303 research outputs found
Neural Distributed Autoassociative Memories: A Survey
Introduction. Neural network models of autoassociative, distributed memory
allow storage and retrieval of many items (vectors) where the number of stored
items can exceed the vector dimension (the number of neurons in the network).
This opens the possibility of a sublinear time search (in the number of stored
items) for approximate nearest neighbors among vectors of high dimension. The
purpose of this paper is to review models of autoassociative, distributed
memory that can be naturally implemented by neural networks (mainly with local
learning rules and iterative dynamics based on information locally available to
neurons). Scope. The survey is focused mainly on the networks of Hopfield,
Willshaw and Potts, that have connections between pairs of neurons and operate
on sparse binary vectors. We discuss not only autoassociative memory, but also
the generalization properties of these networks. We also consider neural
networks with higher-order connections and networks with a bipartite graph
structure for non-binary data with linear constraints. Conclusions. In
conclusion we discuss the relations to similarity search, advantages and
drawbacks of these techniques, and topics for further research. An interesting
and still not completely resolved question is whether neural autoassociative
memories can search for approximate nearest neighbors faster than other index
structures for similarity search, in particular for the case of very high
dimensional vectors.Comment: 31 page
Common Radio Resource Management Strategies for Quality of Service Support in Heterogeneous Wireless Networks
Hoy en día existen varias tecnologías que coexisten en una misma zona formando un sistema heterogéneo. Además, este hecho se espera que se vuelva más acentuado con todas las nuevas tecnologías que se están estandarizando actualmente. Hasta ahora, generalmente son los usuarios los que eligen la tecnología a la que se van a conectar, ya sea configurando sus terminales o usando terminales distintos. Sin embargo, esta solución es incapaz de aprovechar al máximo todos los recursos. Para ello es necesario un nuevo conjunto de estrategias. Estas estrategias deben gestionar los recursos radioeléctricos conjuntamente y asegurar la satisfacción de la calidad de servicio de los usuarios.
Siguiendo esta idea, esta Tesis propone dos nuevos algoritmos. El primero es un algoritmo de asignación dinámica de recusos conjunto (JDRA) capaz de asignar recursos a usuarios y de distribuir usuarios entre tecnologías al mismo tiempo. El algoritmo está formulado en términos de un problema de optimización multi-objetivo que se resuelve usando redes neuronales de Hopfield (HNNs). Las HNNs son interesantes ya que se supone que pueden alcanzar soluciones sub-óptimas en cortos periodos de tiempo. Sin embargo, implementaciones reales de las HNNs en ordenadores pierden esta rápida respuesta. Por ello, en esta Tesis se analizan las causas y se estudian posibles mejoras.
El segundo algoritmo es un algoritmo de control de admisión conjunto (JCAC) que admite y rechaza usuarios teniendo en cuenta todas las tecnologías al mismo tiempo. La principal diferencia con otros algorimos propuestos es que éstos últimos toman las dicisiones de admisión en cada tecnología por separado. Por ello, se necesita de algún mecanismo para seleccionar la tecnología a la que los usuarios se van a conectar. Por el contrario, la técnica propuesta en esta Tesis es capaz de tomar decisiones en todo el sistema heterogéneo. Por lo tanto, los usuarios no se enlazan con ninguna tecnología antes de ser admitidos.Calabuig Soler, D. (2010). Common Radio Resource Management Strategies for Quality of Service Support in Heterogeneous Wireless Networks [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/7348Palanci
Collective stability of networks of winner-take-all circuits
The neocortex has a remarkably uniform neuronal organization, suggesting that
common principles of processing are employed throughout its extent. In
particular, the patterns of connectivity observed in the superficial layers of
the visual cortex are consistent with the recurrent excitation and inhibitory
feedback required for cooperative-competitive circuits such as the soft
winner-take-all (WTA). WTA circuits offer interesting computational properties
such as selective amplification, signal restoration, and decision making. But,
these properties depend on the signal gain derived from positive feedback, and
so there is a critical trade-off between providing feedback strong enough to
support the sophisticated computations, while maintaining overall circuit
stability. We consider the question of how to reason about stability in very
large distributed networks of such circuits. We approach this problem by
approximating the regular cortical architecture as many interconnected
cooperative-competitive modules. We demonstrate that by properly understanding
the behavior of this small computational module, one can reason over the
stability and convergence of very large networks composed of these modules. We
obtain parameter ranges in which the WTA circuit operates in a high-gain
regime, is stable, and can be aggregated arbitrarily to form large stable
networks. We use nonlinear Contraction Theory to establish conditions for
stability in the fully nonlinear case, and verify these solutions using
numerical simulations. The derived bounds allow modes of operation in which the
WTA network is multi-stable and exhibits state-dependent persistent activities.
