One-shot learning with pretrained convolutional neural network

2019 Summer.Includes bibliographical references.Recent progress in convolutional neural networks and deep learning has revolutionized the image classification field, and computers can now classify images with a very high accuracy. However, unlike the human vision system which efficiently recognizes a new object after seeing a similar one, recognizing new classes of images requires a time- and resource-consuming process of retraining a neural network due to several restrictions. Since a pretrained neural network has seen a large amount of training data, it may be generalized to effectively and efficiently recognize new classes considering it may extract patterns from training images. This inspires some research in one-shot learning, which is the process of learning to classify a novel class through one training image from the novel class. One-shot learning can help expand the use of a trained convolutional neural network without costly model retraining. In addition to the practical application of one-shot learning, it is also important to understand how a convolutional neural network supports one-shot learning. More specifically, how does the feature space structure to support one-shot learning? This can potentially help us better understand the mechanisms of convolutional neural networks. This thesis proposes an approximate nearest neighbor-based method for one-shot learning. This method makes use of the features produced by a pretrained convolutional neural network and builds a proximity forest to classify new classes. The algorithm is tested in two datasets with different scales and achieves reasonable high classification accuracy in both datasets. Furthermore, this thesis tries to understand the feature space to explain the success of our proposed method. A novel tool generalized curvature analysis is used to probe the feature space structure of the convolutional neural network. The results show that the feature space curves around samples with both known classes and unknown in-domain classes, but not around transition samples between classes or out-of-domain samples. In addition, the low curvature of out-of-domain samples is correlated with the inability of a pretrained convolutional neural network to classify out-of-domain classes, indicating that a pretrained model cannot generate useful feature representations for out-of-domain samples. In summary, this thesis proposes a new method for one-shot learning, and provides insight into understanding the feature space of convolutional neural networks

Alternating-offer bargaining with endogenous commitment

We revisit the classical alternating-offer bargaining model, further assuming that players cannot reduce their proposals during the game. In equilibrium, players have history-dependent strategies and do not necessarily reach an agreement immediately in the first stage

Topics in Three-Dimensional Imaging, Source Localization and Super-resolution

The realization that twisted light beams with helical phasefronts could carry orbital angular momentum (OAM) that is in excess of the photon\u27s spin angular momentum (SAM) has spawned various important applications. One example is the design of novel imaging systems that achieve three-dimensional (3D) imaging in a single snapshot via the rotation of point spread function (PSF). Based on a scalar-field analysis, a particular simple version of rotating PSF imagery, which was proposed by my advisor Dr. Prasad, furnishes a practical approach to perform 3D source localization using a spiral phase mask that generates a combination of Bessel vortex beams. For a special annular design of the mask, with the spiral-phase winding number in successive annuli changing by a fixed quantum number, this Bessel-beam combination can yield a shape and size invariant PSF that rotates as a function of the axial position of the source, and possesses a superior depth of field (DOF) when compared to other rotating PSFs. In the first part of this dissertation, we present a vector-field analysis of an improved rotating PSF design that encodes both the 3D location and polarization state of a monochromatic point dipole emitter for high numerical aperture (NA) microscopy, in which non-paraxial propagation of the imaging beam and the associated vector character of light fields are properly accounted for. By examining the angle of rotation and the spatial form of the PSF, one can simultaneously localize point sources and determine the polarization state of light emitted by them over a 3D field in a single snapshot. We also propose a more advanced approach for doing joint polarimetry and 3D localization using a SAM-OAM conversion device without the need for high NA is also proposed. A recent paradigm-shifting research proposal has focused on employing the toolbox of quantum parameter estimation for the problem of super-resolution of two incoherent point sources. Surprisingly, the quantum Fisher information (QFI) and associated quantum Cram\\u27er-Rao bound (QCRB) for estimating the one-dimensional transverse separation of the source pair are both finite constants that are achievable with purely classical measurements that utilize coherent projections of the optical wavefront. A second important contribution of this dissertation is the generalization of the previous quantum limited transverse super-resolution work to full 3D imaging with more general PSF. Under the assumption of known centroid, we first derive the general expression of $3\times 3$ QFI matrix with respect to (w.r.t.) the 3D pair separation vector, in terms of the correlation of the wavefront phase gradients in the imaging aperture. For a clear circular aperture, the QFI matrix turns out to be a separation-independent diagonal matrix. Coherent-projection bases that can attain the corresponding QCRB in special cases and small separation limits are also proposed with confirmation by numerical simulations. We next extend our 3D analysis to treat the more general 6-parameter problem of jointly estimating the 3D pair-centroid location and pair-separation vectors. We also present the results of computer simulation of an experimental protocol based on the use of Zernike-mode projections to attain these quantum estimation-limited bounds of performance