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Rajesh P. N. Rao
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Journal Articles
Publisher: Journals Gateway
Neural Computation (2024) 36 (1): 1–32.
Published: 12 December 2023
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There is growing interest in predictive coding as a model of how the brain learns through predictions and prediction errors. Predictive coding models have traditionally focused on sensory coding and perception. Here we introduce active predictive coding (APC) as a unifying model for perception, action, and cognition. The APC model addresses important open problems in cognitive science and AI, including (1) how we learn compositional representations (e.g., part-whole hierarchies for equivariant vision) and (2) how we solve large-scale planning problems, which are hard for traditional reinforcement learning, by composing complex state dynamics and abstract actions from simpler dynamics and primitive actions. By using hypernetworks, self-supervised learning, and reinforcement learning, APC learns hierarchical world models by combining task-invariant state transition networks and task-dependent policy networks at multiple abstraction levels. We illustrate the applicability of the APC model to active visual perception and hierarchical planning. Our results represent, to our knowledge, the first proof-of-concept demonstration of a unified approach to addressing the part-whole learning problem in vision, the nested reference frames learning problem in cognition, and the integrated state-action hierarchy learning problem in reinforcement learning.
Includes: Supplementary data
Journal Articles
Publisher: Journals Gateway
Neural Computation (2016) 28 (8): 1503–1526.
Published: 01 August 2016
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Motivated by the growing evidence for Bayesian computation in the brain, we show how a two-layer recurrent network of Poisson neurons can perform both approximate Bayesian inference and learning for any hidden Markov model. The lower-layer sensory neurons receive noisy measurements of hidden world states. The higher-layer neurons infer a posterior distribution over world states via Bayesian inference from inputs generated by sensory neurons. We demonstrate how such a neuronal network with synaptic plasticity can implement a form of Bayesian inference similar to Monte Carlo methods such as particle filtering. Each spike in a higher-layer neuron represents a sample of a particular hidden world state. The spiking activity across the neural population approximates the posterior distribution over hidden states. In this model, variability in spiking is regarded not as a nuisance but as an integral feature that provides the variability necessary for sampling during inference. We demonstrate how the network can learn the likelihood model, as well as the transition probabilities underlying the dynamics, using a Hebbian learning rule. We present results illustrating the ability of the network to perform inference and learning for arbitrary hidden Markov models.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2007) 19 (10): 2665–2693.
Published: 01 October 2007
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A fundamental problem in biological and machine vision is visual invariance: How are objects perceived to be the same despite transformations such as translations, rotations, and scaling? In this letter, we describe a new, unsupervised approach to learning invariances based on Lie group theory. Unlike traditional approaches that sacrifice information about transformations to achieve invariance, the Lie group approach explicitly models the effects of transformations in images. As a result, estimates of transformations are available for other purposes, such as pose estimation and visuomotor control. Previous approaches based on first-order Taylor series expansions of images can be regarded as special cases of the Lie group approach, which utilizes a matrix-exponential-based generative model of images and can handle arbitrarily large transformations. We present an unsupervised expectation-maximization algorithm for learning Lie transformation operators directly from image data containing examples of transformations. Our experimental results show that the Lie operators learned by the algorithm from an artificial data set containing six types of affine transformations closely match the analytically predicted affine operators. We then demonstrate that the algorithm can also recover novel transformation operators from natural image sequences. We conclude by showing that the learned operators can be used to both generate and estimate transformations in images, thereby providing a basis for achieving visual invariance.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2005) 17 (1): 47–73.
Published: 01 January 2005
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Recent algorithms for sparse coding and independent component analysis (ICA) have demonstrated how localized features can be learned from natural images. However, these approaches do not take image transformations into account. We describe an unsupervised algorithm for learning both localized features and their transformations directly from images using a sparse bilinear generative model. We show that from an arbitrary set of natural images, the algorithm produces oriented basis filters that can simultaneously represent features in an image and their transformations. The learned generative model can be used to translate features to different locations, thereby reducing the need to learn the same feature at multiple locations, a limitation of previous approaches to sparse coding and ICA. Our results suggest that by explicitly modeling the interaction between local image features and their transformations, the sparse bilinear approach can provide a basis for achieving transformation-invariant vision.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2004) 16 (1): 1–38.