Our approach is sufficiently general to reason systematically about the
stability of any network, biological or technological, composed of networks of
small modules that express competition through shared inhibition.Comment: 7 Figure
Asymptotic behavior of memristive circuits
The interest in memristors has risen due to their possible application both
as memory units and as computational devices in combination with CMOS. This is
in part due to their nonlinear dynamics, and a strong dependence on the circuit
topology. We provide evidence that also purely memristive circuits can be
employed for computational purposes. In the present paper we show that a
polynomial Lyapunov function in the memory parameters exists for the case of DC
controlled memristors. Such Lyapunov function can be asymptotically
approximated with binary variables, and mapped to quadratic combinatorial
optimization problems. This also shows a direct parallel between memristive
circuits and the Hopfield-Little model. In the case of Erdos-Renyi random
circuits, we show numerically that the distribution of the matrix elements of
the projectors can be roughly approximated with a Gaussian distribution, and
that it scales with the inverse square root of the number of elements. This
provides an approximated but direct connection with the physics of disordered
system and, in particular, of mean field spin glasses. Using this and the fact
that the interaction is controlled by a projector operator on the loop space of
the circuit. We estimate the number of stationary points of the approximate
Lyapunov function and provide a scaling formula as an upper bound in terms of
the circuit topology only.Comment: 20 pages, 8 figures; proofs corrected, figures changed; results
substantially unchanged; to appear in Entrop
Statistical Physics and Representations in Real and Artificial Neural Networks
This document presents the material of two lectures on statistical physics
and neural representations, delivered by one of us (R.M.) at the Fundamental
Problems in Statistical Physics XIV summer school in July 2017. In a first
part, we consider the neural representations of space (maps) in the
hippocampus. We introduce an extension of the Hopfield model, able to store
multiple spatial maps as continuous, finite-dimensional attractors. The phase
diagram and dynamical properties of the model are analyzed. We then show how
spatial representations can be dynamically decoded using an effective Ising
model capturing the correlation structure in the neural data, and compare
applications to data obtained from hippocampal multi-electrode recordings and
by (sub)sampling our attractor model. In a second part, we focus on the problem
of learning data representations in machine learning, in particular with
artificial neural networks. We start by introducing data representations
through some illustrations. We then analyze two important algorithms, Principal
Component Analysis and Restricted Boltzmann Machines, with tools from
statistical physics
Physics of epigenetic landscapes and statistical inference by cells
Biology is currently in the midst of a revolution. Great technological advances have led to unprecedented quantitative data at the whole genome level. However, new techniques are needed to deal with this deluge of high-dimensional data. Therefore, statistical physics has the potential to help develop systems biology level models that can incorporate complex data. Additionally, physicists have made great strides in understanding non-equilibrium thermodynamics. However, the consequences of these advances have yet to be fully incorporated into biology.
There are three specific problems that I address in my dissertation. First, a common metaphor for describing development is a rugged "epigenetic landscape" where cell fates are represented as attracting valleys resulting from a complex regulatory network. I introduce a framework for explicitly constructing epigenetic landscapes that combines genomic data with techniques from spin-glass physics. The model reproduces known reprogramming protocols and identifies candidate transcription factors for reprogramming to novel cell fates, suggesting epigenetic landscapes are a powerful paradigm for understanding cellular identity.
Second, I examine the dynamics of cellular reprogramming. By reanalyzing all available time-series data, I show that gene expression dynamics during reprogramming follow a simple one-dimensional reaction coordinate that is independent of both the time and details of experimental protocol used. I show that such a reaction coordinate emerges naturally from epigenetic landscape models of cell identity where cellular reprogramming is viewed as a "barrier-crossing" between the starting and ending cell fates. Overall, the analysis and model suggest that gene expression dynamics during reprogramming follow a canonical trajectory consistent with the idea of an "optimal path"' in gene expression space for reprogramming.
Third, an important task of cells is to perform complex computations in response to external signals. Intricate networks are required to sense and process signals, and since cells are inherently non-equilibrium systems, these networks naturally consume energy. Since there is a deep connection between thermodynamics, computation, and information, a natural question is what constraints does thermodynamics place on statistical estimation and learning. I modeled a single chemical receptor and established the first fundamental relationship between the energy consumption and statistical accuracy of a receptor in a cell
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