d = 1.57) (Figure 2I). This pattern supports the COIN model’s prediction that recency becomes the dominant factor in determining which memory is inferred to be active when contextual stability is matched. Bias analysis confirmed this recency-driven shift (bias = −0.62) (Figure 2J). Overall, COIN simulations (using default parameters) exhibited a pattern qualitatively similar to our experimental findings, thereby confirming our hypothesis. On the other hand, the dual-rate model, which updates each cue’s slow process independently (Figure 2H), produced symmetry in the cue-specific expressions, and there was minimal recency bias in expression (bias = −0.12) (Figure 2J).

Distinct contextual memories fail to drive expression under high transitional probability environments

While Experiments 1a and 1b showed that contextual cues could successfully gate memory expression in stable environments, we next asked whether those memories would be expressed distinctly if the cueing environment during the test became highly volatile and dynamic. In Experiment 2a, participants followed the same acquisition schedule as in Experiment 1a (extended training on Task A: 160 trials, followed by shorter training on Task B: 20 trials). This created a stable, low-volatility environment where the transitional probability of a context change was low. However, during the testing phase, the context was switched unpredictably on a trial-by-trial basis (Figure 3A), creating a volatile, high-entropy environment. This mismatch between the stable statistics of training and the volatile statistics of testing was the key manipulation. Participants showed similar magnitude of learning as in 1a (A learning: F_[3,44] = 1.11, p = 0.355, B learning: F_[3,44] = 0.43, p = 0.729). Although overall early expression showed significant cue differences (F_[2,22] = 12.89, p < 0.001, w² = 0.18, Effect size f = 1.08), all three Cue types evoked behavior in the direction of Task A, including Cue B and No Cue trials. Expression in Cue A (mean ± SE: 0.26±0.05) trials was significantly higher than in Cue B (mean ± SE: 0.11±0.02) (p_corrected = 0.005) or No Cue (mean ± SE: 0.14±0.04) trials (p_corrected = 0.005). There was no significant difference between expression under Cue B and No Cue (p_corrected = 0.07). Notably, the sign of early expression under Cue B flipped relative to 1a (Figure 3D), indicating that the Task B memory was not reliably retrieved despite being learned under a distinct cue. Instead, expression under all cues converged toward the more stable Task A, suggesting that participants relied on memory strength rather than cue identity to drive inference in the dynamic context. This reflects a failure of contextual gating: although the learned memories were distinct, the testing environment did not support their selective expression in response to the cue.

Figure 3.

Distinct contextual cues fail to drive expression in dynamic environments, which are biased by the stability and recency of competing memories

(A) Participants learned tasks under the same schedule as Experiment 1a: extensive practice on Task A (160 trials, cue A) followed by brief practice on Task B (20 trials, Cue B), both in a blocked fashion (high environmental stability). During the error-clamp phase, however, cues were presented in a randomly interleaved manner (low environmental stability), creating a mismatch between the stable statistics of training and the volatile statistics of testing. Shaded areas represent ±1 SEM (n=12). Despite the presence of distinct cues, expression converged toward the more extensively practiced Task A memory across all cue conditions, including Cue B and no-cue trials. This indicates a collapse of cue-based retrieval, with behavior dominated by memory stability.

(B) The COIN simulation with default parameters produced near-complete interference, with all cue conditions generating near-baseline output.

(C) The dual-rate simulation maintained strong cue-specific expression, as each cue continues to gate its associated slow process regardless of environmental volatility. Both simulations are shown for qualitative comparison only; parameters were not fitted to the present data.

(D) Early expression (first five error-clamp trials) for Experiment 2a. Behavioral data (left) show that all cue conditions—including Cue B and No Cue—produced motor output biased toward Task A. This graded, non-contextual pattern contrasts with the model simulations: COIN (center) produced uniformly low output, while dual-rate (right) maintained cue-specific expression. Neither simulation captured the graded bias observed in humans.

(E) Expression bias in Experiment 2a. Behavioral data show a strong positive bias, reflecting the dominance of the extensively practiced memory of Task A. COIN and dual-rate simulations with default parameters showed minimal bias.

(F) Experiment 2b design and behavioral results. Participants learned both Task A and Task B for 160 trials each (equal practice) in a blocked fashion (high environmental stability). As in Experiment 2a, the error-clamp phase presented cues in a randomly interleaved manner (low environmental stability). Behavioral data show that expression converged toward the more recently learned Task B memory across all cue conditions, including Cue A and no-cue trials. Again, cue-based retrieval collapsed, with behavior dominated by recency.

(G) The COIN model and (H) the dual-rate model simulations with default parameters. The COIN simulation produced a small, short-lived recency bias in early trials. The dual-rate simulation maintained cue-specific expression throughout with minimal bias.

(I) Early expression for Experiment 2b. Behavioral data (left) show that all cue conditions produced motor output biased toward Task B. This graded, non-contextual pattern was not captured qualitatively by either model: COIN (center) showed only a weak recency bias but minimal overall bias, while dual-rate (right) maintained cue-specific expression.

(J) Expression bias in Experiment 2b. Behavioral data show a strong negative bias, reflecting dominance of the recently learned memory. COIN simulations showed a small negative bias in early trials but minimal overall bias. Dual-rate simulations showed near-zero bias. Data are represented as mean ± SEM.

To assess interference, we compared expression with the performance in Experiment 1a, where only one cue was provided. We have found that expression in both cues A (t₍₂₂₎ = 2.91, p_corrected = 0.016, 95%CI: [2.19 13.1], Cohen’s d = 1.19) and B (t₍₂₂₎ = −2.48, p_corrected = 0.027, 95%CI: [-13.6 -1.22], Cohen’s d = −1.01) is reduced when cues were presented randomly. There was no significant difference between No Cue expression across both experiments (t₍₂₂₎ = 0.18, p_corrected = 0.859, 95%CI: [-4.97 5.91], Cohen’s d = 0.07). Notably, there was a greater bias toward more stable memory (early bias = 0.94) than in Experiment 1a (Figure 3E).

