Aggregating Frame-Level Information in the Spectral Domain With Self-Attention for Speaker Embedding

<pre><pre>Most pooling methods in state-of-the-art speaker embedding networks are implemented in the temporal domain. However, due to the high non-stationarity in the feature maps produced from the last frame-level layer, it is not advantageous to use the global statistics (e.g., means and standard deviations) of the temporal feature maps as aggregated embeddings. This motivates us to explore stationary spectral representations and perform aggregation in the spectral domain. In this paper, we propose attentive short-time spectral pooling (attentive <u>STSP</u>) from a Fourier perspective to exploit the local stationarity of the feature maps. In attentive <u>STSP</u>, for each utterance, we compute the spectral representations through a weighted average of the windowed segments within each spectrogram by attention weights and aggregate their lowest spectral components to form the speaker embedding. Because most energy of the feature maps is concentrated in the low-frequency region in the spectral domain, attentive <u>STSP</u> facilitates the information aggregation by retaining the low spectral components only. Moreover, due to the segment-level attention mechanism, attentive <u>STSP</u> can produce smoother attention weights (weights with less variations) than attentive pooling and generalize better to unseen data, making it more robust against the adverse effect of the non-stationarity in the feature maps. Attentive <u>STSP</u> is shown to consistently outperform attentive pooling on <u>VoxCeleb1</u>, <u>VOiCES19</u>-eval, <u>SRE16</u>-eval, and <u>SRE18</u>-<u>CMN2</u>-eval. This observation suggests that applying segment-level attention and leveraging low spectral components can produce discriminative speaker embeddings.</pre></pre>

Aggregating Frame-Level Information in the Spectral Domain With Self-Attention for Speaker Embedding

<pre><pre>Most pooling methods in state-of-the-art speaker embedding networks are implemented in the temporal domain. However, due to the high non-stationarity in the feature maps produced from the last frame-level layer, it is not advantageous to use the global statistics (e.g., means and standard deviations) of the temporal feature maps as aggregated embeddings. This motivates us to explore stationary spectral representations and perform aggregation in the spectral domain. In this paper, we propose attentive short-time spectral pooling (attentive <u>STSP</u>) from a Fourier perspective to exploit the local stationarity of the feature maps. In attentive <u>STSP</u>, for each utterance, we compute the spectral representations through a weighted average of the windowed segments within each spectrogram by attention weights and aggregate their lowest spectral components to form the speaker embedding. Because most energy of the feature maps is concentrated in the low-frequency region in the spectral domain, attentive <u>STSP</u> facilitates the information aggregation by retaining the low spectral components only. Moreover, due to the segment-level attention mechanism, attentive <u>STSP</u> can produce smoother attention weights (weights with less variations) than attentive pooling and generalize better to unseen data, making it more robust against the adverse effect of the non-stationarity in the feature maps. Attentive <u>STSP</u> is shown to consistently outperform attentive pooling on <u>VoxCeleb1</u>, <u>VOiCES19</u>-eval, <u>SRE16</u>-eval, and <u>SRE18</u>-<u>CMN2</u>-eval. This observation suggests that applying segment-level attention and leveraging low spectral components can produce discriminative speaker embeddings.</pre></pre>

Opacity from Loops in AdS

We investigate how quantum dynamics affects the propagation of a scalar field in Lorentzian AdS. We work in momentum space, in which the propagator admits two spectral representations (denoted “conformal” and “momentum”) in addition to a closed-form one, and all have a simple split structure. Focusing on scalar bubbles, we compute the imaginary part of the self-energy ImΠ in the three representations, which involves the evaluation of seemingly very different objects. We explicitly prove their equivalence in any dimension, and derive some elementary and asymptotic properties of ImΠ.Using a WKB-like approach in the timelike region, we evaluate the propagator dressed with the imaginary part of the self-energy. We find that the dressing from loops exponentially dampens the propagator when one of the endpoints is in the IR region, rendering this region opaque to propagation. This suppression may have implications for field-theoretical model-building in AdS. We argue that in the effective theory (EFT) paradigm, opacity of the IR region induced by higher dimensional operators censors the region of EFT breakdown. This confirms earlier expectations from the literature. Specializing to AdS5, we determine a universal contribution to opacity from gravity.

IMPROVING CLASSIFICATION OF MULTISPECTRAL IMAGES BASED ON SELECTED RELATIONS

A novel classification technique based on definition of unique spectral relations (such as slopes among spectral bands) for all land cover types named (SSF Significant Spectral Features) is presented in the article.A large slopes combination between spectral band pairs is calculated and spectral characterizations that emphasizes the best spectral land cover separation is sought. Increasing in dimensionality of spectral representations is balanced by the simplicity of calculations. The technique has been examined on data acquired by a flown hyperspectral scanner (AISA). The spectral data was narrowed into the equivalent 8 world-view2 channels. The research area was in the city of “Hadera”, Israel, which included 10 land cover types in an urban area, open area and road infrastructure. The comparison between the developed SSF technique and common techniques such as: SVM (Support Vector Machine) and ML (Maximum Likelihood) has shown a clear advantage over ML technique, while produced similar results as SVM. The poorest results of using SSF technique was achieved in an herbaceous area (70%). However, the simplicity of the method, the well-defined parameters it produces for interpreting the results, makes it intuitive over using techniques such as SVM, which is considered as a not explicit classifier.

Automated Spectral Kernel Learning

The generalization performance of kernel methods is largely determined by the kernel, but spectral representations of stationary kernels are both input-independent and output-independent, which limits their applications on complicated tasks. In this paper, we propose an efficient learning framework that incorporates the process of finding suitable kernels and model training. Using non-stationary spectral kernels and backpropagation w.r.t. the objective, we obtain favorable spectral representations that depends on both inputs and outputs. Further, based on Rademacher complexity, we derive data-dependent generalization error bounds, where we investigate the effect of those factors and introduce regularization terms to improve the performance. Extensive experimental results validate the effectiveness of the proposed algorithm and coincide with our theoretical findings.

Analytic Methods of Spectral Representations of Non- Selfadjoint (Non-Unitary) Operators

This book is concerned with model representations theory of linear non- selfadjoint and non-unitary operators, one of booming areas of functional analysis. This area owes its origin to fundamental works by M.S. Livˇsic on the theory of characteristic functions, deep studies of B.S.-Nagy and C. Foias on the dilation theory, and also to the Lax—Phillips scattering theory. A uni- form conceptual approach organically uniting all these research areas in the theory of non-selfadjoint and non-unitary operators is developed in this book. New analytic methods that allow solving some important problems from the theory of spectral representations in this area of analysis are also presented in this book. The book is aimed at the specialists working in this area of analysis and is accessible to senior math students of universities.