This paper proposes a new framework of algorithms that is extended from the celebrated extragradient algorithm. The min-max problem has attracted increasing attention because of its applications in machine learning tasks such as generative adversarial networks (GANs) training. While there has been exhaustive research on convex-concave setting, problem of nonconvex-nonconcave setting faces many challenges, such as convergence to limit cycles. Given that general min-max optimization has been found to be intractable, recent research efforts have shifted towards tackling structured problems. One of these follows the weak Minty variational inequality (weak MVI), which is motivated by relaxing Minty variational inequality (mvi) without compromising convergence guarantee of extragradient algorithm. Existing extragradient-type algorithms involve one exploration step and one update step per iteration. We analyze the algorithms with multiple exploration steps and show that current assumption can be further relaxed when more exploration is introduced. Furthermore, we design an adaptive algorithm that explores until the optimal improvement is achieved. This process exploits information from the whole trajectory and effectively tackles cyclic behaviors.

We introduce a variant of the endpoint (EP) detection problem in automatic speech recognition (ASR), which we call the end-of-speech (EOS) estimation. Given an utterance, EOS estimation aims to identify the timestamp when the utterance waveform has fully decayed and is then used to measure the EP latency. Accurate EOS estimation is difficult in large-scale streaming audio scenarios due to the hefty traffic and hardware limitations. To this end, we develop an efficient and accurate framework by performing force alignment on the 1-best ASR hypothesis. In particular, we propose to use binarized states sequences for alignment, which yields an EOS estimation robust to ASR hypothesis, and the estimation error is reduced by 28% compared to aligning on phoneme states. In addition, we further observe a 30% error reduction by applying the intermediate-stage embeddings of the encoder as additional features to compute the binary probabilities.

We introduce a variant of the speaker localization problem, which we call device arbitration. In the device arbitration problem, a user utters a keyword that is detected by multiple distributed microphone arrays (smart home devices), and we want to determine which device was closest to the user. Rather than solving the full localization problem, we propose an end-to-end machine learning system. This system learns a feature embedding that is computed independently on each device. The embeddings from each device are then aggregated together to produce the final arbitration decision. We use a large-scale room simulation to generate training and evaluation data, and compare our system against a signal-processing baseline.

Cryo-electron microscopy (EM) single particle reconstruction is a general technique for 3D structure determination of macromolecules. However, because the images are taken at low electron dose, it is extremely hard to visualize the individual particle with low contrast and high noise level. In this paper, we propose a novel framework for cryo-EM single particle image denoising, which incorporates the recently developed multi-frequency vector diffusion maps [1] for improving the identification and alignment of images with similar viewing directions. In addition, we propose a novel filtering scheme combining graph signal processing and truncated Fourier-Bessel expansion of the projection images. Through both simulated and publicly available real data, we demonstrate that our proposed method is efficient and robust to noise compared with the state-of-the-art cryo-EM 2D class averaging algorithms.

We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional data sets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other non-linear dimensionality reduction methods. The idea of MFVDM is to incorporates multiple unitary irreducible representations of the alignment group which introduces robustness to noise. We illustrate the efficacy of MFVDM on synthetic and cryo-EM image datasets, achieving better nearest neighbors search and alignment estimation than other baselines as VDM and diffusion maps (DM), especially on extremely noisy data.

We introduce a novel co-learning paradigm for manifolds naturally admitting an action of a transformation group $\mathcal{G}$, motivated by recent developments on learning a manifold from attached fibre bundle structures. We utilize a representation theoretic mechanism that canonically associates multiple independent vector bundles over a common base manifold, which provides multiple views for the geometry of the underlying manifold. The consistency across these fibre bundles provide a common base for performing unsupervised manifold co-learning through the redundancy created artificially across irreducible representations of the transformation group. We demonstrate the efficacy of our proposed algorithmic paradigm through drastically improved robust nearest neighbor identification in cryo-electron microscopy image analysis and the clustering accuracy in community detection.