Do Humans and Deep Convolutional Neural Networks Use Visual Information Similarly for the Categorization of Natural Scenes?

The investigation of visual categorization has recently been aided by the introduction of deep convolutional neural networks (CNNs), which achieve unprecedented accuracy in picture classification after extensive training. Even if the architecture of CNNs is inspired by the organization of the visual brain, the similarity between CNN and human visual processing remains unclear. Here, we investigated this issue by engaging humans and CNNs in a two-class visual categorization task. To this end, pictures containing animals or vehicles were modified to contain only low/high spatial frequency (HSF) information, or were scrambled in the phase of the spatial frequency spectrum. For all types of degradation, accuracy increased as degradation was reduced for both humans and CNNs; however, the thresholds for accurate categorization varied between humans and CNNs. More remarkable differences were observed for HSF information compared to the other two types of degradation, both in terms of overall accuracy and image-level agreement between humans and CNNs. The difficulty with which the CNNs were shown to categorize high-passed natural scenes was reduced by picture whitening, a procedure which is inspired by how visual systems process natural images. The results are discussed concerning the adaptation to regularities in the visual environment (scene statistics); if the visual characteristics of the environment are not learned by CNNs, their visual categorization may depend only on a subset of the visual information on which humans rely, for example, on low spatial frequency information.

Natural Language Statistical Features of LSTM-Generated Texts.

Long short-term memory (LSTM) networks have recently shown remarkable performance in several tasks that are dealing with natural language generation, such as image captioning or poetry composition. Yet, only few works have analyzed text generated by LSTMs in order to quantitatively evaluate to which extent such artificial texts resemble those generated by humans. We compared the statistical structure of LSTM-generated language to that of written natural language, and to those produced by Markov models of various orders. In particular, we characterized the statistical structure of language by assessing word-frequency statistics, long-range correlations, and entropy measures. Our main finding is that while both LSTM- and Markov-generated texts can exhibit features similar to real ones in their word-frequency statistics and entropy measures, LSTM-texts are shown to reproduce long-range correlations at scales comparable to those found in natural language. Moreover, for LSTM networks, a temperature-like parameter controlling the generation process shows an optimal value-for which the produced texts are closest to real language-consistent across different statistical features investigated.

The common origin of symmetry and structure in genetic sequences.

Biologists have long sought a way to explain how statistical properties of genetic sequences emerged and are maintained through evolution. On the one hand, non-random structures at different scales indicate a complex genome organisation. On the other hand, single-strand symmetry has been scrutinised using neutral models in which correlations are not considered or irrelevant, contrary to empirical evidence. Different studies investigated these two statistical features separately, reaching minimal consensus despite sustained efforts. Here we unravel previously unknown symmetries in genetic sequences, which are organized hierarchically through scales in which non-random structures are known to be present. These observations are confirmed through the statistical analysis of the human genome and explained through a simple domain model. These results suggest that domain models which account for the cumulative action of mobile elements can explain simultaneously non-random structures and symmetries in genetic sequences.

Characterization of DNA methylation as a function of biological complexity via dinucleotide inter-distances.

We perform a statistical study of the distances between successive occurrences of a given dinucleotide in the DNA sequence for a number of organisms of different complexity. Our analysis highlights peculiar features of the CG dinucleotide distribution in mammalian DNA, pointing towards a connection with the role of such dinucleotide in DNA methylation. While the CG distributions of mammals exhibit exponential tails with comparable parameters, the picture for the other organisms studied (e.g. fish, insects, bacteria and viruses) is more heterogeneous, possibly because in these organisms DNA methylation has different functional roles. Our analysis suggests that the distribution of the distances between CG dinucleotides provides useful insights into characterizing and classifying organisms in terms of methylation functionalities.

Temporal-varying failures of nodes in networks.

We consider networks in which random walkers are removed because of the failure of specific nodes. We interpret the rate of loss as a measure of the importance of nodes, a notion we denote as failure centrality. We show that the degree of the node is not sufficient to determine this measure and that, in a first approximation, the shortest loops through the node have to be taken into account. We propose approximations of the failure centrality which are valid for temporal-varying failures, and we dwell on the possibility of externally changing the relative importance of nodes in a given network by exploiting the interference between the loops of a node and the cycles of the temporal pattern of failures. In the limit of long failure cycles we show analytically that the escape in a node is larger than the one estimated from a stochastic failure with the same failure probability. We test our general formalism in two real-world networks (air-transportation and e-mail users) and show how communities lead to deviations from predictions for failures in hubs.