In Experiment 2b, we asked whether this failure was due to the weak encoding of Task B. Here, both Task A and B were trained for 160 trials (as in 1b), and test cues were again interleaved. Learning of task A and Task B was similar to that in Experiment 1b (A learning: F_[3,44] = 2.10, p = 0.113, B learning: F_[3,44] = 0.89, p = 0.454) (Figure 3F). Similar to Experiment 2a, early expression differed across cues (F_[2,22] = 12.37, p < 0.001, w² = 0.27, Effect size f = 1.06). Still, in contrast to 1b, all cue types now evoked behavior in the direction of Task B. Expression in Cue B (mean ± SE: −0.38±0.04) trials was significantly higher than that in Cue A (mean ± SE: −0.17±0.04) (p_corrected = 0.002) or No Cue (mean ± SE: −0.24±0.04) trials (p_corrected = 0.004). There was no significant difference between expression under Cue A and No Cue (p_corrected = 0.153).

The sign of early expression under Cue A flipped relative to 1b (Figure 3I), and even No Cue trials aligned with Task B, indicating that recency, and not cue identity, governed retrieval. We have found that expression in Cue A (t₍₂₂₎ = 2.90, p_corrected = 0.016, 95%CI: [2.70 16.3], Cohen’s d = 1.18) was flipped and got reduced in Cue B (t₍₂₂₎ = −2.70, p_corrected = 0.019, 95%CI: [-9.50 -1.25], Cohen’s d = −1.10) when cues were presented randomly in comparison to Experiment 1b, where a single cue was presented. There was no significant difference between No Cue expression across both experiments (t₍₂₂₎ = 0.40, p_corrected = 0.78, 95%CI: [-4.12 6.1], Cohen’s d = 0.16). Notably, there was a greater bias toward more stable memory (early bias = −0.74) than observed in Experiment 1b. Thus, while memories were expressed in a consistent direction, this direction did not depend on the cue but on which memory was more recently experienced (Figure 3J). Notably, while expression in both experiments was biased toward a single memory, Task A in 2a and Task B in 2b, the magnitude of that expression still differed across cues. In Experiment 2a, although all three cues evoked Task A-like outputs, Cue A trials produced stronger expression than Cue B or No Cue trials. A similar pattern was held in Experiment 2b, where Cue B trials evoked more pronounced Task B behavior than the other conditions. This suggests that while cue-memory associations were not strong enough to fully gate expression direction, they still modulated the inferred probability of each memory, consistent with partial cue-based inference. These results reinforce that context recall was degraded but not completely absent in dynamic environments.

Experiments 2a and 2b reveal a critical dissociation: Although contextual memories can be acquired under stable cue-perturbation mappings, their selective expression fails when the retrieval environment is dynamic and there is a mismatch between the stable statistics of training and the volatile statistics of testing. In such cases, behavior is biased by stability or recency but not contextual, a subtle but important distinction. Participants always expressed one of the two learned memories, but this choice was dominated by stability (in 2a, bias = 0.94 toward A, Figure 3E) or recency (in 2b, bias = −0.74 toward B, Figure 3J), regardless of the cue presented.

Interestingly, COIN simulations with default parameters did not reproduce this partial retrieval. The model predicted complete interference in both 2a (Figure 3B) and 2b (Figure 3G), with all cue conditions producing baseline-level output (Figures 3E and 4J). The stability bias toward Task A seen in human data during Experiment 2a was minimal in the simulations (bias = −0.06). In the simulation of Experiment 2b, a small recency bias toward Task B was present in the early trials (bias = −0.22) but dissipated quickly, resulting in minimal overall bias (total expression bias = −0.02). This discrepancy may arise from the COIN model’s reliance on transition statistics learned during training. Because transitions were rare in the acquisition blocks, the model’s inference during the test phase remained tied to the expectation of stable contexts, even when the testing environment became dynamic.

Figure 4.

Learning in a dynamic environment leads to more flexible expression

(A) Participants in Experiment 3a learned both Task A (30° counter-clockwise rotation, Cue A) and Task B (30° clockwise rotation, Cue B) in a randomly interleaved manner for 320 trials (equal practice, low environmental stability). During the subsequent error-clamp phase, cues continued to be presented randomly (Cue A, Cue B, or No Cue). Shaded areas represent ±1 SEM (n=12). Participants exhibited clear cue-specific expression, with motor output corresponding to the memory associated with the presented cue. Unlike Experiments 1 and 2, there was no bias toward either memory, demonstrating that interleaved training promotes flexible, unbiased retrieval even in a volatile test environment. We simulated (B) the COIN model (Heald et al., 2021) and (C) the contextual dual-rate model (Lee & Schweighofer, 2009) using default parameters.

Both simulations produced cue-specific expression with minimal bias, qualitatively resembling the behavioral data.

(D) Early expression (first five error-clamp trials) for Experiment 3a. Behavioral data (left) confirm cue-specific expression with no systematic bias toward either task. COIN (center) and dual-rate (right) simulations show qualitatively similar patterns.

(E) Expression bias in Experiment 3a. Behavioral data show near-zero bias, indicating balanced expression of both memories. Both model simulations also exhibited minimal bias.

(F) Participants in Experiment 3b also learned both tasks under the same interleaved schedule (low environmental stability, equal practice). During the error-clamp phase, however, three independent groups received only one cue type throughout: Cue A (blue), Cue B (yellow), or No Cue (red). This created a mismatch between the low environmental stability of training and the high environmental stability (blocked cue presentation) of testing.

Despite this mismatch, participants in each group expressed the memory appropriate to their assigned cue, with no bias toward either task. This demonstrates that flexibility acquired through interleaved training persists even when the test environment becomes predictable. (G) The COIN model and (H) the dual-rate model simulations with default parameters. Both models produced cue-specific expression qualitatively matching the behavioral pattern.

(I) Behavioral data (left) show that each group expressed the memory corresponding to its assigned cue, with no evidence of bias. COIN (center) and dual-rate (right) simulations qualitatively reproduce this cue-dependent expression.

(J) Expression bias in Experiment 3b. Behavioral data show minimal bias across groups, confirming that interleaved training enables flexible retrieval even when test cues are presented in a blocked fashion. Both model simulations also showed near-zero bias. Data are represented as mean ± SEM.

