To model the underlying affective course of each virtual subject, we construct a latent state trajectory that evolves over a 60-day period. For subject

the daily mood state is represented as a discrete variable

where the four values correspond to Stable (0), Depressive (1), Manic (2), and Mixed (3) states. This formulation aligns with psychiatric models that conceptualize bipolar disorder as a sequence of recurrent mood episodes separated by periods of euthymia or subthreshold symptoms [23]-[27].

The latent state process serves as the generative backbone of the synthetic dataset. All behavioural features at time ( t , h ) are conditionally dependent on the latent state s t , enabling the simulator to encode clinically inspired relationships between internal affective states and observable digital phenotypes.

2.1.1. Episode Durations

Mood episodes do not last for fixed lengths; instead, their durations follow clinically observed ranges. To reflect this variability, each episode duration d s is sampled from a discrete uniform distribution conditioned on its state type:

These ranges were selected to approximate empirical psychiatric observations:

Depressiveepisodes tend to be longer and more persistent, often spanning several weeks.Manicepisodes typically exhibit shorter durations with more abrupt onset and offset.Stableperiods are interspersed throughout the illness trajectory but vary substantially in length.Mixedepisodes tend to be brief and unstable due to rapid fluctuations in symptom polarity.

By sampling durations independently across states, the simulator reproduces the heterogeneous temporal structure characteristic of bipolar disorder, including long stable stretches punctuated by irregular transitions [28]-[30].

2.1.2. Transition Probabilities

After an episode concludes, the next state is selected using a state-dependent transition distribution:

The transition matrix reflects realistic clinical phenomena:

A stableperiod is most likely to transition into a depressive episode (60%) and less frequently into a manic episode (40%).Depressive and manic episodes tend to return to stability (70%) but may progress into mixed states (30%), modelling unstable symptom evolution.Mixedstates often resolve into either pure depression or pure mania with roughly equal probability, consistent with clinical descriptions of mixed affective presentations.

These transition probabilities introduce stochasticity and cyclical patterns into the synthetic dataset, ensuring that the generative model captures the non-linear, recurrent nature of bipolar mood progression [31]-[35].

The formulation closely matches the exact sampling mechanism implemented in the code, where transitions are produced via np.random.choice with state-specific probability vectors. This one-step Markovian structure allows the simulator to encode both predictable episode patterns and random fluctuations, supporting controlled experiments in early-warning prediction [36]-[38].

To simulate realistic digital-phenotyping signatures, each subject is monitored across

measurement intervals per day, corresponding to 2-hour observational windows. For subject i , day t , and interval h ∈ { 1 , ⋯ , 12 } , we define a circadian phase variable:

which encodes intrinsic daily rhythmicity known to influence activity levels, sleep patterns, sociability, and cognitive fluctuations [39]-[41]. This circadian modulation ensures that generated behavioural features exhibit realistic time-of-day oscillations [42]-[46].

Each behavioural feature f ∈ { 1 , ⋯ , 6 } is sampled from a Gaussian distribution conditioned on the current latent mood state s t :

This formulation mirrors the structure of the implementation, where means shift with circadian rhythm and states, variances differ across states, and absolute-value transformation prevents negative behavioural quantities.

The parameters μ s ( f ) , β s ( f ) , and σ s ( f ) encode clinically plausible behavioral patterns:

Depressivestates reduce activity and sociability while increasing sleep.Manicstates elevate activity, speech and keystroke activity, and screen engagement.Stablestates produce moderate, rhythmic behavioural patterns.Mixedstates exhibit high volatility with no consistent directional shift.

Below we provide the exact feature-level distributions used in the simulator.

2.2.1. Exact Feature Distributions

StableState(0)

DepressiveState(1)

ManicState(2)

MixedState(3)

Mixed states were modelled as high-volatility regimes characterized by simultaneous depressive-like and manic-like fluctuations rather than simple random noise. Feature means were dynamically perturbed around both depressive and manic centroids within short intervals, producing rapid polarity oscillations and elevated variance. This design reflects clinical descriptions of mixed episodes as unstable affective states marked by emotional lability, sleep disruption, and psychomotor instability. Unlike the structured circadian modulations of other states, mixed states introduce random deviations:

corresponding directly to the np.random.randn() components in the implementation.

This state produces the highest behavioural unpredictability consistent with clinical observations.

2.2.2. Correlation Structure and Interpretation

To examine dependencies among features, we compute the Pearson correlation matrix over all samples (Figure 1Figure 1). The visualization reveals three important properties:

Figure 1. Correlation matrix of behavioural features and transition labels.

1) Strongcross-featurecoupling: Activity, social interaction, screen time, and keystroke dynamics covary due to shared circadian modulation and state-driven fluctuations.

