Neuroscience: A Face's Journey through Space and Time.

Faces are complex objects of great variety, which the visual brain somehow manages to organize by similarity. Two such orderings in fact exist and one, a new study finds, is transformed into the other over time, enhancing a face's distinctiveness.

Convolutional neural networks explain tuning properties of anterior, but not middle, face-processing areas in macaque inferotemporal cortex.

Recent computational studies have emphasized layer-wise quantitative similarity between convolutional neural networks (CNNs) and the primate visual ventral stream. However, whether such similarity holds for the face-selective areas, a subsystem of the higher visual cortex, is not clear. Here, we extensively investigate whether CNNs exhibit tuning properties as previously observed in different macaque face areas. While simulating four past experiments on a variety of CNN models, we sought for the model layer that quantitatively matches the multiple tuning properties of each face area. Our results show that higher model layers explain reasonably well the properties of anterior areas, while no layer simultaneously explains the properties of middle areas, consistently across the model variation. Thus, some similarity may exist between CNNs and the primate face-processing system in the near-goal representation, but much less clearly in the intermediate stages, thus requiring alternative modeling such as non-layer-wise correspondence or different computational principles.

A mixture of sparse coding models explaining properties of face neurons related to holistic and parts-based processing.

Experimental studies have revealed evidence of both parts-based and holistic representations of objects and faces in the primate visual system. However, it is still a mystery how such seemingly contradictory types of processing can coexist within a single system. Here, we propose a novel theory called mixture of sparse coding models, inspired by the formation of category-specific subregions in the inferotemporal (IT) cortex. We developed a hierarchical network that constructed a mixture of two sparse coding submodels on top of a simple Gabor analysis. The submodels were each trained with face or non-face object images, which resulted in separate representations of facial parts and object parts. Importantly, evoked neural activities were modeled by Bayesian inference, which had a top-down explaining-away effect that enabled recognition of an individual part to depend strongly on the category of the whole input. We show that this explaining-away effect was indeed crucial for the units in the face submodel to exhibit significant selectivity to face images over object images in a similar way to actual face-selective neurons in the macaque IT cortex. Furthermore, the model explained, qualitatively and quantitatively, several tuning properties to facial features found in the middle patch of face processing in IT as documented by Freiwald, Tsao, and Livingstone (2009). These included, in particular, tuning to only a small number of facial features that were often related to geometrically large parts like face outline and hair, preference and anti-preference of extreme facial features (e.g., very large/small inter-eye distance), and reduction of the gain of feature tuning for partial face stimuli compared to whole face stimuli. Thus, we hypothesize that the coding principle of facial features in the middle patch of face processing in the macaque IT cortex may be closely related to mixture of sparse coding models.

Genealogy of Conjugated Acyclic Polyenes.

Based on the total π-electron energies Eπs of Hückel Molecular Orbital (HMO) method for all the possible isomers of conjugated acyclic polyenes (C2nH2n+2) up to n = 7, the structure-stability relation of the possible isomers was analyzed. It was shown that the mean length of conjugation L can roughly predict the ordering of stability among isomers, while the Z-index, or Hosoya-index, can almost perfectly reproduce their stability. Further, the genealogy of the conjugated acyclic polyene family was obtained by drawing systematic diagrams connecting these isomers of different n, and governed by several simple rules. Namely, the stability change of a given isomer in the genealogy connecting n and n + 1 polyenes can be classified into three different modes of vinyl addition (elongation, inner and outer branching) and horn growing, i.e., substitution of -HC=CH- moiety with -HC(=CH2)-C(=CH2)H-. By using the Z-index, we can extend this type of discussion to polyene radicals and even to "cross-conjugated" cyclic polyenes containing only one odd-membered cycle, such as radialene and fulvene.

Learning Visual Spatial Pooling by Strong PCA Dimension Reduction.

In visual modeling, invariance properties of visual cells are often explained by a pooling mechanism, in which outputs of neurons with similar selectivities to some stimulus parameters are integrated so as to gain some extent of invariance to other parameters. For example, the classical energy model of phase-invariant V1 complex cells pools model simple cells preferring similar orientation but different phases. Prior studies, such as independent subspace analysis, have shown that phase-invariance properties of V1 complex cells can be learned from spatial statistics of natural inputs. However, those previous approaches assumed a squaring nonlinearity on the neural outputs to capture energy correlation; such nonlinearity is arguably unnatural from a neurobiological viewpoint but hard to change due to its tight integration into their formalisms. Moreover, they used somewhat complicated objective functions requiring expensive computations for optimization. In this study, we show that visual spatial pooling can be learned in a much simpler way using strong dimension reduction based on principal component analysis. This approach learns to ignore a large part of detailed spatial structure of the input and thereby estimates a linear pooling matrix. Using this framework, we demonstrate that pooling of model V1 simple cells learned in this way, even with nonlinearities other than squaring, can reproduce standard tuning properties of V1 complex cells. For further understanding, we analyze several variants of the pooling model and argue that a reasonable pooling can generally be obtained from any kind of linear transformation that retains several of the first principal components and suppresses the remaining ones. In particular, we show how the classic Wiener filtering theory leads to one such variant.

A Hierarchical Statistical Model of Natural Images Explains Tuning Properties in V2.