By contrast, the contextual dual-rate model, which deterministically maps each cue to a distinct memory state, predicted strong cue-specific expression in both experiments (Figures 3C and 4H) and minimal bias (Experiment 2a, bias = 0.06; Experiment 2b, bias = −0.09) (Figures 3E and 4J), again could not qualitatively capture the observed interference. Neither model, with its default parameters, captured the graded, context-independent bias observed in human participants. This discrepancy indicates that the fixed-volatility assumption in current models may not fully capture how humans adapt their retrieval strategies in response to unexpected environmental change.

Learning in a high transitional probability environment leads to more flexible expression

The interference observed in Experiments 2a and 2b, but not in Experiments 1a and 1b, prompted us to ask whether flexibility in expression depends on the nature of the environment in which memories were acquired. Specifically, we hypothesized that learning in an environment with high context-transition probabilities might promote more adaptable inference during tests, enabling selective expression even under dynamically changing cues.

In Experiment 3a, participants learned Task A and Task B under a dynamic training environment in which cues (Cue A, Cue B, No Cue) were randomly interleaved. Crucially, they experienced an equal number of trials for both tasks (Figure 4A). Participants were able to adapt to both A (F_[1,11] = 71.75, p < 0.001, w² = 0.74) and B (F_[1,11] = 81.06, p < 0.001, w² = 0.67) perturbations without interference. The magnitude of learning by the end of training was comparable across the two tasks (t₍₁₁₎ = 0.93, p = 0.368). During the clamp phase, when contextual cues were again presented in a randomly interleaved manner, participants displayed clean cue-specific expression of the corresponding memories with no evidence of interference (F_[2,22] = 20.71, p < 0.001, w² = 0.56, effect size f = 1.36) (Figure 4D). Participants showed distinct behavior when presented with different cues (mean ± SE: Cue A=0.30±0.07, Cue B=−0.28±0.07, Cue N=−0.01±0.04; maximum p_corrected <0.003). Importantly, there was no discernible bias in expression (−0.01), consistent with the fact that both memories were equally stable and recent (Figure 4E).

These results suggest that learning under high transition probabilities facilitates the creation of cue-tagged memories that can be selectively recalled even when test cues are interleaved. Both the COIN model and the contextual dual-rate model qualitatively matched the behavioral outcome. In the COIN model, the matched structure between learning and test (i.e., dynamic cue switching in both phases) sustained the reliability of the cues, enabling accurate context inference (Figure 4B). Likewise, the dual-rate model produced the expected result because each cue consistently activated its corresponding slow process (Figure 4C). Both models also showed no bias toward any specific memory (COIN: −0.03; dual-rate: −0.02, Figure 4E).

We next asked whether memories acquired in a dynamic environment could also support selective expression when tested in a stable environment. In Experiment 3b, three separate groups learned Tasks A and B under interleaved conditions, but the test phase presented only one contextual cue per group (Cue A, Cue B, or No Cue) (Figure 4F). For Cue A, participants showed improvement over the course of training (F_[1,33] = 237.14, p < 0.001, w² = 0.72), and there was no significant difference across groups (F_[2,33] = 0.85, p = 0.438). Similarly, for Cue B, participants reduced errors over the training period (F_[1,33] = 149.68, p < 0.001, w² = 0.69), and all groups showed similar learning magnitude (F_[2,33] = 0.85, p = 0.435). Participants showed a similar learning magnitude for tasks A and B (F_[2,33] = 0.72, p = 0.494). In the clamp phase, each group expressed the memory corresponding to the cue they received (F_[2,33] = 47.75, p < 0.001, w² = 0.72, Effect size f = 1.69), indicating no interference (Figure 4I). Participants showed distinct behavior when presented with different cues (mean ± SE: Cue A=0.57±0.09, Cue B=−0.40±0.08, Cue N=−0.005±0.02; maximum p_corrected <0.001). Similar to Experiment 3a, there was minimal bias in expression (0.27), suggesting that both memories were equally stable and recent (Figure 4J).

These findings provide further support for the idea that learning in a high transitional probability environment builds more flexible and robust context-memory associations. Both COIN and dual-rate models qualitatively replicated this result: COIN because prior exposure to cue switching enabled the inference of dynamic contextual states (Figure 4G), and the dual-rate model due to its structural mapping of cue to slow state (Figure 4H). Similar to the actual behavior, both models also showed minimal bias (COIN: 0.02; dual-rate: −0.02).

Together, Experiments 3a and 3b demonstrate that training in dynamic environments enables more flexible and context-appropriate memory expression, regardless of whether the testing environment is stable or dynamic. This supports a central prediction of the COIN model: The motor system incorporates the history of contextual cues and their transition statistics into its inference about which memory to express.

Discussion

Our study provides direct behavioral evidence that transition statistics - the learned temporal structure of context switches - shape memory retrieval. Across six visuomotor adaptation experiments, we manipulated training order, stability, and entropy to test how memories of opposing perturbations are recalled under uncertainty. The results reveal that retrieval is not governed by cues alone, but by an arbitration process in which cues are weighted against priors derived from transition statistics. This principle, while demonstrated here in motor learning, extends broadly to memory systems, suggesting a domain-general mechanism of context-sensitive retrieval. These findings align with classic ideas of hippocampal indexing,²⁷ predictive coding models of memory,^28,29 and information-theoretic principles of surprise and uncertainty, situating our results within a broader theoretical landscape.^30,31,32

