Deep Unsupervised Similarity Learning using Partially Ordered Sets

Unsupervised learning of visual similarities is of paramount importance to computer vision, particularly due to lacking training data for fine-grained similarities. Deep learning of similarities is often based on relationships between pairs or triplets of samples. Many of these relations are unreliable and mutually contradicting, implying inconsistencies when trained without supervision information that relates different tuples or triplets to each other. To overcome this problem, we use local estimates of reliable (dis-)similarities to initially group samples into compact surrogate classes and use local partial orders of samples to classes to link classes to each other. Similarity learning is then formulated as a partial ordering task with soft correspondences of all samples to classes. Adopting a strategy of self-supervision, a CNN is trained to optimally represent samples in a mutually consistent manner while updating the classes. The similarity learning and grouping procedure are integrated in a single model and optimized jointly. The proposed unsupervised approach shows competitive performance on detailed pose estimation and object classification.Comment: Accepted for publication at IEEE Computer Vision and Pattern Recognition 201

View-tolerant face recognition and Hebbian learning imply mirror-symmetric neural tuning to head orientation

The primate brain contains a hierarchy of visual areas, dubbed the ventral stream, which rapidly computes object representations that are both specific for object identity and relatively robust against identity-preserving transformations like depth-rotations. Current computational models of object recognition, including recent deep learning networks, generate these properties through a hierarchy of alternating selectivity-increasing filtering and tolerance-increasing pooling operations, similar to simple-complex cells operations. While simulations of these models recapitulate the ventral stream's progression from early view-specific to late view-tolerant representations, they fail to generate the most salient property of the intermediate representation for faces found in the brain: mirror-symmetric tuning of the neural population to head orientation. Here we prove that a class of hierarchical architectures and a broad set of biologically plausible learning rules can provide approximate invariance at the top level of the network. While most of the learning rules do not yield mirror-symmetry in the mid-level representations, we characterize a specific biologically-plausible Hebb-type learning rule that is guaranteed to generate mirror-symmetric tuning to faces tuning at intermediate levels of the architecture

Kramers-Wannier duality and worldline representation for the SU(2) principal chiral model

In this letter we explore different representations of the SU(2) principal chiral model on the lattice. We couple chemical potentials to two of the conserved charges to induce finite density. This leads to a complex action such that the conventional field representation cannot be used for a Monte Carlo simulation. Using the recently developed Abelian color flux approach we derive a new worldline representation where the partition sum has only real and positive weights, such that a Monte Carlo simulation is possible. In a second step we transform the model to new dual variables in the Kramers-Wannier (KW) sense, such that the constraints are automatically fulfilled, and we obtain a second representation free of the complex action problem. We implement exploratory Monte Carlo simulations for both, the worldline, as well as the KW-dual form, for cross-checking the two dualizations and a first assessment of their potential for dual simulations.Comment: Comments and a new plot for the relative errors added. Version to appear in Physics Letters

Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions

Simple to Complex Cross-modal Learning to Rank

The heterogeneity-gap between different modalities brings a significant challenge to multimedia information retrieval. Some studies formalize the cross-modal retrieval tasks as a ranking problem and learn a shared multi-modal embedding space to measure the cross-modality similarity. However, previous methods often establish the shared embedding space based on linear mapping functions which might not be sophisticated enough to reveal more complicated inter-modal correspondences. Additionally, current studies assume that the rankings are of equal importance, and thus all rankings are used simultaneously, or a small number of rankings are selected randomly to train the embedding space at each iteration. Such strategies, however, always suffer from outliers as well as reduced generalization capability due to their lack of insightful understanding of procedure of human cognition. In this paper, we involve the self-paced learning theory with diversity into the cross-modal learning to rank and learn an optimal multi-modal embedding space based on non-linear mapping functions. This strategy enhances the model's robustness to outliers and achieves better generalization via training the model gradually from easy rankings by diverse queries to more complex ones. An efficient alternative algorithm is exploited to solve the proposed challenging problem with fast convergence in practice. Extensive experimental results on several benchmark datasets indicate that the proposed method achieves significant improvements over the state-of-the-arts in this literature.Comment: 14 pages; Accepted by Computer Vision and Image Understandin