Predictive Coding

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Predictive coding studies how systems can infer, learn, or compress information by predicting incoming data and correcting mismatches. In neuroscience, hierarchical Bayesian and free-energy models use precision-weighted prediction errors to explain perception and action; in machine learning, predictive coding networks use local updates, while equilibrium propagation, feedback pathways, and amortized inference aim to make training faster and deeper. Related predictive methods forecast future inputs or code residuals for tasks such as video, language, and data compression, with evaluations spanning CIFAR and ImageNet, time-series benchmarks, and alignment to visual-cortex responses. A central tension is whether local, biologically inspired computation can match backpropagation and scale to deep or long-range tasks without giving up efficiency or hardware simplicity.

Latest papers

59 papers6 papers in the last four weeks, up 20% on the four weeks before. 0.0% of all new papers.

May 29, 2026

Augmented Lagrangian Predictive Coding

Predictive coding (PC) is a local-learning alternative to backpropagation (BP), training deep networks via local energy-minimization dynamics rather than a global backward pass. We introduce Augmented Lagrangian Predictive Coding (PC-ALM), which maintains PC's inference budget but aligns each weight update toward BP by accumulating per-layer constraint errors into a layer-local Lagrange multiplier. In linear PC networks, PC-ALM converges to an equilibrium with exact BP gradients distributed across the network via only layer-local updates. We analyze PC-ALM in nonlinear PC networks up to depth 128 and show that it matches BP performance across all width-depth regimes, notably in deep narrow networks where PC underperforms. PC-ALM introduces recurrent dynamics in each layer's activations. Compared to PC's heat flow on a scalar energy, PC-ALM dynamics are driven by dual ascent on the augmented Lagrangian. We observe "ballistic" credit propagation across very deep networks, with credit signals evenly distributed across layers, compared to PC's slow, diffusive credit propagation. Beyond the algorithm itself, the augmented Lagrangian framework offers a generalization of PC, and may yield insights into how distributed systems could compute and propagate BP-like credit signals through purely local dynamics.

Jeffrey Seely, Julian Gould

Sakana AI

Backpropagation Predictive Coding Augmented Lagrangian Method Neural Network Training Dynamics Local Learning

May 28, 2026

Supervised Training Rapidly Degrades Early Visual Cortex Alignment Across Biologically Plausible Learning Rules

Random, untrained neural networks consistently match or exceed trained networks in representational similarity to early visual cortex. This puzzling finding challenges the assumption that learning improves brain alignment. We investigate it by tracking representational similarity analysis (RSA) alignment to human fMRI data across training for four learning rules: backpropagation (BP), feedback alignment (FA), predictive coding (PC), and spike-timing-dependent plasticity (STDP). Using 720 object images from the THINGS database and fMRI data from three subjects across six visual ROIs, we measure Spearman correlations between model and brain representational dissimilarity matrices at eight training checkpoints (epochs 0-40). We find that (1) a single epoch of training reduces V1 alignment by 25-90%, depending on the learning rule; (2) backpropagation reduces V1 alignment most severely (delta r = -0.080), while predictive coding and STDP preserve substantially more (delta r ~ -0.04); and (3) a weaker, opposite tendency appears in object-selective cortex (LOC), where BP shows the largest increase in alignment during training, although the absolute change is small. These results suggest that untrained architectures capture low-level visual statistics through inductive biases alone, and that global error signals (BP) reshape early representations more aggressively than local learning rules (PC, STDP), which better preserve brain-like structure.

Nils Leutenegger

Independent Researcher, Switzerland

Neural Representation Geometry Predictive Coding Neural Processes Visual Neuroscience Biologically Plausible Learning Neural Network Training Dynamics

May 27, 2026

Exploratory Experience Shapes the Geometry of Predictive Representations

Active sensing links behavior and learning through an action-perception loop: actions determine the observations used to update internal predictive models of perception, which subsequently guide the next actions. Predictive-coding frameworks provide a natural way to model this process, since internal representations are continuously updated to predict future observations. Here, we ask how exploratory and exploitative behavioral strategies shape these internal predictive representations. We build an online learning agent in a tree-like maze with a controllable parameter regulating the balance between exploratory and exploitative regimes. The agent updates a predictive-coding-based perception model from experience generated by its own behavior. The model predicts both future maze states and reward probability, allowing the agent to select actions either by expected information gain during exploration or by predicted reward during exploitation. We show that the resulting internal predictive representations depend strongly on the agent's behavioral regime. Exploratory agents develop representations that are more spatially organized and better preserve the structure of maze transitions in latent space. In contrast, exploitative agents learn less organized representations. We then train this predictive model on natural trajectories of water-deprived mice navigating the same maze and compare the resulting representations with those learned from agent trajectories. More exploratory mice show representational geometries that closely match those of exploratory agents, whereas mice with more restricted visitation patterns resemble reward-driven, exploitative agents. Together, these findings suggest that exploration enables predictive models to form generalized internal representations by organizing latent space around both spatial location and transition context in artificial agents and animals.

