Biological heterogeneity in Alzheimer's Disease (AD) poses a critical diagnostic challenge, particularly for traditional linear methods that fail to capture non-linear neural dynamics. To address this, we propose a diagnostic framework utilizing the Large Brain Model (LaBraM), pretrained on over 2,500 hours of EEG data. By integrating these high-dimensional latent embeddings with a non-linear Random Forest classifier, our approach effectively isolates robust disease markers. Under a rigorous subject-independent 5-fold cross-validation protocol, the method achieves an ROC-AUC of 89.36% +/- 3.49%, PR AUC of 81.45% +/- 4.43%, and Balanced Accuracy of 82.44% +/- 4.34% in distinguishing dementia patients from healthy controls. Notably, this performance uses only 8-second EEG segments, surpassing traditional spectral baselines, including band-power and parameterized oscillatory features (FOOOF). Post-hoc occlusion analysis confirms the model captures clinically validated biomarkers, specifically occipital-frontal Alpha and Theta rhythm degradation. Additional neurophysiological alignment analysis demonstrated that higher LaBraM-predicted dementia probability significantly correlated with worse cognitive performance, greater clinical severity, increased theta and alpha relative power, and higher aperiodic exponent. These findings demonstrate that deep latent representations extract clinically relevant signatures from noisy signals, enabling precise, rapid, and data-efficient diagnosis.

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