A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Classifies Toda-type tt*-structures and their fixed points.
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…
The paper proves an isomorphism between structures of Landau-Ginzburg and Calabi-Yau models.
Analyzes tt*-structures from -type Stokes data.
Solves constant pre-factor problem for tt*-Toda equations using asymptotic data and symplectic structures.
Establishes correspondence between Calabi-Yau and Landau-Ginzburg structures.
We study transverse-tracefree (TT)-tensors on conformally flat 3-manifolds . The Cotton-York tensor linearized at 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…
We propose , 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 -armed bandit setting, we show that there are infinitel…
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…
New surfaces with conjugate points have global blow-down maps in their TT spaces.
Study of symplectic groupoids from tt*-Toda equations.
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.
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 …
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…
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
Bayesian tensor train method recovers streaming data with high accuracy.
Derives smooth homogeneous structures for low-rank tensors.
Investigates neural TTS systems for Japanese and English.
An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever-present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data moti…
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 propose a Lie-theoretic definition of the tt*-Toda equations for any complex simple Lie algebra , based on the concept of topological-antitopological fusion which was introduced by Cecotti and Vafa. Our main result concerns the Stokes data of a certain meromorphic connection, whose isomonodromic deform…
End-to-end Text-to-speech (TTS) system can greatly improve the quality of synthesised speech. But it usually suffers form high time latency due to its auto-regressive structure. And the synthesised speech may also suffer from some error modes, e.g. repeated words, mispronunciations, and skipped words. In this paper, we…
Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
Introduces TT-NF for more compact neural field representations.
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…
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.
In this paper, we analyze the fundamental conditions for low-rank tensor completion given the separation or tensor-train (TT) rank, i.e., ranks of unfoldings. We exploit the algebraic structure of the TT decomposition to obtain the deterministic necessary and sufficient conditions on the locations of the samples to ens…
Study geodesic X-ray transforms on hyperbolic surfaces, proposing new reconstruction methods.
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 …
Solutions of tt*-equation from SU(2)_k fusion algebra.
Proposes Textual Echo Cancellation to improve speech recognition.
Tensor completion estimates missing components by exploiting the low-rank structure of multi-way data. The recently proposed methods based on tensor train (TT) and tensor ring (TR) show better performance in image recovery than classical ones. Compared with TT and TR, the projected entangled pair state (PEPS), which is…
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…
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…
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…
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 .
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.
Shape-constrained convex regression problem deals with fitting a convex function to the observed data, where additional constraints are imposed, such as component-wise monotonicity and uniform Lipschitz continuity. This paper provides a comprehensive mechanism for computing the least squares estimator of a multivariate…
KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.
KReTTaH uses tensor trains and Hadamard overparameterization for fast, interpretable multi-way data imputation.
A new method computes Greeks for multi-asset options using tensor trains and Fourier transforms.