Kseniia Shilova, Abdelrahman Sharafeldin, Advay Balakrishnan +1

School of Mathematics Georgia Institute of Technology Atlanta, GA 30332 · College of Computing Georgia Institute of Technology Atlanta, GA 30332

Computational Cognitive Modeling Predictive Coding RL Exploration Predictive Representation Learning State Representation Learning

May 23, 2026

Motion-Compensated Weight Compression

Neural network weights are increasingly a bottleneck for deployment, yet most compression pipelines treat layers independently and overlook cross-layer redundancy induced by function-preserving symmetries. We propose Motion-Compensated Weight Compression (MCWC), a weight-only codec that aligns permutation-symmetric blocks (e.g., hidden units and attention heads) to maximize cross-layer correspondence, turning depth into a predictable sequence. In the aligned coordinate system, MCWC uses a lightweight layer-sequential predictor with periodic keyframes and encodes only quantized prediction residuals using a learned entropy model trained under a rate distortion objective. A simple decoder reconstructs deployable weights by entropy decoding, dequantization, predictor-driven reconstruction, and inverse alignment, enabling fast weight materialization for inference. Across Transformer language modeling and vision classification, MCWC improves the rate accuracy Pareto frontier over strong quantization and learned weight-codec baselines, while maintaining competitive decode time. Ablations confirm that alignment, prediction, entropy modeling, and keyframe scheduling are each necessary for the full gains. Our code is available via https://github.com/Ism-ail11/MCWC.

Ismail Lamaakal

Multidisciplinary Faculty of Nador · Mohammed Premier University · Oujda 60000, Morocco

Predictive Coding Weight-Only Quantization Neural Network Compression

May 23, 2026

Ontology-constrained multi-LLM scoring of hypothesis support in the predictive processing literature

Fragmentation is common in interdisciplinary fields with diverse methods and theoretical commitments. Predictive coding neuroscience is a clear example: its literature spans computational theory, electrophysiology, imaging, behavior, and modeling, creating a synthesis problem that conventional meta-analysis cannot easily resolve. Here, we describe a local multi-LLM pipeline for ontology-constrained literature synthesis. The pipeline reads papers, extracts evidence, incorporates figure descriptions, assembles constrained prompts, and validates outputs against an expert glossary. We manually defined a predictive-coding glossary of thirty-six concepts grouped into three hypotheses: predictive suppression, feedforward error propagation, and ubiquity. A council of ten local language models scored 31 studies according to their agreement or disagreement with each glossary factor across local and global oddball contexts. This enabled pairwise study-agreement analysis, cross-model comparison, and three-dimensional hypothesis-space mapping. Agreement was high for some hypotheses but weaker for others, revealing structured disagreement, particularly across local versus global oddball paradigms. We further define hypothesis-space temperature, a geometric dispersion metric measuring how compactly studies occupy the hypothesis space. Temperature was lower for local oddball contexts and higher for global oddball contexts, indicating greater dispersion in the latter. The scoring geometry also allowed us to estimate vectors of change between experimental contexts. These results demonstrate that local multi-LLM councils can produce auditable disagreement measurements that map heterogeneous literatures into quantitative evidence spaces. This framework may generalize to cross-study hypothesis mapping where conventional meta-analysis lacks a common comparison space.

Hamed Nejat, Alexander Maier, Jesse Spencer-Smith +1

Department of Psychology and Vanderbilt Brain Institute, Vanderbilt University · Data Science Institute, Vanderbilt University

Ontology-Guided Information Extraction Predictive Coding Multi-LLM Collaboration

May 19, 2026

Closed-form predictive coding via hierarchical Gaussian filters

Predictive coding (PC) offers a local and biologically grounded alternative to backpropagation in the training of artificial neural networks, yet to date, it remains slower, and performance degrades sharply as network depth increases. We trace both problems to a single simplification: current PC networks fix the precision matrix to the identity, discarding precision-weighted prediction errors that the variational derivation requires to be fast, local, and Bayesian. We close this gap by expressing predictive coding networks as deep hierarchical Gaussian filters (HGFs) and restore precision-weighted message passing, yielding dynamic uncertainty estimates and Hebbian-compatible update rules at every layer. The resulting networks can simultaneously learn activations, weights, and precisions under a single free-energy objective, with no global error signal, and resolve inference without requiring iterations or automatic differentiation. On FashionMNIST, our solution approaches backpropagation in epoch-level wall-clock cost while converging in fewer epochs, and outperforms it on online, data efficiency, and concept-drift tasks. We thus establish that closed-form variational inference with online precision learning provides a tractable foundation for deep predictive coding networks, retaining biological and interpretative advantages, without requiring iterative relaxation or global error signals.

Aleksandrs Baskakovs, Sylvain Estebe, Kenneth Enevoldsen +3

Center for Humanities Computing Aarhus University Aarhus, Denmark · Interacting Minds Center Aarhus University Aarhus, Denmark

Predictive Coding Variational Inference Local Learning

May 18, 2026

Inter-LPCM: Learning-based Inter-Frame Predictive Coding for LiDAR Point Cloud Compression

