arXiv research

The paper proves an isomorphism between $tt^*$ structures of Landau-Ginzburg and Calabi-Yau models.

We give an overview on the tt*-geometry defined for isolated hypersurface singularities and tame functions via Brieskorn lattices. We discuss nilpotent orbits in this context, as well as classifying spaces of Brieskorn lattices and (limits of) period maps.

Study of symplectic groupoids from tt*-Toda equations.

We study possible real structures in the space of solutions to the quantum differential equation. We show that, under mild conditions, a real structure in orbifold quantum cohomology yields a pure and polarized tt^*-geometry near the large radius limit. We compute an example of P^1 which is pure and polarized over the …

The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. The aim of this paper is to define a Hermitian geometry on the big phase space. Using the approach of Dijkgraaf and …

Establishes correspondence between Calabi-Yau and Landau-Ginzburg structures.

Derives smooth homogeneous structures for low-rank tensors.

Classifies Toda-type tt*-structures and their fixed points.

For any triple $(W,L,ρ)$, where W is a closed connected and oriented 3-manifold, L is a link in W and $ρ$ is a flat principal B-bundle over W (B is the Borel subgroup of $SL(2,\mc)$), one constructs a $\Dd$-scissors congruence class $\cG_{\Dd}(W,L,ρ)$ which belongs to a (pre)-Bloch group $\Pp (\Dd)$. The class $\cG_{\D…

Using nonlinear pde techniques, we construct a new family of globally smooth tt* structures. This includes tt* structures associated to the (orbifold) quantum cohomology of a finite number of complex projective spaces and weighted projective spaces. The existence of such "magical solutions" of the tt* equations, namely…

Study geodesic X-ray transforms on hyperbolic surfaces, proposing new reconstruction methods.

Relates quantum cohomology to tt*-Toda equations for minuscule flag manifolds.

Recent studies have introduced end-to-end TTS, which integrates the production of context and acoustic features in statistical parametric speech synthesis. As a result, a single neural network replaced laborious feature engineering with automated feature learning. However, little is known about what types of context in…

Study on harmonic Higgs bundles with vanishing endormorphism and eigenvalues of Q.

Analyzes tt*-structures from $ADE$-type Stokes data.

Polynomial growth elements found in all subgroups of Out(F_n).

Explains quantum cohomology of Grassmannians using tt* equations.

Proves existence and uniqueness of solutions for A_n tt*-Toda equations.

We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds $(M,g)$. The Cotton-York tensor linearized at $g$ maps every symmetric tracefree tensor into one which is TT. The question as to whether this is the general solution to the TT-condition is viewed as a cohomological problem within an elliptic com…

Solves constant pre-factor problem for tt*-Toda equations using asymptotic data and symplectic structures.

Solutions of tt*-equation from SU(2)_k fusion algebra.

We propose $\tt RandUCB$, a bandit strategy that builds on theoretically derived confidence intervals similar to upper confidence bound (UCB) algorithms, but akin to Thompson sampling (TS), it uses randomization to trade off exploration and exploitation. In the $K$-armed bandit setting, we show that there are infinitel…

New surfaces with conjugate points have global blow-down maps in their TT spaces.

Proposes Textual Echo Cancellation to improve speech recognition.

This is the first of a series of papers to construct the deformation theory of the form Schrödinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a noncompact complete Kähler manifold with bounded geometry and $f$ is a holomorphic function defined on $M$. This work is also the first …

Investigates neural TTS systems for Japanese and English.

End-to-end text-to-speech (TTS) synthesis is a method that directly converts input text to output acoustic features using a single network. A recent advance of end-to-end TTS is due to a key technique called attention mechanisms, and all successful methods proposed so far have been based on soft attention mechanisms. H…

We present a fully convolutional wav-to-wav network for converting between speakers' voices, without relying on text. Our network is based on an encoder-decoder architecture, where the encoder is pre-trained for the task of Automatic Speech Recognition, and a multi-speaker waveform decoder is trained to reconstruct the…

Bayesian tensor train method recovers streaming data with high accuracy.

We study tt*-geometry on the classifying space for regular singular TERP-structures, e.g., Fourier-Laplace transformations of Brieskorn lattices of isolated hypersurface singularities. We show that (a part of) this classifying space can be canonically equipped with a hermitian structure. We derive an estimate for the h…

We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations, or equations for harmonic maps into SL(n,R)/SO(n)) in terms of (i) asymptotic data, (ii) holomorphic data, and (iii) monodromy data. This allows us to find all solutions with integral Stokes data. These include solu…

Tensor, a multi-dimensional data structure, has been exploited recently in the machine learning community. Traditional machine learning approaches are vector- or matrix-based, and cannot handle tensorial data directly. In this paper, we propose a tensor train (TT)-based kernel technique for the first time, and apply it…

In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (arxiv:1209.2045) we described all smooth solutions of the two-function tt*-Toda equations in terms of asymptotic data, holomorphic data, and monodromy data. In this supplementary article we focus on the holomorphic data and its interpret…

A new TTS method uses diffusion and VAE for better speech synthesis.

End-to-end Sanskrit TTS developed with limited data, achieving good quality.

In this note we prove an existence result for the Einstein conformal constraint equations for metrics with vanishing Yamabe invariant assuming that the TT-tensor is small in $L^2$.

The Lagrangian description of mechanical systems and the Legendre Transformation (considered as a passage from the Lagrangian to the Hamiltonian formulation of the dynamics) for point-like objects, for which the infinitesimal configuration space is TM, is based on the existence of canonical symplectic isomorphisms of d…

We present BOFFIN TTS (Bayesian Optimization For FIne-tuning Neural Text To Speech), a novel approach for few-shot speaker adaptation. Here, the task is to fine-tune a pre-trained TTS model to mimic a new speaker using a small corpus of target utterances. We demonstrate that there does not exist a one-size-fits-all ada…

Characterizes kernel of linearization for minimal surfaces problem

Tensor network surrogate for efficient option pricing in large portfolios.

TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.

A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.

In this note, we prove that for a cobounded,Lipschitz path $γ:I\to\TT$, if the pull back bundle $\mathcal H_γ$ over $I$ is a strongly relatively hyperbolic metric space then there exists a geodesic $ξ$ in $\TT$ such that $γ(I)$ and $ξ$ are close to each other.

Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.

Let π: V \rightarrow M be a (real or holomorphic) vector bundle whose base has an almost Frobenius structure (\circ_{M},e_{M}, g_{M}) and typical fiber has the structure of a Frobenius algebra (\circ_{V},e_{V},g_{V}). Using a connection D on the bundle V and a morphism α: V \rightarrow TM, we construct an almost Froben…

The paper studies automorphisms of free groups with a North-South dynamics.

Paper tackles multivariate shape-constrained convex regression problems.

Introduces TT-NF for more compact neural field representations.