Predictive coding (PC) is a biologically plausible alternative to standard backpropagation (BP) that minimises an energy function with respect to network activities before updating weights. Recent work has improved the training stability of deep PC networks (PCNs) by leveraging some BP-inspired reparameterisations, but the scalability and theoretical basis of these methods remain unclear. To address this gap, we study the infinite width and depth limits of PCNs. For linear networks, we derive stable and "non-lazy" parameterisations when scaling both the model width and depth, revealing that the output of standard PCNs explodes with width during training. Moreover, under stable parameterisations, we show that the gradients computed by PC at activity equilibrium converge to the BP gradients for networks that are much wider than deep ($depth/width\to0$). Experiments show high gradient alignment between PC and BP at large width for different nonlinear models, including convolutional networks and transformers. Overall, this work constrains the parameterisations that are scalable with PC, while suggesting how BP could be implemented using only local updates in much wider than deep networks like the brain.
MRC Brain Network Dynamics Unit, University of Oxford（牛津大学医学研究委员会脑网络动力学研究中心）；University of Oxford（牛津大学）
The backpropagation of error algorithm used to train deep neural networks has been fundamental to the successes of deep learning. However, it requires sequential backward updates and non-local computations, which make it challenging to parallelize at scale and is unlike how learning works in the brain. Neuroscience-inspired learning algorithms, however, such as \emph{predictive coding}, which utilize local learning, have the potential to overcome these limitations and advance beyond current deep learning technologies. While predictive coding originated in theoretical neuroscience as a model of…
There is an increasing convergence between biologically plausible computational models of inference and learning with local update rules and the global gradient-based optimization of neural network models employed in machine learning. One particularly exciting connection is the correspondence between the locally informed optimization in predictive coding networks and the error backpropagation algorithm that is used to train state-of-the-art deep artificial neural networks. Here we focus on the related, but still largely under-explored connection between precision weighting in predictive coding…
In this work, we build upon the Active Inference (AIF) and Predictive Coding (PC) frameworks to propose a neural architecture comprising a generative model for sensory prediction, and a distinct generative model for motor trajectories. We highlight how sequences of sensory predictions can act as rails guiding learning, control and online adaptation of motor trajectories. We furthermore inquire the effects of bidirectional interactions between the motor and the visual modules. The architecture is tested on the control of a simulated robotic arm learning to reproduce handwritten letters.
This paper deals with differentiable dynamical models congruent with neural process theories that cast brain function as the hierarchical refinement of an internal generative model explaining observations. Our work extends existing implementations of gradient-based predictive coding with automatic differentiation and allows to integrate deep neural networks for non-linear state parameterization. Gradient-based predictive coding optimises inferred states and weights locally in for each layer by optimising precision-weighted prediction errors that propagate from stimuli towards latent states. Pr…
ETIS UMR 8051（ETIS UMR 8051实验室）；CY University（塞尔吉-巴黎大学）；ENSEA（法国国立高等电子及应用工程师学院）；CNRS（法国国家科学研究中心）
As a phenomenon in dynamical systems allowing autonomous switching between stable behaviors, chaotic itinerancy has gained interest in neurorobotics research. In this study, we draw a connection between this phenomenon and the predictive coding theory by showing how a recurrent neural network implementing predictive coding can generate neural trajectories similar to chaotic itinerancy in the presence of input noise. We propose two scenarios generating random and past-independent attractor switching trajectories using our model.