Because LiDAR sensors acquire point clouds with a fixed angular resolution, the resulting data can be systematically parameterized and efficiently compressed in the spherical coordinate system. Traditional spherical coordinate-based point cloud compression methods have demonstrated strong rate-distortion (RD) performance, with the predictive geometry coding (PredGeom) method in the geometry-based point cloud compression (G-PCC) standard being a prominent example. Although PredGeom includes an inter-frame prediction mode, it relies on a simple linear model, which limits its ability to capture complex motion patterns and structural dependencies. Meanwhile, existing learning-based compression methods in the spherical domain do not exploit inter-frame correlations to reduce geometry redundancy. To address these limitations, we propose a learning-based inter-frame predictive coding method, termed Inter-LPCM. For azimuth prediction, we employ a delta coding strategy based on the predefined angular resolution. To improve radius compression, we introduce an inter-frame radius predictive (Inter-RP) model that estimates the current point's radius using neighboring points from both the current frame and the registered reference frame. In addition, we design a lightweight attention-based prediction (LAEP) model to predict elevation angles by capturing long-range geometric correlations across different coordinates. For quantization, we propose an RD-optimized method to select quantization steps in the spherical coordinate system. For entropy coding, we design distinct models for each spherical coordinate component. These models are adapted to the statistical priors of each coordinate, enabling more accurate probability estimation. Our source code is publicly available at https://github.com/SDUChangSun/Inter-LPCM

Chang Sun, Hui Yuan, Shiqi Jiang +3

School of Control Science and Engineering, Shandong University, Jinan 250061, China · Key Laboratory of Machine Intelligence and System Control, Ministry of Education, Jinan 250061, China · School of Computer Science and Technology, Shandong University, Qingdao, 266237, China +1

Point Cloud Compression Predictive Coding Airborne Laser Scanning

May 12, 2026

Understanding Sample Efficiency in Predictive Coding

Predictive Coding (PC) is an influential account of cortical learning. Much of recent work has focused on comparing PC to Backpropagation (BP) to find whether PC offers any advantages. Small scale experiments show that PC enables learning that is more sample efficient and effective in many contexts, though a thorough theoretical understanding of the phenomena remains elusive. To address this, we quantify the efficiency of learning in BP and PC through a metric called ``target alignment'', which measures how closely the change in the output of the network is aligned to the output prediction error. We then derive and empirically validate analytical expressions for target alignment in Deep Linear Networks. We show that learning in PC is more efficient than BP, which is especially pronounced in deep, narrow and pre-trained networks. We also derive exact conditions for guaranteed optimal target alignment in PC and validate our findings through experiments. We study full training trajectories of linear and non-linear models, and find the predicted benefits of PC persist in practice even when some assumptions are violated. Overall, this work provides a mechanistic understanding of the higher learning efficiency observed for PC over BP in previous works, and can guide how PC should be parametrised to learn most effectively.

Gaspard Oliviers, Elene Lominadze, Rafal Bogacz

Nuffield Department of Clinical Neurosciences, University of Oxford, United Kingdom · MRC Centre of Research Excellence in Restorative Neural Dynamics, United Kingdom

Backpropagation Predictive Coding Deep Linear Networks Neural Network Training Dynamics Data-Efficient Learning

May 10, 2026

Emergent Communication for Co-constructed Emotion Between Embodied Agents via Collective Predictive Coding

According to the theory of constructed emotion, the brain actively forms emotion categories by integrating multimodal bodily signals, and constructs emotional experiences by using these categories to predict and interpret sensory inputs. While research has advanced in modeling individual emotion construction, the social process of co-construction-how a shared understanding of emotions emerges between individuals-remains computationally underexplored. This study investigates this process by modeling emergent communication between two embodied agents using the Metropolis-Hastings Naming Game (MHNG), grounded in the Collective Predictive Coding (CPC) framework. Our experiments, using visual, auditory, and simulated interoceptive inputs, yield two main findings. First, MHNG-based communication significantly improves the alignment, clarity, and inter-agent agreement of the learned emotion categories compared to non-communicative and non-selective baselines, with the alignment effect concentrated at the symbolic layer rather than the perceptual latent representation. Second, even when the two agents have systematically divergent interoceptive dynamics, communication still produces robust categorical alignment, with distinct, category-specific reshaping patterns of each agent's emotion categories-consistent with the constructed-emotion view that interoceptive heterogeneity is constitutive of, rather than an obstacle to, shared emotional meaning. These findings provide computational support for the co-constructionist view of emotion and extend the CPC framework from physical to socially-grounded domains.

Zehang Zhang, Nguyen Le Hoang, Tadahiro Taniguchi +1

Graduate School of Engineering Science, The University of Osaka, Toyonaka 560-8531, Japan · Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

Computational Cognitive Modeling Predictive Coding Multi-Agent Communication Emergent Communication Affective Computing

May 8, 2026

Dynamic Representational Synchrony through Collective Predictive Coding: A Computational Model of Parent-Infant Homeostatic Co-Regulation

Inter-brain synchrony (IBS) observed in real-time dyadic interactions, including parent-infant exchanges, suggests that two agents can align their internal representations through interaction. Yet computational accounts of how such alignment can arise between agents that have only local sensory access and asymmetric internal knowledge remain underdeveloped. We propose a constructive model of parent-infant homeostatic co-regulation that integrates a POMDP formulation of active interoceptive inference with the Metropolis-Hastings Naming Game (MHNG) derived from the Collective Predictive Coding (CPC) hypothesis. In our model, the parent and infant agents agree on homeostatic regulatory actions for the infant's visceral state through a shared communicative variable generated by a locally computable Metropolis-Hastings probability. The parent observes the infant through body-generated exteroceptive cues, whereas the infant directly senses its own visceral state through interoception. This difference in access modality is implemented as asymmetric generative-model knowledge: the parent knows how actions transform visceral states but must learn what the infant's bodily cues indicate, whereas the infant perceives its visceral state directly but must learn how actions affect it. We quantify the degree of representational alignment using the Jensen-Shannon divergence between the two agents' latent representations. Notably, this synchrony emerged far earlier than the generative-model convergence and was maintained despite heterogeneous generative-model knowledge, indicating that it does not require fully shared world models. These findings support CPC as a candidate computational framework for explaining how dynamic representational synchrony relevant to IBS can emerge through local interactions.

