The backpropagation algorithm has experienced remarkable success in training large-scale artificial neural networks; however, its biological plausibility has been strongly criticized, and it remains an open question whether the brain employs supervised learning mechanisms akin to it. Here, we propose correlative information maximization between layer activations as an alternative normative approach to describe the signal propagation in biological neural networks in both forward and backward directions. This new framework addresses many concerns about the biological-plausibility of conventional artificial neural networks and the backpropagation algorithm. The coordinate descent-based optimization of the corresponding objective, combined with the mean square error loss function for fitting labeled supervision data, gives rise to a neural network structure that emulates a more biologically realistic network of multi-compartment pyramidal neurons with dendritic processing and lateral inhibitory neurons. Furthermore, our approach provides a natural resolution to the weight symmetry problem between forward and backward signal propagation paths, a significant critique against the plausibility of the conventional backpropagation algorithm. This is achieved by leveraging two alternative, yet equivalent forms of the correlative mutual information objective. These alternatives intrinsically lead to forward and backward prediction networks without weight symmetry issues, providing a compelling solution to this long-standing challenge.

Neural Information Processing Systems http://nips.cc/

Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is currently no SFA algorithm with a biologically plausible neural network implementation, by which we mean an algorithm operates in the online setting and can be mapped onto a neural network with local synaptic updates. In this work, starting from an SFA objective, we derive an SFA algorithm, called Bio-SFA, with a biologically plausible neural network implementation.

Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e., they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise?

Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is currently no SFA algorithm with a biologically plausible neural network implementation, by which we mean an algorithm operates in the online setting and can be mapped onto a neural network with local synaptic updates. In this work, starting from an SFA objective, we derive an SFA algorithm, called Bio-SFA, with a biologically plausible neural network implementation.

Summary and Contributions: This paper produces a so-called biologically plausible neural network for slow-feature analysis. Biological plausibility here means that network learning is online and based on local synaptic learning rules. These online and locality requirements might lead to low computational overhead. While Foldiak, Wiskott, and many others have explored online local learning for SFA in the last thirty years, this paper attempts to relate SFA to a normative theory through an MDS objective.

All reviewers agreed that the proposed normative approach to deriviing a biologically plausible implementation of SFA in multiple dimensions represents a strong contribution.

Learning latent features from time series data is an important problem in both machine learning and brain function. One approach, called Slow Feature Analysis (SFA), leverages the slowness of many salient features relative to the rapidly varying input signals. Furthermore, when trained on naturalistic stimuli, SFA reproduces interesting properties of cells in the primary visual cortex and hippocampus, suggesting that the brain uses temporal slowness as a computational principle for learning latent features. However, despite the potential relevance of SFA for modeling brain function, there is currently no SFA algorithm with a biologically plausible neural network implementation, by which we mean an algorithm operates in the online setting and can be mapped onto a neural network with local synaptic updates. In this work, starting from an SFA objective, we derive an SFA algorithm, called Bio-SFA, with a biologically plausible neural network implementation.

Many neurons in the brain, such as place cells in the rodent hippocampus, have localized receptive fields, i.e., they respond to a small neighborhood of stimulus space. What is the functional significance of such representations and how can they arise? Here, we propose that localized receptive fields emerge in similarity-preserving networks of rectifying neurons that learn low-dimensional manifolds populated by sensory inputs. Numerical simulations of such networks on standard datasets yield manifold-tiling localized receptive fields. More generally, we show analytically that, for data lying on symmetric manifolds, optimal solutions of objectives, from which similarity-preserving networks are derived, have localized receptive fields. Therefore, nonnegative similarity-preserving mapping (NSM) implemented by neural networks can model representations of continuous manifolds in the brain.