Bayesian predictive coding is a putative neuromorphic method for acquiring higher-level neural representations to account for sensory input. Although originating in the neuroscience community, there are also efforts in the machine learning community to study these models. This paper reviews some of the more well known models. Our review analyzes module connectivity and patterns of information transfer, seeking to find general principles used across the models. We also survey some recent attempts to cast these models within a deep learning framework. A defining feature of Bayesian predictive co…
University of Edinburgh（爱丁堡大学）；University of Sussex（萨塞克斯大学）
Backpropagation of error (backprop) is a powerful algorithm for training machine learning architectures through end-to-end differentiation. However, backprop is often criticised for lacking biological plausibility. Recently, it has been shown that backprop in multilayer-perceptrons (MLPs) can be approximated using predictive coding, a biologically-plausible process theory of cortical computation which relies only on local and Hebbian updates. The power of backprop, however, lies not in its instantiation in MLPs, but rather in the concept of automatic differentiation which allows for the optimi…
While recent progress in deep reinforcement learning has enabled robots to learn complex behaviors, tasks with long horizons and sparse rewards remain an ongoing challenge. In this work, we propose an effective reward shaping method through predictive coding to tackle sparse reward problems. By learning predictive representations offline and using these representations for reward shaping, we gain access to reward signals that understand the structure and dynamics of the environment. In particular, our method achieves better learning by providing reward signals that 1) understand environment dy…
A Stable, Fast, and Fully Automatic Learning Algorithm for Predictive Coding Networks
VERSES AI Research Lab（VERSES AI研究实验室）；Institute of Logic and Computation, TU Wien（维也纳技术大学逻辑与计算研究所）；MRC Brain Network Dynamics Unit, University of Oxford（牛津大学医学研究委员会脑网络动力学单元）；Department of Computer Science, University of Oxford（牛津大学计算机科学系）；State Key Laboratory of Reliability and Intelligence of Electrical Equipment, Hebei University（河北大学电力设备可靠性与智能化国家重点实验室）
This thesis describes our ongoing work on Contrastive Predictive Coding (CPC) features for speaker verification. CPC is a recently proposed representation learning framework based on predictive coding and noise contrastive estimation. We focus on incorporating CPC features into the standard automatic speaker verification systems, and we present our methods, experiments, and analysis. This thesis also details necessary background knowledge in past and recent work on automatic speaker verification systems, conventional speech features, and the motivation and techniques behind CPC.
Self-supervised learning methods overcome the key bottleneck for building more capable AI: limited availability of labeled data. However, one of the drawbacks of self-supervised architectures is that the representations that they learn are implicit and it is hard to extract meaningful information about the encoded world states, such as 3D structure of the visual scene encoded in a depth map. Moreover, in the visual domain such representations only rarely undergo evaluations that may be critical for downstream tasks, such as vision for autonomous cars. Herein, we propose a framework for evaluat…
Faster Predictive Coding Networks via Better Initialization
Department of Computer Science, University of Oxford（牛津大学计算机科学系）；Institute of Logic and Computation, Vienna University of Technology（维也纳技术大学逻辑与计算研究所）；VERSES AI Research Lab（VERSES AI研究实验室）
Rochester Institute of Technology（罗切斯特理工学院）；University of South Florida（南佛罗里达大学）
In this work, we develop convolutional neural generative coding (Conv-NGC), a generalization of predictive coding to the case of convolution/deconvolution-based computation. Specifically, we concretely implement a flexible neurobiologically-motivated algorithm that progressively refines latent state feature maps in order to dynamically form a more accurate internal representation/reconstruction model of natural images. The performance of the resulting sensory processing system is evaluated on complex datasets such as Color-MNIST, CIFAR-10, and Street House View Numbers (SVHN). We study the eff…
We propose that the Continual Learning desiderata can be achieved through a neuro-inspired architecture, grounded on Mountcastle's cortical column hypothesis. The proposed architecture involves a single module, called Self-Taught Associative Memory (STAM), which models the function of a cortical column. STAMs are repeated in multi-level hierarchies involving feedforward, lateral and feedback connections. STAM networks learn in an unsupervised manner, based on a combination of online clustering and hierarchical predictive coding. This short paper only presents the architecture and its connectio…
Institute for Informatics, University of Munich (LMU)（信息学院，慕尼黑大学（LMU））
Robotic systems operating at the edge require efficient online learning algorithms that can continuously adapt to changing environments while processing streaming sensory data. Traditional backpropagation, while effective, conflicts with biological plausibility principles and may be suboptimal for continuous adaptation scenarios. The Predictive Coding (PC) framework offers a biologically plausible alternative with local, Hebbian-like update rules, making it suitable for neuromorphic hardware implementation. However, PC's main limitation is its computational overhead due to multiple inference i…
