The increasing need for intelligent sensors in a wide range of everyday objects requires the existence of low power information processing systems which can operate autonomously in their environment. In particular, merging and processing the outputs
of different sensors efficiently is a necessary requirement for mobile agents with cognitive abilities. In this work, we present a multi-layer spiking neural network for inference of relations between stimuli patterns in dedicated neuromorphic systems. The system is trained with a new version of the backpropagation algorithm adapted to on-chip learning in neuromorphic hardware: Error gradients are encoded as spike signals which are propagated through symmetric synapses, using the same integrate-and-fire hardware infrastructure as used during forward propagation. We demonstrate the strength of the approach on an arithmetic relation inference task and on visual XOR on the MNIST dataset. Compared to previous, biologically-inspired implementations of networks for learning and inference of relations, our approach is able to achieve better performance with less neurons. Our architecture is the first spiking neural network architecture with on-chip learning capabilities, which is able to perform relational inference on complex visual stimuli. These features make our system interesting for sensor fusion applications and embedded learning in autonomous neuromorphic agents.
We investigate the unconditional basis property of martingale differences in weighted $L^2$ spaces in the non-homogeneous situation (i.e. when the reference measure is not doubling). Specifically, we prove that finiteness of the quantity $[w]_{A_2}
=sup_I , < w>_I < w^{-1}>_I$, defined through averages $ <cdot >_I$ relative to the reference measure $ u$, implies that each martingale transform relative to $ u$ is bounded in $L^2(w, d u)$. Moreover, we prove the linear in $[w]_{A_2}$ estimate of the unconditional basis constant of the Haar system. Even in the classical case of the standard dyadic lattice in $mathbb{R}^n$, where the results about unconditional basis and linear in $[w]_{A_2}$ estimates are known, our result gives something new, because all the estimates are independent of the dimension $n$. Our approach combines the technique of outer measure spaces with the Bellman function argument.
We discuss the possibility of quantum interferences and entanglement of photons which exist at different intervals of time, i.e., one photon being recorded before the other has been created. The corresponding two-photon correlation function is shown to violate Bells inequalities.
We demonstrate that intensity correlations of second order in the fluorescence light of N > 2 single- photon emitters may violate locality while the visibility of the signal remains below 71%. For this, we derive a homogeneous Bell-Wigner-type inequa
lity, which can be applied to a broad class of experimental setups. We trace the violation of this inequality back to path entanglement created by the process of detection.
We demonstrate a novel approach of violating position dependent Bell inequalities by photons emitted via independent photon sources in free space. We trace this violation back to path entanglement created a posteriori by the selection of modes due to the process of detection.
Incoherent scattering of photons off two remote atoms with a Lambda-level structure is used as a basic Young-type interferometer to herald long-lived entanglement of an arbitrary degree. The degree of entanglement, as measured by the concurrence, is
found to be tunable by two easily accessible experimental parameters. Fixing one of them to certain values unveils an analog to the Malus law. An estimate of the variation in the degree of entanglement due to uncertainties in an experimental realization is given.
We present a physical setup with which it is possible to produce arbitrary symmetric long-lived multiqubit entangled states in the internal ground levels of photon emitters, including the paradigmatic GHZ and W states. In the case of three emitters,
where each tripartite entangled state belongs to one of two well-defined entanglement classes, we prove a one-to-one correspondence between well-defined sets of experimental parameters, i.e., locally tunable polarizer orientations, and multiqubit entanglement classes inside the symmetric subspace.
We propose a technique capable of imaging a distinct physical object with sub-Rayleigh resolution in an ordinary far-field imaging setup using single-photon sources and linear optical tools only. We exemplify our method for the case of a rectangular
aperture and two or four single-photon emitters obtaining a resolution enhanced by a factor of two or four, respectively.