Stability, recency, and volatility

Blocked training established strong priors for continuity. In Experiment 1a, where one memory (Task A) was practiced extensively and the other (Task B) only briefly (∼20 trials), retrieval largely defaulted to the stable memory - the one with greater cumulative practice - even when cues signaled the alternative mapping. This indicates that even minimal exposure to Task B was sufficient to form a distinct, context-linked memory, but its expression was overshadowed by the stronger stability prior. In Experiment 1b, where stabilities were matched, retrieval was biased toward the more recent memory, underscoring that in the absence of a stability advantage, recency dominates. These patterns show that retrieval biases are lawful consequences of learned transition statistics: stability priors weight older, more experienced memories, while volatility priors bias toward more recent ones. Such biases mirror those in the broader memory literature. For instance, the recency effect - recent items being readily recalled due to lingering availability in short-term memory^33,34 - parallels the dominance of recent memories in volatile or equal-stability contexts. Conversely, the primacy effect (favoring early, well-practiced items) is analogous to stability priors weighting older memories.³⁴ Additionally, stability biases in metamemory lead people to overestimate the durability of memories (underestimating forgetting), aligning with the persistent influence of stable memories in our experiments.^35,36

By contrast, interleaved training (Experiments 3a and 3b) cultivated high-entropy priors that preserved cue-specific memory separation even in volatile test conditions. Retrieval remained highly flexible, with minimal stability or recency bias, because participants had learned to expect frequent context switches. This suggests that interleaved exposure induces a meta-learning of volatility - effectively training the learner’s inference policies to maintain multiple competing memories in readiness and to arbitrate retrieval flexibly based on context cues.

Arbitration between cues and transition priors

Together, our findings converge on a single principle: Retrieval is an arbitration between cue information and transition priors. In stable environments, priors favor continuity, yielding persistence or stability biases. When stabilities are equal, priors favor recency, yielding recency biases. When training and testing structures mismatch, priors dominate and cue-based gating collapses, producing biased but non-contextual behavior. Conversely, when volatility is high, priors flatten, allowing cues to regain control of behavior.

Empirically, when training and test structures mismatched (Experiments 2a and 2b), cue-based retrieval collapsed. Despite valid cues at test, participants defaulted almost entirely to the stable memory (Experiment 2a) or the recent memory (Experiment 2b), with contextual cues modulating only the magnitude of responses, not the direction. This demonstrates that retrieval failure arises not from an inability to encode or recall cue associations, but from a mismatch between the learned transition structure and the test environment. It reframes anterograde interference not as an encoding deficit, but as a problem of inference: strong stability or recency priors from earlier training overwhelm contradictory cue evidence when the context suddenly becomes unpredictable. In other words, what traditionally has been described as failure to learn or express a new memory due to prior learning can be recast as an arbitration issue - where robust transition priors from a stable or recent history suppress the expression of newly acquired mappings (even when cues indicate a switch), resulting in inference-based “blocking” rather than true learning failure.

This arbitration framework also helps reinterpret spontaneous recovery - where a dormant memory re-emerges after a delay or context change - as a shift in inferred transition statistics. When the environment appears stable, the system reweights older, more practiced memories with high stability priors, allowing a previously suppressed memory to resurface. Similarly, anterograde interference reflects the converse: When the context is perceived as continuous or when recent practice dominates, strong continuity or recency priors hinder the retrieval of a newer memory. This underscores how spontaneous recovery and anterograde interference phenomena can be explained by models that incorporate transition statistics to adjust memory expression under changing environmental structures. Likewise, partial retrieval effects - where cues influence the extent of expression, but not which memory is expressed (as seen in our volatile test conditions) - reflect a probabilistic weighting of multiple memories rather than an all-or-none gating. These ideas mirror latent-state inference mechanisms in memory and perception, and align with recent Bayesian models such as the COIN model^9,10,11 that jointly infer context identity and its dynamics.

The COIN model’s Bayesian framework provides a natural account of such arbitration through posterior inference: P(context|cue, prior) ∝ P(cue|context) × P(context|prior). Although the COIN model framework explains that the stability effects emerge through Bayesian weighting of transition probabilities, where high self-transition probabilities (κ ≈ 0.7) favor persistent memories. However, our simulations revealed that COIN’s default implementation could not capture the partial retrieval patterns in Experiment 2. Importantly, this failure persisted across the full parameter range tested in our sensitivity analysis (Figure S1), suggesting it reflects a structural limitation of the model rather than mis-specification of particular parameter values. This discrepancy highlights a difference between the model’s assumptions—specifically, that volatility is a fixed parameter learned during training—and human behavior, which appeared to adapt when the testing environment became unexpectedly volatile. Whether this adaptation reflects online updating of volatility estimates, changes in retrieval strategy, or other cognitive processes cannot be determined from the present data. Addressing this question will require new experimental designs and computational models specifically designed to track how volatility beliefs evolve over time.

Recent theoretical work has begun to explore how probabilistic context inference could be extended to account for a wider range of adaptation phenomena. Heald, Lengyel and Wolpert (2023), in their review of COIN in learning and memory, explicitly discuss the possibility that learners may infer not only the current context but also higher-order statistics such as the volatility of the environment.¹⁰ Similarly, hierarchical Bayesian models developed outside the motor domain have demonstrated how the brain can dynamically update its estimate of environmental volatility and adjust learning rates accordingly.^22,37,38 Shivkumar, Lengyel, and Wolpert (2025) have recently argued that such hierarchical inference may be necessary to explain curriculum effects across motor and perceptual learning, while Heald, Lengyel, and Wolpert (2023) have applied this framework to understand how the brain builds and maintains repertoires of motor memories, suggesting that extensions of this kind are a promising direction for future computational work.^10,39

In contrast, simple dual-rate state-space models⁴⁰ can approximate the empirical stability and recency biases via fast and slow learning processes, but they lack explicit representation of context and transition statistics - limiting their explanatory power. Our data suggest that retrieval phenomena such as contextual interference, cue-induced collapse, and spontaneous recovery require models that explicitly represent transition priors.

Cross-domain parallels and cognitive theory

The logic of transition-guided retrieval appears to generalize beyond motor learning. In episodic memory, for example, event boundaries (i.e., abrupt increases in volatility) segment experiences into distinct contexts and reduce interference between events.^14,21 In working memory, recall sequences naturally cluster according to learned transition probabilities,²³ paralleling the recency-weighted arbitration we observed in motor adaptation. In language acquisition, infants extract word boundaries from statistical transitions in syllables,¹⁸ and bilinguals with extensive switching experience show reduced switch costs¹⁹ - akin to our interleaved-training participants who learned to switch seamlessly. Even in perception and decision-making, adaptation slows in volatile environments,^8,22 consistent with a dampening of cue-driven updating when transitions are unpredictable.