Yushi Tsubamoto, Takato Horii

Graduate School of Medicine The University of Osaka 565-0871, Yamadaoka, Suita, Osaka · Graduate School of Engineering Science The University of Osaka 560-0043, Machikaneyama, Toyonaka Osaka

Computational Cognitive Modeling Predictive Coding Active Inference

May 4, 2026

Online Generalised Predictive Coding

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.

Mehran H. Z. Bazargani, Szymon Urbas, Adeel Razi +2

Insight Research Ireland Centre, UCD, Dublin, Ireland. · UCD School of Mathematics and Statistics, UCD, Belfield, Dublin, Ireland. · Turner Institute for Brain and Mental Health, School of Psychological Sciences, Monash University, Melbourne, Victoria, Australia. +5

Parameter Estimation Latent Dynamics Modeling Predictive Coding Data Assimilation Expectation-Maximization

May 4, 2026

Video Generation with Predictive Latents

Video Variational Autoencoder (VAE) enables latent video generative modeling by mapping the visual world into compact spatiotemporal latent spaces, improving training efficiency and stability. While existing video VAEs achieve commendable reconstruction quality, continued optimization of reconstruction does not necessarily translate into improved generative performance. How to enhance the diffusability of video latents remains a critical and unresolved challenge. In this work, inspired by principles of predictive world modeling, we investigate the potential of predictive learning to improve the video generative modeling. To this end, we introduce a simple and effective predictive reconstruction objective that unifies predictive learning with video reconstruction. Specifically, we randomly discard future frames and encode only partial past observations, while training the decoder to reconstruct the observed frames and predict future ones simultaneously. This design encourages the latent space to encode temporally predictive structures and build a more coherent understanding of video dynamics, thereby improving generation quality. Our model, termed Predictive Video VAE (PV-VAE), achieves superior performance on video generation, with 52% faster convergence and a 34.42 FVD improvement over the Wan2.2 VAE on UCF101. Furthermore, comprehensive analyses demonstrate that PV-VAE not only exhibits favorable scalability, with generative performance improving alongside VAE training, but also yields consistent gains in downstream video understanding, underscoring a latent space that effectively captures temporal coherence and motion priors.

Yian Zhao, Feng Wang, Qiushan Guo +4

ByteDance Seed · Tsinghua University · Peking University

Variational Autoencoders Predictive Coding Video Representation Learning Video Generation

Apr 23, 2026

Cross-Entropy Is Load-Bearing: A Pre-Registered Scope Test of the K-Way Energy Probe on Bidirectional Predictive Coding

Cacioli (2026) showed that the K-way energy probe on standard discriminative predictive coding networks reduces approximately to a monotone function of the log-softmax margin. The reduction rests on five assumptions, including cross-entropy (CE) at the output and effectively feedforward inference dynamics. This pre-registered study tests the reduction's sensitivity to CE removal using two conditions: standard PC trained with MSE instead of CE, and bidirectional PC (bPC; Oliviers, Tang & Bogacz, 2025). Across 10 seeds on CIFAR-10 with a matched 2.1M-parameter backbone, we find three results. The negative result replicates on standard PC: the probe sits below softmax (Delta = -0.082, p < 10^-6). On bPC the probe exceeds softmax across all 10 seeds (Delta = +0.008, p = 0.000027), though a pre-registered manipulation check shows that bPC does not produce materially greater latent movement than standard PC at this scale (ratio 1.6, threshold 10). Removing CE alone without changing inference dynamics halves the probe-softmax gap (Delta_MSE = -0.037 vs Delta_stdPC = -0.082). CE is a major empirically load-bearing component of the decomposition at this scale. CE training produces output logit norms approximately 15x larger than MSE or bPC training. A post-hoc temperature scaling ablation decomposes the probe-softmax gap into two components: approximately 66% is attributable to logit-scale effects removable by temperature rescaling, and approximately 34% reflects a scale-invariant ranking advantage of CE-trained representations. We use "metacognitive" operationally to denote Type-2 discrimination of a readout over its own Type-1 correctness, not to imply human-like introspective access.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Predictive Coding Confidence Estimation

Apr 22, 2026

Response time of lateral predictive coding and benefits of modular structures

Lateral predictive coding (LPC) is a simple theoretical framework to appreciate feature detection in biological neural circuits. Recent theoretical work [Huang et al., Phys.Rev.E 112, 034304 (2025)] has successfully constructed optimal LPC networks capable of extracting non-Gaussian hidden input features by imposing the tradeoff between energetic cost and information robustness, but the resulting dynamical systems of recurrent interactions can be very slow in responding to external inputs. We investigate response-time reduction in the present paper. We find that the characteristic response time of the LPC system can be minimized to closely approaching the lower-bound value without compromising the mean predictive error (energetic cost) and the information robustness of signal transmission. We further demonstrate that optimal LPC networks taking a modular structural organization with extensively reduced number of lateral interactions are equally excellent as all-to-all completely connected networks, in terms of feature detection performance, response time, energetic cost and information robustness.

