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.
Bayesian model improves image completion accuracy by automatically learning low rank structure.
BRTR improves robust tensor completion with automatic rank detection.
Bayesian Tensor Ring factorization improved for scalability and handling of discrete data.
T-Basis represents neural network tensors with fewer parameters.
A new tensor ring mixture model improves density estimation efficiency.
Scalable and robust TR decomposition for large-scale data with missing entries and outliers.
We show that near-horizon geometries in the presence of a positive cosmological constant cannot exist with ring topology. In particular, de Sitter black rings with vanishing surface gravity do not exist. Our result relies on a known mathematical theorem which is a straightforward consequence of a type of energy conditi…
Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To further deal with its sensitivity to sparse component as it does in tensor princ…
Paper proposes a new model for noisy tensor completion.
The paper studies the metric and algebraic structures on section rings of projective manifolds.
Tensor completion recovers a multi-dimensional array from a limited number of measurements. Using the recently proposed tensor ring (TR) decomposition, in this paper we show that a d-order tensor of dimensional size n and TR rank r can be exactly recovered with high probability by solving a convex optimization program,…
Deep neural networks have demonstrated state-of-the-art performance in a variety of real-world applications. In order to obtain performance gains, these networks have grown larger and deeper, containing millions or even billions of parameters and over a thousand layers. The trade-off is that these large architectures r…
We construct certain tensor categories that are dominated by finitely many simple objects. Objects in these categories are modules over rings of algebra integers. We show how to obtain TQFTs defined over algebra integers from these categories.
The study connects norms and filtrations on section rings of projective manifolds.
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model possibilities grows exponentially with the tensor order, which makes it rather ch…
Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace W^{\bot} of W within the dual space of K[S_r] yield linear identities needed for a t…
We construct an explicit categorification of the action of tangles on tensor powers of the fundamental representation of quantum sl(2).
Bayesian tensor train method recovers streaming data with high accuracy.
We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as u…
A novel Laplace-approximated Bayesian Tensor Network Kernel Machine (LA-TNKM) provides principled uncertainty estimates.
Paper bounds tensor decomposition's RLCT, aiding Bayesian inference.
We compute the Kauffman skein module of the complement of torus knots in S^3. Precisely, we show that these modules are isomorphic to the algebra of Sl(2,C)-characters tensored with the ring of Laurent polynomials.
The paper proposes a method to compute higher infinitesimals in numerical and symbolic analysis.
We compute the integer cohomology rings of the ``polygon spaces'' introduced in [Hausmann,Klyachko,Kapovich-Millson]. This is done by embedding them in certain toric varieties; the restriction map on cohomology is surjective and we calculate its kernel using ideas from the theory of Gröbner bases. Since we do not inver…
Tensor decomposition is an important technique for capturing the high-order interactions among multiway data. Multi-linear tensor composition methods, such as the Tucker decomposition and the CANDECOMP/PARAFAC (CP), assume that the complex interactions among objects are multi-linear, and are thus insufficient to repres…
Algorithm learns polynomial transformations of Gaussian distributions.
We generalize the Khovanov-Rozansky cohomology for n=2 by means of a homogeneous potential that depends on two parameters, to obtain the universal Khovanov-Rozansky sl(2) link cohomology. This theory is equivalent to the universal foam sl(2) link cohomology, after tensoring both theories with appropriate rings.
Bayesian Tensor Network combines prior and data likelihood for efficient prediction and parameter estimation.
Generative models produce realistic objects in many domains, including text, image, video, and audio synthesis. Most popular models---Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs)---usually employ a standard Gaussian distribution as a prior. Previous works show that the richer family of pri…
Tensor decomposition is an effective approach to compress over-parameterized neural networks and to enable their deployment on resource-constrained hardware platforms. However, directly applying tensor compression in the training process is a challenging task due to the difficulty of choosing a proper tensor rank. In o…
If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M. We show that S(M_1 connect sum M_2) is isomorphic to S(M_1) tensor S(M_2) modulo torsion. In fact, we show that S(M_1 connect sum M_2) is isomorphic to S(M_1) tensot S(M_2) if we are working over a certain localized ring. We show the simila…
Bayesian tensor train kernel machine uses Laplace approximation for scalable GP regression.
Anomaly Detection has several important applications. In this paper, our focus is on detecting anomalies in seller-reviewer data using tensor decomposition. While tensor-decomposition is mostly unsupervised, we formulate Bayesian semi-supervised tensor decomposition to take advantage of sparse labeled data. In addition…
Adaptive algorithm learns tensor network structures from data.
A new tensor completion method using tensor networks with Tucker wrapper.
Bayesian TNKMs automatically infer model complexity and feature relevance.
Bayesian method for imputing missing values in tensor data.
A new method reduces Volterra kernel complexity and uncertainty quantification.
Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…
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…
Probabilistic approaches for tensor factorization aim to extract meaningful structure from incomplete data by postulating low rank constraints. Recently, variational Bayesian (VB) inference techniques have successfully been applied to large scale models. This paper presents full Bayesian inference via VB on both single…
Develops a two-stage approach for robust tensor completion of visual data.
Defines tensor product of profinitely many vector spaces over F2.
Bayesian hierarchical tensor factorization model for international trade flows
Paper identifies tensor ranks via prior predictive matching, solving system of equations.
Paper presents a method for imputing and forecasting structural response from incomplete sensor data.
BKTF uses tensor factorization for Bayesian optimization of complex functions.
The Kähler cone of a compact manifold carries a natural Riemannian metric, given by the intersection product of its cohomology ring. We write down the curvature tensor of this metric by embedding the Kähler cone in the space of hermitian metrics on the underlying manifold. After discussing weak functorality and complet…