Our results also reinforce principles such as event segmentation theory⁴¹ and the classic encoding-specificity principle.^42,43 When transitions are predictable and stable, cue-context associations are strengthened, and memory retrieval is more straightforward. When environmental entropy rises, cue efficacy declines as the system places more weight on recent experience. In essence, the brain encodes not only what cues occur, but how reliably they occur in sequence. This enables context-sensitive retrieval guided by latent statistical structure: Memory recall is tuned not just to the presence of a cue, but to the learned reliability of that cue given the history of context switches.

Neural implementation: Precision gating and memory arbitration

The interaction between contextual cues and transition statistics is likely supported by a network involving the prefrontal cortex (PFC), basal ganglia, and cerebellum, which collectively learn transitional probabilities to gate motor memory expression in the primary motor cortex (M1). The PFC is hypothesized to maintain and flexibly apply contextual priors,²⁸ the basal ganglia learns state transition statistics through reinforcement mechanisms,⁴⁴ and the cerebellum fine-tunes the predictive timing of these transitions.⁴⁵ These brain areas then bias competition between memory representations in M1, which are thought to be stored in distinct neural subspaces.²⁵ Our findings - that expression is governed by stability and recency of learned memory and collapses under statistical mismatch-support this framework, suggesting that these fronto-subcortical circuits gate memory retrieval.⁴⁶ Future studies could test these interactions using fMRI to track PFC-basal ganglia connectivity during volatility shifts, EEG to measure theta-band oscillations as a signature of context switching, or TMS to disrupt PFC or cerebellar processing and probe their causal roles in the arbitration of competing motor memories.

By demonstrating that retrieval reflects an arbitration between cues and transition priors, our study reframes memory recall as a predictive process governed by learned environmental dynamics. This principle has direct implications across domains. For example, interleaved practice (high-context variability) in skill acquisition and coaching could promote volatility-tuned retrieval policies that generalize better across changing environments, aligning with classical findings that variable practice enhances long-term adaptability. In rehabilitation settings, manipulating contextual entropy (e.g., practicing tasks in unpredictable sequences) could help patients to regain flexible switching between motor memories, potentially reducing interference in re-learning movements.

More broadly, this work contributes to a domain-general theory of memory retrieval. It argues that memory is not a static cache indexed only by cues, but rather a dynamic inference process guided by the brain’s internal model of temporal structure. Transition statistics - how often things change and in what patterns - become an integral part of the memory code. Whether in perception, action, language, or episodic recall, the same principle applies: The brain learns not only what to expect, but when to expect it-and uses this temporal knowledge to decide which memory to recall in a given moment.

Limitations of the study

Several limitations of the present study should be acknowledged, and together they define clear directions for future work. First, the order of blocked training was not counterbalanced across participants: Task A was always learned before Task B in Experiments 1 and 2. Although the reversal from a stability bias (Experiment 1a) to a recency bias (Experiment 1b) under identical task order argues against a pure primacy account, a formally counterbalanced design would provide a cleaner separation of order-related from stability-related contributions to memory expression. Second, the present study did not assess participants’ explicit awareness of the cue-rotation contingencies, nor did we collect trial-by-trial aiming reports. Visuomotor adaptation reflects both implicit recalibration and explicit re-aiming, and these processes are likely both engaged when contextual cues reliably predict perturbation direction. The relatively rapid decay of adaptation observed during the error-clamp phase is consistent with the disengagement of explicit strategies once error feedback is removed,^47,48,49 and interleaved training may provide greater opportunity to form explicit cue-rotation associations than blocked training, representing a potential alternative explanation for some effects. Future studies incorporating trial-by-trial aiming probes or post-experiment awareness questionnaires will be essential for dissociating implicit and explicit contributions to the reported effects. Third, the model simulations presented here used default parameters from the original publications and were intended as qualitative illustrations rather than formal model fits. A definitive adjudication between competing computational accounts—including whether fitted parameters could capture the graded retrieval failures in Experiments 2a and 2b—will require parameter estimation and formal model comparison procedures, which we identify as a priority for future computational work. Finally, the present experiments were conducted within a single sensorimotor domain. Whether the transition-statistics principle generalizes to episodic, working, or semantic memory systems in the manner we propose remains to be directly tested. Studies pairing motor and non-motor memory paradigms within the same participants, or tracking the neural signatures of context inference across domains, would provide the strongest test of the domain-generality of the framework.

Resource availability

Lead contact

Further information and requests for resources should be directed to and will be fulfilled by the lead contact, Neeraj Kumar (neeraj.kumar@la.iith.ac.in).

Materials availability

This study did not generate any new unique reagents.

Data and code availability

• •The datasets used and/or analyzed in the current study are available on the OSF repository (https://osf.io/g7za6).
• •This paper does not report original code.
• •Any additional information required to reanalyze the data reported in this paper is available from the lead contact upon request.

Acknowledgments

This work was supported by a DST CSRI (DST/CSRI/2021/164(C) (G)) grant to N.K. We thank the Indian Institute of Technology Hyderabad for all the institutional-level support. A.K. is currently affiliated with the Centre for Neuroscience Studies, Queen’s University, Kingston, ON, Canada.

Author contributions

Conceptualization, A.K., A.D.K., and N.K.; methodology, A.K., A.D.K., and N.K.; investigation, A.D.K. and N.K.; data curation, A.D.K., S.S., and N.K.; formal analysis, A.K., A.D.K., S.S., and N.K.; writing – original draft, A.K., A.D.K., and N.K.; writing – review and editing, A.K., A.D.K., S.S., and N.K.; visualization, A.K., A.D.K., S.S., and N.K.; supervision, A.K. and N.K.; funding acquisition, N.K.

Declaration of interests

The authors declare no competing interests.

