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 information processing in the cortex, recent work has developed the idea into a general-purpose algorithm able to train neural networks using only local computations. In this survey, we review works that have contributed to this perspective and demonstrate the close theoretical connections between predictive coding and backpropagation, as well as works that highlight the multiple advantages of using predictive coding models over backpropagation-trained neural networks. Specifically, we show the substantially greater flexibility of predictive coding networks against equivalent deep neural networks, which can function as classifiers, generators, and associative memories simultaneously, and can be defined on arbitrary graph topologies. Finally, we review direct benchmarks of predictive coding networks on machine learning classification tasks, as well as its close connections to control theory and applications in robotics.
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…
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…
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…
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）
Integration of Contrastive Predictive Coding and Spiking Neural Networks
Université Paris-Saclay（巴黎萨克雷大学）；İstanbul Teknik Üniversitesi（伊斯坦布尔技术大学）；Osmaniye Korkut Ata Üniversitesi（奥斯曼耶·科鲁特阿大学）；Erzincan Binali Yıldırım Üniversitesi（埃尔津詹·比纳利·伊利德里姆大学）；Hacettepe Üniversitesi（哈恰特佩大学）
The Ohio State University（俄亥俄州立大学）；Carnegie Mellon University（卡内基梅隆大学）；Massachussetts Institute of Technology（麻省理工学院）
We explore the use of a neural network inspired by predictive coding for modeling human music perception. This network was developed based on the computational neuroscience theory of recurrent interactions in the hierarchical visual cortex. When trained with video data using self-supervised learning, the model manifests behaviors consistent with human visual illusions. Here, we adapt this network to model the hierarchical auditory system and investigate whether it will make similar choices to humans regarding the musicality of a set of random pitch sequences. When the model is trained with a l…
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…
The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivati…
We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with an…
Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation
College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）；ZJU-UIUC Institute, Zhejiang University（浙江大学-伊利诺伊大学厄巴纳-香槟分校联合学院）
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…
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…
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.
University of Edinburgh（爱丁堡大学）；University of Sussex（萨塞克斯大学）
Predictive coding offers a potentially unifying account of cortical function -- postulating that the core function of the brain is to minimize prediction errors with respect to a generative model of the world. The theory is closely related to the Bayesian brain framework and, over the last two decades, has gained substantial influence in the fields of theoretical and cognitive neuroscience. A large body of research has arisen based on both empirically testing improved and extended theoretical and mathematical models of predictive coding, as well as in evaluating their potential biological plau…
Predictive coding (PC) is a general theory of cortical function. The local, gradient-based learning rules found in one kind of PC model have recently been shown to closely approximate backpropagation. This finding suggests that this gradient-based PC model may be useful for understanding how the brain solves the credit assignment problem. The model may also be useful for developing local learning algorithms that are compatible with neuromorphic hardware. In this paper, we modify this PC model so that it better fits biological constraints, including the constraints that neurons can only have po…
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…
The algorithm of brain learning and memory is still undetermined. The backpropagation algorithm of artificial neural networks was thought not suitable for brain cortex, and there is a lack of algorithm for memory engram. We designed a brain version of backpropagation algorithm, which are biologically plausible and could be implemented with virtual neurons to complete image classification task. An encoding algorithm that can automatically allocate engram cells is proposed, which is an algorithm implementation for memory engram theory, and could simulate how hippocampus achieve fast associative …
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…
Predictive coding can be regarded as a function which reduces the error between an input signal and a top-down prediction. If reducing the error is equivalent to reducing the influence of stimuli from the environment, predictive coding can be regarded as stimulation avoidance by prediction. Our previous studies showed that action and selection for stimulation avoidance emerge in spiking neural networks through spike-timing dependent plasticity (STDP). In this study, we demonstrate that spiking neural networks with random structure spontaneously learn to predict temporal sequences of stimuli ba…
