Efficiency of Local Learning Rules in Threshold-Linear Associative Networks

A theory of hippocampal function: New developments

We develop further here the only quantitative theory of the storage of information in the hippocampal episodic memory system and its recall back to the neocortex. The theory is upgraded to account for a revolution in understanding of spatial representations in the primate, including human, hippocampus, that go beyond the place where the individual is located, to the location being viewed in a scene. This is fundamental to much primate episodic memory and navigation: functions supported in humans by pathways that build 'where' spatial view representations by feature combinations in a ventromedial visual cortical stream, separate from those for 'what' object and face information to the inferior temporal visual cortex, and for reward information from the orbitofrontal cortex. Key new computational developments include the capacity of the CA3 attractor network for storing whole charts of space; how the correlations inherent in self-organizing continuous spatial representations impact the storage capacity; how the CA3 network can combine continuous spatial and discrete object and reward representations; the roles of the rewards that reach the hippocampus in the later consolidation into long-term memory in part via cholinergic pathways from the orbitofrontal cortex; and new ways of analysing neocortical information storage using Potts networks.

Linear Classification of Neural Manifolds with Correlated Variability

Understanding how the statistical and geometric properties of neural activity relate to performance is a key problem in theoretical neuroscience and deep learning. Here, we calculate how correlations between object representations affect the capacity, a measure of linear separability. We show that for spherical object manifolds, introducing correlations between centroids effectively pushes the spheres closer together, while introducing correlations between the axes effectively shrinks their radii, revealing a duality between correlations and geometry with respect to the problem of classification. We then apply our results to accurately estimate the capacity of deep network data.

Applying the Properties of Neurons in Machine Learning: A Brain-like Neural Model with Interactive Stimulation for Data Classification

Some neural models achieve outstanding results in image recognition, semantic segmentation and natural language processing. However, their classification performance on structured and small-scale datasets that do not involve feature extraction is worse than that of traditional algorithms, although they require more time to train. In this paper, we propose a brain-like neural model with interactive stimulation (NMIS) that focuses on data classification. It consists of a primary neural field and a senior neural field that play different cognitive roles. The former is used to correspond to real instances in the feature space, and the latter stores the category pattern. Neurons in the primary field exchange information through interactive stimulation and their activation is transmitted to the senior field via inter-field interaction, simulating the mechanisms of neuronal interaction and synaptic plasticity, respectively. The proposed NMIS is biologically plausible and does not involve complex optimization processes. Therefore, it exhibits better learning ability on small-scale and structured datasets than traditional BP neural networks. For large-scale data classification, a nearest neighbor NMIS (NN_NMIS), an optimized version of NMIS, is proposed to improve computational efficiency. Numerical experiments performed on some UCI datasets show that the proposed NMIS and NN_NMIS are significantly superior to some classification algorithms that are widely used in machine learning.

Restricted Boltzmann Machines as Models of Interacting Variables

We study the type of distributions that restricted Boltzmann machines (RBMs) with different activation functions can express by investigating the effect of the activation function of the hidden nodes on the marginal distribution they impose on observed bi nary nodes. We report an exact expression for these marginals in the form of a model of interacting binary variables with the explicit form of the interactions depending on the hidden node activation function. We study the properties of these interactions in detail and evaluate how the accuracy with which the RBM approximates distributions over binary variables depends on the hidden node activation function and the number of hidden nodes. When the inferred RBM parameters are weak, an intuitive pattern is found for the expression of the interaction terms, which reduces substantially the differences across activation functions. We show that the weak parameter approximation is a good approximation for different RBMs trained on the MNIST data set. Interestingly, in these cases, the mapping reveals that the inferred models are essentially low order interaction models.

From synapse to network: models of information storage and retrieval in neural circuits

The mechanisms of information storage and retrieval in brain circuits are still the subject of debate. It is widely believed that information is stored at least in part through changes in synaptic connectivity in networks that encode this information and that these changes lead in turn to modifications of network dynamics, such that the stored information can be retrieved at a later time. Here, we review recent progress in deriving synaptic plasticity rules from experimental data and in understanding how plasticity rules affect the dynamics of recurrent networks. We show that the dynamics generated by such networks exhibit a large degree of diversity, depending on parameters, similar to experimental observations in vivo during delayed response tasks.

Recognition capabilities of a Hopfield model with auxiliary hidden neurons

We study the recognition capabilities of the Hopfield model with auxiliary hidden layers, which emerge naturally upon a Hubbard-Stratonovich transformation. We show that the recognition capabilities of such a model at zero temperature outperform those of the original Hopfield model, due to a substantial increase of the storage capacity and the lack of a naturally defined basin of attraction. The modified model does not fall abruptly into the regime of complete confusion when memory load exceeds a sharp threshold. This latter circumstance, together with an increase of the storage capacity, renders such a modified Hopfield model a promising candidate for further research, with possible diverse applications.