2,378 research outputs found
Noise-induced behaviors in neural mean field dynamics
The collective behavior of cortical neurons is strongly affected by the
presence of noise at the level of individual cells. In order to study these
phenomena in large-scale assemblies of neurons, we consider networks of
firing-rate neurons with linear intrinsic dynamics and nonlinear coupling,
belonging to a few types of cell populations and receiving noisy currents.
Asymptotic equations as the number of neurons tends to infinity (mean field
equations) are rigorously derived based on a probabilistic approach. These
equations are implicit on the probability distribution of the solutions which
generally makes their direct analysis difficult. However, in our case, the
solutions are Gaussian, and their moments satisfy a closed system of nonlinear
ordinary differential equations (ODEs), which are much easier to study than the
original stochastic network equations, and the statistics of the empirical
process uniformly converge towards the solutions of these ODEs. Based on this
description, we analytically and numerically study the influence of noise on
the collective behaviors, and compare these asymptotic regimes to simulations
of the network. We observe that the mean field equations provide an accurate
description of the solutions of the network equations for network sizes as
small as a few hundreds of neurons. In particular, we observe that the level of
noise in the system qualitatively modifies its collective behavior, producing
for instance synchronized oscillations of the whole network, desynchronization
of oscillating regimes, and stabilization or destabilization of stationary
solutions. These results shed a new light on the role of noise in shaping
collective dynamics of neurons, and gives us clues for understanding similar
phenomena observed in biological networks
Deep Learning of Representations: Looking Forward
Deep learning research aims at discovering learning algorithms that discover
multiple levels of distributed representations, with higher levels representing
more abstract concepts. Although the study of deep learning has already led to
impressive theoretical results, learning algorithms and breakthrough
experiments, several challenges lie ahead. This paper proposes to examine some
of these challenges, centering on the questions of scaling deep learning
algorithms to much larger models and datasets, reducing optimization
difficulties due to ill-conditioning or local minima, designing more efficient
and powerful inference and sampling procedures, and learning to disentangle the
factors of variation underlying the observed data. It also proposes a few
forward-looking research directions aimed at overcoming these challenges
Past, Present, and Future of Simultaneous Localization And Mapping: Towards the Robust-Perception Age
Simultaneous Localization and Mapping (SLAM)consists in the concurrent
construction of a model of the environment (the map), and the estimation of the
state of the robot moving within it. The SLAM community has made astonishing
progress over the last 30 years, enabling large-scale real-world applications,
and witnessing a steady transition of this technology to industry. We survey
the current state of SLAM. We start by presenting what is now the de-facto
standard formulation for SLAM. We then review related work, covering a broad
set of topics including robustness and scalability in long-term mapping, metric
and semantic representations for mapping, theoretical performance guarantees,
active SLAM and exploration, and other new frontiers. This paper simultaneously
serves as a position paper and tutorial to those who are users of SLAM. By
looking at the published research with a critical eye, we delineate open
challenges and new research issues, that still deserve careful scientific
investigation. The paper also contains the authors' take on two questions that
often animate discussions during robotics conferences: Do robots need SLAM? and
Is SLAM solved
On Dynamics of Integrate-and-Fire Neural Networks with Conductance Based Synapses
We present a mathematical analysis of a networks with Integrate-and-Fire
neurons and adaptive conductances. Taking into account the realistic fact that
the spike time is only known within some \textit{finite} precision, we propose
a model where spikes are effective at times multiple of a characteristic time
scale , where can be \textit{arbitrary} small (in particular,
well beyond the numerical precision). We make a complete mathematical
characterization of the model-dynamics and obtain the following results. The
asymptotic dynamics is composed by finitely many stable periodic orbits, whose
number and period can be arbitrary large and can diverge in a region of the
synaptic weights space, traditionally called the "edge of chaos", a notion
mathematically well defined in the present paper. Furthermore, except at the
edge of chaos, there is a one-to-one correspondence between the membrane
potential trajectories and the raster plot. This shows that the neural code is
entirely "in the spikes" in this case. As a key tool, we introduce an order
parameter, easy to compute numerically, and closely related to a natural notion
of entropy, providing a relevant characterization of the computational
capabilities of the network. This allows us to compare the computational
capabilities of leaky and Integrate-and-Fire models and conductance based
models. The present study considers networks with constant input, and without
time-dependent plasticity, but the framework has been designed for both
extensions.Comment: 36 pages, 9 figure
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