This paper reviews predictive coding, from theoretical neuroscience, and variational autoencoders, from machine learning, identifying the common origin and mathematical framework underlying both areas. As each area is prominent within its respective field, more firmly connecting these areas could prove useful in the dialogue between neuroscience and machine learning. After reviewing each area, we discuss two possible correspondences implied by this perspective: cortical pyramidal dendrites as analogous to (non-linear) deep networks and lateral inhibition as analogous to normalizing flows. Thes…
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…
Naval Surface Warfare Center（海军水面作战中心）；US Naval Sea Systems Command（美国海军海上系统司令部）；University of Florida（佛罗里达大学）
Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial element of DPCNs is a forward-backward inference procedure to uncover sparse, invariant features. However, this inference is a major computational bottleneck. It severely limits the network depth due to learning stagnation. Here, we prove why this bottleneck occurs. We then propose a new forward-inference strategy based on accelerated proximal gradients. This st…
National Institute of Advanced Industrial Science and Technology (AIST)（产业技术综合研究所）；Plymouth University（普利茅斯大学）；Waseda University（早稻田大学）
Studies suggest that within the hierarchical architecture, the topological higher level possibly represents a conscious category of the current sensory events with slower changing activities. They attempt to predict the activities on the lower level by relaying the predicted information. On the other hand, the incoming sensory information corrects such prediction of the events on the higher level by the novel or surprising signal. We propose a predictive hierarchical artificial neural network model that examines this hypothesis on neurorobotic platforms, based on the AFA-PredNet model. In this…
PC-SNN: Predictive Coding-based Local Hebbian Plasticity Learning in Spiking Neural Networks
Sun Yat-Sen University (Shenzhen Campus)（中山大学（深圳校区））；Harbin Institute of Technology Shenzhen（哈尔滨工业大学（深圳））；City University of Hong Kong（香港城市大学）；The University of South Dakota（南达科他大学）；Lingnan University（岭南大学）
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…
Predictive coding (PC) networks are a biologically interesting class of neural networks. Their layered hierarchy mimics the reciprocal connectivity pattern observed in the mammalian cortex, and they can be trained using local learning rules that approximate backpropagation [Bogacz, 2017]. However, despite having feedback connections that enable information to flow down the network hierarchy, discriminative PC networks are not generative. Clamping the output class and running the network to equilibrium yields an input sample that typically does not resemble the training input. This paper studie…
Rochester Institute of Technology（罗切斯特理工学院）；AI Research Lab（AI研究实验室）；University of Washington（华盛顿大学）；Rochester, New York, USA（纽约罗切斯特市）；Los Angeles, California, USA（加州洛杉矶市）；Seattle, Washington, USA（华盛顿州西雅图市）
Shahid Beheshti University（沙希德·贝赫什提大学）；Amirkabir University of Technology（阿米尔卡比尔理工大学）；CerCo UMR 5549, CNRS Université Toulouse 3（法国国家科学研究中心图卢兹第三大学 CerCo UMR 5549 实验室）
We recently proposed the S4NN algorithm, essentially an adaptation of backpropagation to multilayer spiking neural networks that use simple non-leaky integrate-and-fire neurons and a form of temporal coding known as time-to-first-spike coding. With this coding scheme, neurons fire at most once per stimulus, but the firing order carries information. Here, we introduce BS4NN, a modification of S4NN in which the synaptic weights are constrained to be binary (+1 or -1), in order to decrease memory (ideally, one bit per synapse) and computation footprints. This was done using two sets of weights: f…
The predictive processing (PP) hypothesizes that the predictive inference of our sensorimotor system is encoded implicitly in the regularities between perception and action. We propose a neural architecture in which such regularities of active inference are encoded hierarchically. We further suggest that this encoding emerges during the embodied learning process when the appropriate action is selected to minimize the prediction error in perception. Therefore, this predictive stream in the sensorimotor loop is generated in a top-down manner. Specifically, it is constantly modulated by the motor…
A Spiking Neural Network (SNN) can be trained indirectly by first training an Artificial Neural Network (ANN) with the conventional backpropagation algorithm, then converting it into an SNN. The conventional rate-coding method for SNNs uses the number of spikes to encode magnitude of an activation value, and may be computationally inefficient due to the large number of spikes. Temporal-coding is typically more efficient by leveraging the timing of spikes to encode information. In this paper, we present Logarithmic Temporal Coding (LTC), where the number of spikes used to encode an activation v…
