## 3 Methods
### Facial Expression Recognition
This close proximity suggests a strong joint contribution of both modalities in estimating engagement, where the game score reflects direct performance feedback and EEG captures underlying cognitive attention levels. Interestingly, peaks in EEG concentration often preceded increases in game score by a few seconds, indicating that higher concentration may anticipate better gameplay outcomes. This subtle lag reinforces the temporal dynamics between cognitive state and performance, aligning with expected neurocognitive responses in adaptive learning contexts. Facial expression consistently held the lowest weight, although it showed small increases that followed game score peaks with a slight delay. This behavior likely reflects the reduced expressiveness common in neurodivergent populations such as ASD and ADHD, where emotional cues are less explicit but still present and reactive under certain conditions. The lower discriminative power of facial expressions is thus mitigated by assigning them less influence in the final engagement score while still preserving their contribution in the multimodal model. Overall, this averaged modality profile illustrates a coherent and realistic weighting strategy: performance (game score) and cognitive attention (EEG) dominate engagement estimation, while facial emotion recognition supports additional context with lower but non-negligible importance. This insight reinforces the value of dynamically adjusting the modality weights based on observed temporal responses, rather than relying on fixed assumptions. To understand how the engagement evolved throughout the gameplay, Figure 13 presents the average multimodal engagement scores calculated from the ASD and ADHD groups over a 3 min interaction involving three different games. The engagement score, ranging from 1 to 5, was dynamically computed using a weighted fusion of EEG concentration, facial expressions, and game performance metrics. The ADHD group consistently demonstrated higher levels of engagement throughout most of the session, particularly in the early phase (0-60 s) and again between 85-130 s, with pronounced peaks around 20-30 s and 90-100 s. These peaks align with BIFL's adaptive use of auditory and high-frequency visual stimuli, which appear particularly effective for individuals with ADHD--likely due to their increased responsiveness to dynamic sensory input. In contrast, the ASD group exhibited a more gradual engagement trajectory, with

Figure 12: Average modality weights over time (normalized). The BIFL system dynamically adjusted importance based on modality consistency. Game scores were consistently most informative, followed closely by EEG, with facial expressions weighted least. a modest local peak between 70-80 s where their engagement briefly approached that of the ADHD group. This suggests that, for many participants with ASD, engagement may require longer exposure to structured stimuli before meaningful responses are observed. Toward the end of the session (150-180 s), the engagement scores for both groups converged, indicating stable attention once consistent and individualized stimuli were provided. It is also important to consider the difference in sample size between groups (ADHD: 25 participants, ASD: 15 participants), which may introduce variability in engagement metrics. Naturally, larger sample sizes introduce greater variability and offer more robust insights. Nevertheless, our experimental results demonstrate that the proposed BIFL framework, combined with multimodal engagement scoring, performs effectively in real-time, real-world scenarios. These promising findings suggest that the approach is both scalable and adaptable to larger and more diverse populations. Overall, the average engagement score across the 3 min session with three games was approximately 3.9 for ADHD and 3.7 for ASD. This small difference highlights the effectiveness of the BIFL framework in supporting engagement for both groups, helping to reduce disparities through adaptive and personalized interaction strategies.