Large-Scale Optical Neural Networks based on Photoelectric Multiplication

Recent success in deep neural networks has generated strong interest in hardware accelerators to improve speed and energy consumption. This paper presents a new type of photonic accelerator based on coherent detection that is scalable to large ($N \gtrsim 10^6$) networks and can be operated at high (GHz) speeds and very low (sub-aJ) energies per multiply-and-accumulate (MAC), using the massive spatial multiplexing enabled by standard free-space optical components. In contrast to previous approaches, both weights and inputs are optically encoded so that the network can be reprogrammed and trained on the fly. Simulations of the network using models for digit- and image-classification reveal a "standard quantum limit" for optical neural networks, set by photodetector shot noise. This bound, which can be as low as 50 zJ/MAC, suggests performance below the thermodynamic (Landauer) limit for digital irreversible computation is theoretically possible in this device. The proposed accelerator can implement both fully-connected and convolutional networks. We also present a scheme for back-propagation and training that can be performed in the same hardware. This architecture will enable a new class of ultra-low-energy processors for deep learning.Comment: Text: 10 pages, 5 figures, 1 table. Supplementary: 8 pages, 5, figures, 2 table

Factory of realities: on the emergence of virtual spatiotemporal structures

The ubiquitous nature of modern Information Retrieval and Virtual World give rise to new realities. To what extent are these "realities" real? Which "physics" should be applied to quantitatively describe them? In this essay I dwell on few examples. The first is Adaptive neural networks, which are not networks and not neural, but still provide service similar to classical ANNs in extended fashion. The second is the emergence of objects looking like Einsteinian spacetime, which describe the behavior of an Internet surfer like geodesic motion. The third is the demonstration of nonclassical and even stronger-than-quantum probabilities in Information Retrieval, their use. Immense operable datasets provide new operationalistic environments, which become to greater and greater extent "realities". In this essay, I consider the overall Information Retrieval process as an objective physical process, representing it according to Melucci metaphor in terms of physical-like experiments. Various semantic environments are treated as analogs of various realities. The readers' attention is drawn to topos approach to physical theories, which provides a natural conceptual and technical framework to cope with the new emerging realities.Comment: 21 p

Qubit representation of qudit states: correlations and state reconstruction

A method to establish a qubit decomposition of a general qudit state is presented. This new representation allows a geometrical depiction of any qudit state in the Bloch sphere. Additionally, we show that the nonnegativity conditions of the qudit state imply the existence of quantum correlations between the qubits which compose it. These correlations are used to define new inequalities which the density matrices components must satisfy. The importance of such inequalities in the reconstruction of a qudit state is addressed. As an example of the general procedure the qubit decomposition of a qutrit system is shown, which allows a classification of the qutrit states by fixing their invariants ${\rm Tr}(\hat{\rho}^2)$, ${\rm Tr}(\hat{\rho}^3)$.Comment: Accepted in Quantum Information Processing journa