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Matthias Franz

Publications and source records attributed to Matthias Franz.

At least 19 recordsLinked to original sources
arXiv2026

Noise-Robust AV-ASR Using Visual Features Both in the Whisper Encoder and Decoder

In audiovisual automatic speech recognition (AV-ASR) systems, information fusion of visual features in a pre-trained ASR has been proven as a promising method to improve noise robustness. In this work, based on the prominent Whisper ASR, first, we propose a simple and effective visual fusion method -- use of visual features both in encoder and decoder (dual-use) -- to learn the audiovisual interactions in the encoder and to weigh modalities in the decoder. Second, we compare visual fusion methods in Whisper models of various sizes. Our proposed dual-use method shows consistent noise robustness improvement, e.g., a 35% relative improvement (WER: 4.41% vs. 6.83%) based on Whisper small, and a 57% relative improvement (WER: 4.07% vs. 9.53%) based on Whisper medium, compared to typical reference middle fusion in babble noise with a signal-to-noise ratio (SNR) of 0dB. Third, we conduct ablation studies examining the impact of various module designs and fusion options. Fine-tuned on 1929 hours of audiovisual data, our dual-use method using Whisper medium achieves 4.08% (MUSAN babble noise) and 4.43% (NoiseX babble noise) average WER across various SNRs, thereby establishing a new state-of-the-art in noisy conditions on the LRS3 AV-ASR benchmark. Our code is at https://github.com/ifnspaml/Dual-Use-AVASR

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arXiv2025

The Szczarba map and the cubical cobar construction

We consider a twisting function from a 1-reduced simplicial set $X$ to a simplicial group $G$. We prove in detail that the associated Szczarba operators induce a simplicial map from the triangulation of the cubical cobar construction of $X$ to $G$. This confirms a result due to Minichiello-Rivera-Zeinalian and gives, as pointed out by these authors, a conceptual proof of the fact that the dga map $\Omega\,C(X) \to C(G)$ induced by Szczarba's twisting cochain is comultiplicative.

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arXiv2023

An $A_\infty$-version of the Eilenberg-Moore theorem

We construct an $A_\infty$-structure on the two-sided bar construction involving homotopy Gerstenhaber algebras (hgas). It extends the non-associative product defined by Carlson and the author and generalizes the dga structure on the one-sided bar construction due to Kadeishvili-Saneblidze. As a consequence, the multiplicative cohomology isomorphism from the Eilenberg-Moore theorem is promoted to a quasi-isomorphism of $A_\infty$-algebras. We also show that the resulting product on the differential torsion product involving cochain algebras agrees with the one defined by Eilenberg-Moore and Smith, for all triples of spaces. This is a consequence of the following result, which is of independent interest: The strongly homotopy commutative (shc) structure on cochains inductively constructed by Gugenheim-Munkholm agrees with the one previously defined by the author for all hgas.

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arXiv2023

Big polygon spaces

We study a new class of compact orientable manifolds, called big polygon spaces. They are intersections of real quadrics and related to polygon spaces, which appear as their fixed point set under a canonical torus action. What makes big polygon spaces interesting is that they exhibit remarkable new features in equivariant cohomology: The Chang-Skjelbred sequence can be exact for them and the equivariant Poincare pairing perfect although their equivariant cohomology is never free as a module over the cohomology ring of BT. More generally, big polygon spaces show that a certain bound on the syzygy order of the equivariant cohomology of compact orientable T-manifolds obtained by Allday, Puppe and the author is sharp.

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arXiv2023

The Chang-Skjelbred lemma and generalizations

We review the Chang-Skjelbred lemma for torus-equivariant cohomology and discuss several generalizations of it: to other coefficients, other groups and also to syzygies in equivariant cohomology and the Atiyah-Bredon sequence.

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arXiv2021

The cohomology rings of homogeneous spaces

Let $G$ be a compact connected Lie group and $K$ a closed connected subgroup. Assume that the order of any torsion element in the integral cohomology of $G$ and $K$ is invertible in a given principal ideal domain $k$. It is known that in this case the cohomology of the homogeneous space $G/K$ with coefficients in $k$ and the torsion product of $H^{*}(BK)$ and $k$ over $H^{*}(BG)$ are isomorphic as $k$-modules. We show that this isomorphism is multiplicative and natural in the pair $(G,K)$ provided that 2 is invertible in $k$. The proof uses homotopy Gerstenhaber algebras in an essential way. In particular, we show that the normalized singular cochains on the classifying space of a torus are formal as a homotopy Gerstenhaber algebra.