STAR★Methods

Key resources table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Deposited data
Behavioral data	This Experiment, and Open Science Framework Repository	https://osf.io/g7za6
Software and algorithms
MATLAB (R2023a)	MathWorks	https://www.mathworks.com/
Psychtoolbox-3	Psychtoolbox	http://psychtoolbox.org/
RStudio 2023.06.1	RStudio Posit	https://www.r-project.org/
Illustrator	Adobe	https://www.adobe.com/

Experimental model and study participant details

Participants

A total of 144 healthy right-handed participants (81 men, 63 women, age [mean ± SD] = 22.24 ± 2.6 years, 12 individuals per experimental group) with normal or corrected-to-normal vision participated in the study. The participants reported no neurological disorders, cognitive impairments, or orthopedic injuries. The Edinburgh Handedness Inventory was used to evaluate the handedness of the participants.⁵⁰ Participants provided written informed consent before participating in the study in accordance with the Declaration of Helsinki, and were naive to the purpose of the study. On successful completion of the task, participants were monetarily compensated for their time. All experimental procedures were approved by the Institutional Review Board (IITH/IEC/2022/07/13).

Sensitivity power analyses were conducted using G∗Power (version 3.1.9.7) to determine the minimum detectable effect size given our sample size (N = 12 per group), significance level (α = 0.05), and desired power = 0.80. The analyses indicated that the minimum detectable effect size was f = 0.39 for within-subject comparisons and f = 0.54 for between-subject comparisons. The observed effect sizes in all experiments exceeded these thresholds, indicating that the sample size was sufficient to detect the effects reported in this study. The sample size used in this study is also consistent with prior studies investigating context-dependent visuomotor adaptation and contextual inference, which have demonstrated robust and reproducible effects using similar sample sizes.^5,9,51,52

Method details

Experimental setup

The participants sat in a dark and sound-attenuated room on a height-adjustable chair in front of a virtual reality frame setup on which a digitizing tablet was placed (GTCO CalComp). Participants made planar reaching movements on the tablet using a stylus. A high-definition display screen (1920 × 1080 Pixels, 120 Hz) was mounted on top and projected downwards onto a semi-transparent mirror. The mirror was placed between the screen and the tablet, which occluded participants’ view of their arms, and they had to rely on the cursor projected onto the mirror from the screen for indirect visual feedback of their hand (Figure 1A). The hand position was recorded at a sampling rate of 120 Hz by the digitizing tablet.

The hand-controlled yellow cursor (0.3 cm diameter) indicated the stylus position. Each trial began when the cursor entered a blue start circle (0.8 cm diameter). After 550 ms, the start circle turned green, signaling the participants to initiate a reach to the primary and secondary targets (red, diameter = 0.8 cm), which appeared simultaneously.^51,52 Participants were first required to reach the primary target (straight in front of the participant, distance: 12 cm) and then to the secondary target located 30° to the right (contextual Cue A) or to the left (contextual Cue B), at the same radial distance from the primary target. The primary reach was treated as the main task, while the secondary reach served as a contextual cue (Figure 1B).

After familiarization with the setup, instructions for the task, and a few practice trials, participants were asked to perform three consistent blocks: a baseline block (150 trials), a memory acquisition block (variable number of trials depending on the experiment), and a memory expression block (100 trials). In the baseline block, the cursor feedback was veridical to the hand movement, and it established unperturbed motor behavior and familiarized participants with the trial structure. For the first 50 trials, the secondary target was not presented, and participants had only to make the primary reach. For the subsequent 100 trials, one of the two secondary targets was also presented randomly.

Following the baseline session, the memory acquisition block was introduced, where the cursor movement was rotated relative to the hand movement during the primary reach. After the cursor reached the primary target, the rotation was removed, and the cursor moved in the same direction as the hand for the secondary reach. The location of the secondary target was linked with the direction of the perturbation imposed during primary reach. If the second target was presented on a clockwise/right side (Cue A), then the perturbation for primary reach was a 30° counterclockwise cursor rotation (Task A). If it was presented on a counterclockwise/left side (Cue B), then the cursor rotation for primary reach was 30° clockwise (Task B). This way, the secondary target acted as an explicit contextual cue about the upcoming perturbation in each trial. The number and order of these perturbation trials during the acquisition block varied across groups. The acquisition block was followed by a memory expression block (Task N) where the cursor movement from the primary reach was clamped at 0° to the target, and the movement feedback to the secondary target from the first was veridical. The secondary target was presented either on the right for Context A, on the left for Context B, the same as the memory acquisition block, or was absent (no-cue) for No Context trials. Participants were not notified about the change in the block (Figure 1B).

At the end of each trial, participants were provided feedback about performance and speed. A numerical score represented the performance/reward about the reach where 10 points were given if the cursor ended within the target circle at the end of the movement, 5 points if the cursor was within 0.25 cm from the target edge, 1 point if within 0.4 cm and 0 points was provided if the endpoint of the cursor was beyond this distance. The overall score was also presented with the cumulative sum of the points obtained. Participants were asked to maximize the score. Participants also received text on screen as “Too slow” in red if their peak velocity was less than 32 cm/s, “Good” in green if it was between 32 and 50 cm/s, and “Too Fast” in red if the peak velocity was above 50 cm/s. The points obtained did not impact the compensation provided to the participants at the end of the experiment, and the points were also not analyzed. The performance feedback was not provided during the memory expression block.

Throughout this paper, we distinguish two forms of stability. Environmental stability refers to the probability that the current context persists across trials - a property of the learning environment. Learning rates in motor adaptation adjust to such environmental volatility, accelerating when perturbations are stable and slowing when unpredictable switches occur, consistent with Bayesian inference about context dynamics.⁸ Memory stability refers to the precision, strength, and resistance to interference of a memory representation acquired through practice. Foundational work on motor consolidation has demonstrated that memories undergo stabilization over time and with extended practice, transforming from fragile states to stable states resistant to disruption.^{53,54,55,56,57} These two forms of stability are orthogonally manipulated in our experiments (see below). The COIN framework provides a unified account of how both factors influence retrieval: environmental stability shapes the transition prior, while memory stability influences the precision of the latent state estimate and thus the likelihood term during inference.

