Adaptive behavior under partial observability depends on internal organization that carries information beyond the current observation. Drawing on Barrett and Miller's account of categorization as predictive, compressive, functionally organized, and allostatically constrained, we test whether recurrent and spiking agents develop internal states with corresponding computational properties. Agents operate in an energy-constrained foraging task requiring resource acquisition, threat avoidance, contact-dependent consumption, and regulation of an internal energy variable. In a frozen benchmark, learned agents outperform random and heuristic baselines; the trace-augmented recurrent policy is strongest overall, while spiking variants show stress-specific differences. Early internal dynamics predict later full-safe-efficient success above permutation baseline, reaching a maximum ROC-AUC of 0.802. Reduced PCA subspaces retain behaviorally relevant information. Feature-family controls show that predictive signal is distributed across trace, policy-head, internal-dynamics, observation, and allostatic variables, and low-energy state remains strongly decodable after explicit energy-related features are removed. Evaluation-time perturbations to temporal state, sensory information, operating conditions, and allostatic mechanisms alter behavior and/or internal prediction. Seed-balanced event probes show weaker but measurable information about future contact, successful consumption, and threat events, alongside strong low-energy decoding. We interpret this pattern as a computational analogue of predictive allostatic organization: distributed control regimes that are predictive, energy-sensitive, action-relevant, and partly causally involved, without claiming biological validation or discrete symbolic categories.
We propose IM-LEPP (Integrated Multimodal Latent Energy-based Predictive Processing), a hierarchical, energy-based model of multimodal cognition that extends a previously proposed single-modality model (LEPP) to integrate vision and language. Following the view that generative neural networks are effective theories of cognitive dynamics, analogous to how statistical mechanics relates to thermodynamics, IM-LEPP models cognition as latent states flowing through learned energy landscapes rather than as an account of neural circuitry. The architecture is a hub-and-spoke hierarchy, grounded in the controlled semantic cognition framework of Lambon Ralph et al., in which predictive-coding pipelines for visual objects, scenes, and linguistic units converge on a shared amodal hub modeled on the anterior temporal lobe. Each pipeline's own prediction is conditioned by, rather than overwritten by, the current hub state, preserving pipeline-specific identity while letting every prediction reflect the full multimodal context. We show this architecture gives a mechanistic account of attentional phenomena such as inattentional blindness and Necker-cube bistability, and that its structure recovers or motivates independently established findings in psycholinguistics, including surprisal theory, the N400/P600 ERP components, and garden-path reanalysis, alongside a falsifiable contrast with transformer language models on trajectory-sensitivity in next-word prediction. We also discuss data-efficient language acquisition relative to LLMs, outline a semantic/episodic memory subsystem, situate the model against predictive coding, the free-energy principle, JEPA, and Hierarchical Temporal Memory, and propose concrete experimental predictions to test its central claims Key Words: predictive processing; predictive coding; energy-based models; diffusion models; effective theory; computational neuroscience.
Predictive coding offers a powerful framework for cortical computation, yet scalable implementations that respect both Bayesian exactness and neurobiological constraints remain scarce. We bridge this gap by formally connecting predictive coding to Recursive Gaussian Processes (RGPs). RGPs employ a single Gaussian process \( g(t, \cdot) \) indexed by layer index and input value, preventing the representational collapse of standard deep Gaussian processes while allowing learnable cross-layer dependence via \( r_{1g} \). We demonstrate that RGPs intrinsically implement hierarchical Bayesian inference, uncertainty propagation, and precision-weighted prediction error. Critically, we map RGP components---the shared GP, spike-and-slab variable selection, and MCMC dynamics---onto the canonical cortical microcircuit, providing a neurobiological substrate for these computations. Drawing on the free energy principle, we show that RGP inference minimizes variational free energy, formally linking Bayesian mechanics to neuronal dynamics. Our synthesis positions RGPs as both a principled computational tool and a candidate model for the brain's predictive machinery, generating testable predictions for laminar-specific dynamics and spectral asymmetries between feedforward and feedback processing.
Predictive coding offers a powerful theory of cortical computation, but corresponding scalable algorithmic implementations for artificial intelligence have remained elusive. This paper introduces the Bayesian reflex, a computational framework that directly instantiates predictive coding through three pillars: belief maintenance via hierarchical generative models, sequential Bayesian updating via prediction-error minimization, and uncertainty-driven action via active inference. We show that recent breakthroughs---ellipsoidal decomposition for exact $i.i.d.$ sampling, recursive Gaussian processes for deep hierarchical inference, and derivative-aware Bayesian optimization---provide the missing algorithmic ingredients. The resulting framework enables mathematically principled, scalable, and brain-inspired continual learning, perception, and decision-making. We illustrate its versatility through applications ranging from climate model evaluation to prime number discovery, offering a blueprint for truly adaptive artificial intelligence.