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arXiv2021

Cohomology of smooth toric varieties: naturality

Building on the recent computation of the cohomology rings of smooth toric varieties and partial quotients of moment-angle complexes, we investigate the naturality properties of the resulting isomorphism between the cohomology of such a space and the torsion product involving the Stanley-Reisner ring. If 2 is invertible in the chosen coefficient ring, then the isomorphism is natural with respect to toric morphisms, which for partial quotients are defined in analogy with toric varieties. In general there are deformation terms that we describe explicitly.

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arXiv2021

The cohomology rings of real toric spaces and smooth real toric varieties

We compute the cohomology rings of smooth real toric varieties and of real toric spaces, which are quotients of real moment-angle complexes by freely acting subgroups of the ambient 2-torus. The differential graded algebra we present is in fact an equivariant dga model, valid for arbitrary coefficients. We deduce from our description that smooth toric varieties are M-varieties.

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arXiv2021

Homotopy Gerstenhaber formality of Davis-Januszkiewicz spaces

A homotopy Gerstenhaber structure on a differential graded algebra is essentially a family of operations defining a multiplication on its bar construction. We prove that the normalized singular cochain algebra of a Davis-Januszkiewicz space is formal as a homotopy Gerstenhaber algebra, for any coefficient ring. This generalizes a recent result by the author about classifying spaces of tori and also strengthens the well-known dga formality result for Davis-Januszkiewicz spaces due to the author and Notbohm-Ray. As an application, we determine the cohomology rings of free and based loop spaces of Davis-Januszkiewicz spaces.

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arXiv2020

Syzygies in equivariant cohomology in positive characteristic

We develop a theory of syzygies in equivariant cohomology for tori as well as $p$-tori and coefficients in $\mathbb{F}_p$. A noteworthy feature is a new algebraic approach to the partial exactness of the Atiyah-Bredon sequence, which also covers all instances considered so far.

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arXiv2020

Homotopy Gerstenhaber algebras are strongly homotopy commutative

We show that any homotopy Gerstenhaber algebra is naturally a strongly homotopy commutative (shc) algebra in the sense of Stasheff-Halperin with a homotopy associative structure map. In the presence of certain additional operations corresponding to a cup-1 product on the bar construction, the structure map becomes homotopy commutative, so that one obtains an shc algebra in the sense of Munkholm.

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arXiv2020

Szczarba's twisting cochain is comultiplicative

We prove that Szczarba's twisting cochain is comultiplicative. In particular, the induced map from the cobar construction of the chains on a 1-reduced simplicial set X to the chains on the Kan loop group of X is a quasi-isomorphism of dg bialgebras. We also show that Szczarba's twisted shuffle map is a dgc map connecting a twisted Cartesian product with the associated twisted tensor product. This gives a natural dgc model for fibre bundles. We apply our results to finite covering spaces and to the Serre spectral sequence.

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arXiv2020

Szczarba's twisting cochain and the Eilenberg-Zilber maps

We show that Szczarba's twisting cochain for a twisted Cartesian product is essentially the same as the one constructed by Shih. More precisely, Szczarba's twisting cochain can be obtained via the basic perturbation lemma if one uses a 'reversed' version of the classical Eilenberg-MacLane homotopy for the Eilenberg-Zilber contraction. Along the way we prove several new identities involving these homotopies.

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arXiv2020

Dga models for moment-angle complexes

A dga model for the integral singular cochains on a moment-angle complex is given by the twisted tensor product of the corresponding Stanley-Reisner ring and an exterior algebra. We present a short proof of this fact and extend it to real moment-angle complexes. We also compare various descriptions of the cohomology rings of these spaces, including one stated without proof by Gitler and L\'opez de Medrano.

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arXiv2019

The cohomology rings of smooth toric varieties and quotients of moment-angle complexes

Partial quotients of moment-angle complexes are topological analogues of smooth, not necessarily compact toric varieties. In 1998, Buchstaber and Panov proposed a formula for the cohomology ring of such a partial quotient in terms of a torsion product involving the corresponding Stanley-Reisner ring. We show that their formula gives the correct cup product if 2 is invertible in the chosen coefficient ring, but not in general. We rectify this by defining an explicit deformation of the canonical multiplication on the torsion product.

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