Deferring the learning for better generalization in radial basis neural networks

Proceeding of: International Conference Artificial Neural Networks — ICANN 2001. Vienna, Austria, August 21–25, 2001The level of generalization of neural networks is heavily dependent on the quality of the training data. That is, some of the training patterns can be redundant or irrelevant. It has been shown that with careful dynamic selection of training patterns, better generalization performance may be obtained. Nevertheless, generalization is carried out independently of the novel patterns to be approximated. In this paper, we present a learning method that automatically selects the most appropriate training patterns to the new sample to be predicted. The proposed method has been applied to Radial Basis Neural Networks, whose generalization capability is usually very poor. The learning strategy slows down the response of the network in the generalisation phase. However, this does not introduces a significance limitation in the application of the method because of the fast training of Radial Basis Neural Networks

Characterizing the Implicit Bias of Regularized SGD in Rank Minimization

We study the bias of Stochastic Gradient Descent (SGD) to learn low-rank weight matrices when training deep neural networks. Our results show that training neural networks with mini-batch SGD and weight decay causes a bias towards rank minimization over the weight matrices. Specifically, we show, both theoretically and empirically, that this bias is more pronounced when using smaller batch sizes, higher learning rates, or increased weight decay. Additionally, we predict and observe empirically that weight decay is necessary to achieve this bias. Unlike previous literature, our analysis does not rely on assumptions about the data, convergence, or optimality of the weight matrices and applies to a wide range of neural network architectures of any width or depth. Finally, we empirically investigate the connection between this bias and generalization, finding that it has a marginal effect on generalization

Cambios florísticos en comunidades de malezas : un marco conceptual basado en reglas de ensamblaje

150-158Agriculture provides interesting situations to study ecological succession in weed communities. There is empirical evidence of floristic shifts in weed communities due to both environmental and technological changes, which have been interpreted in the light of succession theory. In turn, the assembly rules framework has proved to be useful to describe and predict patterns of change in communities. The aim of this paper is to present the application of an approach based on community assembly rules to study floristic changes in weed communities. Assembly rules are associated with specific factors that explain the patterns observed in a community. Assembly rules operate as a filter restricting the number of species of the regional pool that occur in local communities. The regional species pool is defined by means of a hierarchical classification as three nested spatial domains: geographic, landscape and habitat type. At large spatial scales (1000-10000 km 2), the species pool is determined by the factors regulating the rates of both speciation and extinction and plant migrations between distant regions. Landscape complexity effects are higher at regional level. While dispersion increases its influence in mosaics of patches (100 m 2-10 ha), habitat heterogeneity is more important in smaller patches (1-1000 m 2-1 ha). In small plots (<10 m 2), plant communities are modulated by biotic interactions, soil fertility, abiotic stress and microdisturbances. Species from the regional pool are filtering out by the limitations to dispersal within the region and the restrictions imposed by both the abiotic environment and biotic interaction at local scale. Community assembly rules provide a flexible framework for building descriptive models of successional trajectories in weed communities in response to changes in agricultural systems

Cambios florísticos en comunidades de malezas : un marco conceptual basado en reglas de ensamblaje

150-158Agriculture provides interesting situations to study ecological succession in weed communities. There is empirical evidence of floristic shifts in weed communities due to both environmental and technological changes, which have been interpreted in the light of succession theory. In turn, the assembly rules framework has proved to be useful to describe and predict patterns of change in communities. The aim of this paper is to present the application of an approach based on community assembly rules to study floristic changes in weed communities. Assembly rules are associated with specific factors that explain the patterns observed in a community. Assembly rules operate as a filter restricting the number of species of the regional pool that occur in local communities. The regional species pool is defined by means of a hierarchical classification as three nested spatial domains: geographic, landscape and habitat type. At large spatial scales (1000-10000 km 2), the species pool is determined by the factors regulating the rates of both speciation and extinction and plant migrations between distant regions. Landscape complexity effects are higher at regional level. While dispersion increases its influence in mosaics of patches (100 m 2-10 ha), habitat heterogeneity is more important in smaller patches (1-1000 m 2-1 ha). In small plots (<10 m 2), plant communities are modulated by biotic interactions, soil fertility, abiotic stress and microdisturbances. Species from the regional pool are filtering out by the limitations to dispersal within the region and the restrictions imposed by both the abiotic environment and biotic interaction at local scale. Community assembly rules provide a flexible framework for building descriptive models of successional trajectories in weed communities in response to changes in agricultural systems