Previous theoretical and experimental studies have demonstrated tight relationships between natural image statistics and neural representations in V1. In particular, receptive field properties similar to simple and complex cells have been shown to be inferable from sparse coding of natural images. However, whether such a relationship exists in higher areas has not been clarified. To address this question for V2, we trained a sparse coding model that took as input the output of a fixed V1-like model, which was in its turn fed a large variety of natural image patches as input. After the training, the model exhibited response properties that were qualitatively and quantitatively compatible with three major neurophysiological results on macaque V2, as follows: (1) homogeneous and heterogeneous integration of local orientations (Anzai et al., 2007); (2) a wide range of angle selectivities with biased sensitivities to one component orientation (Ito and Komatsu, 2004); and (3) exclusive length and width suppression (Schmid et al., 2014). The reproducibility was stable across variations in several model parameters. Further, a formal classification of the internal representations of the model units offered detailed interpretations of the experimental data, emphasizing that a novel type of model cell that could detect a combination of local orientations converging toward a single spatial point (potentially related to corner-like features) played an important role in reproducing tuning properties compatible with V2. These results are consistent with the idea that V2 uses a sparse code of natural images. Significance statement: Sparse coding theory has successfully explained a number of receptive field properties in V1; but how about in V2? This question has recently become important since a variety of properties distinct from V1 have been discovered in V2, and thus a more integrative understanding is called for. Our study shows that a hierarchical sparse coding model of natural images explains three major response properties known in the macaque V2. We further provide a detailed analysis revealing the roles of different kinds of model cells in explaining the V2-specific properties. Our results thus offer the first sparse coding account for receptive field properties in V2 that has extensive biological relevance.

Multinomial Bayesian learning for modeling classical and nonclassical receptive field properties.

We study the interplay of Bayesian inference and natural image learning in a hierarchical vision system, in relation to the response properties of early visual cortex. We particularly focus on a Bayesian network with multinomial variables that can represent discrete feature spaces similar to hypercolumns combining minicolumns, enforce sparsity of activation to learn efficient representations, and explain divisive normalization. We demonstrate that maximal-likelihood learning using sampling-based Bayesian inference gives rise to classical receptive field properties similar to V1 simple cells and V2 cells, while inference performed on the trained network yields nonclassical context-dependent response properties such as cross-orientation suppression and filling in. Comparison with known physiological properties reveals some qualitative and quantitative similarities.

How can we explain the stability of conjugated hydrocarbon-and heterosubstituted networks by topological descriptors?

Correlation between the π-electronic stability (Hückel's Eπ) and several topological descriptors, including Hosoya's Z, Wiener's W, and Randic's 1χ , was compared for the isomeric acyclic conjugated hydrocarbon molecules from hexatriene to decapentaene. From the analysis of the best descriptor Z and mean length of conjugated paths L, the origin of π-electronic stability was logically explained. The effect of heteroatom substitution to polyenes was studied and analyzed by graph-theoretical techniques. The difference in the stability and electron flow for this heteroatom substitution was also quantitatively and easily explained. Discussion was given for the difference in the topological dependency of HOMO level of these networks with even and odd number of skeletal carbon atoms. An efficient determinantal method for calculating the Z-index for tree graphs is introduced.

Sparse codes of harmonic natural sounds and their modulatory interactions.

Sparse coding and its related theories have been successful to explain various response properties of early stages of sensory information processing such as primary visual cortex and peripheral auditory system, which suggests that the emergence of such properties results from adaptation of the nerve system to natural stimuli. The present study continues this line of research in a higher stage of auditory processing, focusing on harmonic structures that are often found in behaviourally important natural sound like animal vocalization. It has been physiologically shown that monkey primary auditory cortices (A1) have neurons with response properties capturing such harmonic structures: their response and modulation peaks are often found at frequencies that are harmonically related to each other. We hypothesize that such relations emerge from sparse coding of harmonic natural sounds. Our simulation shows that similar harmonic relations emerge from frequency-domain sparse codes of harmonic sounds, namely, piano performance and human speech. Moreover, the modulatory behaviours can be explained by competitive interactions of model neurons that capture partially common harmonic structures.

Important mathematical structures of the topological index Z for tree graphs.

Mathematical importance of the topological index, ZG, or the so-called Hosoya index is stressed by presenting and giving supporting evidence for the proposed conjecture. That is, for a given pair of positive integers (n1or=3), with Z(G1) = n1 and Z(G2) = n2.

Analysis of the relationship among the graphs isomorphic to multilayered cyclic fence graphs (MLCFG).

Multilayered cyclic fence graphs (MLCFG, E(m,n), F(m,n), D(m,n), G(m,n), X(m,n)) are proposed to be defined, all of which are composed of m 2n-membered cycles with periodic bridging. They are also cubic and bipartite. Hamiltonian wheel graph, H (n,[j(k)]), and parallelogram-shaped polyhex graph are also defined. All the members of MLCFGs are found to be isomorphic to the so-called "torus benzenoid graphs", while some members of MLCFGs are found to be related to the Hamilton wheel graphs. Through the construction of Hamilton wheel graph and the matrix representation by Kirby, a number of isomorphic relations among MLCFGs, Hamilton wheel graphs, and polyhex graphs were obtained. These relations among the MLCFG members were found also by the help of the characteristic quantities of MLCFGs.