Bump formation in a binary attractor neural network

Retrieval of noisy fingerprint patterns using metric attractor networks

This work experimentally analyzes the learning and retrieval capabilities of the diluted metric attractor neural network when applied to collections of fingerprint images. The computational cost of the network decreases with the dilution, so we can increase the region of interest to cover almost the complete fingerprint. The network retrieval was successfully tested for different noisy configurations of the fingerprints, and proved to be robust with a large basin of attraction. We showed that network topologies with a 2D-Grid arrangement adapt better to the fingerprints spatial structure, outperforming the typical 1D-Ring configuration. An optimal ratio of local connections to random shortcuts that better represent the intrinsic spatial structure of the fingerprints was found, and its influence on the retrieval quality was characterized in a phase diagram. Since the present model is a set of nonlinear equations, it is possible to go beyond the naïve static solution (consisting in matching two fingerprints using a fixed distance threshold value), and a crossing evolution of similarities was shown, leading to the retrieval of the right fingerprint from an apparently more distant candidate. This feature could be very useful for fingerprint verification to discriminate between fingerprints pairs.

Structured information in small-world neural networks

The retrieval abilities of spatially uniform attractor networks can be measured by the global overlap between patterns and neural states. However, we found that nonuniform networks, for instance, small-world networks, can retrieve fragments of patterns (blocks) without performing global retrieval. We propose a way to measure the local retrieval using a parameter that is related to the fluctuation of the block overlaps. Simulation of neural dynamics shows a competition between local and global retrieval. The phase diagram shows a transition from local retrieval to global retrieval when the storage ratio increases and the topology becomes more random. A theoretical approach confirms the simulation results and predicts that the stability of blocks can be improved by dilution.

Representing where along with what information in a model of a cortical patch

Behaving in the real world requires flexibly combining and maintaining information about both continuous and discrete variables. In the visual domain, several lines of evidence show that neurons in some cortical networks can simultaneously represent information about the position and identity of objects, and maintain this combined representation when the object is no longer present. The underlying network mechanism for this combined representation is, however, unknown. In this paper, we approach this issue through a theoretical analysis of recurrent networks. We present a model of a cortical network that can retrieve information about the identity of objects from incomplete transient cues, while simultaneously representing their spatial position. Our results show that two factors are important in making this possible: A) a metric organisation of the recurrent connections, and B) a spatially localised change in the linear gain of neurons. Metric connectivity enables a localised retrieval of information about object identity, while gain modulation ensures localisation in the correct position. Importantly, we find that the amount of information that the network can retrieve and retain about identity is strongly affected by the amount of information it maintains about position. This balance can be controlled by global signals that change the neuronal gain. These results show that anatomical and physiological properties, which have long been known to characterise cortical networks, naturally endow them with the ability to maintain a conjunctive representation of the identity and location of objects.

Localized activity profiles and storage capacity of rate-based autoassociative networks

We study analytically the effect of metrically structured connectivity on the behavior of autoassociative networks. The steady state equations are derived for a generic input-output function, and then we focus on their solutions in the case of networks composed of three alternative simple rate-based model neurons: threshold-linear, binary or smoothly saturating units. For a connectivity which is short range enough the threshold-linear network shows localized retrieval states. The saturating and binary models also exhibit spatially modulated retrieval states if the highest activity level that they can achieve is above the maximum activity of the units in the stored patterns. We show that this saturation level together with the linear gain of the transfer function are important parameters that determine the possibility of localized retrieval. If the ratio of the number of stored patterns to the number of connections per unit goes to zero, while the latter goes to infinity, it is possible to derive an analytical formula for the critical value of the connectivity width, below which one observes spatially nonuniform retrieval states. The formula is also shown to offer a good first approximation for higher storage loads. We show that even in the case of localized retrieval the storage capacity remains proportional to the number of connections per neurons, with the proportionality constant lower by a factor of 3-4 compared to uniform retrieval. The approach that we present here is generic in the sense that there are no specific assumptions on the single unit input-output function nor on the exact connectivity structure.