339 research outputs found
Dreaming neural networks: forgetting spurious memories and reinforcing pure ones
The standard Hopfield model for associative neural networks accounts for
biological Hebbian learning and acts as the harmonic oscillator for pattern
recognition, however its maximal storage capacity is , far
from the theoretical bound for symmetric networks, i.e. . Inspired
by sleeping and dreaming mechanisms in mammal brains, we propose an extension
of this model displaying the standard on-line (awake) learning mechanism (that
allows the storage of external information in terms of patterns) and an
off-line (sleep) unlearningconsolidating mechanism (that allows
spurious-pattern removal and pure-pattern reinforcement): this obtained daily
prescription is able to saturate the theoretical bound , remaining
also extremely robust against thermal noise. Both neural and synaptic features
are analyzed both analytically and numerically. In particular, beyond obtaining
a phase diagram for neural dynamics, we focus on synaptic plasticity and we
give explicit prescriptions on the temporal evolution of the synaptic matrix.
We analytically prove that our algorithm makes the Hebbian kernel converge with
high probability to the projection matrix built over the pure stored patterns.
Furthermore, we obtain a sharp and explicit estimate for the "sleep rate" in
order to ensure such a convergence. Finally, we run extensive numerical
simulations (mainly Monte Carlo sampling) to check the approximations
underlying the analytical investigations (e.g., we developed the whole theory
at the so called replica-symmetric level, as standard in the
Amit-Gutfreund-Sompolinsky reference framework) and possible finite-size
effects, finding overall full agreement with the theory.Comment: 31 pages, 12 figure
On the cusp anomalous dimension in the ladder limit of SYM
We analyze the cusp anomalous dimension in the (leading) ladder limit of
SYM and present new results for its higher-order perturbative
expansion. We study two different limits with respect to the cusp angle .
The first is the light-like regime where . This limit is
characterised by a non-trivial expansion of the cusp anomaly as a sum of powers
of , where the maximum exponent increases with the loop order. The
coefficients of this expansion have remarkable transcendentality features and
can be expressed by products of single zeta values. We show that the whole
logarithmic expansion is fully captured by a solvable Woods-Saxon like
one-dimensional potential. From the exact solution, we extract generating
functions for the cusp anomaly as well as for the various specific
transcendental structures appearing therein. The second limit that we discuss
is the regime of small cusp angle. In this somewhat simpler case, we show how
to organise the quantum mechanical perturbation theory in a novel efficient way
by means of a suitable all-order Ansatz for the ground state of the associated
Schr\"odinger problem. Our perturbative setup allows to systematically derive
higher-order perturbative corrections in powers of the cusp angle as explicit
non-perturbative functions of the effective coupling. This series approximation
is compared with the numerical solution of the Schr\"odinger equation to show
that we can achieve very good accuracy over the whole range of coupling and
cusp angle. Our results have been obtained by relatively simple techniques.
Nevertheless, they provide several non-trivial tests useful to check the
application of Quantum Spectral Curve methods to the ladder approximation at
non zero , in the two limits we studied.Comment: 21 pages, 3 figure
Chiral trace relations in -deformed theories
We consider gauge theories in four dimensions (pure or
mass deformed) and discuss the properties of the simplest chiral observables in
the presence of a generic -deformation. We compute them by equivariant
localization and analyze the structure of the exact instanton corrections to
the classical chiral ring relations. We predict exact relations valid at all
instanton number among the traces , where
is the scalar field in the gauge multiplet. In the
Nekrasov-Shatashvili limit, such relations may be explained in terms of the
available quantized Seiberg-Witten curves. Instead, the full two-parameter
deformation enjoys novel features and the ring relations require non trivial
additional derivative terms with respect to the modular parameter. Higher rank
groups are briefly discussed emphasizing non-factorization of correlators due
to the -deformation. Finally, the structure of the deformed ring
relations in the theory is analyzed from the point of
view of the Alday-Gaiotto-Tachikawa correspondence proving consistency as well
as some interesting universality properties.Comment: 36 pages. v2 references adde
Reactive immunization on complex networks
Epidemic spreading on complex networks depends on the topological structure
as well as on the dynamical properties of the infection itself. Generally
speaking, highly connected individuals play the role of hubs and are crucial to
channel information across the network. On the other hand, static topological
quantities measuring the connectivity structure are independent on the
dynamical mechanisms of the infection. A natural question is therefore how to
improve the topological analysis by some kind of dynamical information that may
be extracted from the ongoing infection itself. In this spirit, we propose a
novel vaccination scheme that exploits information from the details of the
infection pattern at the moment when the vaccination strategy is applied.
