1,721,070 research outputs found
Retrieving mismatched memory patterns in the Hopfield model of neural networks
Get PDFThe main objective of this thesis is to explore the physical mechanisms of the so called Hopfield model of neural networks and to recover some quantitative results regarding a few of its possible variations. The Hopfield model is a paradigm of theoretical physics and computational neuroscience because it is a model of interacting neurons that shows how such simple units are able to store and retrieve memories in a statistical mechanical framework. Though the structure of the Hopfield model has been inspired by neuroscience, just like neural networks, its applications can be various and a simulation of such a model has been done also in the context of random optical systems.
A modern application of the Hopfield network has been found by Hopfield himself, he was able to build an associative memory model related to the original Hopfield model, but with multiple neuron interactions. He, then, mapped it onto a neural network with one hidden layer and an unusual activation function and its utility has been illustrated for two test cases: the logical gate XOR and the recognition of handwritten digits from the MNIST data set.
The Hopfield model is useful also in the case of inference problems and, in the context of neural networks, it has been proven to be equivalent to the so called attention mechanism used by Transformers if the update rule is replaced with a particular one.
In recent decades, with the improvement of human computational power, neural networks have proven themselves very useful and they have been widely used not only in the academic world. For this reason, scientists started to wonder more and more about the physical reasons and laws that allow such networks to work.
In order to do that, we start, in Section 2, by studying a class of Hopfield models where the memories are represented by a mixture of Gaussian and binary variables and the neurons are Ising spins and for this reason we say that the continuous pattern variables are partially mismatched with the binary system variables. We study the properties of this family of models as the relative weight of the two kinds of variables in the patterns varies. We quantitatively determine how the maximum number of memories that can be stored without letting the system lose the property to act as an associative memory squeezes towards zero as the memory patterns contain a larger fraction of mismatched variables. As the memory is purely Gaussian retrieval is lost for any positive storage capacity. It is shown that this comes about because of the spherical symmetry of the free energy in the Gaussian case. Introducing two different memory pattern overlaps between spin configurations and each contribution to the pattern from the two kinds of variables one can observe that the Gaussian parts of the patterns act as a noise, making retrieval more difficult. The basins of attraction of the states, the accuracy of the retrieval and the storage capacity are studied by means of Monte Carlo numerical simulations. We uncover that even in the limit where the network capacity shrinks to zero, the (few) retrieval states maintain a large basin of attraction and large overlaps with the mismatched patterns. So the network can be used for retrieval, but with a very small capacity.
In Section 3, we take into account other possible variations of the Hopfield model and, precisely, the spherical Hopfield model with Gaussian and bimodal memorized patterns. In both cases, the same spherical symmetry that causes the aforementioned lack of retrieval persists and, this time, we use a higher order term in the Hamiltonian (4-bodies interactions) to recover retrieval.
In Section 4 we obtain the mean field dynamical equation of the spherical (2+4)- Hopfield model for the macroscopic observables and we present a gradient descent analysis of the out of equilibrium dynamics of such a model in order to better understand its retrieval properties
Effective interactions in group competition with strategic diffusive dynamics
No full textWe analyze, on a random graph, a diffusive strategic dynamics with pairwise interactions, where
nor Glauber prescription, neither detailed balance hold. We observe numerically that such a dynamics reaches a well defined steady state that fulfills a shift property: the critical temperature of
the canonical ferromagnetic phase transition is higher with respect to the expected equilibrium one,
known both numerically via Glauber relaxation or Monte Carlo simulations as well as analytically
via cavity techniques or replica approaches.
We show how the relaxed states of this kind of dynamics can be described by statistical mechanics
equilibria of a diluted p-spin model, for a suitable non-integer real p. Several implications from both
theoretical physics and quantitative sociology points of view are discussed
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
How glassy are neural networks?
No full textIn this paper we continue our investigation on the high storage regime of a neural network with Gaussian patterns. Through an exact mapping between its partition function and one of a bipartite spin glass (whose parties consist of Ising and Gaussian spins respectively), we give a complete control of the whole annealed region. The strategy explored is based on an interpolation between the bipartite system and two independent spin glasses built respectively by dichotomic and Gaussian spins: critical line, behavior of the principal thermodynamic observables and their fluctuations as well as overlap fluctuations are obtained and discussed. Then, we move further, extending such an equivalence beyond the critical line, to explore the broken ergodicity phase under the assumption of replica symmetry and show that the quenched free energy of this (analogical) Hopfield model can be described as a linear combination of the two quenched spin glass free energies even in the replica symmetric framework. © 2012 IOP Publishing Ltd and SISSA Medialab srl
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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