This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in su(2) k WZW models. Here we present a constructive derivation of the fermionic character at level k based on these paths. The starting point is the expression of a path in terms of a sequence of nonlocal (formal) operators acting on the vacuum ground-state path. Within this framework, the key step is the construction of the level-k operator sequences out of those at level-1 by the action of a new type of operators. These actions of operators on operators turn out to have a path interpretation: these paths are precisely the finitized RSOS paths related to the unitary minimal models M(k + 1, k + 2). We thus unravel -at the level of the path representation of the states -, a direct factorization into a k = 1 spinon part times a RSOS factor. It is also pointed out that since there are two fermionic forms describing these finite RSOS paths, the resulting fermionic su(2) k characters arise in two versions. Finally, the relation between the present construction and the Nagoya spectral decomposition of the path space is sketched.

This is the first of two articles devoted to the analysis of the path description of the states in su(2) k WZW models, a representation well suited for constructive derivations of the fermionic characters. In this first article, the cases k = 1, 2 are treated in detail, emphasizing a different description in each case (operators vs particles). For k = 1, we first prove, as a side result, the equivalence of two known path representations for the finitized su(2) 1 states by displaying an explicit bijection. An immediate offshoot is the gain of a new and simple weighting for the (Kyoto) path representation that generalizes to level k. The bijection also suggests two operator constructions for the su(2) 1 paths, a local and a nonlocal one, both interrelated. These are formal operators that map a path to another path, so that any path can be obtained by successive applications of these operators on a simple reference (ground-state) path. The nonlocal operator description is the starting point for a direct and elementary derivation of the su(2) 1 spinon character. The second part presents an extensive study of the su(2) 2 paths from their particle point of view, where the particles are defined as the path building blocks. The resulting generating functions appear to provide new (at least superficially) fermionic forms of the characters. In particular, a nice relationship between the sum of the j = 0, 1 characters at k = 2 and the two ones at k = 1 is unravelled.

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We present Hinted Networks: a collection of architectural transformations for improving the accuracies of neural network models for regression tasks, through the injection of a prior for the output prediction (i.e. a hint). We ground our investigations within the camera relocalization domain, and propose two variants, namely the Hinted Embedding and Hinted Residual networks, both applied to the PoseNet base model for regressing camera pose from an image. Our evaluations show practical improvements in localization accuracy for standard outdoor and indoor localization datasets, without using additional information. We further assess the range of accuracy gains within an aerial-view localization setup, simulated across vast areas at different times of the year.