Numerical simulations of the infection process show that the proposed
immunization strategy is effective and robust on a wide class of complex
networks
An evolutionary game model for behavioral gambit of loyalists: Global awareness and risk-aversion
We study the phase diagram of a minority game where three classes of agents
are present. Two types of agents play a risk-loving game that we model by the
standard Snowdrift Game. The behaviour of the third type of agents is coded by
{\em indifference} w.r.t. the game at all: their dynamics is designed to
account for risk-aversion as an innovative behavioral gambit. From this point
of view, the choice of this solitary strategy is enhanced when innovation
starts, while is depressed when it becomes the majority option. This implies
that the payoff matrix of the game becomes dependent on the global awareness of
the agents measured by the relevance of the population of the indifferent
players. The resulting dynamics is non-trivial with different kinds of phase
transition depending on a few model parameters. The phase diagram is studied on
regular as well as complex networks
The relativistic Hopfield model with correlated patterns
In this work we introduce and investigate the properties of the
"relativistic" Hopfield model endowed with temporally correlated patterns.
First, we review the "relativistic" Hopfield model and we briefly describe the
experimental evidence underlying correlation among patterns. Then, we face the
study of the resulting model exploiting statistical-mechanics tools in a
low-load regime. More precisely, we prove the existence of the thermodynamic
limit of the related free-energy and we derive the self-consistence equations
for its order parameters. These equations are solved numerically to get a phase
diagram describing the performance of the system as an associative memory as a
function of its intrinsic parameters (i.e., the degree of noise and of
correlation among patterns). We find that, beyond the standard retrieval and
ergodic phases, the relativistic system exhibits correlated and symmetric
regions -- that are genuine effects of temporal correlation -- whose width is,
respectively, reduced and increased with respect to the classical case.Comment: 23 pages, 6 figure
Dreaming neural networks: rigorous results
Recently a daily routine for associative neural networks has been proposed:
the network Hebbian-learns during the awake state (thus behaving as a standard
Hopfield model), then, during its sleep state, optimizing information storage,
it consolidates pure patterns and removes spurious ones: this forces the
synaptic matrix to collapse to the projector one (ultimately approaching the
Kanter-Sompolinksy model). This procedure keeps the learning Hebbian-based (a
biological must) but, by taking advantage of a (properly stylized) sleep phase,
still reaches the maximal critical capacity (for symmetric interactions). So
far this emerging picture (as well as the bulk of papers on unlearning
techniques) was supported solely by mathematically-challenging routes, e.g.
mainly replica-trick analysis and numerical simulations: here we rely
extensively on Guerra's interpolation techniques developed for neural networks
and, in particular, we extend the generalized stochastic stability approach to
the case. Confining our description within the replica symmetric approximation
(where the previous ones lie), the picture painted regarding this
generalization (and the previously existing variations on theme) is here
entirely confirmed. Further, still relying on Guerra's schemes, we develop a
systematic fluctuation analysis to check where ergodicity is broken (an
analysis entirely absent in previous investigations). We find that, as long as
the network is awake, ergodicity is bounded by the Amit-Gutfreund-Sompolinsky
critical line (as it should), but, as the network sleeps, sleeping destroys
spin glass states by extending both the retrieval as well as the ergodic
region: after an entire sleeping session the solely surviving regions are
retrieval and ergodic ones and this allows the network to achieve the perfect
retrieval regime (the number of storable patterns equals the number of neurons
in the network)
Spunti di riflessione sulle tecniche di conciliazione telematica delle controversie
Even though the remarkable development of on line negotiation methods, the inclination at purchasing goods or services from foreign countries is still low, probably due to a widespread distrust in the systems that have to manage eventual pathological stages. Among all cross countries recent initiatives that aim at increasing and improving the litigate resolution mechanism between customers and professionals, a particular attention has to be paid on those that run conciliation processes only by means of on line systems. The current scenario, where rule definition on ODR is slowly in progress while new methods of resolution already are taking place instead of ordinary justice path, stimulates considerations and suggests research
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