What grid cells convey about rat location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code

ForestHash: Semantic Hashing With Shallow Random Forests and Tiny Convolutional Networks

Hash codes are efficient data representations for coping with the ever growing amounts of data. In this paper, we introduce a random forest semantic hashing scheme that embeds tiny convolutional neural networks (CNN) into shallow random forests, with near-optimal information-theoretic code aggregation among trees. We start with a simple hashing scheme, where random trees in a forest act as hashing functions by setting `1' for the visited tree leaf, and `0' for the rest. We show that traditional random forests fail to generate hashes that preserve the underlying similarity between the trees, rendering the random forests approach to hashing challenging. To address this, we propose to first randomly group arriving classes at each tree split node into two groups, obtaining a significantly simplified two-class classification problem, which can be handled using a light-weight CNN weak learner. Such random class grouping scheme enables code uniqueness by enforcing each class to share its code with different classes in different trees. A non-conventional low-rank loss is further adopted for the CNN weak learners to encourage code consistency by minimizing intra-class variations and maximizing inter-class distance for the two random class groups. Finally, we introduce an information-theoretic approach for aggregating codes of individual trees into a single hash code, producing a near-optimal unique hash for each class. The proposed approach significantly outperforms state-of-the-art hashing methods for image retrieval tasks on large-scale public datasets, while performing at the level of other state-of-the-art image classification techniques while utilizing a more compact and efficient scalable representation. This work proposes a principled and robust procedure to train and deploy in parallel an ensemble of light-weight CNNs, instead of simply going deeper.Comment: Accepted to ECCV 201

Using correlation matrix memories for inferencing in expert systems

Outline of The Chapter… Section 16.2 describes CMM and the Dynamic Variable Binding Problem. Section 16.3 deals with how CMM is used as part of an inferencing engine. Section 16.4 details the important performance characteristics of CMM

On the origin of the mitochondrial genetic code: Towards a unified mathematical framework for the management of genetic information

The origin of the genetic code represents one of the most challenging problems in molecular evolution. The genetic code is an important universal feature of extant organisms and indicates a common ancestry of different forms of life on earth. Known variants of the genetic code can be mainly divided in mitochondrial and nuclear classes. Here we provide a new insight on the origin of the mitochondrial genetic code: we found that its degeneracy distribution can be explained by using a mathematical approach recently developed for the description of the Euplotes nuclear variant of the genetic code. The results point to a primeval mitochondrial genetic code composed of four base codons, which we call tesserae, that, among other features, exhibit outstanding error detection capabilities. The theoretical description suggests also a formulation of a plausible biological theory about the origin of protein coding. Such theory is based on the symmetry properties of hypothetical primeval chemical adaptors between nucleic acids and amino acids (ancient tRNA’s). Our paper provides a unified mathematical framework for different hypotheses on the origin of genetic coding. Also, it contributes to revisit our present view about the evolutionary steps that led to extant genetic codes by giving a new first-principles perspective on the difficult problem of the origin of the genetic code, and consequently, on the origin of life on earth