The study proposes a multimodal Bayesian homeostatic recurrent neural network (MBH-RNN) that models autonomous behavioral allostasis – the predictive regulation of nutritional status in anticipation of future needs. Extending the variational Bayesian framework to future predictive processing, the model minimizes not only current sensory prediction errors but also predicted future sensory entropy. This meta-goal drives self-organized switching between goal-directed movement (feeding) and sensory-focused rest, without explicit training or hand-coded goals. Simulation experiments in a dynamic navigation survival task demonstrate that the agent survives longer than a control setpoint model by predictively regulating its interoceptive (energy) state. The MBH-RNN architecture integrates sensorimotor and homeostatic modules with a temporal hierarchy, and its latent variables develop specialized representations for modality-specific, bimodal, and uncertainty-related information. The model provides a computational account of mode switching, linking Bayesian brain theories with homeostatic regulation and offering insights into allostatic-interoceptive brain networks.
Key Points
Behavioral allostasis involves mode switching between goal-directed movement and sensory-focused perception, driven by minimization of predicted future sensory entropy.
The MBH-RNN is a structurally and temporally hierarchical multimodal neural network based on predictive-coding-inspired variational RNNs.
The cost function for autonomous behavior includes variational free energy for the past (sensory prediction error + complexity) and a future term (predicted sensory entropy + predicted complexity), derived as a bound on future expected surprisal.
In a survival task, the allostasis model survives significantly longer than a setpoint model that uses a fixed interoceptive target (t(9)=3.38, p=0.0082).
Mode switching is characterized by shifts in which components of variational free energy are minimized: strong beliefs (“intention”) dominate during goal-directed movement, while weak beliefs (“recognition”) characterize sensory-focused rest.
Ablation analysis reveals specialized latent representations: lower-perceptual modules are modality-specific; multimodal-associative module integrates interoception with proprioception/exteroception; unexpected-uncertainty-cause module encodes the cause of sensory uncertainty; higher-cognitive module integrates multimodal information with uncertainty.
The model shows predictive interoceptive regulation: food acquisitions peak in Period III after increased cue acquisition in Period II, while the setpoint model shows monotonic declines.
Limitations include only addressing cognitive aspects of allostasis; future work should test on physical robots and explore applications to psychiatric disorders.
Concepts
Behavioral allostasis: Predictive regulation of internal state (e.g., energy) in anticipation of future needs, as opposed to reactive homeostatic setpoint maintenance. In the model, it is achieved by minimizing predicted future sensory entropy.
Bayesian brain / Free-energy principle: Agents infer causes of sensations by minimizing variational free energy (VFE), which balances sensory prediction errors (accuracy) and Kullback–Leibler divergence between posterior and prior beliefs (complexity).
Active inference: The concept that actions are generated to minimize expected free energy; here, movement is driven by strong posterior beliefs (“intentions”) that shape proprioceptive predictions.
Variational free energy for the future (VFEF): Extension of VFE to future time steps, where the sensory prediction error term is replaced by the conditional Shannon entropy of predicted sensations. Minimizing VFEF corresponds to minimizing predicted future sensory uncertainty.
PV-RNN: Predictive-coding-inspired variational recurrent neural network that learns to predict sensations by updating latent state posteriors and priors through free-energy minimization.
Mode switching: Autonomous alternation between goal-directed movement and sensory-focused rest, enabled by dynamic regulation of the precision (sigma) of posterior beliefs and the relative contribution of VFEF components.
Setpoint model: Control model where the future cost includes a negative log-likelihood for the interoceptive state relative to a fixed target of 0.0, rather than the predicted sensory entropy term.
Unexpected-uncertainty-cause module: Module that encodes perception of unexpected causes of uncertainty and generates top-down predictions of sensory uncertainty for all modalities; it responds only to actual deviations from homeostasis, not to predicted future uncertainty.
Details
Experimental Setup and Environment
The agent operates in a 2D square space ([-1.0, 1.0] \times [-1.0, 1.0]) with a food item that appears at random positions. The food’s nutritional value gradually decreases over a 100-timestep cycle, after which a new food appears at another random position. A fixed-position cue at (0.0, 0.4) provides the current food’s x‑y coordinates only when the agent approaches it. The agent receives three types of sensations: 2D x‑y body position (proprioceptive), 2D cue signal (exteroceptive, meaningful only near the cue; otherwise ((-0.8, -0.8))), and 1D energy state (interoceptive, range ([-1.0, 1.0])). Low or high interoceptive states (deviations from 0.0) add Gaussian noise to all sensory modalities, simulating homeostatic deviation. The agent dies if the interoceptive state exceeds ±1.0. Movements consume energy (decrease interoceptive state). The sensory noise (\sigma_{x,t}) is defined as a function of the interoceptive state: (\sigma_{x,t} = \gamma \left{ \frac{1}{1+e^{-20(-x_{t,\text{intero}} -0.5)}} + \frac{1}{1+e^{-20(x_{t,\text{intero}} -0.5)}} \right}), with (\gamma = \sqrt{0.1}). Energy expenditure due to movement: (EE_t = k(0.1 + MD_t)), where (MD_t) is moving distance and (k=0.013).
MBH-RNN Architecture
The MBH-RNN is built from PV-RNN modules arranged in a structural and temporal hierarchy. It comprises:
Lower-perceptual modules: Modality-specific for proprioceptive, exteroceptive, and interoceptive sensations.
Multimodal-associative module: Integrates information across modalities.
Unexpected-uncertainty-cause module: Perceives the cause of sensory uncertainty and generates top-down predictions of sensory uncertainty for all modalities.
