Backpropagating neurons from bichromatic interaction with a three-level system

Optical implementation of a backpropagating neuron by means of a nonlinear Fabry-Perot etalon requires thresholding a forward signal beam while the transmittance of a backpropagating beam is multiplied by the differential of the forward signal. This is achievable by inputting a bichromatic field to a three-level system in an optical cavity. The response characteristics of this device have the added possibility of adaptability of the threshold by the backward probe input intensity

The Minimal Modal Interpretation of Quantum Theory

We introduce a realist, unextravagant interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact. Much as classical systems have specific states that evolve along definite trajectories through configuration spaces, the traditional formulation of quantum theory asserts that closed quantum systems have specific states that evolve unitarily along definite trajectories through Hilbert spaces, and our interpretation extends this intuitive picture of states and Hilbert-space trajectories to the case of open quantum systems as well. We provide independent justification for the partial-trace operation for density matrices, reformulate wave-function collapse in terms of an underlying interpolating dynamics, derive the Born rule from deeper principles, resolve several open questions regarding ontological stability and dynamics, address a number of familiar no-go theorems, and argue that our interpretation is ultimately compatible with Lorentz invariance. Along the way, we also investigate a number of unexplored features of quantum theory, including an interesting geometrical structure---which we call subsystem space---that we believe merits further study. We include an appendix that briefly reviews the traditional Copenhagen interpretation and the measurement problem of quantum theory, as well as the instrumentalist approach and a collection of foundational theorems not otherwise discussed in the main text.Comment: 73 pages + references, 9 figures; cosmetic changes, added figure, updated references, generalized conditional probabilities with attendant changes to the sections on the EPR-Bohm thought experiment and Lorentz invariance; for a concise summary, see the companion letter at arXiv:1405.675

Avoiding Braess' Paradox through Collective Intelligence

In an Ideal Shortest Path Algorithm (ISPA), at each moment each router in a network sends all of its traffic down the path that will incur the lowest cost to that traffic. In the limit of an infinitesimally small amount of traffic for a particular router, its routing that traffic via an ISPA is optimal, as far as cost incurred by that traffic is concerned. We demonstrate though that in many cases, due to the side-effects of one router's actions on another routers performance, having routers use ISPA's is suboptimal as far as global aggregate cost is concerned, even when only used to route infinitesimally small amounts of traffic. As a particular example of this we present an instance of Braess' paradox for ISPA's, in which adding new links to a network decreases overall throughput. We also demonstrate that load-balancing, in which the routing decisions are made to optimize the global cost incurred by all traffic currently being routed, is suboptimal as far as global cost averaged across time is concerned. This is also due to "side-effects", in this case of current routing decision on future traffic. The theory of COllective INtelligence (COIN) is concerned precisely with the issue of avoiding such deleterious side-effects. We present key concepts from that theory and use them to derive an idealized algorithm whose performance is better than that of the ISPA, even in the infinitesimal limit. We present experiments verifying this, and also showing that a machine-learning-based version of this COIN algorithm in which costs are only imprecisely estimated (a version potentially applicable in the real world) also outperforms the ISPA, despite having access to less information than does the ISPA. In particular, this COIN algorithm avoids Braess' paradox.Comment: 28 page

Using Collective Intelligence to Route Internet Traffic

A COllective INtelligence (COIN) is a set of interacting reinforcement learning (RL) algorithms designed in an automated fashion so that their collective behavior optimizes a global utility function. We summarize the theory of COINs, then present experiments using that theory to design COINs to control internet traffic routing. These experiments indicate that COINs outperform all previously investigated RL-based, shortest path routing algorithms.Comment: 7 page