Guanghui Cai, Zhen-Ye Huang, Weikang Wang +1

Institute of Theoretical Physics, Chinese Academy of Sciences, ZhongGuanCun East Road 55, Beijing 100190, China · Westlake Institute for Advanced Study, Hangzhou 310024, China · Center for Interdisciplinary Studies and Department of Physics, School of Science, Westlake University, Hangzhou 310030, China +2

Predictive Coding Modular Neural Networks

Apr 16, 2026

Lossless Compression via Chained Lightweight Neural Predictors with Information Inheritance

This paper is dedicated to lossless data compression with probability estimation using neural networks. First, we propose a probability estimation architecture based on a chain of neural predictors, so that each unit of the chain is defined as a neural network with the minimum possible number of weights, which is sufficient for efficient compression of data generated by Markov sources of a given order. We show that this architecture allows us to minimize the overall number of weights participating in the probability estimation process depending on the statistical properties of the input data. Second, in order to improve compression efficiency, we introduce an information inheritance mechanism, where the probability estimate obtained by a low-order unit is used at the next higher-order unit. Experimental results show that the proposed lossless data compressor equipped with the chained probability estimation architecture provides compression ratios close to the state-of-the-art PAC compressor. At the same time, it outperforms PAC by a factor of 1.2 to 6.3 in encoding throughput and by a factor of 2.8 to 12.3 in decoding throughput on a consumer GPU.

Yuriy Kim, Evgeny Belyaev

ITMO University, Saint-Petersburg, Russia

Predictive Coding Lossless Data Compression

Apr 14, 2026

DINO-Explorer: Active Underwater Discovery via Ego-Motion Compensated Semantic Predictive Coding

Marine ecosystem degradation necessitates continuous, scientifically selective underwater monitoring. However, most autonomous underwater vehicles (AUVs) operate as passive data loggers, capturing exhaustive video for offline review and frequently missing transient events of high scientific value. Transitioning to active perception requires a causal, online signal that highlights significant phenomena while suppressing maneuver-induced visual changes. We propose DINO-Explorer, a novelty-aware perception framework driven by a continuous semantic surprise signal. Operating within the latent space of a frozen DINOv3 foundation model, it leverages a lightweight, action-conditioned recurrent predictor to anticipate short-horizon semantic evolution. An efference-copy-inspired module utilizes globally pooled optical flow to discount self-induced visual changes without suppressing genuine environmental novelty. We evaluate this signal on the downstream task of asynchronous event triage under variant telemetry constraints. Results demonstrate that DINO-Explorer provides a robust, bandwidth-efficient attention mechanism. At a fixed operating point, the system retains 78.8% of post-discovery human-reviewer consensus events with a 56.8% trigger confirmation rate, effectively surfacing mission-relevant phenomena. Crucially, ego-motion conditioning suppresses 45.5% of false positives relative to an uncompensated surprise signal baseline. In a replay-side Pareto ablation study, DINO-Explorer robustly dominates the validated peak F1 versus telemetry bandwidth frontier, reducing telemetry bandwidth by 48.2% at the selected operating point while maintaining a 62.2% peak F1 score, successfully concentrating data transmission around human-verified novelty events.

Yuhan Jin, Nayari Marie Lessa, Mariela De Lucas Alvarez +4

Robotics Innovation Center, German Research Center for Artificial Intelligence, Bremen, Germany · Robotics Research Group, University of Bremen, Bremen, Germany · Computing Department, SENAI CIMATEC, Salvador, Brazil

Active Visual Perception Underwater Robotics Predictive Coding

Apr 13, 2026

K-Way Energy Probes for Metacognition Reduce to Softmax in Discriminative Predictive Coding Networks

We present this as a negative result with an explanatory mechanism, not as a formal upper bound. Predictive coding networks (PCNs) admit a K-way energy probe in which each candidate class is fixed as a target, inference is run to settling, and the per-hypothesis settled energies are compared. The probe appears to read a richer signal source than softmax, since the per-hypothesis energy depends on the entire generative chain. We argue this appearance is misleading under the standard Pinchetti-style discriminative PC formulation. We present an approximate reduction showing that with target-clamped CE-energy training and effectively-feedforward latent dynamics, the K-way energy margin decomposes into a monotone function of the log-softmax margin plus a residual that is not trained to correlate with correctness. The decomposition predicts that the structural probe should track softmax from below. We test this across six conditions on CIFAR-10: extended deterministic training, direct measurement of latent movement during inference, a post-hoc decoder fairness control on a backpropagation network, a matched-budget PC vs BP comparison, a five-point Langevin temperature sweep, and trajectory-integrated MCPC training. In every condition the probe sat below softmax. The gap was stable across training procedures within the discriminative PC family. Final-state and trajectory-integrated training produced probes whose AUROC_2 values differed by less than 10^-3 at deterministic evaluation. The empirical regime is small: single seed, 2.1M-parameter network, 1280 test images. We frame the result as a preprint inviting replication. We discuss conditions under which the decomposition does not apply (bidirectional PC, prospective configuration, generative PC, non-CE energy formulations) and directions for productive structural probing the analysis does not foreclose.

