Bayesian tensor train method recovers streaming data with high accuracy.
problem Recovering high-order, incomplete, and noisy streaming data.
method Bayesian tensor train decomposition using streaming variational Bayes method.
result The proposed SPTT algorithm excels in recovering streaming data compared to state-of-the-art methods.
The paper analyzes conditions for low-rank tensor completion using TT decomposition.
problem Conditions for finite completability of low-rank tensors.
method Algebraic geometric analysis on the TT manifold, focusing on the independence of polynomials defined by sampling patterns and TT decompositions.
result Deterministic and probabilistic conditions for finite completability of tensors with high probability.
Paper addresses statistical efficiency and scalability in tensor train decomposition.
problem Statistical inefficiency and scalability issues in tensor train decomposition.
method Introduces a convex relaxation and alternating optimization method with randomization.
result Derives error bounds and demonstrates method's performance on real data.
Tensorized random projections reduce high-dimensional tensor size efficiently.
problem Efficiently reducing the dimension of very high-dimensional tensors.
method Proposes two tensorized random projection maps using TT and CP decompositions.
result TT format offers superior performance in terms of required random projection size.
Study geodesic X-ray transforms on hyperbolic surfaces, proposing new reconstruction methods.
problem Inverting geodesic X-ray transforms for symmetric tensor fields on asymptotically hyperbolic surfaces.
method Developed a decomposition theorem for m-tensor fields, used Guillemin-Kazhdan operators and 0-calculus, and provided explicit reconstruction methods.
result Explicit reconstruction methods for even tensor fields from their X-ray transform or normal operator.
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
problem Reducing the dimension of high-dimensional tensors for machine learning.
method Tensorized Rademacher random projections using Tensor Train decomposition.
result Tensorized Rademacher projections can replace Gaussian projections in tensor compression.
Characterizes kernel of linearization for minimal surfaces problem
problem Characterizing kernel of linearization for minimal surfaces problem
method Show kernel consists of potential fields and TT fields
result In whole-space Euclidean decomposition, kernel consists of potential fields and TT fields
Tensor networks constrain kernel machines to Gaussian processes.
problem Speeding up kernel machines with reduced model complexity.
method Proving CPD and TT-constrained models recover Gaussian processes with i.i.d. priors.
result TT-constrained models exhibit more Gaussian process behavior than CPD for the same parameters.
New LSH methods for tensor data improve efficiency and space usage.
problem Efficiency and space usage issues in LSH for tensor data.
method Proposes new LSH methods using CP and TT decompositions for Euclidean and cosine similarity.
result Space-efficient and scalable LSH for tensor data.
We introduce a new parameterization method for deep learning layers using spectral tensor train decomposition.
problem Efficiency and stability in deep learning models with weight matrix compression.
method Spectral Tensor Train Parameterization (STTP) of weight matrices.
result Improved compression and training stability in neural networks.
Develops a new tensor classification method for high-dimensional data.
problem Efficient learning algorithms exploiting tensorial structure in high-dimensional multi-way arrays.
method Tensor Train Multi-way Multi-level Kernel (TT-MMK) combining Canonical Polyadic decomposition, Dual Structure-preserving Support Vector Machine, and Tensor Train approximation.
result The TT-MMK method provides higher prediction accuracy and is more reliable computationally compared to other techniques.
Proposes a new tensor grid method for image completion.
problem Image completion from missing data.
method Low-rank tensor grid with two-stage density matrix renormalization group initialization and alternating least squares factorization.
result The proposed tensor grid method outperforms existing methods in image recovery accuracy.
TensorGuide improves LoRA efficiency and expressivity through joint tensor-train optimization.
problem Limited expressivity and generalization of standard LoRA.
method TensorGuide uses a unified tensor-train structure with controlled Gaussian noise to generate correlated low-rank matrices.
result TensorGuide achieves superior accuracy and scalability with fewer parameters compared to standard LoRA and TT-LoRA.
Adaptive algorithm learns tensor network structures from data.
problem Identifying optimal tensor network structure from data.
method Greedy approach starting from rank one tensor, small rank increments.
result Adaptive algorithm identifies efficient tensor network structures.
Unified algorithm for tensor decomposition supports multiple loss functions and models.
problem Efficient tensor decomposition for various models and loss functions.
method Hierarchical combination of ADMM and MM for optimization.
result Wide-range applications can be solved by the proposed algorithm.