Higher-cognitive module: Integrates multimodal information with uncertainty (homeostatic context) and controls goal-directed behavior.
Temporal hierarchy is implemented via multiple timescale RNN (MT-RNN): higher-level modules (higher-cognitive, multimodal-associative, unexpected-uncertainty-cause) have slower neural dynamics ((\tau = 4) or (8) or (8)/(16)) than lower perceptual modules ((\tau = 2) or (4)). Each module contains deterministic recurrent states (\mathbf{d}_t^{(m)}) and probabilistic latent states (\mathbf{z}t^{(m)}) (multivariate Gaussian with diagonal covariance). Latent states represent Bayesian beliefs about causes of sensations or uncertainty. Priors (p(\mathbf{z}t^{(m)}|\mathbf{d}{t-1}^{(m)})) are generated from previous deterministic states; posteriors (q(\mathbf{z}t^{(m)}|\mathbf{e}{t:T})) are determined by backpropagated errors (\mathbf{e}{t:T}).
Prediction generation is top-down: mean predictions (\hat{\mathbf{x}}t) for each sensation are generated from the corresponding lower-perceptual module (using tanh activation). Sensory uncertainty predictions (\hat{\boldsymbol{\sigma}}{x,t}) for all sensations are generated from the unexpected-uncertainty-cause module (exponential activation). The higher-cognitive module acts as the information hub, dissociating sensorimotor from homeostatic processing.
The diagram below illustrates the information flow among modules.
Rendering diagram…
Learning Procedure
Learning uses random exploration data collected over 100 food cycles (10,000 timesteps). Movement is generated by a predefined random algorithm, and the agent is rescued when near death. The MBH-RNN with fixed synaptic weights experiences the sensations and learns to reconstruct them by minimizing the accumulated variational free energy over timesteps: (F_{\text{learning}} = \sum_{t=1}^T \text{VFE}_t), where
Synaptic weights (\boldsymbol{\omega}) and adaptive variables (\mathbf{a}_{1:T}) are updated via gradient descent with rectified Adam (learning rate 0.01, (\beta_1=0.9), (\beta_2=0.999)) over 100,000 iterations, using BPTT.
Latent Representation Analysis via Ablation
Ablation analysis removes each latent variable one-by-one and measures effects on predictions. Across 10 trained networks:
Multimodal-associative module develops bimodal and trimodal latent variables, representing interoceptive integration with proprioception and exteroception.
Unexpected-uncertainty-cause module is involved only in sensory uncertainty predictions.
Higher-cognitive module represents integration of multimodal information and sensory uncertainty.
Autonomous Behavior Generation
In the autonomous survival task, at each sensorimotor timestep (t_c), the MBH-RNN (with fixed weights) performs inference over a time window from (t_c - win_p + 1) to (t_c + win_f) through 200 iterations of prediction generation and posterior update. Past window length (win_p = 10) (or (t_c+1) if (t_c<10)); future window (win_f = 200). The cost function minimizes the accumulated past VFE and future VFEF:
Action is generated by a proportional–integral–derivative controller based on the proprioceptive prediction at current time. Sequential future predictions are regarded as planning.
Results: Mode Switching and VFE Dynamics
Example trial (Fig. 3b) shows the agent alternating between moving (feeding) and resting. From rest to movement, before movement onset ((t_c \approx -9) to 0), adjustments of postdictive posteriors in the higher-cognitive and interoceptive modules occur, accompanied by increased KLDs, driven by rising VFEF. During movement, strong postdictive posteriors (low sigma) in these modules are maintained as “intention,” enabling movement despite large sensory prediction errors (NLL) in sensorimotor modules. From movement to rest, interoceptive state is regulated to appropriate level; sigma of postdictive posteriors increases, weakening beliefs, and NLL decreases due to reduced environmental interaction.
VFE dynamics analysis (Fig. 5): During the switch to goal-directed mode, both VFEP and VFEF increase from t=0 to 10, with large KLDs in higher-cognitive and interoceptive modules driving the shift. After intention realization, VFEP decreases. During the switch to sensory-focused mode, VFEF and VFEP alternate decrease, converging to low free energy.
Comparison with Setpoint Model
The setpoint model replaces predicted sensory entropy in VFEF with predicted negative accuracy for interoceptive state relative to a fixed target of 0.0. Using the same trained networks, the allostasis model survives significantly longer (paired t-test: t(9)=3.38, p=0.0082). In the allostasis model, interoceptive level rises until Period III and returns to near Period I by Period V, with food acquisitions peaking in Period III following increased cue acquisitions in Period II. The setpoint model shows monotonic declines in interoceptive level, food acquisition, and cue acquisition across periods II–IV. The allostasis model also shows smaller energy expenditure throughout.
Contributions and Limitations
The model is the first predictive processing model of autonomous behavioral allostasis with an endogenously generated goal mechanism, integrating reward from reinforcement learning into the Bayesian brain by considering interoceptive predictive processing under increasing physiological entropy. It reconciles sensory attenuation (strong beliefs reduce prediction error responses) and sensory gating (ignoring sensory prediction errors during movement). Mode switching corresponds to meta-control over which VFE components are minimized.
Limitations: Only cognitive aspects of allostasis requiring behavioral interactions are addressed; interoceptive reflex arcs with hard-wired setpoints are not modeled. MBH-RNN is computationally complex; scalability and real-time applicability are open. Future work should test on physical robots, combine with hippocampal navigation models for cluttered environments, and explore applications to psychiatric disorders (depression, eating disorders, autism spectrum).