Jon-Paul Cacioli

Independent Researcher, Melbourne, Australia

Confidence Estimation Predictive Coding

Apr 10, 2026

Sequential KV Cache Compression via Probabilistic Language Tries: Beyond the Per-Vector Shannon Limit

Recent work on KV cache quantization, culminating in TurboQuant, has approached the Shannon entropy limit for per-vector compression of transformer key-value caches. We observe that this limit applies to a strictly weaker problem than the one that actually matters: compressing the KV cache as a sequence. The tokens stored in a KV cache are not arbitrary floating-point data -- they are samples from the exact formal language the model was trained on, and the model is by construction a near-optimal predictor of that language. We introduce sequential KV compression, a two-layer architecture that exploits this structure. The first layer, probabilistic prefix deduplication, identifies semantically equivalent shared prefixes across sessions using the trie metric d_T(s, s') = -log_2 P_M(s ^ s') from Probabilistic Language Tries (PLTs). The second layer, predictive delta coding, stores only the residual of each new KV vector from the model's own prediction of it, achieving a per-token entropy bound of H(KV_{i+1} | KV_{<=i}) <= H(token_{i+1} | token_{<=i}). We prove that at typical language model perplexity -- approximately 10-20 for fluent English text -- this bound is 3.3-4.3 bits on average per token position, compared to TurboQuant's 3 bits per vector component (with typical attention heads having 64-128 components). The theoretical compression ratio over TurboQuant is approximately 914,000x at the Shannon limit. Even at 1000x above the entropy floor -- a deliberately pessimistic worst-case overhead, two orders of magnitude above the 2-5x typical of practical source coders -- the ratio remains approximately 914x over TurboQuant, with compression improving rather than degrading as context length grows. The two layers are orthogonal and compose with existing per-vector quantization methods including TurboQuant.

Gregory Magarshak

KV-Cache Compression Memory Compression Predictive Coding

Apr 10, 2026

Across the Levels of Analysis: Explaining Predictive Processing in Humans Requires More Than Machine-Estimated Probabilities

Under the lens of Marr's levels of analysis, we critique and extend two claims about language models (LMs) and language processing: first, that predicting upcoming linguistic information based on context is central to language processing, and second, that many advances in psycholinguistics would be impossible without large language models (LLMs). We further outline future directions that combine the strengths of LLMs with psycholinguistic models.

Sathvik Nair, Colin Phillips

University of Maryland Department of Linguistics · University of Maryland Institute for Advanced Computer Studies · Oxford University Faculty of Linguistics, Philology and Phonetics

Computational Psycholinguistics Predictive Coding

Mar 24, 2026

LiZIP: An Auto-Regressive Compression Framework for LiDAR Point Clouds

The massive volume of data generated by LiDAR sensors in autonomous vehicles creates a bottleneck for real-time processing and vehicle-to-everything (V2X) transmission. Existing lossless compression methods often force a trade-off: industry standard algorithms (e.g., LASzip) lack adaptability, while deep learning approaches suffer from prohibitive computational costs. This paper proposes LiZIP, a lightweight, near-lossless zero-drift compression framework based on neural predictive coding. By utilizing a compact Multi-Layer Perceptron (MLP) to predict point coordinates from local context, LiZIP efficiently encodes only the sparse residuals. We evaluate LiZIP on the NuScenes and Argoverse datasets, benchmarking against GZip, LASzip, and Google Draco (configured with 24-bit quantization to serve as a high-precision geometric baseline). Results demonstrate that LiZIP consistently achieves superior compression ratios across varying environments. The proposed system achieves a 7.5%-14.8% reduction in file size compared to the industry-standard LASzip and outperforms Google Draco by 8.8%-11.3% across diverse datasets. Furthermore, the system demonstrates generalization capabilities on the unseen Argoverse dataset without retraining. Against the general purpose GZip algorithm, LiZIP achieves a reduction of 38%-48%. This efficiency offers a distinct advantage for bandwidth constrained V2X applications and large scale cloud archival.

Aditya Shibu, Kayvan Karim, Claudio Zito

MACS, Heriot Watt University, Dubai, United Arab Emirates

Point Cloud Compression Predictive Coding

Mar 19, 2026

Authority-Level Priors: An Under-Specified Constraint in Hierarchical Predictive Processing

Hierarchical predictive processing explains adaptive behaviour through precision-weighted inference. Explicit belief revision often fails to produce corresponding changes in stress reactivity or autonomic regulation. This asymmetry suggests the framework leaves under-specified a governance-level constraint concerning which identity-level hypotheses regulate autonomic and behavioural control under uncertainty. We introduce Authority-Level Priors (ALPs) as meta-structural constraints defining a regulatory-admissible subset (Hauth, a subset of H) of identity-level hypotheses. ALPs are not additional representational states nor hyperpriors over precision; they constrain which hypotheses are admissible for regulatory control. Precision determines influence conditional on admissibility; ALPs determine admissibility itself. This explains why explicit belief updating modifies representational beliefs while autonomic threat responses remain stable. A computational formalisation restricts policy optimisation to policies generated by authorised hypotheses, yielding testable predictions concerning stress-reactivity dynamics, recovery time constants, compensatory control engagement, and behavioural persistence. Neurobiologically, ALPs manifest through distributed prefrontal arbitration and control networks. The proposal is compatible with variational active inference and introduces no additional inferential operators, instead formalising a boundary condition required for determinate identity-regulation mapping. The model generates falsifiable predictions: governance shifts should produce measurable changes in stress-reactivity curves, recovery dynamics, compensatory cognitive effort, and behavioural change durability. ALPs are advanced as an architectural hypothesis to be evaluated through computational modelling and longitudinal stress-induction paradigms.

