Neural Kalman Filtering

Millidge, Beren; Tschantz, Alexander; Seth, Anil; Buckley, Christopher

doi:10.48550/arxiv.2102.10021

Cited by 8 publications

(9 citation statements)

References 25 publications

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“…active inference agents, can perform laser-based localization and navigation tasks. The results obtained in the localization experiment, where we compared our approach against a state-of-the-art alternative (particle filter), show the potential of predictive stochastic neural filtering in robot localization, and estimation in general [6,15]. Furthermore, the navigation experiment showcased how to compute actions as a dual filtering process.…”

Section: Discussionmentioning

confidence: 90%

Robot Localization and Navigation through Predictive Processing using LiDAR

Burghardt¹,

Lanillos²

2021

Preprint

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Knowing the position of the robot in the world is crucial for navigation. Nowadays, Bayesian filters, such as Kalman and particlebased, are standard approaches in mobile robotics. Recently, end-to-end learning has allowed for scaling-up to high-dimensional inputs and improved generalization. However, there are still limitations to providing reliable laser navigation. Here we show a proof-of-concept of the predictive processing-inspired approach to perception applied for localization and navigation using laser sensors, without the need for odometry. We learn the generative model of the laser through self-supervised learning and perform both online state-estimation and navigation through stochastic gradient descent on the variational free-energy bound. We evaluated the algorithm on a mobile robot (TIAGo Base) with a laser sensor (SICK) in Gazebo. Results showed improved state-estimation performance when comparing to a state-of-the-art particle filter in the absence of odometry. Furthermore, conversely to standard Bayesian estimation approaches our method also enables the robot to navigate when providing the desired goal by inferring the actions that minimize the prediction error.

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Section: Discussionmentioning

confidence: 90%

Robot Localization and Navigation through Predictive Processing using LiDAR

Burghardt¹,

Lanillos²

2021

Preprint

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“…However, it is unclear how BayesPCN's locally conjugate Bayesian weight update can be realized in the brain unlike GPCN's Hebbian weight update arising from gradient descent. Nevertheless given that the Kalman filter can be approximated by gradient descent Millidge et al [2021b] and the fact that BayesPCN's weight update is related to the mixture Kalman filter, there may be a biologically plausible way of approximating BayesPCN's write. In addition, there are similarities between BayesPCN's diffusion-based f orget and the synaptic homeostasis hypothesis [Cirelli and Tononi, 2022], where during sleep the synaptic weight strengths are decreased on average to facilitate future learning.…”

Section: Discussionmentioning

confidence: 99%

BayesPCN: A Continually Learnable Predictive Coding Associative Memory

Yoo¹,

Wood²

2022

Preprint

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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 (f orget) to free its memory. Experiments show that BayesPCN can recall corrupted i.i.d. high-dimensional data observed hundreds of "timesteps" ago without a significant drop in recall ability compared to the state-of-the-art offline-learned associative memory models.Preprint. Under review.

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“…Other models explicitly compare deterministic and probabilistic implementations to predictive coding [16]. Gradient based predictive coding, the approach we will use here, is largely biologically plausible as all optimization can be described with Hebbian updates rules [5,17]. Gradient based predictive coding is deterministic based on the nature of its updates without explicit sampling.…”

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%

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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Neural Kalman Filtering

Cited by 8 publications

References 25 publications

Robot Localization and Navigation through Predictive Processing using LiDAR

Robot Localization and Navigation through Predictive Processing using LiDAR

BayesPCN: A Continually Learnable Predictive Coding Associative Memory

Predictive coding, precision and natural gradients

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