There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks. This motivates longer term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation, and manifold learning.

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Representation Learning: A Review and New Perspectives

Most current speech recognition systems use hidden Markov models (HMMs) to deal with the temporal variability of speech and Gaussian mixture models (GMMs) to determine how well each state of each HMM fits a frame or a short window of frames of coefficients that represents the acoustic input. An alternative way to evaluate the fit is to use a feed-forward neural network that takes several frames of coefficients as input and produces posterior probabilities over HMM states as output. Deep neural networks (DNNs) that have many hidden layers and are trained using new methods have been shown to outperform GMMs on a variety of speech recognition benchmarks, sometimes by a large margin. This article provides an overview of this progress and represents the shared views of four research groups that have had recent successes in using DNNs for acoustic modeling in speech recognition.

Deep Neural Networks for Acoustic Modeling in Speech Recognition: The Shared Views of Four Research Groups

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

Topological photonics is a rapidly emerging field of research in which geometrical and topological ideas are exploited to design and control the behavior of light. Drawing inspiration from the discovery of the quantum Hall effects and topological insulators in condensed matter, recent advances have shown how to engineer analogous effects also for photons, leading to remarkable phenomena such as the robust unidirectional propagation of light, which hold great promise for applications. Thanks to the flexibility and diversity of photonics systems, this field is also opening up new opportunities to realize exotic topological models and to probe and exploit topological effects in new ways. This article reviews experimental and theoretical developments in topological photonics across a wide range of experimental platforms, including photonic crystals, waveguides, metamaterials, cavities, optomechanics, silicon photonics, and circuit QED. A discussion of how changing the dimensionality and symmetries of photonics systems has allowed for the realization of different topological phases is offered, and progress in understanding the interplay of topology with non-Hermitian effects, such as dissipation, is reviewed. As an exciting perspective, topological photonics can be combined with optical nonlinearities, leading toward new collective phenomena and novel strongly correlated states of light, such as an analog of the fractional quantum Hall effect.

Topological Photonics

One-way quantum computing achieves the full power of quantum computation by performing single particle measurements on some many-body entangled state, known as the resource state. As single particle measurements are relatively easy to implement, the preparation of the resource state becomes a crucial task. An appealing approach is simply to cool a strongly correlated quantum many-body system to its ground state. In addition to requiring the ground state of the system to be universal for one-way quantum computing, we also want the Hamiltonian to have non-degenerate ground state protected by a fixed energy gap, to involve only two-body interactions, and to be frustration-free so that measureme nts in the course of the computation leave the remaining particles in the ground space. Recently, significant eff orts have been made to the search of resource states that appear naturally as ground states in spin lattice syste ms. The approach is proved to be successful in spin- 5 and spin- 3 systems. Yet, it remains an open question whether there could be such a natural resource state in a spin- 1 , i.e., qubit system. Here, we give a negative answer to this question by proving that it is impossible for a genuinely entangled qubit states to be a non-degenerate ground state of any two-body frustration-free Hamiltonian. What is more, we prove that every spin- 1 frustration-free Hamiltonian with two-body interaction always has a ground state that is a product of single- or two-qubit st ates, a stronger result that is interesting independent of the context of one-way quantum computing.

No-go theorem for one-way quantum computing on naturally occurring two-level systems

Integrating external language models (LMs) into end-to-end (E2E) models remains a challenging task for domain-adaptive speech recognition. Recently, internal language model estimation (ILME)-based LM fusion has shown significant word error rate (WER) reduction from Shallow Fusion by subtracting a weighted internal LM score from an interpolation of E2E model and external LM scores during beam search. However, on different test sets, the optimal LM interpolation weights vary over a wide range and have to be tuned extensively on well-matched validation sets. In this work, we perform LM fusion in the minimum WER (MWER) training of an E2E model to obviate the need for LM weights tuning during inference. Besides MWER training with Shallow Fusion (MWER-SF), we propose a novel MWER training with ILME (MWER-ILME) where the ILME-based fusion is conducted to generate N-best hypotheses and their posteriors. Additional gradient is induced when internal LM is engaged in MWER-ILME loss computation. During inference, LM weights pre-determined in MWER training enable robust LM integrations on test sets from different domains. Experimented with 30K-hour trained transformer transducers, MWER-ILME achieves on average 8.8% and 5.8% relative WER reductions from MWER and MWER-SF training, respectively, on 6 different test sets

Minimum Word Error Rate Training with Language Model Fusion for End-to-End Speech Recognition

In Liu et al. [Phys. Rev. B 84, 075135 (2011)] we studied eight gapped symmetric quantum phases in $S=1$ spin chains/ladders which respect a discrete spin rotation ${D}_{2}\ensuremath{\subset}SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of one-dimensional (1D) integer spin systems with ${D}_{2}+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in $S=1$ spin chain or spin ladder models. The gapped symmetric phases protected by subgroups of ${D}_{2}+T$ are also studied. Again, all these phases can be distinguished by physically measuring their end ``spins.''

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Symmetry-protected topological orders of one-dimensional spin systems with D 2 + T symmetry

Xie Chen would like to thank Toshiba Research Europe Ltd, Cambridge Research Lab, for funding his work. The authors would like to thank the Toshiba Cambridge Speech Group for allowing the data to be collected, also would like to thank Chao Zhang and Eric Wang for providing DNN and CMLLR transform tools.

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An initial investigation of long-term adaptation for meeting transcription

Any quantum system inevitably interacts with the environment which causes decoherence. While the environment is generally inaccessible, can we protect our system against noise to maintain its quantum coherence? One technique developed in quantum information science, called the quantum error-correcting codes, does the job. The main idea is to “encode” the system into a subspace of the entire N-qubit space, called the “code space”, such that the errors caused by decoherence of the system can be “corrected”.

Xie Chen

Papers

No-go theorem for one-way quantum computing on naturally occurring two-level systems

Minimum Word Error Rate Training with Language Model Fusion for End-to-End Speech Recognition

Symmetry-protected topological orders of one-dimensional spin systems with D 2 + T symmetry

An initial investigation of long-term adaptation for meeting transcription

Quantum Error-Correcting Codes