Machta-Zwanzig regime of anomalous diffusion in infinite-horizon billiards.

We study diffusion on a periodic billiard table with an infinite horizon in the limit of narrow corridors. An effective trapping mechanism emerges according to which the process can be modeled by a Lévy walk combining exponentially distributed trapping times with free propagation along paths whose precise probabilities we compute. This description yields an approximation of the mean squared displacement of infinite-horizon billiards in terms of two transport coefficients, which generalizes to this anomalous regime the Machta-Zwanzig approximation of normal diffusion in finite-horizon billiards [J. Machta and R. Zwanzig, Phys. Rev. Lett. 50, 1959 (1983)PRLTAO0031-900710.1103/PhysRevLett.50.1959].

Sparre-Andersen theorem with spatiotemporal correlations.

The Sparre-Andersen theorem is a remarkable result in one-dimensional random walk theory concerning the universality of the ubiquitous first-passage-time distribution. It states that the probability distribution ρ(n) of the number of steps needed for a walker starting at the origin to land on the positive semiaxes does not depend on the details of the distribution for the jumps of the walker, provided this distribution is symmetric and continuous, where in particular ρ(n) ∼ n(-3/2) for large number of steps n. On the other hand, there are many physical situations in which the time spent by the walker in doing one step depends on the length of the step and the interest concentrates on the time needed for a return, not on the number of steps. Here we modify the Sparre-Andersen proof to deal with such cases, in rather general situations in which the time variable correlates with the step variable. As an example we present a natural process in 2D that shows that deviations from normal scaling are present for the first-passage-time distribution on a semiplane.

Measuring logarithmic corrections to normal diffusion in infinite-horizon billiards.

We perform numerical measurements of the moments of the position of a tracer particle in a two-dimensional periodic billiard model (Lorentz gas) with infinite corridors. This model is known to exhibit a weak form of superdiffusion, in the sense that there is a logarithmic correction to the linear growth in time of the mean-squared displacement. We show numerically that this expected asymptotic behavior is easily overwhelmed by the subleading linear growth throughout the time range accessible to numerical simulations. We compare our simulations to analytical results for the variance of the anomalously rescaled limiting normal distributions.

On the origin of long-range correlations in texts.

The complexity of human interactions with social and natural phenomena is mirrored in the way we describe our experiences through natural language. In order to retain and convey such a high dimensional information, the statistical properties of our linguistic output has to be highly correlated in time. An example are the robust observations, still largely not understood, of correlations on arbitrary long scales in literary texts. In this paper we explain how long-range correlations flow from highly structured linguistic levels down to the building blocks of a text (words, letters, etc..). By combining calculations and data analysis we show that correlations take form of a bursty sequence of events once we approach the semantically relevant topics of the text. The mechanisms we identify are fairly general and can be equally applied to other hierarchical settings.

Recurrence for quenched random Lorentz tubes.

We consider the billiard dynamics in a striplike set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called quenched random Lorentz tube. We prove that under general conditions, almost every system in the ensemble is recurrent.

Dynamical and transport properties in a family of intermittent area-preserving maps.

We introduce a family of area-preserving maps representing a (nontrivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations, providing analytical and numerical estimates. We study the transport properties of a suitable lift and use a probabilistic argument to derive the full spectrum of transport moments. Finally, the dynamical effects of a stochastic perturbation are considered.

Anomalous deterministic transport.

We present a series of results on deterministic transport in chaotic system, obtained in the framework of periodic orbits theory. The emphasis is on intermittent systems, where deviations from complete chaos may induce anomalies on the asymptotic moments' growth.

Anomalous transport: a deterministic approach.

We introduce a cycle-expansion (fully deterministic) technique to compute the asymptotic behavior of arbitrary order transport moments. The theory is applied to different kinds of one-dimensional intermittent maps and Lorentz gas with an infinite horizon, confirming the typical appearance of phase transitions in the transport spectrum.