Decoding Prediction Errors in the Brain: A Laminar Neural Mass Model Approach

Introduction

In this post, we explore how a new modeling study by our research team and collaborators sheds light on the neural mechanisms of prediction error evaluation and precision weighting, offering a physiologically grounded implementation of core predictive coding principles [1].

In the predictive coding framework, the brain is viewed not as a passive receiver of sensory inputs, but as an active inferential machine. It continuously generates predictions about the world and compares these to incoming sensory data. When the actual input deviates from the expected, the mismatch—known as a prediction error—is propagated forward to update internal models [2, 3].

But what are the neural mechanisms that implement this comparison? And how are prediction errors evaluated and precision-weighted in real cortical circuits?

In this recent work, we propose a biophysical solution to this problem, grounded in cross-frequency coupling (CFC) and instantiated in a Laminar Neural Mass Model (LaNMM). By simulating how different oscillatory components interact across cortical layers, the model provides a plausible implementation of the neural process that evaluates the difference between sensory inputs and top-down predictions.

Encoding Information in Neural Oscillations

Before diving into the model, it’s worth unpacking a central idea: that information in the brain is encoded not only in spike trains but also in the amplitude and phase of neural oscillations.

This principle is analogous to amplitude modulation (AM) radio, where a low-frequency signal (e.g., voice) modulates the envelope of a high-frequency carrier wave. Similarly, in the brain, fast oscillations (e.g., gamma) can be modulated by slower rhythms (e.g., theta or alpha) to encode relevant information across timescales [4, 5]. This modulation scheme is not only theoretical: studies of speech perception have shown that slow cortical rhythms track the temporal envelope of speech, while gamma-band activity encodes its finer acoustic features [6].

Such cross-frequency interactions are widespread in the brain and are thought to coordinate local processing with global context. For example, phase–amplitude coupling has been linked to attention, memory, and sensory integration [4,5,7]. This offers a rich substrate for predictive processing: prediction errors are typically conveyed in fast (gamma, ~30–100 Hz) oscillations, while top-down predictions are communicated via slower rhythms, such as alpha (~8–12 Hz) and beta (~13–30 Hz) [3,4,8]. This spectral separation is supported by both laminar electrophysiology and modeling studies, and aligns with the anatomical distinction between feedforward and feedback pathways in cortical hierarchies.

Cross-Frequency Coupling and Predictive Coding

Cross-frequency coupling provides a plausible physiological mechanism by which the brain integrates predictions and sensory inputs across timescales—a core requirement for implementing predictive coding. Cross-frequency coupling refers to the interaction between brain rhythms of different frequencies. In particular, two forms of CFC are present in the laminar model:

• Signal-Envelope Coupling (SEC): Similar to phase-amplitude coupling, slow oscillations modulate the amplitude envelope of fast oscillations.

• Envelope-Envelope Coupling (EEC): Similar to amplitude-amplitude coupling, the envelopes of slow oscillations modulate the envelopes of faster rhythms.

  
  

We hypothesized that SEC supports the fast-time evaluation of prediction error by comparing bottom-up input (encoded in the fast oscillatory envelope) with top-down predictions (encoded in slower oscillations). EEC, on the other hand, governs slow-time gating and precision modulation, key for selective attention and sensory attenuation.

Figure 1 – SEC and EEC mechanisms (and their combination) for computation of prediction error and precision modulation. Adapted from [1].

The Laminar Neural Mass Model (LaNMM)

The LaNMM is a biophysically inspired model combining features of the Jansen-Rit model and Pyramidal-Interneuron Network Gamma (PING) oscillators, producing slow (alpha) and fast (gamma) oscillations respectively. Through dynamic interactions and parameter tuning, the model mimics electrophysiological signatures observed in laminar recordings, including signal-amplitude and envelope-amplitude interactions across frequencies [9].

Figure 2 – Laminar NMM architecture, composed of a PING population in superficial layers generating gamma activity and a Jansen-Rit population in deep layers generating alpha activity. Adapted from [1].

Computing prediction error with LaNMM

To test the hypothesis that we prediction error computation can be carried out in the LaNMM through CFC, we simulated various input-prediction scenarios:

• When predictions match the fast oscillation envelope, gamma power at the output node is suppressed (low prediction error).

• When predictions are absent or mismatched, gamma power increases (high prediction error)

  
  

This supports the idea that LaNMM can reproduce a functional computation of prediction error, akin to the difference between internal models and sensory input.

Figure 3 – Computing prediction error with LaNMM: we obtain a low prediction error for predictions matching the input (blue line), and a high error for predictions not matching the input (yellow and red lines). Adapted from [1].

