Changes in sleep dynamics are increasingly recognized as early biomarkers of neurodegenerative diseases. We present a machine learning framework for predicting cognitive impairment (CI) from polysomnographic (PSG) recordings by jointly modeling two complementary dimensions of sleep quality: sleep depth and sleep fragmentation. Across 6,600 multi-site PSG recordings, we extract a multimodal feature space from electroencephalogram, electrocardiogram and respiratory. Sleep depth is quantified via slow-wave activity, odds ratio product, and delta power entropy, while sleep fragmentation is assessed through cyclic alternating pattern (CAP), arousal temporal distributions and respiratory event indices. To mitigate overfitting given the high feature-to-sample ratio, features were filtered using combined ANOVA and mutual information ranking, compressing the candidate pool by over 99%. Gradient-boosted trees (XGBoost) were trained with class-imbalance weighting and interpreted using Shapley additive explanations (SHAP). Our approach achieved an age-conditioned AUROC of 0.661 ± 0.037 in stratified 5-fold cross-validation and 0.636 on the official hidden validation set. For the sleep depth dimension, SHAP analysis identified cycle-dependent frontal slow-oscillation (SO) frequency as the top predictor, where reduced SO frequency was associated with increased CI risk, alongside θ-variability during non-REM stage 2 and reduced sleep spindle power across sleep thirds. As SO and sleep spindles orchestrate memory consolidation and glymphatic clearance, their reduction in frequency and power mirrors established links between slow-wave loss and early tau and amyloid pathology. Within the sleep fragmentation dimension, mean CAP A-phase and cycle durations contributed substantially to prediction, consistent with evidence that slow-wave disruption promotes shallower, more fragmented sleep associated with neurodegenerative pathology. Because sleep depth and fragmentation are physiologically coupled, their joint modeling captures complementary facets of sleep quality. Cross-site testing confirmed cohort-invariance for four of the top five features, supporting the physiological rather than site-dependent basis of these markers and the potential of combined micro-structural biomarkers for early CI screening.