Predictive Neural Dynamics

• Predictive Neural Dynamics are mechanisms by which biological and artificial neural systems form, transmit, and utilize predictions across multiple scales.
• They integrate hierarchical predictive coding, recurrent network architectures, and information-theoretic metrics to reduce prediction error and enable robust control.
• Recent advances apply these principles to model predictive control in robotics and AI, achieving real-time, interpretable, and adaptive system behaviors.

Predictive neural dynamics encompasses the mechanisms by which neural systems—biological or artificial—form, transmit, and utilize predictions about future states at multiple scales, from cellular electrophysiology to high-level perception and motor planning. This domain integrates models of recurrent and hierarchical neural circuits, information-theoretic quantification of prediction and error, and learning algorithms enabling robust forecasting and control. Recent research combines neural network architectures, dynamical system theory, information theory, and optimal control to dissect the roles of prediction in brain function, provide interpretable tools for neuroscience, and inspire advanced machine learning and control frameworks.

1. Theoretical Foundations: Predictive Coding and Hierarchical Neural Dynamics

At the core of predictive neural dynamics lies the predictive coding framework, formalizing perception and action as processes of hierarchical inference and prediction error minimization. The canonical architecture involves recurrent, multi-layered networks in which each layer generates top-down predictions of activity in the subordinate layer, while bottom-up signals convey discrepancies (prediction errors) (Choi et al., 2016, Choi et al., 2017, Ofner et al., 2021). Key properties include:

• Bidirectional hierarchical architectures: Higher areas send generative predictions; lower areas feed back surprise signals.
• Temporal and spatial hierarchies: Distinct layers operate at different timescales and spatial granularities, reflecting the multiscale organization of biological cortex (Choi et al., 2016, Choi et al., 2017, Hwang et al., 2017).
• Iterative inference: Network states are updated recurrently to reduce free energy or prediction error, with gradients or local Hebbian/plasticity rules guiding weight and state adaptation (Ofner et al., 2021, Hwang et al., 2017, Huang et al., 2022).

Analytical models describe explicit stability and wave propagation properties in these architectures. Mathematical results show how joint settings of bottom-up and top-down correction weights ($\alpha, \lambda$), recurrent feedback, and activation nonlinearities generate regimes of upward, downward, or stalled propagation of activity (i.e., prediction-error or signal waves), with natural parameter regions corresponding to sensory-driven, hyperprior-driven, or balanced “healthy” predictive coding (Alamia et al., 14 May 2025, Faye et al., 2023).

2. Neural and Machine Learning Models: Architectures and Algorithms

Predictive neural dynamics are instantiated in diverse model classes spanning biological plausibility and engineering utility:

• Predictive state-space models and deep RNNs: Long Short-Term Memory (LSTM) networks and Echo State Networks (ESN) have been trained to forecast spiking and bursting behavior of biological neurons as well as high-dimensional chaotic and regime-shifting systems. These architectures can anticipate both time-local fluctuations and large-scale transitions, with ESNs demonstrating capacity to predict regimes never seen in training (Plaster et al., 2019, Pershin et al., 2021).
• Hierarchical, multiscale RNNs: Models such as predictive multiple spatio-temporal scales RNN (P-MSTRNN) and Predictive Visuo-Motor Deep Dynamic Neural Network (P-VMDNN) achieve robust prediction and intention inference by aligning spatial and temporal representational hierarchies, with higher levels encoding slow, intention-like attractors and lower levels tracking fine sensory or motor detail (Choi et al., 2016, Choi et al., 2017, Hwang et al., 2017).
• Memory In Memory (MIM) networks: Directly embed time-differencing operations in recurrent blocks to handle higher-order non-stationary signals, decomposing spatio-temporal trends and enabling deep hierarchies to capture multi-scale structure (Wang et al., 2018).
• Pulse-gated and oscillatory circuits: Pulse-gated information routing, layered Hebbian circuits, and explicitly oscillatory gating mechanisms have been analyzed for their role in online AR-process prediction, emphasizing both biological plausibility and functional oscillatory multiplexing (Shao et al., 2017).
• Differentiable generalised predictive coding: Implements variational free energy objectives integrating hierarchical and dynamical predictions using deep neural parameterizations with automatic differentiation, yielding biological interpretability and scalability to nonlinear, high-dimensional tasks (Ofner et al., 2021).

3. Information-Theoretic and Empirical Quantification

Quantitative understanding of predictive neural dynamics is advanced through tools from information theory and multimodal data analysis:

• Local active information storage (AIS) and transfer entropy (TE): Core metrics for quantifying, at each time point, how much of a neural process is explainable by its own past and how much new information is transferred between processes. Positive correlation between AIS and TE at a synapse quantitatively distinguishes “predict-and-pass-predictable” from “predict-and-pass-errors” strategies (Wollstadt et al., 2022).
• Partial information decomposition (PID): Dissects unique vs. synergistic information transfer, isolating pure bottom-up versus state-dependent (prediction-error) routing (Wollstadt et al., 2022).
• Coherence analysis in brain recordings: Spatiotemporal coherence between EEG frequency bands and stimulus dynamics reveals predictive neural signatures in natural vision and language, discriminating conditions with intact versus disrupted statistical structure and mapping experience-dependent tuning of generative models (Borneman et al., 24 Dec 2025).