Marcy Palejova

Anglia Ruskin University

Predictive Coding Active Inference Computational Cognitive Modeling

Mar 18, 2026

A Synthesizable RTL Implementation of Predictive Coding Networks

Backpropagation has enabled modern deep learning but is difficult to realize as an online, fully distributed hardware learning system due to global error propagation, phase separation, and heavy reliance on centralized memory. Predictive coding offers an alternative in which inference and learning arise from local prediction-error dynamics between adjacent layers. This paper presents a digital architecture that implements a discrete-time predictive coding update directly in hardware. Each neural core maintains its own activity, prediction error, and synaptic weights, and communicates only with adjacent layers through hardwired connections. Supervised learning and inference are supported via a uniform per-neuron clamping primitive that enforces boundary conditions while leaving the internal update schedule unchanged. The design is a deterministic, synthesizable RTL substrate built around a sequential MAC datapath and a fixed finite-state schedule. Rather than executing a task-specific instruction sequence inside the learning substrate, the system evolves under fixed local update rules, with task structure imposed through connectivity, parameters, and boundary conditions. The contribution of this work is not a new learning rule, but a complete synthesizable digital substrate that executes predictive-coding learning dynamics directly in hardware.

Timothy Oh

University of California, Riverside

Neural Network Hardware Acceleration Predictive Coding Neuromorphic Computing Online Learning

Mar 12, 2026

LPC-SM: Local Predictive Coding and Sparse Memory for Long-Context Language Modeling

Most current long-context language models still rely on attention to handle both local interaction and long-range state, which leaves relatively little room to test alternative decompositions of sequence modeling. We propose LPC-SM, a hybrid autoregressive architecture that separates local attention, persistent memory, predictive correction, and run-time control within the same block, and we use Orthogonal Novelty Transport (ONT) to govern slow-memory writes. We evaluate a 158M-parameter model in three stages spanning base language modeling, mathematical continuation, and 4096-token continuation. Removing mHC raises the Stage-A final LM loss from 12.630 to 15.127, while adaptive sparse control improves the Stage-B final LM loss from 12.137 to 10.787 relative to a matched fixed-ratio continuation. The full route remains stable at sequence length 4096, where Stage C ends with final LM loss 11.582 and improves the delayed-identifier diagnostic from 14.396 to 12.031 in key cross-entropy. Taken together, these results show that long-context autoregressive modeling can be organized around a broader division of labor than attention alone.

Keqin Xie

Independent Researcher, Suzhou, China

Long-Context Language Modeling Autoregressive Language Modeling Long-Range Dependency Modeling Memory-Augmented Language Models Persistent Memory for Language Models Predictive Coding

Mar 6, 2026

Predictive Coding Graphs are a Superset of Feedforward Neural Networks

Predictive coding graphs (PCGs) are a recently introduced generalization to predictive coding networks, a neuroscience-inspired probabilistic latent variable model. Here, we prove how PCGs define a mathematical superset of feedforward artificial neural networks (multilayer perceptrons). This positions PCNs more strongly within contemporary machine learning (ML), and reinforces earlier proposals to study the use of non-hierarchical neural networks for ML tasks, and more generally the notion of topology in neural networks.

Björn van Zwol

Department of Information & Computing Sciences, Utrecht University, Utrecht, The Netherlands

Predictive Coding Neural Network Expressivity Feedforward Neural Networks

Mar 3, 2026

Expectation and Acoustic Neural Network Representations Enhance Music Identification from Brain Activity

During music listening, cortical activity encodes both acoustic and expectation-related information. Prior work has shown that ANN representations resemble cortical representations and can serve as supervisory signals for EEG recognition. Here we show that distinguishing acoustic and expectation-related ANN representations as teacher targets improves EEG-based music identification. Models pretrained to predict either representation outperform non-pretrained baselines, and combining them yields complementary gains that exceed strong seed ensembles formed by varying random initializations. These findings show that teacher representation type shapes downstream performance and that representation learning can be guided by neural encoding. This work points toward advances in predictive music cognition and neural decoding. Our expectation representation, computed directly from raw signals without manual labels, reflects predictive structure beyond onset or pitch, enabling investigation of multilayer predictive encoding across diverse stimuli. Its scalability to large, diverse datasets further suggests potential for developing general-purpose EEG models grounded in cortical encoding principles.

Shogo Noguchi, Taketo Akama, Tai Nakamura +2

Sony Computer Science Laboratories, Inc., Tokyo, Japan

EEG Decoding Predictive Representation Learning Neural Encoding Predictive Coding

Feb 20, 2026

Learning Long-Range Dependencies with Temporal Predictive Coding

Temporal Predictive Coding provides a layer-local, parallelisable mechanism for learning in recurrent systems, making it an attractive candidate for online local learning on neuromorphic and edge hardware. However, its recurrent parameter update captures only local temporal relationships, neglecting the historic influence of parameters along the latent-state trajectory, and therefore struggles to assign credit over longer temporal horizons. This work combines for the first time Temporal Predictive Coding with Real-Time Recurrent Learning (tPC-RTRL), incorporating an online influence matrix that tracks this historic effect whilst preserving the spatial and temporal locality properties valued by neuromorphic implementations. Under explicit assumptions, we prove that tPC-RTRL recovers the gradients of backpropagation-through-time exactly. Empirically, a near-equivalence holds across several tasks of varying scale and complexity, including byte-level language modelling on WikiText-103 (tPC-RTRL vs. BPTT: 1.865 vs. 1.864 validation BPC), English--French translation on a CCMatrix subset (20.23 vs. 20.29 BLEU), and a realistic nanodrone system-identification benchmark (0.506m vs. 0.505m mean position error). Finally, we show that the iterative inference mechanism used during training can be reused at deployment time to incorporate intermittent state observations, halving final-position error relative to open-loop rollout on the nanodrone task (0.402m vs. 0.805m) and suggesting a path towards unifying learning and filtering within the same computational framework.