2) Weaklinearrelationshipwithlabels: The switch-imminent label shows minimal linear correlation with individual features, confirming that impending transitions are not manifested through simple magnitude shifts but through temporal micro-patterns.

3) Necessityofsequencemodels: Since individual features do not exhibit clear univariate separation between classes, architectures such as transformers capable of modelling multi-feature temporal dependencies are essential for capturing prodromal behaviour.

Heatmap illustrating the Pearson correlation coefficients among four representative behavioural modalities (physical activity, sleep duration, social interaction, and voice features) and the binary switch-imminent label. Strong intra-feature correlations reflect shared behavioural drivers such as circadian rhythms and state-dependent patterns, whereas near-zero cannot correlations with the transition label indicate that single features linearly predict imminent state changes. These patterns underscore the necessity of temporal, multimodal sequence modelling for mood transition forecasting.

A primary objective of this work is to determine whether short multimodal behavioural sequences contain information predictive of an impending shift in the latent mood state. To this end, we construct a binary label sequence indicating whether a given behavioural observation belongs to the pre-transition window the interval immediately preceding a transition in the underlying affective trajectory.

2.3.1. Identification of Latent Mood Transitions

For each subject, the latent mood state is defined as a daily sequence

representing Stable, Depressive, Manic, and Mixed conditions.

A transition occurs whenever the state on day t differs from the following day:

This event marks the onset of a new mood episode. In clinical terms, such transitions often capture the beginning of depressive relapse, manic escalation, or mixed-state destabilization.

2.3.2. Mapping Behavioural Samples to Daily Indices

Each day contains

behavioural measurements, yielding a flattened index

which uniquely identifies sample n in the full time series.

Thus, a 60-day trajectory contains

measurements per subject.

This indexing scheme allows precise identification of which behavioural samples fall within the pre-transition horizon.

2.3.3. Definition of the Pre-Transition Window

To label samples that precede an episode boundary, we define a fixed prediction horizon

corresponding to the 12 samples (≈12 hours) immediately prior to a transition.

For a transition at day t \* , the set of behavioural indices belonging to the pre-transition window is:

This ensures that all samples classified as “switch imminent” strictly precede the first measurement of the next latent state, preventing any contamination with future information.

The binary label sequence is therefore defined as:

A label of y [ n ] = 1 indicates that the sample occurs within the critical pre-transition window where prodromal behavioral signatures are hypothesized to emerge.

2.3.4. Clinical Interpretation of the Label

This labelling strategy directly corresponds to a short-horizon early-warning task:

Given the last 12 behavioural observations, can we determine whether the subject is approaching a mood-state change? The choice of a 12-sample horizon is motivated by:

Evidence that prodromal signals often appear within hours rather than days,The desire to construct a challenging yet clinically meaningful prediction task,Practical considerations of continuous mobile monitoring.

The resulting labels reflect imminent risk, without incorporating any information about the future mood trajectory.

2.3.5. Distributional Properties and Predictive Difficulty

Given that transitions are relatively rare events in bipolar disorder, the fraction of samples satisfying y [ n ] = 1 is small. Consequently, the dataset is characterized by severe class imbalance, with stable windows dominating the distribution.

This imbalance is visualized in Figure 2Figure 2, which depicts the frequency of stable versus switch-imminent samples. The rarity of transitions mirrors clinical reality and underscores the difficulty of detecting early prodromal signatures from short behavioural sequences.

This figure illustrates the proportion of behavioural samples labelled as “switch imminent” (within 12 samples before a latent state transition) relative to stable samples. The distribution is highly imbalanced, with transition-proximal observations forming only a small minority. This reflects real-world affective dynamics in bipolar disorder, where long stable periods are punctuated by infrequent episode shifts, and highlights the inherent difficulty of short-horizon early-warning prediction.

Figure 2. Distribution of switch-imminent and stable samples across the full dataset.

To transform the continuous behavioural time series into a supervised learning dataset, we extract fixed-length temporal windows using a sliding-window procedure. Let

denote the six-dimensional multimodal feature vector at flattened time index n .

Each sequence X k is constructed as:

where the window length of 12 samples corresponds to approximately 12 hours of behavioural history.

The label assigned to this sequence is simply the label of its final time step:

ensuring that each input window is aligned with the outcome that follows immediately after it.

A sliding stride of 3 samples is applied:

producing overlapping windows that capture rich temporal variability while maintaining sufficient sample diversity. Over all subjects, this yields a total of:

11,800 training sequences.

This formulation provides the model with short, partially overlapping windows resembling those obtainable from continuous real-world mobile sensing streams.