Compact RNNs reduce parameters and improve efficiency.
problem High computational cost of RNNs with large inputs.
method Block-Term Tensor Decomposition (BT-TD) to reduce RNN parameters.
result BT-RNN achieves better accuracy and faster convergence than standard RNNs.
The main construction of this paper contains a serious error, and I am withdrawing it. I owe Andrew Stacey and Ralph Cohen thanks for seeing the problem; in particular, Stacey has shown that the projections constructed in §3.1 will fail in general to have constant rank, so the family TV of vector spaces defined…
Tensor networks improve data privacy and robustness in convolutional neural networks.
problem Improving data privacy and robustness in convolutional neural networks.
method Tensor network decomposition for data partitioning and adversarial defense.
result Tensor networks can protect data privacy and resist adversarial attacks.
Classifies Toda-type tt*-structures and their fixed points.
problem Classifying Toda-type tt*-structures and their fixed points.
method Fixed point description and reduction of anti-symmetry conditions.
result Reduces possibilities of anti-symmetry condition to two cases.
A new method uses CPD to efficiently model feature interactions in non-sequential data.
problem Efficiently modeling feature interactions in non-sequential data with high computational and memory costs.
method Implicitly represent model parameters as a tensor, factorize into a compact Tensor Train (TT) format, and use Canonical Polyadic (CP) Decomposition for invariance to feature ordering.
result The proposed CP-based predictor outperforms other TN-based predictors on sparse data and matches neural network performance on dense non-sequential tasks.
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…
End-to-end TTS learns context features from text input.
problem Lack of understanding of context features learned by end-to-end TTS.
method Evaluated encoder outputs against context criteria derived from parametric TTS.
result Encoder outputs reflect linguistic and phonetic context features.
The paper proves an isomorphism between tt∗ structures of Landau-Ginzburg and Calabi-Yau models.
problem Establishing an isomorphism between tt∗ structures of different geometries. method Using Landau-Ginzburg models and Calabi-Yau hypersurfaces, proving the isomorphism via the big residue map.
result An isomorphism between tt∗ structures of Landau-Ginzburg and Calabi-Yau models is proven. Existence proof for Einstein equations with small TT-tensor and vanishing Yamabe invariant.
problem Existence of metrics with vanishing Yamabe invariant and small TT-tensor.
method Existence proof for Einstein conformal constraint equations assuming small TT-tensor and vanishing Yamabe invariant.
result Existence result for Einstein equations under specified conditions.
Paper compresses RNNs using HT decomposition for better performance.
problem Large model sizes of RNNs in sequence analysis.
method Hierarchical Tucker (HT) tensor decomposition for model compression.
result HT-LSTM achieves better compression and accuracy than state-of-the-art methods.
Relates quantum cohomology to tt*-Toda equations for minuscule flag manifolds.
problem Quantum cohomology of minuscule flag manifolds.
method Combining Lie-theoretic treatments of tt*-Toda equations and quantum cohomology.
result Relates quantum cohomology to tt*-Toda equations for minuscule flag manifolds.
Analyzes tt*-structures from ADE-type Stokes data.
problem Classifying tt*-structures over C∗. method Isomonodromic deformations with upper unitriangular real Stokes matrices.
result Establishes a direct analytic realization of the ADE classification. Polynomial growth elements found in all subgroups of Out(F_n).
problem Understanding polynomial growth in subgroups of Out(F_n).
method Analyzing conjugacy classes and elements of Out(F_n).
result Polynomial growth elements exist in all subgroups of Out(F_n).
Explains quantum cohomology of Grassmannians using tt* equations.
problem Relates quantum cohomology of complex Grassmannians to projective space.
method Uses tt* equations and Lie-theoretic connections.
result Illustrates relations between tt* equations and quantum cohomology.
Proves existence and uniqueness of solutions for A_n tt*-Toda equations.
problem Existence and uniqueness of solutions for A_n tt*-Toda equations.
method Proof of existence and uniqueness for any n, new treatment of asymptotic data.
result Existence and uniqueness of global solutions for any n.
