We investigate opportunities and challenges for improving unsupervised machine learning using four common strategies with a long history in physics: divide-and-conquer, Occam's razor, unification and lifelong learning. Instead of using one model to learn everything, we propose a novel paradigm centered around the learning and manipulation of theories, which parsimoniously predict both aspects of the future (from past observations) and the domain in which these predictions are accurate. Specifically, we propose a novel generalized-mean-loss to encourage each theory to specialize in its comparatively advantageous domain, and a differentiable description length objective to downweight bad data and "snap" learned theories into simple symbolic formulas. Theories are stored in a "theory hub", which continuously unifies learned theories and can propose theories when encountering new environments. We test our implementation, the toy "AI Physicist" learning agent, on a suite of increasingly complex physics environments. From unsupervised observation of trajectories through worlds involving random combinations of gravity, electromagnetism, harmonic motion and elastic bounces, our agent typically learns faster and produces mean-squared prediction errors about a billion times smaller than a standard feedforward neural net of comparable complexity, typically recovering integer and rational theory parameters exactly. Our agent successfully identifies domains with different laws of motion also for a nonlinear chaotic double pendulum in a piecewise constant force field.

The theory to calculate circular dichroism (CD) of chiral molecules in a finite cluster with arbitrarily disposed objects has been developed by means of T-matrix method. The interactions between chiral molecules and nanostructures have been investigated. Our studies focus on the case of chiral molecules inserted into plasmonic hot spots of nanostructures. Our results show that the total CD of the system with two chiral molecules is not sum for two cases when two chiral molecules inserted respectively into the hot spots of nanoparticle clusters as the distances among nanoparticles are small, although the relationship is established at the case of large interparticle distances. The plasmonic CD arising from structure chirality of nanocomposites depends strongly on the relative positions and orientations of nanospheroids, and are much greater than that from molecule-induced chirality. However, the molecule-induced plasmonic CD effect from the molecule-NP nanocomposites with special chiral structures can be spectrally distinguishable from the structure chirality-based optical activity. Our results provide a new theoretical framework for understanding the two different aspects of plasmonic CD effect in molecule-NP nanocomposites, which would be helpful for the experimental design of novel biosensors to realize ultrasensitive probe of chiral information of molecules by plasmon-based nanotechnology.

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The Information Bottleneck (IB) method (Tishby et al. (2000)) provides an insightful and principled approach for balancing compression and prediction for representation learning. The IB objective I(X; Z) − βI(Y ; Z) employs a Lagrange multiplier β to tune this trade-off. However, in practice, not only is β chosen empirically without theoretical guidance, there is also a lack of theoretical understanding between β, learnability, the intrinsic nature of the dataset and model capacity. In this paper, we show that if β is improperly chosen, learning cannot happen -the trivial representation P (Z|X) = P (Z) becomes the global minimum of the IB objective. We show how this can be avoided, by identifying a sharp phase transition between the unlearnable and the learnable which arises as β is varied. This phase transition defines the concept of IB-Learnability. We prove several sufficient conditions for IB-Learnability, which provides theoretical guidance for choosing a good β. We further show that IB-learnability is determined by the largest confident, typical, and imbalanced subset of the examples (the conspicuous subset), and discuss its relation with model capacity. We give practical algorithms to estimate the minimum β for a given dataset. We also empirically demonstrate our theoretical conditions with analyses of synthetic datasets, MNIST, and CIFAR10.• We show that improperly chosen β may result in a failure to learn: the trivial solution P (Z|X) = P (Z) becomes the global minimum of the IB objective, even for β 1 (Section 1.1).• We introduce the concept of IB-Learnability, and show that when we vary β, the IB objective will un-arXiv:1907.07331v1 [cs.LG]

High-finesse optical cavities placed under vacuum are foundational platforms in quantum information science with photons and atoms. We study the vacuum-induced degradation of high-finesse optical cavities with mirror coatings composed of SiO₂-Ta₂O₅ dielectric stacks, and present methods to protect these coatings and to recover their initial low loss levels. For separate coatings with reflectivities centered at 370 nm and 422 nm, a vacuum-induced continuous increase in optical loss occurs if the surface-layer coating is made of Ta₂O₅, while it does not occur if it is made of SiO₂. The incurred optical loss can be reversed by filling the vacuum chamber with oxygen at atmospheric pressure, and the recovery rate can be strongly accelerated by continuous laser illumination at 422 nm. Both the degradation and the recovery processes depend strongly on temperature. We find that a 1 nm-thick layer of SiO₂ passivating the Ta₂O₅ surface layer is sufficient to reduce the degradation rate by more than a factor of 10, strongly supporting surface oxygen depletion as the primary degradation mechanism.

