arXiv subjects

Masato Mimura

Publications and source records attributed to Masato Mimura.

At least 37 records · Page 2Linked to original sources

arXiv2023

Invariant quasimorphisms for groups acting on the circle and non-equivalence of SCL

We construct invariant quasimorphisms for groups acting on the circle. Furthermore, we provide a criterion for the non-extendablity of the resulting quasimorphisms and an explicit formula which relates the values of our quasimorphisms to those of the Poincaré translation number. By using them, we show that the stable commutator length $\mathrm{scl}_G$ and the stable mixed commutator length $\mathrm{scl}_{G,N}$ are not bi-Lipschitzly equivalent for the surface group $G=π_1(Σ_{\ell})$ of genus at least $2$ and its commutator subgroup $N = [π_1(Σ_{\ell}), π_1(Σ_{\ell})]$. We also show the non-equivalence for a pair $(G,N)$ such that $G$ is the fundamental group of a $3$-dimensional closed hyperbolic mapping torus. These pairs serve as the first family of examples of such $(G,N)$ in which $G$ is finitely generated.

math.GT↗

arXiv2023

Mixed commutator lengths, wreath products and general ranks

In the present paper, for a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the mixed commutator length $\mathrm{cl}_{G,N}$ on the mixed commutator subgroup $[G,N]$. We focus on the setting of wreath products: $ (G,N)=(\mathbb{Z}\wr Γ, \bigoplus_Γ\mathbb{Z})$. Then we determine mixed commutator lengths in terms of the general rank in the sense of Malcev. As a byproduct, when an abelian group $Γ$ is not locally cyclic, the ordinary commutator length $\mathrm{cl}_G$ does not coincide with $\mathrm{cl}_{G,N}$ on $[G,N]$ for the above pair. On the other hand, we prove that if $Γ$ is locally cyclic, then for every pair $(G,N)$ such that $1\to N\to G\to Γ\to 1$ is exact, $\mathrm{cl}_{G}$ and $\mathrm{cl}_{G,N}$ coincide on $[G,N]$. We also study the case of permutational wreath products when the group $Γ$ belongs to a certain class related to surface groups.

math.GR↗

arXiv2022

Survey on invariant quasimorphisms and stable mixed commutator length

A homogeneous quasimorphism $\phi$ on a normal subgroup $N$ of $G$ is said to be $G$-invariant if $\phi(gxg^{-1}) = \phi(x)$ for every $g \in G$ and for every $x \in N$. Invariant quasimorphisms have naturally appeared in symplectic geometry and the extension problem of quasimorphisms. Moreover, it is known that the existence of non-extendable invariant quasimorphisms is closely related to the behavior of the stable mixed commutator length $\mathrm{scl}_{G,N}$, which is a certain generalization of the stable commutator length $\mathrm{scl}_G$. In this survey, we review the history and recent developments of invariant quasimorphisms and stable mixed commutator length. The topics we treat include several examples of invariant quasimorphisms, Bavard's duality theorem for invariant quasimorphisms, Aut-invariant quasimorphisms, and the estimation of the dimension of spaces of non-extendable quasimorphisms. We also mention the extension problem of partial quasimorphisms.

math.GR↗

arXiv2022

Non-autoregressive Error Correction for CTC-based ASR with Phone-conditioned Masked LM

Connectionist temporal classification (CTC) -based models are attractive in automatic speech recognition (ASR) because of their non-autoregressive nature. To take advantage of text-only data, language model (LM) integration approaches such as rescoring and shallow fusion have been widely used for CTC. However, they lose CTC's non-autoregressive nature because of the need for beam search, which slows down the inference speed. In this study, we propose an error correction method with phone-conditioned masked LM (PC-MLM). In the proposed method, less confident word tokens in a greedy decoded output from CTC are masked. PC-MLM then predicts these masked word tokens given unmasked words and phones supplementally predicted from CTC. We further extend it to Deletable PC-MLM in order to address insertion errors. Since both CTC and PC-MLM are non-autoregressive models, the method enables fast LM integration. Experimental evaluations on the Corpus of Spontaneous Japanese (CSJ) and TED-LIUM2 in domain adaptation setting shows that our proposed method outperformed rescoring and shallow fusion in terms of inference speed, and also in terms of recognition accuracy on CSJ.

