179,563 research outputs found
Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings
Spiking Neural Networks (SNNs) are a promising research direction for
building power-efficient information processing systems, especially for
temporal tasks such as speech recognition. In SNNs, delays refer to the time
needed for one spike to travel from one neuron to another. These delays matter
because they influence the spike arrival times, and it is well-known that
spiking neurons respond more strongly to coincident input spikes. More
formally, it has been shown theoretically that plastic delays greatly increase
the expressivity in SNNs. Yet, efficient algorithms to learn these delays have
been lacking. Here, we propose a new discrete-time algorithm that addresses
this issue in deep feedforward SNNs using backpropagation, in an offline
manner. To simulate delays between consecutive layers, we use 1D convolutions
across time. The kernels contain only a few non-zero weights - one per synapse
- whose positions correspond to the delays. These positions are learned
together with the weights using the recently proposed Dilated Convolution with
Learnable Spacings (DCLS). We evaluated our method on three datasets: the
Spiking Heidelberg Dataset (SHD), the Spiking Speech Commands (SSC) and its
non-spiking version Google Speech Commands v0.02 (GSC) benchmarks, which
require detecting temporal patterns. We used feedforward SNNs with two or three
hidden fully connected layers, and vanilla leaky integrate-and fire neurons. We
showed that fixed random delays help and that learning them helps even more.
Furthermore, our method outperformed the state-of-the-art in the three datasets
without using recurrent connections and with substantially fewer parameters.
Our work demonstrates the potential of delay learning in developing accurate
and precise models for temporal data processing. Our code is based on PyTorch /
SpikingJelly and available at: https://github.com/Thvnvtos/SNN-delay
A modified Next Reaction Method for simulating chemical systems with time dependent propensities and delays
Chemical reaction systems with a low to moderate number of molecules are
typically modeled as discrete jump Markov processes. These systems are
oftentimes simulated with methods that produce statistically exact sample paths
such as the Gillespie Algorithm or the Next Reaction Method. In this paper we
make explicit use of the fact that the initiation times of the reactions can be
represented as the firing times of independent, unit rate Poisson processes
with internal times given by integrated propensity functions. Using this
representation we derive a modified Next Reaction Method and, in a way that
achieves efficiency over existing approaches for exact simulation, extend it to
systems with time dependent propensities as well as to systems with delays.Comment: 25 pages, 1 figure. Some minor changes made to add clarit
Network tomography based on 1-D projections
Network tomography has been regarded as one of the most promising
methodologies for performance evaluation and diagnosis of the massive and
decentralized Internet. This paper proposes a new estimation approach for
solving a class of inverse problems in network tomography, based on marginal
distributions of a sequence of one-dimensional linear projections of the
observed data. We give a general identifiability result for the proposed method
and study the design issue of these one dimensional projections in terms of
statistical efficiency. We show that for a simple Gaussian tomography model,
there is an optimal set of one-dimensional projections such that the estimator
obtained from these projections is asymptotically as efficient as the maximum
likelihood estimator based on the joint distribution of the observed data. For
practical applications, we carry out simulation studies of the proposed method
for two instances of network tomography. The first is for traffic demand
tomography using a Gaussian Origin-Destination traffic model with a power
relation between its mean and variance, and the second is for network delay
tomography where the link delays are to be estimated from the end-to-end path
delays. We compare estimators obtained from our method and that obtained from
using the joint distribution and other lower dimensional projections, and show
that in both cases, the proposed method yields satisfactory results.Comment: Published at http://dx.doi.org/10.1214/074921707000000238 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Privacy Leakages in Approximate Adders
Approximate computing has recently emerged as a promising method to meet the
low power requirements of digital designs. The erroneous outputs produced in
approximate computing can be partially a function of each chip's process
variation. We show that, in such schemes, the erroneous outputs produced on
each chip instance can reveal the identity of the chip that performed the
computation, possibly jeopardizing user privacy. In this work, we perform
simulation experiments on 32-bit Ripple Carry Adders, Carry Lookahead Adders,
and Han-Carlson Adders running at over-scaled operating points. Our results
show that identification is possible, we contrast the identifiability of each
type of adder, and we quantify how success of identification varies with the
extent of over-scaling and noise. Our results are the first to show that
approximate digital computations may compromise privacy. Designers of future
approximate computing systems should be aware of the possible privacy leakages
and decide whether mitigation is warranted in their application.Comment: 2017 IEEE International Symposium on Circuits and Systems (ISCAS
Simulating non-Markovian stochastic processes
We present a simple and general framework to simulate statistically correct
realizations of a system of non-Markovian discrete stochastic processes. We
give the exact analytical solution and a practical an efficient algorithm alike
the Gillespie algorithm for Markovian processes, with the difference that now
the occurrence rates of the events depend on the time elapsed since the event
last took place. We use our non-Markovian generalized Gillespie stochastic
simulation methodology to investigate the effects of non-exponential
inter-event time distributions in the susceptible-infected-susceptible model of
epidemic spreading. Strikingly, our results unveil the drastic effects that
very subtle differences in the modeling of non-Markovian processes have on the
global behavior of complex systems, with important implications for their
understanding and prediction. We also assess our generalized Gillespie
algorithm on a system of biochemical reactions with time delays. As compared to
other existing methods, we find that the generalized Gillespie algorithm is the
most general as it can be implemented very easily in cases, like for delays
coupled to the evolution of the system, where other algorithms do not work or
need adapted versions, less efficient in computational terms.Comment: Improvement of the algorithm, new results, and a major reorganization
of the paper thanks to our coauthors L. Lafuerza and R. Tora
- …