Magnetic anisotropy of individual maghemite mesocrystals

Interest in creating magnetic metamaterials has led to methods for growing superstructures of magnetic nanoparticles. Mesoscopic crystals of maghemite (gamma-Fe2O3) nanoparticles can be arranged into highly ordered body-centered tetragonal lattices of up to a few micrometers. Although measurements on disordered ensembles have been carried out, determining the magnetic properties of individual mesoscopic crystals is challenging due to their small total magnetic moment. Here, we overcome these challenges by utilizing sensitive dynamic cantilever magnetometry to study individual micrometer-sized gamma-Fe2O3 mesocrystals. These measurements reveal an unambiguous cubic anisotropy, resulting from the crystalline anisotropy of the constituent maghemite nanoparticles and their alignment within the mesoscopic lattice. The signatures of anisotropy and its origins come to light because we combine the self-assembly of highly ordered mesocrystals with the ability to resolve their individual magnetism. This combination is promising for future studies of the magnetic anisotropy of other nanoparticles, which are too small to investigate individually

Implicitly Constrained Semi-Supervised Least Squares Classification

We introduce a novel semi-supervised version of the least squares classifier. This implicitly constrained least squares (ICLS) classifier minimizes the squared loss on the labeled data among the set of parameters implied by all possible labelings of the unlabeled data. Unlike other discriminative semi-supervised methods, our approach does not introduce explicit additional assumptions into the objective function, but leverages implicit assumptions already present in the choice of the supervised least squares classifier. We show this approach can be formulated as a quadratic programming problem and its solution can be found using a simple gradient descent procedure. We prove that, in a certain way, our method never leads to performance worse than the supervised classifier. Experimental results corroborate this theoretical result in the multidimensional case on benchmark datasets, also in terms of the error rate.Comment: 12 pages, 2 figures, 1 table. The Fourteenth International Symposium on Intelligent Data Analysis (2015), Saint-Etienne, Franc

Harnessing nuclear spin polarization fluctuations in a semiconductor nanowire

Soon after the first measurements of nuclear magnetic resonance (NMR) in a condensed matter system, Bloch predicted the presence of statistical fluctuations proportional to $1/\sqrt{N}$ in the polarization of an ensemble of $N$ spins. First observed by Sleator et al., so-called "spin noise" has recently emerged as a critical ingredient in nanometer-scale magnetic resonance imaging (nanoMRI). This prominence is a direct result of MRI resolution improving to better than 100 nm^3, a size-scale in which statistical spin fluctuations begin to dominate the polarization dynamics. We demonstrate a technique that creates spin order in nanometer-scale ensembles of nuclear spins by harnessing these fluctuations to produce polarizations both larger and narrower than the natural thermal distribution. We focus on ensembles containing ~10^6 phosphorus and hydrogen spins associated with single InP and GaP nanowires (NWs) and their hydrogen-containing adsorbate layers. We monitor, control, and capture fluctuations in the ensemble's spin polarization in real-time and store them for extended periods. This selective capture of large polarization fluctuations may provide a route for enhancing the weak magnetic signals produced by nanometer-scale volumes of nuclear spins. The scheme may also prove useful for initializing the nuclear hyperfine field of electron spin qubits in the solid-state.Comment: 18 pages, 5 figure

Non-perturbative effects in semi-leptonic B_c decays

We discuss the impact of the soft degrees of freedom inside the B_c meson on its rate in the semi-leptonic decay B_c -> X l nu_l where X denotes light hadrons below the D^0 threshold. In particular we identify contributions involving soft hadrons which are non-vanishing in the limit of massless leptons. These contributions become relevant for a measurement of the purely leptonic B_c decay rate, which due to helicity suppression involves a factor m_l^2 and thus is much smaller than the contributions involving soft hadrons.Comment: LaTeX, 22 pages, 1 figur

Charmed decays of the B-meson in the quark model

Exclusive and inclusive, semileptonic and non-leptonic, charmed decays of the B-meson are investigated in the context of a phenomenological quark model. Bound-state effects are taken care of by adopting a single (model-dependent) non-perturbative wave function, describing the motion of the light spectator quark in the B-meson. A nice reproduction of both exclusive and inclusive semileptonic data is obtained. Our predictions for the electron spectrum are presented and compared with those of the Isgur-Scora-Grinstein-Wise quark model. Finally, our approach is applied to the calculation of inclusive non-leptonic widths, obtaining a remarkable agreement with experimental findings.Comment: to appear in the Proc. of the 2^{nd} Int. Conf. on Hyperons, Charm and Beauty Hadrons, Montreal, Canada, 27-30 August 199