To evaluate model performance, the full set of 11,800 sequences is partitioned into:

Trainingset: 80% of sequences

9440 sequences

Held-outset(“testset”): 20% of sequences

2360 sequences

To ensure unbiased evaluation, the dataset was divided into three non-overlapping subsets:

Training set: 70% of sequencesValidation set: 10% of sequencesTest set: 20% of sequences

The validation set was used exclusively for monitoring epoch-wise performance and early stopping. The test set remained completely unseen during training and was used only once for final performance reporting. All splits were stratified to preserve the class imbalance (~8% switch-imminent windows). No sequence from the test set was used during model development.

The lightweight transformer model processes each sequence X k through several stages designed to capture temporal dependencies and cross-feature interactions.

2.6.1. Input Projection

Each six-dimensional feature vector is linearly projected into a d = 64 -dimensional embedding space:

This expansion enhances the representational capacity of the model.

2.6.2. Positional Encoding

Transformers lack inherent temporal ordering, so positional information is incorporated by adding a learnable positional encoding matrix P :

ensuring the model can distinguish between early and late elements of a behavioural sequence.

2.6.3. Multi-Head Self-Attention

The core mechanism enabling temporal reasoning is self-attention, which relates each time step to every other within the window. Query, key, and value projections are computed as:

Self-attention is then computed as:

where the denominator d stabilizes gradient magnitudes. This operation enables the model to assign greater weight to specific time steps e.g., sudden behavioural fluctuations believed to precede transitions. Multiple attention heads run in parallel, allowing the model to learn diverse interaction patterns (e.g., sleep–activity coupling, keystroke–screen-time synchrony).

2.6.4. Position-Wise Feed-Forward Network

Each time step is then transformed independently through a nonlinear feed-forward block:

which increases expressiveness and filters high-level temporal patterns. Residual connections and layer normalization (implicit in the architecture) stabilize training and improve generalization.

2.6.5. Classification Head

After repeated layers of attention and feed-forward transformations, the resulting sequence representation is flattened:

and mapped to a 2-class probability distribution:

The output y ^ estimates the probability that the sequence lies within the imminent-transition window.

Because the dataset exhibits severe class imbalance only ≈8% of sequences correspond to upcoming transitions the model is optimized using weighted cross-entropy, which compensates for unequal class frequencies.

Let:

N be the total number of training sequences N c the number of sequences in class c ∈ { 0 , 1 }

Then the class weights are:

The weighted cross-entropy loss for a single sequence is:

where:

y ∈ { 0 , 1 } is the ground-truth label, p ^ is the predicted probability of the switch-imminent class.

This formulation penalizes misclassification of transition windows more strongly than misclassification of stable windows, thereby encouraging sensitivity to prodromal patterns while preserving model stability.

To evaluate whether temporal modelling provides added value beyond static feature analysis, we implemented two baseline classifiers. For each sequence, the six behavioural features were averaged across the 12-time steps, resulting in a 6-dimensional static representation.

LogisticRegression: A weighted logistic regression model was trained using the same class-weighting scheme as the transformer.

RandomForest: A Random Forest classifier (100 trees) was trained on the same aggregated features with class weighting to address imbalance.

These baselines assess whether imminent transitions can be predicted using static magnitude features alone.

To characterize the behavioural landscape of the synthetic dataset and to assess whether prodromal changes manifest in individual modalities, we examined the label-conditioned distributions of all six digital phenotyping features. Figure 3 (panels 3a-3f) presents histograms comparing each feature’s distribution during stable periods versus switch-imminent windows [47][48].

Across all modalities, distributions overlap substantially, indicating that imminent transitions cannot be identified from single-feature magnitude alone. Nevertheless, subtle yet meaningful patterns emerge. In Figure 3(a), physical activity shows a mild reduction prior to depressive shifts and increased variability preceding manic escalation, reflecting bipolar disorder’s bidirectional motor signatures. Figure 3(b) demonstrates that sleep duration is slightly elevated in transition-proximal periods consistent with depressive prodromes while also exhibiting shortened sleep associated with emerging manic states, resulting in a wide, heterogeneous distribution. The distribution of social interaction (Figure 3(c)) reveals lower central tendency and increased irregularity before transitions, reflecting behavioural withdrawal, mood lability, or agitation. Figure 3(d), representing voice-related features, shows subtle broadening of the distribution in switch-imminent windows, capturing the heightened vocal instability often observed before manic or mixed episodes. Keystroke dynamics in Figure 3(e) exhibit a notable increase in variance, consistent with psychomotor agitation or slowing, both of which may precede state shifts [49]-[51]. Finally, Figure 3(f) shows greater dispersion in screen-time behaviour, likely driven by nocturnal wakefulness, increased stimulation seeking, or pre-episode behavioural dysregulation. Altogether, these results demonstrate that while individual features do not yield strong static separation between classes, they exhibit state-dependent variability and destabilization patterns that can serve as valuable temporal cues. This reinforces the need for sequence-aware models such as transformers to capture distributed micro-dynamics rather than relying on single-snapshot measurements.

