942,572 research outputs found
Towards Fast-Convergence, Low-Delay and Low-Complexity Network Optimization
Distributed network optimization has been studied for well over a decade.
However, we still do not have a good idea of how to design schemes that can
simultaneously provide good performance across the dimensions of utility
optimality, convergence speed, and delay. To address these challenges, in this
paper, we propose a new algorithmic framework with all these metrics
approaching optimality. The salient features of our new algorithm are
three-fold: (i) fast convergence: it converges with only
iterations that is the fastest speed among all the existing algorithms; (ii)
low delay: it guarantees optimal utility with finite queue length; (iii) simple
implementation: the control variables of this algorithm are based on virtual
queues that do not require maintaining per-flow information. The new technique
builds on a kind of inexact Uzawa method in the Alternating Directional Method
of Multiplier, and provides a new theoretical path to prove global and linear
convergence rate of such a method without requiring the full rank assumption of
the constraint matrix
Emergence and Growth of Complex Networks in Adaptive Systems
We consider the population dynamics of a set of species whose network of
catalytic interactions is described by a directed graph. The relationship
between the attractors of this dynamics and the underlying graph theoretic
structures like cycles and autocatalytic sets is discussed. It is shown that
when the population dynamics is suitably coupled to a slow dynamics of the
graph itself, the network evolves towards increasing complexity driven by
autocatalytic sets. Some quantitative measures of network complexity are
described.Comment: 10 pages (including figures), 3 Postscript figure
Insights into the relation between noise and biological complexity
Understanding under which conditions the increase of systems complexity is
evolutionary advantageous, and how this trend is related to the modulation of
the intrinsic noise, are fascinating issues of utmost importance for synthetic
and systems biology. To get insights into these matters, we analyzed chemical
reaction networks with different topologies and degrees of complexity,
interacting or not with the environment. We showed that the global level of
fluctuations at the steady state, as measured by the sum of the Fano factors of
the number of molecules of all species, is directly related to the topology of
the network. For systems with zero deficiency, this sum is constant and equal
to the rank of the network. For higher deficiencies, we observed an increase or
decrease of the fluctuation levels according to the values of the reaction
fluxes that link internal species, multiplied by the associated stoichiometry.
We showed that the noise is reduced when the fluxes all flow towards the
species of higher complexity, whereas it is amplified when the fluxes are
directed towards lower complexity species.Comment: 5 pages, 3 figure
A Faster Counting Protocol for Anonymous Dynamic Networks
We study the problem of counting the number of nodes in a slotted-time
communication network, under the challenging assumption that nodes do not have
identifiers and the network topology changes frequently. That is, for each time
slot links among nodes can change arbitrarily provided that the network is
always connected. Tolerating dynamic topologies is crucial in face of mobility
and unreliable communication whereas, even if identifiers are available, it
might be convenient to ignore them in massive networks with changing topology.
Counting is a fundamental task in distributed computing since knowing the size
of the system often facilitates the design of solutions for more complex
problems. Currently, the best upper bound proved on the running time to compute
the exact network size is double-exponential. However, only linear complexity
lower bounds are known, leaving open the question of whether efficient Counting
protocols for Anonymous Dynamic Networks exist or not. In this paper we make a
significant step towards answering this question by presenting a distributed
Counting protocol for Anonymous Dynamic Networks which has exponential time
complexity. Our algorithm ensures that eventually every node knows the exact
size of the system and stops executing the algorithm. Previous Counting
protocols have either double-exponential time complexity, or they are
exponential but do not terminate, or terminate but do not provide running-time
guarantees, or guarantee only an exponential upper bound on the network size.
Other protocols are heuristic and do not guarantee the correct count
Emergence of Invariance and Disentanglement in Deep Representations
Using established principles from Statistics and Information Theory, we show
that invariance to nuisance factors in a deep neural network is equivalent to
information minimality of the learned representation, and that stacking layers
and injecting noise during training naturally bias the network towards learning
invariant representations. We then decompose the cross-entropy loss used during
training and highlight the presence of an inherent overfitting term. We propose
regularizing the loss by bounding such a term in two equivalent ways: One with
a Kullbach-Leibler term, which relates to a PAC-Bayes perspective; the other
using the information in the weights as a measure of complexity of a learned
model, yielding a novel Information Bottleneck for the weights. Finally, we
show that invariance and independence of the components of the representation
learned by the network are bounded above and below by the information in the
weights, and therefore are implicitly optimized during training. The theory
enables us to quantify and predict sharp phase transitions between underfitting
and overfitting of random labels when using our regularized loss, which we
verify in experiments, and sheds light on the relation between the geometry of
the loss function, invariance properties of the learned representation, and
generalization error.Comment: Deep learning, neural network, representation, flat minima,
information bottleneck, overfitting, generalization, sufficiency, minimality,
sensitivity, information complexity, stochastic gradient descent,
regularization, total correlation, PAC-Baye
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