Tom Potter, Oliver Rhodes

International Centre for Neuromorphic Systems, The University of Manchester, Manchester, United Kingdom

Predictive Coding Recurrent Neural Networks Local Learning

Feb 17, 2026

Accelerated Predictive Coding Networks via Direct Kolen-Pollack Feedback Alignment

Predictive coding (PC) is a biologically inspired algorithm for training neural networks that relies only on local updates, allowing parallel learning across layers. However, practical implementations face two key limitations: error signals must still propagate from the output to early layers through multiple inference-phase steps, and feedback decays exponentially during this process, leading to vanishing updates in early layers. We propose direct Kolen-Pollack predictive coding (DKP-PC), which simultaneously addresses both feedback delay and exponential decay, yielding a more efficient and scalable variant of PC while preserving update locality. Leveraging direct feedback alignment and direct Kolen-Pollack algorithms, DKP-PC introduces learnable feedback connections from the output layer to all hidden layers, establishing a direct pathway for error transmission. This yields an algorithm that reduces the theoretical error propagation time complexity from O(L), with L being the network depth, to O(1), removing depth-dependent delay in error signals. Moreover, empirical results demonstrate that DKP-PC achieves performance at least comparable to, and often exceeding, that of standard PC, while offering improved latency and computational performance, supporting its potential for custom hardware-efficient implementations.

Davide Casnici, Martin Lefebvre, Justin Dauwels +1

Department of Microelectronics, Delft University of Technology, Delft, Netherlands.

Predictive Coding Deep Learning Optimization

Nov 16, 2025

Predicting upcoming visual features during eye movements yields scene representations aligned with human visual cortex

Natural scenes are complex arrangements of objects, surfaces, and backgrounds. For the brain's visual system to effectively operate, it needs to extract not only what objects are present, but also their spatial and semantic relations. We hypothesize that such structures may be learned, in a self-supervised fashion, by exploiting temporal regularities of natural active vision: each fixation reveals a glimpse that is related to the previous one via co-occurrence and saccade-conditioned spatial regularities. We instantiate this idea with Glimpse Prediction Networks (GPNs), recurrent models trained to predict the embedding of the next glimpse along human-like scanpaths. GPNs are shown to successfully extract complex scene information, including object co-occurrences and spatial object arrangements, and integrate information across glimpses. Importantly, GPN representations align strongly with human fMRI responses in mid and higher-level visual cortex and match, often outperform, alternative state-of-the-art ANN models, establishing next-glimpse-prediction as a biologically plausible route towards brain-aligned scene representations.

Sushrut Thorat, Adrien Doerig, Alexander Kroner +2

Institute of Cognitive Science, Osnabrück University, Osnabrück 49069, Germany. · Lossfunk, Bengaluru 560038, India. · Department of Education and Psychology, Freie Universität, Berlin 14195, Germany. +1

Predictive Coding Visual Neuroscience Predictive Representation Learning Active Visual Perception Self-Supervised Visual Representation Learning

Mar 22, 2025

Meta-Representational Predictive Coding: Neuroscience-Informed Self-Supervised Learning

Self-supervised learning has become an increasingly important paradigm in the domain of machine intelligence. Furthermore, evidence for self-supervised adaptation, such as contrastive formulations, has emerged in recent computational neuroscience and brain-inspired research. Nevertheless, current work on self-supervised learning relies on biologically implausible credit assignment -- in the form of backpropagation of errors -- and feedforward inference, typically a forward-locked pass. Predictive coding, in its mechanistic form, offers a biologically plausible means to sidestep these backprop-specific limitations. However, unsupervised predictive coding rests on learning a generative model of raw input (akin to "generative AI" approaches), which entails predicting a potentially high dimensional input; on the other hand, supervised predictive coding, which learns a mapping between inputs to target labels, requires human annotation, and thus incurs the drawbacks of supervised learning. In this work, we present a scheme for self-supervised learning, specifically for an emerging research sub-domain that we label as neuroscience-informed self-supervised learning (NeuroSSL), within a neurobiologically plausible framework that appeals to the free energy principle, constructing a new form of predictive coding that we call meta-representational predictive coding (MPC). MPC sidesteps the need for learning a generative model of sensory input (e.g., pixel-level features) by learning to predict representations of the input across parallel streams, resulting in an encoder-only learning and inference scheme. This formulation notably rests on active inference (in the form of sensory glimpsing) to drive the learning of representations, i.e., the representational dynamics are driven by sequences of decisions made by the model to sample informative portions of its sensorium.

Alexander Ororbia, Karl Friston, Rajesh P. N. Rao

Rochester Institute of Technology · Rochester, New York, USA · VERSES AI Research Lab +3

Self-Supervised Learning Predictive Coding Predictive Representation Learning