Figure 3. Label-conditioned distributions of six behavioural features arranged in two rows: Row 1 (a) Physical Activity (left), (b) Sleep Duration (middle), (c) Social Interaction (right); Row 2 (d) Voice Features (left), (e) Keystroke Dynamics (middle), and (f) Screen Time (right). Each panel compares the distribution of stable windows (label = 0) with switch-imminent windows (label = 1). Although substantial overlap exists across all modalities, the switch-imminent class exhibits distinct increases in variance, broader tails, and subtle shifts in central tendency, reflecting the destabilized behavioural patterns that often precede mood-state transitions [52]-[54]. These findings underscore the need for temporal sequence modelling to capture prodromal micro-dynamics beyond static feature magnitudes.

The training dynamics of the lightweight transformer reveal a stable and interpretable learning trajectory across 50 epochs. As illustrated in Figure 4(a) and Figure 4(b), the training loss exhibits a consistent downward trend, indicating that the model can extract meaningful temporal representations from the multimodal behavioural sequences. In contrast, the validation loss fluctuates within a narrow band around a stable plateau, reflecting the inherent noise of the synthetic environment and the difficulty of predicting rare transition events [55]-[60]. Such oscillatory behaviour is expected in settings characterized by severe class imbalance and highly overlapping feature distributions. Despite these challenges, the model does not collapse into degenerate solutions such as majority-class prediction. Instead, both training and validation accuracy remain significantly above chance, demonstrating partial but robust learnability. The divergence between the training and validation curves is moderate and stable, suggesting that the model captures generalizable dynamics without overfitting to spurious temporal patterns [61]-[63]. These results support the capacity of even a compact transformer to model subtle, temporally distributed variations associated with prodromal mood instability.

Figure 4. Training dynamics of the lightweight transformer model: (a) Training and validation loss across epochs; (b) Training and validation accuracy. Training loss decreases monotonically, while validation metrics oscillate around stable plateaus, reflecting noisy data conditions, class imbalance, and the complexity of predicting rare transition windows.

The predictive performance of the transformer on the held-out sequence set demonstrates its ability to detect non-trivial early-warning signals. The model achieves an overall accuracy of 55.38%, which exceeds the 50% chance-level baseline despite substantial distributional overlap between stable and switch-imminent windows. Sensitivity reaches 0.597, indicating that the model successfully identifies nearly 60% of imminent transitions. Specificity remains moderate at 0.550, suggesting a tendency toward false positives during behaviourally volatile but non-transitioning periods an expected artifact of noisy prodromal-like fluctuations. The F1-score of 0.174, though modest, reflects the severe imbalance of the dataset. The ROC-AUC of 0.622 demonstrates meaningful discriminative power, confirming that the model captures temporal structure beyond random guessing. The confusion matrix in Figure 5Figure 5 provides further insight into classification behaviour. True positives occur predominantly in cases where behavioural signatures express clear destabilization, whereas false negatives tend to arise in abrupt transitions lacking prodromal buildup. Conversely, false positives frequently align with irregular but non-transitioning periods, highlighting the challenge of distinguishing genuine early-warning signals from routine behavioural variability.

The ROC curve shown in Figure 6Figure 6 rises consistently above the diagonal reference line, validating that the model reliably ranks transition-proximal sequences higher than stable ones across decision thresholds. This property is especially important for clinical applications, where threshold tuning may vary according to risk tolerance or intervention requirements. Overall, the model exhibits promising discriminative capacity given the challenging nature of the task and the lightweight architecture employed.

Figure 5. Confusion matrix showing true and predicted labels for the held-out sequence set. The model captures a substantial proportion of switch-imminent windows (true positives) while generating false positives during noisy stable periods and false negatives during abrupt transitions, reflecting the inherent difficulty of early-warning prediction.

Figure 6. Receiver operating characteristic (ROC) curve for imminent-transition classification. The ROC-AUC of 0.622 demonstrates above-chance discrimination, indicating that the lightweight transformer successfully captures temporal patterns predictive of mood-state transitions.

The Logistic Regression baseline achieved an ROC-AUC of 0.541 and F1-score of 0.098.

The Random Forest achieved an ROC-AUC of 0.566 and F1-score of 0.121. Both baselines underperformed relative to the transformer (ROC-AUC 0.622), supporting the hypothesis that temporal micro-patterns contribute meaningfully to early-warning prediction.