VERSES Research Lab（VERSES研究实验室）；Institute of Logic and Computation, Vienna University of Technology（维也纳技术大学逻辑与计算研究所）；University of Oxford（牛津大学）；MRC Brain Network Dynamics Unit, University of Oxford（牛津大学医学研究委员会脑网络动力学单元）；Zyphra（Zyphra公司）
Associative memory plays an important role in human intelligence and its mechanisms have been linked to attention in machine learning. While the machine learning community's interest in associative memories has recently been rekindled, most work has focused on memory recall ($read$) over memory learning ($write$). In this paper, we present BayesPCN, a hierarchical associative memory capable of performing continual one-shot memory writes without meta-learning. Moreover, BayesPCN is able to gradually forget past observations ($forget$) to free its memory. Experiments show that BayesPCN can recal…
As large-scale time-series data can easily be found in real-world applications, multivariate time-series anomaly detection has played an essential role in diverse industries. It enables productivity improvement and maintenance cost reduction by preventing malfunctions and detecting anomalies based on time-series data. However, multivariate time-series anomaly detection is challenging because real-world time-series data exhibit complex temporal dependencies. For this task, it is crucial to learn a rich representation that effectively contains the nonlinear temporal dynamics of normal behavior. …
Ritsumeikan University（立命馆大学）；Keio University（庆应义塾大学）；The University of Tokyo（东京大学）；Università Milano-Bicocca（米兰比可卡大学）；University of Essex（埃塞克斯大学）；Donders Institute for Brain, Cognition and Behaviour（唐德斯脑、认知与行为研究所）；Cajal International Neuroscience Center, Spanish National Research Council（西班牙国家研究委员会卡哈尔国际神经科学中心）；Bogazici University（博阿齐奇大学）；Queen Mary University of London（伦敦玛丽女王大学）；The University of Electro-Communications（电气通信大学）；National Autonomous University of Mexico（墨西哥国立自治大学）；Universidad Autónoma del Estado de Morelos（莫雷洛斯州自治大学）；Institute of Cognitive Sciences and Technologies, National Research Council of Italy（意大利国家研究委员会认知科学与技术研究所）
Creating autonomous robots that can actively explore the environment, acquire knowledge and learn skills continuously is the ultimate achievement envisioned in cognitive and developmental robotics. Their learning processes should be based on interactions with their physical and social world in the manner of human learning and cognitive development. Based on this context, in this paper, we focus on the two concepts of world models and predictive coding. Recently, world models have attracted renewed attention as a topic of considerable interest in artificial intelligence. Cognitive systems learn…
University of Sussex（萨塞克斯大学）；VERSES Research Lab（VERSES研究实验室）；University of Oxford（牛津大学）
Predictive coding is an influential model of cortical neural activity. It proposes that perceptual beliefs are furnished by sequentially minimising "prediction errors" - the differences between predicted and observed data. Implicit in this proposal is the idea that perception requires multiple cycles of neural activity. This is at odds with evidence that several aspects of visual perception - including complex forms of object recognition - arise from an initial "feedforward sweep" that occurs on fast timescales which preclude substantial recurrent activity. Here, we propose that the feedforwar…
This study is focused on the development of the cortex-like visual object recognition system. We propose a general framework, which consists of three hierarchical levels (modules). These modules functionally correspond to the V1, V4 and IT areas. Both bottom-up and top-down connections between the hierarchical levels V4 and IT are employed. The higher the degree of matching between the input and the preferred stimulus, the shorter the response time of the neuron. Therefore information about a single stimulus is distributed in time and is transmitted by the waves of spikes. The reciprocal conne…
University of Potsdam（波茨坦大学）；Otto von Guericke University（奥托·冯·格里克大学）
PredNet, a deep predictive coding network developed by Lotter et al., combines a biologically inspired architecture based on the propagation of prediction error with self-supervised representation learning in video. While the architecture has drawn a lot of attention and various extensions of the model exist, there is a lack of a critical analysis. We fill in the gap by evaluating PredNet both as an implementation of the predictive coding theory and as a self-supervised video prediction model using a challenging video action classification dataset. We design an extended model to test if condit…
KAIST（韩国科学技术院）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）
The current paper proposes a novel variational Bayes predictive coding RNN model, which can learn to generate fluctuated temporal patterns from exemplars. The model learns to maximize the lower bound of the weighted sum of the regularization and reconstruction error terms. We examined how this weighting can affect development of different types of information processing while learning fluctuated temporal patterns. Simulation results show that strong weighting of the reconstruction term causes the development of deterministic chaos for imitating the randomness observed in target sequences, whil…
Federated learning can enable remote workers to collaboratively train a shared machine learning model while allowing training data to be kept locally. In the use case of wireless mobile devices, the communication overhead is a critical bottleneck due to limited power and bandwidth. Prior work has utilized various data compression tools such as quantization and sparsification to reduce the overhead. In this paper, we propose a predictive coding based compression scheme for federated learning. The scheme has shared prediction functions among all devices and allows each worker to transmit a compr…
