Cross-Frequency Coupling as a Neural Substrate for Prediction Error Evaluation: A Laminar Neural Mass Modeling Approach

Cross-frequency coupling (CFC), where brain rhythms at different speeds interact, may be the mechanism the brain uses to compare sensory input with internal predictions. Using a laminar neural mass model, the authors show that two forms of CFC—signal-envelope coupling and envelope-envelope coupling—can implement hierarchical prediction-error computation and precision-weighting. In Alzheimer's disease, disruptions in fast-spiking interneurons lead to aberrant prediction errors: inflated early on, then attenuated. Serotonergic psychedelics reduce the influence of predictions, increasing prediction-error signals. These findings suggest that CFC across multiple timescales is a key computational mechanism supporting predictive coding, with disruptions central to certain disorders.

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Abstract

Abstract Predictive coding frameworks suggest that neural computations rely on hierarchical error minimization, where sensory signals are evaluated against internal model predictions. However, the neural implementation of this inference process remains unclear. We propose that cross-frequency coupling (CFC) furnishes a fundamental mechanism for this form of inference. We first demonstrate that our previously described Laminar Neural Mass Model (LaNMM) supports two key forms of CFC: (i) Signal-Envelope Coupling (SEC), where lowfrequency rhythms modulate the amplitude envelope of higher-frequency oscillations and (ii) Envelope-Envelope Coupling (EEC), where the envelopes of slower oscillations modulate the envelopes of higher-frequency rhythms. Then, we propose that, by encoding information in signals and their envelopes, these processes instantiate a hierarchical “Comparator” mechanism at the columnar level. Specifically, SEC generates fast prediction-error signals by subtracting top-down predictions from bottom-up oscillatory envelopes, while EEC operates at slower timescales to instantiate gating—a critical computational mechanism for precision-weighting and selective information routing. To establish the face validity and clinical implications of this proposal, we model perturbations of these CFC mechanisms to investigate their roles in pathophysiological and altered neuronal function. We illustrate how, in disorders such as Alzheimer’s disease, disruptions in gamma oscillations following dysfunction in fast-spiking inhibitory interneurons impact Comparator function with an aberrant amplification of prediction errors in the early stages and a drastic attenuation in late phases of the disease. In contrast, by increasing excitatory gain, serotonergic psychedelics diminish the modulatory effect of predictions, resulting in a failure to attenuate prediction error signals (c.f., a failure of sensory attenuation). Collectively, these findings implicate cross-frequency coupling across multiple temporal scales as a key computational mechanism supporting predictive coding and suggest that disruptions in these processes play a central role in disease. Highlights Using an encoding scheme where information is encoded in signals, their envelopes, and envelopes of envelopes, we show how to implement prediction error and precision modulation in a neural mass model through cross-frequency coupling (CFC). We use the laminar neural mass model (LaNMM), which integrates Jansen-Rit and pyramidal interneuron gamma (PING) submodels to display fast and slow rhythms and provides mechanisms for a) Signal-Envelope Coupling (SEC) , where slow-wave activity modulates the amplitude envelope of fast oscillations (analogous to phase-amplitude coupling), and b) Envelope-Envelope Coupling (EEC) , where the envelopes of slower oscillations modulate the envelopes of higher-frequency rhythms. We show how to use the LaNMM to implement information-based prediction-error evaluation (as used in Active Inference and Kolmogorov Theory), computing the approximate precision-weighted difference between incoming sensory data (envelopes) and internal model predictions (signals or envelopes). We show that using these mechanisms, the Comparator mechanism can operate at multiple levels and timescales, generating fast prediction-error signals (via SEC) and slower gating signals that encode context (e.g., precision) (via EEC). Our model provides insights into the physiological and cognitive consequences of mesoscale circuital alterations in the context of predictive coding. First, we study disorders of fast-spiking interneurons, such as Alzheimer’s Disease (AD). In the early stages of AD, error evaluation and precision are disrupted (inflated error and reduced gating/weight of predictions), leading to higher prediction errors. In later stages, prediction errors are suppressed regardless of predictions or their precision. Then, we show how serotonergic psychedelics increase the effective weight of inputs and diminish that of predictions, resulting in higher prediction error signals. These observations link oscillatory mechanisms and predictive coding alterations, and potentially with the subjective phenomena in each condition—including cognitive decline in AD and hallucinatory states under psychedelics.