cs.CL↗

arXiv2022

Distilling the Knowledge of BERT for CTC-based ASR

Connectionist temporal classification (CTC) -based models are attractive because of their fast inference in automatic speech recognition (ASR). Language model (LM) integration approaches such as shallow fusion and rescoring can improve the recognition accuracy of CTC-based ASR by taking advantage of the knowledge in text corpora. However, they significantly slow down the inference of CTC. In this study, we propose to distill the knowledge of BERT for CTC-based ASR, extending our previous study for attention-based ASR. CTC-based ASR learns the knowledge of BERT during training and does not use BERT during testing, which maintains the fast inference of CTC. Different from attention-based models, CTC-based models make frame-level predictions, so they need to be aligned with token-level predictions of BERT for distillation. We propose to obtain alignments by calculating the most plausible CTC paths. Experimental evaluations on the Corpus of Spontaneous Japanese (CSJ) and TED-LIUM2 show that our method improves the performance of CTC-based ASR without the cost of inference speed.

cs.CL↗

arXiv2022

On the spectrum and linear programming bound for hypergraphs

The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigenvalue, is widely seen an algebraic measure of connectivity and plays a key role in the theory of expander graphs. In this paper, we extend previous work done for graphs and bipartite graphs and present a linear programming method for obtaining an upper bound on the order of a regular uniform hypergraph with prescribed distinct eigenvalues. Furthermore, we obtain a general upper bound on the order of a regular uniform hypergraph whose second eigenvalue is bounded by a given value. Our results improve and extend previous work done by Feng-Li (1996) on Alon-Boppana theorems for regular hypergraphs and by Dinitz-Schapira-Shahaf (2020) on the Moore or degree-diameter problem. We also determine the largest order of an $r$-regular $u$-uniform hypergraph with second eigenvalue at most $θ$ for several parameters $(r,u,θ)$. In particular, orthogonal arrays give the structure of the largest hypergraphs with second eigenvalue at most $1$ for every sufficiently large $r$. Moreover, we show that a generalized Moore geometry has the largest spectral gap among all hypergraphs of that order and degree.

math.CO↗

arXiv2022

Constellations in prime elements of number fields

Given any number field, we prove that there exist arbitrarily shaped constellations consisting of pairwise non-associate prime elements of the ring of integers. This result extends the celebrated Green-Tao theorem on arithmetic progressions of rational primes and Tao's theorem on constellations of Gaussian primes. Furthermore, we prove a constellation theorem on prime representations of binary quadratic forms with integer coefficients. More precisely, for a non-degenerate primitive binary quadratic form $F$ which is not negative definite, there exist arbitrarily shaped constellations consisting of pairs of integers $(x,y)$ for which $F(x,y)$ is a rational prime. The latter theorem is obtained by extending the framework from the ring of integers to the pair of an order and its invertible fractional ideal.

math.NT↗

arXiv2022

Bavard's duality theorem for mixed commutator length

Let $N$ be a normal subgroup of a group $G$. A quasimorphism $f$ on $N$ is $G$-invariant if $f(gxg^{-1}) = f(x)$ for every $g \in G$ and every $x \in N$. The goal in this paper is to establish Bavard's duality theorem of $G$-invariant quasimorphisms, which was previously proved by Kawasaki and Kimura in the case $N = [G,N]$. Our duality theorem provides a connection between $G$-invariant quasimorphisms and $(G,N)$-commutator lengths. Here for $x \in [G,N]$, the $(G,N)$-commutator length $\mathrm{cl}_{G,N}(x)$ of $x$ is the minimum number $n$ such that $x$ is a product of $n$ commutators which are written as $[g,x]$ with $g \in G$ and $h \in N$. In the proof, we give a geometric interpretation of $(G,N)$-commutator lengths. As an application of our Bavard duality, we obtain a sufficient condition on a pair $(G,N)$ under which $\mathrm{scl}_G$ and $\mathrm{scl}_{G,N}$ are bi-Lipschitzly equivalent on $[G,N]$.