Predictive coding, currently a highly influential theory in neuroscience, has not been widely adopted in machine learning yet. In this work, we transform the seminal model of Rao and Ballard (1999) into a modern deep learning framework while remaining maximally faithful to the original schema. The resulting network we propose (PreCNet) is tested on a widely used next frame video prediction benchmark, which consists of images from an urban environment recorded from a car-mounted camera, and achieves state-of-the-art performance. Performance on all measures (MSE, PSNR, SSIM) was further improved…
Directorate of Technology and Innovation（技术与创新局）；Chamber of Deputies（众议院）
Deep predictive coding networks are neuroscience-inspired unsupervised learning models that learn to predict future sensory states. We build upon the PredNet implementation by Lotter, Kreiman, and Cox (2016) to investigate if predictive coding representations are useful to predict brain activity in the visual cortex. We use representational similarity analysis (RSA) to compare PredNet representations to functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG) data from the Algonauts Project. In contrast to previous findings in the literature (Khaligh-Razavi &Kriegeskorte, …
High-dimensional observations are a major challenge in the application of model-based reinforcement learning (MBRL) to real-world environments. To handle high-dimensional sensory inputs, existing approaches use representation learning to map high-dimensional observations into a lower-dimensional latent space that is more amenable to dynamics estimation and planning. In this work, we present an information-theoretic approach that employs temporal predictive coding to encode elements in the environment that can be predicted across time. Since this approach focuses on encoding temporally-predicta…
A large amount of recent research has the far-reaching goal of finding training methods for deep neural networks that can serve as alternatives to backpropagation (BP). A prominent example is predictive coding (PC), which is a neuroscience-inspired method that performs inference on hierarchical Gaussian generative models. These methods, however, fail to keep up with modern neural networks, as they are unable to replicate the dynamics of complex layers and activation functions. In this work, we solve this problem by generalizing PC to arbitrary probability distributions, enabling the training o…
For energy-efficient computation in specialized neuromorphic hardware, we present spiking neural coding, an instantiation of a family of artificial neural models grounded in the theory of predictive coding. This model, the first of its kind, works by operating in a never-ending process of "guess-and-check", where neurons predict the activity values of one another and then adjust their own activities to make better future predictions. The interactive, iterative nature of our system fits well into the continuous time formulation of sensory stream prediction and, as we show, the model's structure…
Paul G. Allen School of Computer Science and Engineering（保罗·G·艾伦计算机科学与工程学院）；University of Washington, Seattle（华盛顿大学西雅图分校）
We introduce Active Predictive Coding Networks (APCNs), a new class of neural networks that solve a major problem posed by Hinton and others in the fields of artificial intelligence and brain modeling: how can neural networks learn intrinsic reference frames for objects and parse visual scenes into part-whole hierarchies by dynamically allocating nodes in a parse tree? APCNs address this problem by using a novel combination of ideas: (1) hypernetworks are used for dynamically generating recurrent neural networks that predict parts and their locations within intrinsic reference frames condition…
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Okinawa Institute of Science Technology（冲绳科学技术大学院大学）
This study presents a dynamic neural network model based on the predictive coding framework for perceiving and predicting the dynamic visuo-proprioceptive patterns. In our previous study [1], we have shown that the deep dynamic neural network model was able to coordinate visual perception and action generation in a seamless manner. In the current study, we extended the previous model under the predictive coding framework to endow the model with a capability of perceiving and predicting dynamic visuo-proprioceptive patterns as well as a capability of inferring intention behind the perceived vis…
Predictive coding is a message-passing framework initially developed to model information processing in the brain, and now also topic of research in machine learning due to some interesting properties. One of such properties is the natural ability of generative models to learn robust representations thanks to their peculiar credit assignment rule, that allows neural activities to converge to a solution before updating the synaptic weights. Graph neural networks are also message-passing models, which have recently shown outstanding results in diverse types of tasks in machine learning, providin…
Early Exiting Predictive Coding Neural Networks for Edge AI
TICLab, International University of Rabat, Morocco（TICLab，拉巴特国际大学，摩洛哥）；College of Computing, University Mohammed VI Polytechnic, Morocco（计算机学院，穆罕默德六世理工大学，摩洛哥）；School of Electronic and Electrical Engineering, University of Leeds, UK（电子与电气工程学院，利兹大学，英国）
