Predictive Coding Approximates Backprop along Arbitrary Computation Graphs

Millidge, Beren; Tschantz, Alexander; Buckley, Christopher L.

doi:10.48550/arxiv.2006.04182

Cited by 29 publications

(70 citation statements)

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“…It's these uncertainties that we will focus on in this work. Previous research revolving around gradient based predictive coding has illuminated its close connection to the error backpropagation algorithm, whose gradients have been shown to be directly approximated by discriminative predictive coding [4]. Predictive coding models have also been compared to other popular inference methods, such as the Kalman filter or variational inference in general [2].…”

Section: Related Workmentioning

confidence: 99%

“…There are many conceptual similarities between the state-of-the-art in machine learning, namely deep neural networks and the error back-propagation algorithm, and predictive coding models. Work that aims at directly connecting these fields, however, is still relatively sparse [4,5,6,7,8]. Recently, it has been suggested that gradient based predictive coding, when it includes precision estimations, directly implements a form of Natural Gradient Descent, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, it has been suggested that gradient based predictive coding, when it includes precision estimations, directly implements a form of Natural Gradient Descent, i.e. second order, uncertainty-aware optimization of the network's parameters [4]. Within the domain of Deep Learning, Natural Gradient Descent (NGD) is a highly attractive optimization method, due to the speed and stability of convergence [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Predictive coding, precision and natural gradients

Ofner¹,

Ratul²,

Ghosh³

et al. 2021

Preprint

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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 networks and the Natural Gradient Descent algorithm for deep neural networks. Precision-weighted predictive coding is an interesting candidate for scaling up uncertainty-aware optimizationparticularly for models with large parameter spaces -due to its distributed nature of the optimization process and the underlying local approximation of the Fisher information metric, the adaptive learning rate that is central to Natural Gradient Descent. Here, we show that hierarchical predictive coding networks with learnable precision indeed are able to solve various supervised and unsupervised learning tasks with performance comparable to global backpropagation with natural gradients and outperform their classical gradient descent counterpart on tasks where high amounts of noise are embedded in data or label inputs. When applied to unsupervised auto-encoding of image inputs, the deterministic network produces hierarchically organized and disentangled embeddings, hinting at the close connections between predictive coding and hierarchical variational inference.

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Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Predictive coding, precision and natural gradients

Ofner¹,

Ratul²,

Ghosh³

et al. 2021

Preprint

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“…This last property is fundamental for the functioning of different brain areas, such as the hippocampus [19]. PC also shares the generalization capabilities of standard deep learning, as it is able to approximate BP on any neural structure [20], and a variation of PC is able to exactly replicate the weight update of BP on any computational graph [21,22]. Moreover, PC only uses local information to update synapses, allowing the network to be fully parallelized, and to train on networks with any topology.…”

Section: Introductionmentioning

confidence: 98%

Learning on Arbitrary Graph Topologies via Predictive Coding

Salvatori¹,

Luca²,

Millidge³

et al. 2022

Preprint

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Training with backpropagation (BP) in standard deep learning consists of two main steps: a forward pass that maps a data point to its prediction, and a backward pass that propagates the error of this prediction back through the network. This process is highly effective when the goal is to minimize a specific objective function. However, it does not allow training on networks with cyclic or backward connections. This is an obstacle to reaching brain-like capabilities, as the highly complex heterarchical structure of the neural connections in the neocortex are potentially fundamental for its effectiveness. In this paper, we show how predictive coding (PC), a theory of information processing in the cortex, can be used to perform inference and learning on arbitrary graph topologies. We experimentally show how this formulation, called PC graphs, can be used to flexibly perform different tasks with the same network by simply stimulating specific neurons, and investigate how the topology of the graph influences the final performance. We conclude by comparing against simple baselines trained with BP.

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“…In turn, this induces timing mismatches between instructive signals and neural activity, which disrupts learning. For example, recent proposals for bio-plausible implementations of error backpropagation (BP) [1][2][3][4] in the brain all require some form of relaxation, both for inference and during learning [5][6][7][8][9][10][11]. Notably, this also affects some purely algorithmic methods involving auxiliary variables [12].…”

Section: Introductionmentioning

confidence: 99%

Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons

Haider¹,

Ellenberger²,

Kriener³

et al. 2021

Preprint

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The response time of physical computational elements is finite, and neurons are no exception. In hierarchical models of cortical networks each layer thus introduces a response lag. This inherent property of physical dynamical systems results in delayed processing of stimuli and causes a timing mismatch between network output and instructive signals, thus afflicting not only inference, but also learning. We introduce Latent Equilibrium, a new framework for inference and learning in networks of slow components which avoids these issues by harnessing the ability of biological neurons to phase-advance their output with respect to their membrane potential. This principle enables quasi-instantaneous inference independent of network depth and avoids the need for phased plasticity or computationally expensive network relaxation phases. We jointly derive disentangled neuron and synapse dynamics from a prospective energy function that depends on a network's generalized position and momentum. The resulting model can be interpreted as a biologically plausible approximation of error backpropagation in deep cortical networks with continuous-time, leaky neuronal dynamics and continuously active, local plasticity. We demonstrate successful learning of standard benchmark datasets, achieving competitive performance using both fully-connected and convolutional architectures, and show how our principle can be applied to detailed models of cortical microcircuitry. Furthermore, we study the robustness of our model to spatio-temporal substrate imperfections to demonstrate its feasibility for physical realization, be it in vivo or in silico.

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Predictive Coding Approximates Backprop along Arbitrary Computation Graphs

Cited by 29 publications

References 0 publications

Predictive coding, precision and natural gradients

Predictive coding, precision and natural gradients

Learning on Arbitrary Graph Topologies via Predictive Coding

Latent Equilibrium: A unified learning theory for arbitrarily fast computation with arbitrarily slow neurons

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