Precision Modulation via Envelope-Envelope Coupling

Beyond detecting mismatches, the brain must also weigh the reliability—or precision—of prediction errors. In predictive coding theory, precision plays a critical role in determining how strongly prediction errors influence belief updating [2]. It has been proposed that precision is encoded in the gain or excitability of the neural populations that carry prediction errors, and that this gain is modulated by slower oscillatory activity, particularly in the alpha and beta bands [5, 7].

EEC mechanisms in the LaNMM capture this functionality. By injecting slow envelope signals that mimic precision modulation, the model shows how top-down control can scale the amplitude of prediction error signals—akin to Bayesian gain control. This provides a concrete, physiologically plausible mechanism for implementing context-sensitive gating and attentional filtering at the level of cortical columns.

Figure 4 – Precision modulation in LaNMM: a precision-modulation signal sent to P1 modulates the precision-weighting of the prediction error. Adapted from [1]. 

Pathophysiological Implications: Psychedelics and Alzheimer’s Disease

The Comparator function is susceptible to disruption in disease and altered states. We simulated two cases:

1. Serotonergic Psychedelics: Increased excitability (via 5-HT2A agonism) reduces alpha power (predictions) and enhances gamma power (inputs). This imbalance inflates prediction error signals, echoing the REBUS model of “relaxed priors” under psychedelics [10]. The model shows a breakdown in both error suppression (SEC) and precision gating (EEC).

2. Alzheimer’s Disease (AD): Modeled as a gradual loss of PV interneuron inhibition, AD simulations reveal a biphasic dysfunction:

   • In early stages (MCI), there’s excess gamma and alpha power, leading to exaggerated prediction errors and reduced gating.

   • In later stages (full AD), both signals collapse, leading to an overall suppression of error signaling—akin to the clinical observation of reduced mismatch negativity and P300 in AD [11].

Looking Ahead

This computational framework is a compelling step toward understanding how the brain might compute and regulate prediction errors at the circuit level. But like any model, it comes with limitations and exciting opportunities for expansion.

Currently, the model represents a single cortical column, capturing the local dynamics of cross-frequency coupling between prediction and input signals. Yet, real brains operate across distributed, hierarchical networks, where information flows through recurrent loops connecting multiple brain areas and layers. Capturing these long-range asymmetric interactions and modeling how prediction errors are routed and integrated across space will be essential for extending the model’s realism.

Still, the LaNMM lays a strong foundation. It brings predictive coding out of the abstract and into a testable, biophysically grounded framework. Going forward, researchers could expand this model into multi-column networks, explore oscillatory hierarchies, or link model outputs to empirical data from EEG, MEG, and behavior. These extensions will be crucial for validating predictive coding theories in real-world brain dynamics and for understanding how these processes go awry in disorders like Alzheimer’s, schizophrenia, or under psychedelics.

References

[1] Ruffini, G., Lopez-Sola, E., Palma, R., Sanchez-Todo, R., Vohryzek, J., Castaldo, F., & Friston, K. (2025). Cross-Frequency Coupling as a Neural Substrate for Prediction Error Evaluation: A Laminar Neural Mass Modeling Approach. bioRxiv. https://doi.org/10.1101/2025.03.19.644090

[2] Friston, K. (2009). The free-energy principle: a rough guide to the brain. Trends in Cognitive Sciences, 13(7), 293–301.

[3] Bastos, A. M., et al. (2012). Canonical microcircuits for predictive coding. Neuron, 76(4), 695–711.

[4] Buzsáki, G., & Watson, B. O. (2012). Brain rhythms and neural syntax. Dialogues in Clinical Neuroscience, 14(4), 345–367.

[5] Hyafil, A., et al. (2015). Neural cross-frequency coupling: connecting architectures, mechanisms, and functions. Trends in Neurosciences, 38(11), 725–740.

[6] Pasley, B. N., et al. (2012). Reconstructing speech from human auditory cortex. PLoS Biology, 10(1), e1001251.

[7] Jensen, O., & Mazaheri, A. (2010). Shaping functional architecture by oscillatory alpha activity: gating by inhibition. Frontiers in Human Neuroscience, 4, 186.

[8] Fries, P. (2015). Rhythms for cognition: communication through coherence. Neuron, 88(1), 220–235.

[9] Sanchez-Todo R, Bastos AM, Lopez-Sola E, Mercadal B, Santarnecchi E, Miller EK, Deco G, Ruffini G. A physical neural mass model framework for the analysis of oscillatory generators from laminar electrophysiological recordings. NeuroImage. 2023 Apr 15;270:119938.

[10] Carhart-Harris, R. L., & Friston, K. J. (2019). REBUS and the Anarchic Brain: Toward a Unified Model of the Brain Action of Psychedelics. Pharmacological Reviews, 71(3), 316–344.

[11] Pekkonen, E. (2000). Mismatch negativity in aging and in Alzheimer’s and Parkinson’s diseases. Audiology and Neurotology, 5(3-4), 216–224.