Experiment 1

The first experiment was designed to investigate whether the stability of acquired memory would affect how the memories are expressed. We hypothesized that a more stable memory would have a higher chance of being expressed. Furthermore, when multiple memories are equally stable, we expect the most recent memory to influence expression more.

Experiment 1a

In our first experiment (1a, N=36), we aimed to determine whether contextual cues can prevent interference even when one of the memories is acquired for a very short time. We manipulated memory stability by providing extensive practice on Task A (160 trials) and brief practice on Task B (20 trials), while holding environmental stability constant (both tasks were learned in a blocked, low-volatility schedule). This design allowed us to test whether a more stable memory (i.e., one with greater precision due to extended practice) would be preferentially expressed even when the sensory cue signaled the alternative memory. In three separate groups (N=12 per group), participants either received cue A, B, or no secondary target during the memory expression block (Task N).

Experiment 1b

Experiment 1b (N=36) aimed to determine whether the most recent memory would be expressed if multiple memories were equally stable. The experimental groups were similar to the first experiment, except that Task B was learned for the same number of trials as Task A (160 trials) during the acquisition block (Figure 1D).

Experiment 2

Experiment 1 established that both environmental stability (blocked training) and memory stability (practice quantity) influence retrieval in stable test environments. We next asked whether these memories would be expressed distinctly if the testing environment itself became highly volatile. Specifically, we investigated whether memories acquired under high environmental stability (blocked training) could support cue-appropriate retrieval when tested under low environmental stability (randomly interleaved cues).

Experiment 2a

In Experiment 2a (N=12), participants learned Task A and Task B under the same schedule as Experiment 1a: extensive practice on Task A (160 trials) followed by brief practice on Task B (20 trials), both in a blocked fashion. Thus, during acquisition, environmental stability was high (rare context switches) while memory stability differed between tasks (Task A was more stable than Task B). During the subsequent expression block (Task N), participants were presented with Cue A, Cue B, or No Cue trials in a randomly interleaved manner (Figure 1E). This introduced a mismatch between the high environmental stability experienced during learning and the low environmental stability (volatile cue presentations) of the test phase. We asked whether memories acquired under stable environmental statistics could be flexibly retrieved when the testing environment became unpredictable.

Experiment 2b

In this experiment (N=12), we asked whether any observed retrieval failure in Experiment 2a was attributable to the unequal memory stability of the two tasks. Participants learned Task A and Task B under the same schedule as Experiment 1b: equal practice on both tasks (160 trials each) in blocked fashion. Thus, during acquisition, environmental stability was high and memory stability was equated across tasks. As in Experiment 2a, the expression block (Task N) presented Cue A, Cue B, and No Cue trials in a randomly interleaved manner (Figure 1F). This design allowed us to isolate the effect of environmental stability mismatch while controlling for differences in memory stability.

Experiment 3

Experiments 1 and 2 demonstrated that memories acquired under high environmental stability (blocked training) are expressed with biases reflecting either memory stability differences (Experiment 1a) or recency (Experiment 1b), and that these memories fail to support cue-appropriate retrieval when the testing environment becomes volatile (Experiments 2a and 2b). In Experiment 3, we asked whether acquiring memories in a high transitional probability environment (low environmental stability - interleaved training) would promote more flexible, cue-driven retrieval regardless of the testing environment.

Experiment 3a

In Experiment 3a (N=12), participants learned Task A and Task B in a randomly interleaved manner during acquisition (320 trials, equal practice on both tasks). Thus, during acquisition, environmental stability was low (frequent context switches), while memory stability was equated across tasks (equal practice, 160 trials each). During the subsequent expression block (Task N, 100 trials), participants were presented with Cue A, Cue B, or No Cue trials in a randomly interleaved manner (Figure 1G). Here, both the learning and testing environments had low environmental stability. We asked whether learning under volatile conditions would enable participants to maintain distinct, cue-appropriate memories that could be flexibly retrieved even when the testing environment remained unpredictable.

Experiment 3b

Experiment 3b (N=36) asked whether memories acquired under low environmental stability could support cue-appropriate retrieval even when the testing environment returned to high stability. Participants learned Task A and Task B under the same interleaved schedule as Experiment 3a (320 trials, equal practice). Thus, during acquisition, environmental stability was low, and memory stability was equated across tasks. During the expression block (Task N), participants were randomly assigned to one of three groups, each receiving only a single cue type throughout: Cue A, Cue B, or No Cue (Figure 1H). This created a mismatch between the low environmental stability experienced during learning and the high environmental stability (blocked cue presentation) of the test phase.

The six experiments implement a factorial design in which two factors are independently varied: training transition structure (blocked, high environmental stability: Experiments 1a, 1b, 2a, 2b; vs. interleaved, low environmental stability: Experiments 3a, 3b) and testing transition structure (stable, between-subjects cue presentation: Experiments 1a, 1b, 3b; vs. volatile, within-subjects interleaved cue presentation: Experiments 2a, 2b, 3a). This 2 × 2 structure allows the independent and interactive contributions of training and testing statistics to be evaluated. The comparison that most cleanly isolates the effect of training structure is the contrast between Experiments 2a/2b and Experiment 3a: all three experiments used an identical volatile, within-subjects testing phase, and differed only in training schedule. Under these matched testing conditions, blocked training yielded degraded cue-based retrieval whereas interleaved training preserved it, providing the strongest evidence that training transition statistics - not testing structure - determine whether memories can be selectively expressed. The stable, between-subjects experiments (1a, 1b, 3b) served the complementary role of establishing retrieval under low-volatility conditions and characterising how stability and recency biases manifest when the test environment itself does not introduce uncertainty about context identity.

Quantification and statistical analysis

Behavioral data analysis

The data obtained were analyzed using custom MATLAB scripts. The hand position data were filtered using a low-pass Butterworth filter with a 10 Hz cut-off frequency. The speed of movement was calculated by differentiating the position data. The moment at which hand speed initially exceeded 5% of maximum movement speed was identified as the movement onset. The direction error was calculated as the angle between the line connecting the center of the start circle and the target and the line connecting the start of the movement and the hand position at peak tangential velocity.