math.GR↗

arXiv2021

ASR Rescoring and Confidence Estimation with ELECTRA

In automatic speech recognition (ASR) rescoring, the hypothesis with the fewest errors should be selected from the n-best list using a language model (LM). However, LMs are usually trained to maximize the likelihood of correct word sequences, not to detect ASR errors. We propose an ASR rescoring method for directly detecting errors with ELECTRA, which is originally a pre-training method for NLP tasks. ELECTRA is pre-trained to predict whether each word is replaced by BERT or not, which can simulate ASR error detection on large text corpora. To make this pre-training closer to ASR error detection, we further propose an extended version of ELECTRA called phone-attentive ELECTRA (P-ELECTRA). In the pre-training of P-ELECTRA, each word is replaced by a phone-to-word conversion model, which leverages phone information to generate acoustically similar words. Since our rescoring method is optimized for detecting errors, it can also be used for word-level confidence estimation. Experimental evaluations on the Librispeech and TED-LIUM2 corpora show that our rescoring method with ELECTRA is competitive with conventional rescoring methods with faster inference. ELECTRA also performs better in confidence estimation than BERT because it can learn to detect inappropriate words not only in fine-tuning but also in pre-training.

cs.CL↗

arXiv2021

The space of non-extendable quasimorphisms

For a pair $(G,N)$ of a group $G$ and its normal subgroup $N$, we consider the space of quasimorphisms and quasi-cocycles on $N$ non-extendable to $G$. To treat this space, we establish the five-term exact sequence of cohomology relative to the bounded subcomplex. As its application, we study the spaces associated with the kernel of the (volume) flux homomorphism, the IA-automorphism group of a free group, and certain normal subgroups of Gromov-hyperbolic groups. Furthermore, we employ this space to prove that the stable commutator length is equivalent to the stable mixed commutator length for certain pairs of a group and its normal subgroup.

math.GR↗

arXiv2020

Enhancing Monotonic Multihead Attention for Streaming ASR

We investigate a monotonic multihead attention (MMA) by extending hard monotonic attention to Transformer-based automatic speech recognition (ASR) for online streaming applications. For streaming inference, all monotonic attention (MA) heads should learn proper alignments because the next token is not generated until all heads detect the corresponding token boundaries. However, we found not all MA heads learn alignments with a naïve implementation. To encourage every head to learn alignments properly, we propose HeadDrop regularization by masking out a part of heads stochastically during training. Furthermore, we propose to prune redundant heads to improve consensus among heads for boundary detection and prevent delayed token generation caused by such heads. Chunkwise attention on each MA head is extended to the multihead counterpart. Finally, we propose head-synchronous beam search decoding to guarantee stable streaming inference.

eess.AS↗

arXiv2020

End-to-end Music-mixed Speech Recognition

Automatic speech recognition (ASR) in multimedia content is one of the promising applications, but speech data in this kind of content are frequently mixed with background music, which is harmful for the performance of ASR. In this study, we propose a method for improving ASR with background music based on time-domain source separation. We utilize Conv-TasNet as a separation network, which has achieved state-of-the-art performance for multi-speaker source separation, to extract the speech signal from a speech-music mixture in the waveform domain. We also propose joint fine-tuning of a pre-trained Conv-TasNet front-end with an attention-based ASR back-end using both separation and ASR objectives. We evaluated our method through ASR experiments using speech data mixed with background music from a wide variety of Japanese animations. We show that time-domain speech-music separation drastically improves ASR performance of the back-end model trained with mixture data, and the joint optimization yielded a further significant WER reduction. The time-domain separation method outperformed a frequency-domain separation method, which reuses the phase information of the input mixture signal, both in simple cascading and joint training settings. We also demonstrate that our method works robustly for music interference from classical, jazz and popular genres.

eess.AS↗

arXiv2020

Distilling the Knowledge of BERT for Sequence-to-Sequence ASR

Attention-based sequence-to-sequence (seq2seq) models have achieved promising results in automatic speech recognition (ASR). However, as these models decode in a left-to-right way, they do not have access to context on the right. We leverage both left and right context by applying BERT as an external language model to seq2seq ASR through knowledge distillation. In our proposed method, BERT generates soft labels to guide the training of seq2seq ASR. Furthermore, we leverage context beyond the current utterance as input to BERT. Experimental evaluations show that our method significantly improves the ASR performance from the seq2seq baseline on the Corpus of Spontaneous Japanese (CSJ). Knowledge distillation from BERT outperforms that from a transformer LM that only looks at left context. We also show the effectiveness of leveraging context beyond the current utterance. Our method outperforms other LM application approaches such as n-best rescoring and shallow fusion, while it does not require extra inference cost.