We develop a fiber based probe that is capable of two-dimensional scanning applicable in optical coherence tomography (OCT). Based on the resonance of the fiber cantilever with asymmetry structure which has two distinguished resonant frequencies in orthogonal directions, Lissajous pattern is produced suitable for two-dimensional scanning upon a sample. Orthogonal resonances of the fiber cantilever are simultaneously excited by single piezo bender actuator with one driving signal consisting of two components corresponding to above-mentioned two resonant frequencies. By integrating a backward-placed two-dimensional position sensitive detector (PSD) into the probe, real-time lateral position of the scanning pattern is registered simultaneously for image reconstruction. Dynamical characteristics of the fiber cantilever are experimentally studied with special consideration on factors determining the resolution of the scanning pattern, including frequency and amplitude ratios between two components of the driving signal and fetching duration used for an en face image. With the developed probe implemented in our established OCT system, en face OCT images of typical samples are obtained with satisfying resolution and contrast, demonstrating the feasibility of such fiber cantilever with asymmetry structure for realizing two dimensional scanning by single actuator, potentially applicable to endoscopic OCT imaging.

Whether or not chiral interaction exists between the optical orbital angular momentum (OAM) and a chiral molecule remains unanswered. So far, such an interaction has not been observed experimentally. Here we present a T-matrix method to study the interaction between optical OAM and the chiral molecule in a cluster of nanoparticles. We find that strong interaction between the chiral molecule and OAM can be induced by the excitation of plasmon resonances. An experimental scheme to observe such an interaction has been proposed. Furthermore, we have found that the signal of the OAM dichroism can be either positive or negative, depending on the spatial positions of nanocomposites in the cross-sections of OAM beams. The cancellation between positive and negative signals in the spatial average can explain why the interaction has not been observed in former experiments.

ABSTRACT:We present a rigorous finite element method to calculate circular dichroism (CD) in various systems consisting of nanostructures and oriented chiral molecules with electric quadrupole transitions. The interaction between oriented molecule materials, which are regarded as anisotropic chiral media, and metallic nanostructures has been investigated. Our results show that the plasmon-induced CD is sensitive to the orientations of the molecules. In many cases, the contribution of molecular electric quadrupole transitions to the total CD signal can play a key role. More interesting, we have demonstrated that both the quadrupole-and dipole-based CD signals can be improved greatly by matching the phases for the electromagnetic fields and their gradients at different regions around the nanostructures, which are occupied by the oriented chiral molecules. Different regions might produce CD of opposite sign. When integrating over regions with only one side of the proposed nanostructure, we find that the CD-peak may be nearly hundreds-fold over the case of integrating both sides. We believe that these findings would be helpful for realizing ultrasensitive probing of chiral information for oriented molecules by plasmon-based nanotechnology. 2 I.INTRODUCTIONChirality, which refers to structures lacking any mirror symmetry planes, is a very intriguing property of molecules. Many biologically active molecules are chiral, which plays a pivotal role in biochemistry and the evolution of life itself.1-2 Detecting and characterizing chiral enantiomers of these biomolecules are of considerable importance for biomedical diagnostics and pathogen analyses. 3 A common technique for chirality discrimination is CD spectroscopy describing the difference in molecular absorption of left-and right-handed circularly polarized photons. [4][5] In general, the molecular CD signal is typically weak, thus, chiral analyses by such a spectroscopic technique have usually been restricted to analysis at a relatively high concentration. 1-5Recent investigations have shown that superchiral fields allow measuring the chiroptical properties of small amounts of molecules with high sensitivity. 6-7 A weak molecular CD signal in the ultraviolet spectral region can be both enhanced and transferred to the visible-near-infrared region when chiral molecules are adsorbed at the surfaces of metallic nanoparticles or in the nanogaps (i.e., hot spots) of particle clusters. However, many related discussions assume that the molecules are randomly oriented, 6, 21-24 and the results have been obtained by averaging over the solid angles of the molecular directions. In fact, this rotational degree of freedom for molecules is absent in many cases, i.e. chiral molecules adopt geometries in which they have an axis with a well-defined orientation with respect to the surface of the nanostructures. 9,[26][27][28][29] This leads to several orientation-selective signals for appropriately sculpted fields. Although there are also some theoretical researches concentrating o...