Published: 01 January 2004
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A large number of human psychophysical results have been successfully explained in recent years using Bayesian models. However, the neural implementation of such models remains largely unclear. In this article, we show that a network architecture commonly used to model the cerebral cortex can implement Bayesian inference for an arbitrary hidden Markov model. We illustrate the approach using an orientation discrimination task and a visual motion detection task. In the case of orientation discrimination, we show that the model network can infer the posterior distribution over orientations and correctly estimate stimulus orientation in the presence of significant noise. In the case of motion detection, we show that the resulting model network exhibits direction selectivity and correctly computes the posterior probabilities over motion direction and position. When used to solve the well-known random dots motion discrimination task, the model generates responses that mimic the activities of evidence-accumulating neurons in cortical areas LIP and FEF. The framework we introduce posits a new interpretation of cortical activities in terms of log posterior probabilities of stimuli occurring in the natural world.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2001) 13 (10): 2221–2237.
Published: 01 October 2001
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A spike-timing-dependent Hebbian mechanism governs the plasticity of recurrent excitatory synapses in the neocortex: synapses that are activated a few milliseconds before a postsynaptic spike are potentiated, while those that are activated a few milliseconds after are depressed. We show that such a mechanism can implement a form of temporal difference learning for prediction of input sequences. Using a biophysical model of a cortical neuron, we show that a temporal difference rule used in conjunction with dendritic backpropagating action potentials reproduces the temporally asymmetric window of Hebbian plasticity observed physiologically. Furthermore, the size and shape of the window vary with the distance of the synapse from the soma. Using a simple example, we show how a spike-timing-based temporal difference learning rule can allow a network of neocortical neurons to predict an input a few milliseconds before the input's expected arrival.
Journal Articles
Publisher: Journals Gateway
Neural Computation (2001) 13 (6): 1243–1253.
Published: 01 June 2001
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When a flash is aligned with a moving object, subjects perceive the flash to lag behind the moving object. Two different models have been proposed to explain this “flash-lag” effect. In the motion extrapolation model, the visual system extrapolates the location of the moving object to counteract neural propagation delays, whereas in the latency difference model, it is hypothesized that moving objects are processed and perceived more quickly than flashed objects. However, recent psychophysical experiments suggest that neither of these interpretations is feasible (Eagleman & Sejnowski, 2000a, 2000b, 2000c), hypothesizing instead that the visual system uses data from the future of an event before committing to an interpretation. We formalize this idea in terms of the statistical framework of optimal smoothing and show that a model based on smoothing accounts for the shape of psychometric curves from a flash-lag experiment involving random reversals of motion direction. The smoothing model demonstrates how the visual system may enhance perceptual accuracy by relying not only on data from the past but also on data collected from the immediate future of an event.
Journal Articles
Publisher: Journals Gateway
Neural Computation (1997) 9 (4): 721–763.
Published: 15 May 1997
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The responses of visual cortical neurons during fixation tasks can be significantly modulated by stimuli from beyond the classical receptive field. Modulatory effects in neural responses have also been recently reported in a task where a monkey freely views a natural scene. In this article, we describe a hierarchical network model of visual recognition that explains these experimental observations by using a form of the extended Kalman filter as given by the minimum description length (MDL) principle. The model dynamically combines input-driven bottom-up signals with expectation-driven top-down signals to predict current recognition state. Synaptic weights in the model are adapted in a Hebbian manner according to a learning rule also derived from the MDL principle. The resulting prediction-learning scheme can be viewed as implementing a form of the expectation-maximization (EM) algorithm. The architecture of the model posits an active computational role for the reciprocal connections between adjoining visual cortical areas in determining neural response properties. In particular, the model demonstrates the possible role of feedback from higher cortical areas in mediating neurophysiological effects due to stimuli from beyond the classical receptive field. Simulations of the model are provided that help explain the experimental observations regarding neural responses in both free viewing and fixating conditions.