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.
problem Constant pre-factor problem for the tt*-Toda equations.
method Explicit evaluation using asymptotic data and introduction of symplectic structures.
result Preservation of symplectic structures by Riemann-Hilbert correspondence for wider class of solutions.
BOFFIN TTS optimizes hyper-parameters for new speaker adaptation.
problem Fine-tuning a pre-trained TTS model for a new speaker with limited data.
method Bayesian optimization to efficiently find optimal hyper-parameters.
result Average 30% improvement in speaker similarity over standard techniques.
Study of symplectic groupoids from tt*-Toda equations.
problem Geometry of meromorphic connections with irregular singularities.
method Holomorphic symplectic groupoid structure over Steinberg cross section.
result Proves the space of tt*-Toda connections is a symplectic Lie groupoid.
End-to-end TTS framework uses hard alignment to improve accuracy.
problem End-to-end TTS systems struggle with accurate alignment between input text and output acoustic features.
method Proposes a constrained alignment scheme with hard monotonic alignments, marginalized during training.
result Improves alignment learning and prediction in end-to-end TTS systems.
Convolutional network converts speaker voices without text.
problem Speaker conversion without text-based methods.
method Fully convolutional wav-to-wav network with ASR pre-training.
result Successfully converts TTS robot's voice to narrated audiobook voices.
Solutions of tt*-equation from SU(2)_k fusion algebra.
problem Describe solutions to the tt*-equation from a specific algebra.
method Use DPW method and representations of SU(2).
result Construct solutions corresponding to A_k minimal model.
New surfaces with conjugate points have global blow-down maps in their TT spaces.
problem Constructing global blow-down maps for surfaces with conjugate points.
method Explicit construction of a family of non-trapping Riemannian surfaces with global blow-down maps.
result Global blow-down maps exist for some non-simple surfaces with conjugate points.
Proposes Textual Echo Cancellation to improve speech recognition.
problem Improving speech recognition performance and user experience for smart devices.
method A novel sequence-to-sequence model with multi-source attention that processes both the microphone mixture signal and source text of TTS playback.
result Demonstrates enhanced speech recognition performance and reduced latency.
Representation mixing combines character and phoneme inputs for flexible TTS synthesis.
problem Limited control over pronunciation in character or phoneme-based TTS systems.
method Representation mixing combines multiple linguistic inputs in a single encoder.
result Flexibility in choosing between character, phoneme, or mixed representations during inference.
Investigates neural TTS systems for Japanese and English.
problem Improving neural TTS systems for high-quality speech synthesis.
method Comparative study of neural sequence-to-sequence TTS vs. DNN pipeline TTS, varying model architecture, parameter size, and language.
result A neural sequence-to-sequence TTS system requires sufficient model parameters and a powerful encoder for high-quality speech synthesis.
RandUCB combines UCB and TS for optimal bandit performance.
problem Optimizing decision-making in uncertain environments with limited feedback.
method Randomized UCB algorithm using confidence intervals.
result Achieves minimax-optimal regret in various bandit settings.
New Lie-theoretic definition of tt*-Toda equations with remarkable structure.
problem Defining tt*-Toda equations for any complex simple Lie algebra.
method Topological-antitopological fusion, isomonodromic deformations, Kostant's theory, Steinberg's theory.
result Remarkable structure of Stokes data for tt*-Toda equations.
FPETS speeds up TTS by 600X and reduces errors.
problem High latency and errors in end-to-end TTS systems.
method Non-autoregressive, fully parallel approach with UFANS and trainable position encoding.
result Significant speed up and better quality audios with fewer errors.
The paper describes solutions to the tt* equations using various mathematical methods.
problem Solving the tt* equations and understanding their global and local properties.
method Combination of p.d.e., isomonodromic deformations, and loop groups.
result Explicit computation of Stokes data and connection matrix for global solutions.
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…
Paper proposes efficient tensor completion method using Gaussian Process.
problem Tensor completion in high-dimensional data with unknown smooth functions.
method Gaussian Process Regression for initialization and TT-cross approximation for tensor rank selection.
result Improved reconstruction error compared to random initialization.
Efficiently trains GPs with billions of inducing inputs using Tensor Train decomposition.
problem Training GPs with large numbers of inducing inputs.
method Tensor Train decomposition for variational parameters in stochastic variational inference.
result Achieves state-of-the-art results on several benchmarks.