cs.CL↗

arXiv2020

CTC-synchronous Training for Monotonic Attention Model

Monotonic chunkwise attention (MoChA) has been studied for the online streaming automatic speech recognition (ASR) based on a sequence-to-sequence framework. In contrast to connectionist temporal classification (CTC), backward probabilities cannot be leveraged in the alignment marginalization process during training due to left-to-right dependency in the decoder. This results in the error propagation of alignments to subsequent token generation. To address this problem, we propose CTC-synchronous training (CTC-ST), in which MoChA uses CTC alignments to learn optimal monotonic alignments. Reference CTC alignments are extracted from a CTC branch sharing the same encoder with the decoder. The entire model is jointly optimized so that the expected boundaries from MoChA are synchronized with the alignments. Experimental evaluations of the TEDLIUM release-2 and Librispeech corpora show that the proposed method significantly improves recognition, especially for long utterances. We also show that CTC-ST can bring out the full potential of SpecAugment for MoChA.

cs.CL↗

arXiv2020

Generative Adversarial Training Data Adaptation for Very Low-resource Automatic Speech Recognition

It is important to transcribe and archive speech data of endangered languages for preserving heritages of verbal culture and automatic speech recognition (ASR) is a powerful tool to facilitate this process. However, since endangered languages do not generally have large corpora with many speakers, the performance of ASR models trained on them are considerably poor in general. Nevertheless, we are often left with a lot of recordings of spontaneous speech data that have to be transcribed. In this work, for mitigating this speaker sparsity problem, we propose to convert the whole training speech data and make it sound like the test speaker in order to develop a highly accurate ASR system for this speaker. For this purpose, we utilize a CycleGAN-based non-parallel voice conversion technology to forge a labeled training data that is close to the test speaker's speech. We evaluated this speaker adaptation approach on two low-resource corpora, namely, Ainu and Mboshi. We obtained 35-60% relative improvement in phone error rate on the Ainu corpus, and 40% relative improvement was attained on the Mboshi corpus. This approach outperformed two conventional methods namely unsupervised adaptation and multilingual training with these two corpora.

eess.AS↗

arXiv2020

Speech Corpus of Ainu Folklore and End-to-end Speech Recognition for Ainu Language

Ainu is an unwritten language that has been spoken by Ainu people who are one of the ethnic groups in Japan. It is recognized as critically endangered by UNESCO and archiving and documentation of its language heritage is of paramount importance. Although a considerable amount of voice recordings of Ainu folklore has been produced and accumulated to save their culture, only a quite limited parts of them are transcribed so far. Thus, we started a project of automatic speech recognition (ASR) for the Ainu language in order to contribute to the development of annotated language archives. In this paper, we report speech corpus development and the structure and performance of end-to-end ASR for Ainu. We investigated four modeling units (phone, syllable, word piece, and word) and found that the syllable-based model performed best in terms of both word and phone recognition accuracy, which were about 60% and over 85% respectively in speaker-open condition. Furthermore, word and phone accuracy of 80% and 90% has been achieved in a speaker-closed setting. We also found out that a multilingual ASR training with additional speech corpora of English and Japanese further improves the speaker-open test accuracy.

cs.CL↗

arXiv2019

Avoiding a star of three-term arthmetic progressions

We provide an upper bound of the size of a subset A of F_p^n that does not admit a k-star of 3-APs (three-term arithmetic progressions). Namely, the subset A is assumed to contain no configuration of k 3-APs, sharing the middle term, such that all 2k+1 terms are distinct. In the proof, we adapt a new method in the recent work of Sauermann.

math.CO↗

arXiv2019

Avoiding a shape, and the slice rank method for a system of equations

Fix a vector space over a finite field and a system of linear equations. We provide estimates, in terms of the dimension of the vector space, of the maximum of the sizes of subsets of the space that do not admit solutions of the system consisting of more than one point. That from above is derived by slice rank method of Tao; to obtain one from below, we define the notion of 'dominant reductions' of the system. Furthermore, by adapting a recent argument of Sauermann, we make an estimation of the maximum of the sizes of subsets that are 'W shape'-free, that means, there exist no five distinct points forming two overlapping parallelograms.

math.CO↗