Hierarchical predictive coding provides an interpretable framework for perception as error-driven inference in multi-layer models, while sparse coding imposes parsimonious latent representations through explicit sparsity constraints. Their combination yields hierarchical sparse predictive coding models with appealing computational and neuroscientific properties, but practical use is often limited by the cost of iterative latent inference. In such models, each input may require many recurrent refinement steps before a useful sparse representation is obtained, and this burden becomes more severe as the hierarchy deepens. We study this bottleneck by comparing training-and-inference procedures that share the same hierarchical sparse objective formulation and architecture but use different latent-inference mechanisms. The comparison includes classical iterative inference based on ISTA, an accelerated MFISTA reference, structurally informed amortized inference using a LISTA-style bottom-up encoder adapted to the hierarchical model, and a Hybrid procedure in which this fast amortized initialization is followed by a small number of corrective energy-based refinement steps. Each procedure is trained separately, allowing its inference mechanism to interact with dictionary learning and, where applicable, encoder learning. We measure the resulting reconstruction quality, sparsity, latency, and run-to-run variability across random seeds on static image benchmarks. The results show that Hybrid improves over pure amortization in the tested settings while remaining substantially faster than procedures based on long iterative inference.
We recast predictive coding as continuous-time proximal gradient descent applied to a regularized maximum-a-posteriori (MAP) objective. We study first a single-level problem and then a multi-level hierarchy. For the single-level problem, we show that proximal gradient descent is precisely a leaky firing-rate network: the membrane leak, the effective recurrent matrix, the local synaptic drive, and the static nonlinearity all follow from one optimization principle, and the resulting circuit is the one proposed by Rao and Ballard. The prior selects the nonlinearity through its proximal operator, and the likelihood precision sets the gain on the observation. For the hierarchy, we show that a classical variable-splitting relaxation of the deep MAP problem yields hierarchical predictive coding as the interconnection of local and distributed solvers. In probabilistic modeling terms, this relaxation replaces the directed generative chain by an undirected Markov random field whose node potentials are the level-wise priors. Each level then applies its own activation function, namely the proximal operator of its prior.
Dahye Kim, Bhuvan Sachdeva, Karan Uppal +3cs.CV cs.AI
While most frames in long-form video are redundant, the critical information resides in temporal surprises: moments where the actual visual features deviate from their predicted evolution. Inspired by the human brain's predictive coding, we introduce Swift Sampling, an elegant, training-free frame selection algorithm that automatically identifies high-information moments in a video. Specifically, we model a video as a differentiable trajectory in the visual latent space and compute the velocity and acceleration of its features. Then, we apply Taylor expansion to project the expected path of subsequent frames. Frames that diverge sharply from this predicted manifold are identified as temporally surprising frames and selected for sampling. Unlike prior training-free methods that rely on auxiliary networks or video-specific hyperparameter tuning, Swift Sampling is incredibly lightweight, adding only 0.02x additional computational cost over baseline making it 30x cheaper overhead than leading baselines. Across three long-video question answering benchmarks and 10 different downstream tasks, Swift Sampling outperforms uniform sampling and prior query-agnostic baselines. It is especially powerful for long videos with limited frame budgets improving accuracy by up to +12.5 points.
Mehran H. Z. Bazargani, Szymon Urbas, Adeel Razi +2stat.ML cs.LG q-bio.NC
This paper introduces an extension of generalised filtering for online applications. Generalised filtering refers to data assimilation schemes that jointly infer latent states, learn unknown model parameters, and estimate uncertainty in an integrated framework -- e.g., estimate state and observation noise -- at the same time (i.e., triple estimation). This framework appears across disciplines under different names, including variational Kalman-Bucy filtering in engineering, generalised predictive coding in neuroscience, and Dynamic Expectation Maximisation (DEM) in time-series analysis. Here, we specialise DEM for ``online'' data assimilation, through a separation of temporal scales. We describe the variational principles and procedures that allow one to assimilate data in a way that allows for a slow updating of parameters and precisions, which contextualise fast Bayesian belief updating about the dynamic hidden states. Using numerical studies, we demonstrate the validity of online DEM (ODEM) using a non-linear -- and potentially chaotic -- generative model, to show that the ODEM scheme can track the latent states of the generative process, even when its functional form differs fundamentally from the dynamics of the generative model. Framed from a neuro-mimetic predictive coding perspective, ODEM offers a biologically inspired solution to online inference, learning, and uncertainty estimation in dynamic environments.