A total of 0.24% of trials were removed due to failure to initiate movement or because data were not recorded. From the remaining trials, 0.07% were excluded due to extreme hand angles greater than ±60°. All analyses were performed on the remaining trials. No participant was excluded from the analysis.

Statistical analysis

All statistical analyses were conducted using the R programming environment. One-way analyses of variance (ANOVAs) were used to compare expression between groups in Experiments 1a, 2a, and 3b. For Experiments 1 b, 2b, and 3a, one-way repeated-measures ANOVA was used to compare within-group expression. Post hoc comparisons were conducted when suitable, and p-values were adjusted using the Benjamini-Hochberg (BH) method to account for multiple comparisons. Furthermore, independent-samples t-tests were used to perform planned contrast comparisons of expression measures between Experiment 1a and 1b, 1a and 2a, and 1b and 2b. The p-values from these tests were also adjusted using the BH correction.

Model simulations

We used the explicit cues and perturbation sequence presented across trials to simulate predictions of the COIN model according to our experimental design in all of our experiments. We ran COIN model simulations for our experiments to test whether the model’s predictions qualitatively match our experimental results (See supplementary information for the COIN model simulations). In our simulations, we used the original article’s default parameter values (noise and model parameters.^9,10,11 We also ran the Contextual Dual Rate State Space model to test whether adding context to the individual processes would lead to tagging and recall of distinct memories (See Supplemental information for the dual-rate model simulation).

All model simulations presented in this paper were performed using default parameters taken directly from the original publications (Heald et al., 2021 for the COIN model; Lee & Schweighofer, 2009 for the dual-rate model). These parameters were estimated from independent datasets and experimental paradigms and were not fitted to the data from the present experiments. The simulations are therefore intended as qualitative illustrations of how each computational framework might behave under the experimental conditions we tested, not as quantitative fits or rigorous tests of the models.⁵⁷ Comparisons between model outputs and human data should be interpreted with this limitation in mind. The primary value of these simulations lies in highlighting qualitative similarities and differences between the frameworks’ predictions and observed behavior, which can inform future modeling efforts.

To assess whether the qualitative patterns reported in the Results depend on the specific parameter choices, we conducted a sensitivity analysis for the COIN model. We varied each of the eight free parameters independently across a plausible range (50%–150% of the default values) and recomputed the predicted expression biases for each experiment. This analysis allowed us to determine whether the discrepancies between simulations and experimental data (e.g., the graded bias in Experiments 2a/2b) could be resolved by tuning parameters within physiologically meaningful bounds. Details of the sensitivity analysis are provided in Figure S1.

Transitional probability

We calculated transition probabilities directly from the trial sequences presented to participants during the acquisition block. These probabilities are objective statistics of the experimental design, reflecting the frequency with which contexts switched or remained the same across consecutive trials. For each experiment, we computed local transition probabilities (the probability of switching given the current context). The local transition probability for a given context was calculated as the number of switches away from that context, divided by the total number of trials in which that context was present and followed by another trial. In Experiments 1a and 2a, which used a blocked training schedule with 160 trials of Task A followed by 20 trials of Task B, the local transition probabilities from Task A, the probability of switching to Task B was 1/160 = 0.00625; from Task B, the probability of switching was zero as the block ended after Task B (Figure 1I). Similarly, in Experiments 1b and 2b (160 trials of Task A followed by 160 trials of Task B), the local transition probabilities were 1/160 = 0.00625 from Task A and zero from Task B (Figure 1J).

In contrast, Experiments 3a and 3b used an interleaved training schedule in which Task A and Task B trials were randomly alternated. For the specific random sequences used in our experiments (generated with a fixed random seed for reproducibility), the local transition probabilities from Task A to Task B were 0.58, and from Task B to Task A were 0.42 (Figure 1K). These values reflect the fact that on any given trial, the probability of switching to the other context was roughly equal to the probability of staying in the current context.

These design-based transition probabilities characterize the statistical structure of the learning environment in each experiment. They are identical for all participants within a given experiment (because all participants experienced the same cue sequence or sequences drawn from the same random distribution) and are independent of any computational model. They serve to quantify the volatility (environmental stability) manipulation central to our experimental design.

Bias quantification

We computed a context-specific bias for every participant to assess whether the stability and recency generated any biases during expression. For each cue (Cue A, Cue B, and the No Cue), we first obtained a pre-clamp “peak” (Peak_c) by averaging the motor output of the last five learning trials separately from Task A and Task B. We then averaged the motor output during the clamp phase to obtain the expression. Two time windows were used: for “early bias” - the mean of the first five clamp trials, capturing the initial, most rapid expression for the corresponding cue, was used, while the mean across the entire clamp block was used to calculate the total expression for each cue.

In order to match the scale of the motor output from behavior and simulation data, the learning data from participants were transformed to −1 to 1 scale by dividing the direction error by 30 (perturbation size).

For each cue c (A, B, No Cue), the fractional retention (d_c) was

$$\left\{d_c=\frac{{Expression}_c}{{Peak}_c}\right\}\text{,}$$ (Equation 1)

where d_c = 1 indicates perfect complete contextual expression and dc = 0, no expression. We then calculated the contextual bias d_AB (only concerning Cue A and Cue B):

$$\left\{ContextualBias\left(d_{AB}\right)=d_A-d_B\right\}\text{.}$$ (Equation 2)

A positive value of the bias will indicate that expression is biased toward Task A memory, whereas a negative value will indicate that bias is toward Task B memory. Both early and total expressions were computed per participant, and then the bias factor was calculated for each experiment separately for early and total trials. The early window was chosen to capture the initial expression of the retrieved motor memory immediately after entering the clamp phase, before it could be substantially influenced by decay of the memory trace or changes in contextual belief. During clamp trials, visual feedback is decoupled from the participant’s movement, eliminating sensory prediction errors. In the absence of error signals, the system receives no evidence to maintain separation between competing memories associated with different contexts. As a result, contextual beliefs may gradually collapse and memory expression can decay or become averaged across memories over the course of the clamp block.^9,10,11 The earliest clamp trials, therefore, provide the clearest measure of the initially retrieved memory state, uncontaminated by these subsequent processes.