These frameworks are directly operationalized in experiments, including retinogeniculate synapse analyses (demonstrating predictable input transfer) and EEG–optical flow coherence studies (showing hierarchical predictive signatures in language comprehension).

4. Model Predictive Control and Engineering Applications

Predictive neural dynamics underpin advanced real-world control strategies by embedding learned neural models within model predictive control (MPC) schemes:

• Neural MPC for robotics: Deep neural networks (DNNs), including large architectures and residual MLPs, are coupled to multiple-shooting or sequential quadratic programming MPC loops. Techniques such as local Taylor expansion of the learned dynamics and batched autodiff enable real-time operation on embedded hardware, outperforming both small-model and analytical approaches in high-agility tasks (Salzmann et al., 2022).
• Mixed-integer predictive control (MIPC): Aggressively sparsified ReLU networks, found by continuous relaxation and architectural co-optimization, facilitate globally optimal planning by encoding nonlinear neural dynamics in a form directly amenable to MIP solvers, outperforming both unsparsified networks and RL baselines (Liu et al., 2023).
• Neural MPC with finite-time convergence: Neural-dynamic QP solvers (e.g., finite-time convergent neural dynamics, FTCND) can be embedded in MPC loops, achieving sub-millimeter trajectory tracking with finite-time convergence and robustness to mechanical disturbances (Su et al., 2024).
• Probabilistic and exploration-aware MPC: Reservoir computing models (ESNs) are integrated into model predictive path integral (MPPI) control schemes, achieving rapid online identification and uncertainty-driven exploration, outperforming standard QP-based MPC in nonlinear, model-uncertain settings (Inoue et al., 4 Sep 2025).

These control-theoretic advances demonstrate translation of predictive neural principles into practical engineering systems.

5. Predictive Neural Dynamics in Perception, Mental Simulation, and AI

Predictive dynamics enable the brain’s—and artificial models’—capacity for flexible simulation, planning, and “mental time travel”:

• Latent-state future prediction: Sensory-cognitive networks trained to predict the evolution of compact latent representations—especially those derived from video foundation models—best align with both human behavioral judgments and detailed primate cortical firing patterns, indicating the brain's internal models operate at the level of future latent, not raw sensory, prediction (Nayebi et al., 2023).
• Mental simulation and intention inference: Networks equipped with predictive coding and error-regression schemes perform internal generation of multi-modal trajectories and inverse inference of hidden intentions, paralleling biological mechanisms in the mirror neuron system and high-level motor control (Hwang et al., 2017).
• Robustness and denoising: Predictive coding dynamics embedded in conventional CNNs (“Predify”) provide iterative error-correcting layers that denoise representations, enhance adversarial robustness, and induce brain-like temporal inference properties (Choksi et al., 2021).

These findings constrain both neuroscience models and inspire architectures for Embodied AI, emphasizing hierarchical, temporally extended, and generative latent prediction as key organizing principles.

6. Analytical Phenomena: Wave Propagation, Stability, and Dysfunction

Explicit mathematical models describe how predictive neural dynamics support stability, wave transmission, and, by parameter sweep, various dysfunctions:

• Traveling wave and propagation failures: Systems analysis reveals parameter domains in which activity propagates up (feedforward error), down (top-down prediction), or becomes pinned, with threshold phenomena for input amplitude and duration (Alamia et al., 14 May 2025, Faye et al., 2023). Phase maps in feedback/threshold parameter space reveal “healthy,” “sensory-gated,” and “hyperprior-dominated” regimes, linking to perceptual disorders such as “blindsight,” autism, and schizophrenia.
• Oscillatory regimes and delays: Inter-layer transmission delays and the interplay of bottom-up/top-down strengths yield oscillatory phenomena observed in electrophysiological recordings (α-, β-, γ-bands) and clone features of empirical EEG/MEG wave propagation (Faye et al., 2023).
• Lateral predictive coding and response acceleration: Single-layer models show learned lateral weights drive redundancy reduction, accelerated responses to familiar inputs, and symmetry breaking, again mirroring experimentally observed cortical motifs (Huang et al., 2022).

These analyses unify dynamical systems and information processing perspectives, extending predictive coding to rigorously defined multi-scale and multi-regime settings.

7. Outlook and Implications

Predictive neural dynamics now encompass unified principles—hierarchical generative modeling, prediction error minimization, spatio-temporal and information-theoretic quantification, and optimal control—that are quantitatively realized in both biological and artificial systems. Cross-disciplinary progress continues in:

• Scaling hierarchical, multiscale architectures to real-world tasks and large-scale data.
• Unifying information-theoretic diagnostics (AIS, TE, PID) across modalities and model classes.
• Embedding explicit predictive structures in engineering systems for anticipatory, robust, and interpretable control.
• Bridging neural, behavioral, and computational axes of mental simulation, inference, and planning.
• Analytically dissecting the stability, propagation, and failure phenomena associated with parameter regimes, both for model validation and the understanding of cognitive dysfunction.

The continued interplay of theoretical, empirical, and engineering advances is expected to further clarify the neural basis and computational power of prediction across domains (Choi et al., 2016, Hwang et al., 2017, Ofner et al., 2021, Nayebi et al., 2023, Borneman et al., 24 Dec 2025, Alamia et al., 14 May 2025, Wollstadt et al., 2022, Su et al., 2024, Inoue et al., 4 Sep 2025, Liu et al., 2023, Pershin et al., 2021, Wang et al., 2018).