The paper uses tensor decompositions to improve neural network models for tree data.
problem Encoding structural knowledge from tree-structured data efficiently.
method Introduces new aggregation functions using Canonical and Tensor-Train decompositions.
result Proposed models outperform traditional methods on tree classification tasks.
Paper proposes a new method for density estimation using tree tensor-network states.
problem Density estimation for complex graphical models with loops.
method Determines tree topology with Chow-Liu algorithm and uses sketching techniques to define tensor-network components.
result Sample complexity guarantees and empirical validation provided.
Extends geometrical description of tensor manifolds in tree-based formats.
problem Geometrical description of tensor manifolds in tree-based formats.
method Provided a new geometrical description of manifolds of tensors in tree-based format.
result Geometrical description compatible with Tucker format.
Tree tensor networks balance model complexity and empirical risk for high-dimensional function approximation.
problem Selecting optimal tree structure and ranks for high-dimensional function approximation.
method Proposes a complexity-based model selection method for tree tensor networks in empirical risk minimization.
result Demonstrates near-minimax adaptive performance across various smoothness classes.
Estimates high-dimensional distributions using tree tensor networks.
problem Estimating high-dimensional probability distributions from i.i.d. samples.
method Tree-based tensor formats, empirical risk minimization, L2 contrast, orthogonal bases.
result Effective approximation of classical probabilistic models like Gaussian and graphical models.
Tensor networks improve generative modeling of natural images.
problem Exponential decay of correlation in Matrix Product States limits their use for complex data.
method Introduced Tree Tensor Networks (TTN) for 2D data, developed efficient learning and sampling algorithms.
result TTN outperforms Matrix Product States in keeping pixel correlations and log-likelihood scores.
Improved machine learning with reduced tensor rank constraints and dropout.
problem Efficiently approximating large tensors in machine learning.
method Tree tensor networks with CP rank constraints and tensor dropout.
result Low-rank TTN classifier achieves 90.3% accuracy in Fashion-MNIST.
TensorNetwork speeds up quantum spin chain calculations using GPU.
problem Efficiently approximating ground states of quantum spin chains.
method Tree tensor network (TTN) algorithm implemented in TensorNetwork.
result Significant computational speed-ups using GPUs (up to 100x faster).
New model uses PEPS for image classification, outperforming tree-like networks.
problem Efficiently modeling and classifying 2D data like images.
method Feature map followed by PEPS contraction with trainable parameters.
result Significantly superior to tree-like networks on MNIST and Fashion-MNIST.
A new tree method for tensor data improves regression accuracy.
problem Efficiently modeling tensor data for regression problems.
method Scalar-output regression tree models for scalar-on-tensor problems, and tensor-on-tensor problems using additive tree ensemble approaches.
result The tensor-input tree (TT) method outperforms tensor-input GP models in efficiency and accuracy.
Optimizes tensor program execution time using graph neural networks.
problem Finding optimal configurations for tensor programs is infeasible due to large configuration space.
method Trains a graph convolutional network on an abstract syntax tree to predict execution time.
result Graph-based surrogate model outperforms heuristic-based methods.
Bayesian tensor network reduces conditional probability calculation to polynomial time.
problem Exponential cost of calculating conditional probabilities for multiple events.
method Bayesian tensor network (BTN) with polynomial complexity.
result Competitive performance in image recognition with simple tree structures.
Tensor networks improve exotic option pricing efficiency.
problem Challenges in pricing exotic financial derivatives using standard methods.
method Combining binomial pricing with tensor network techniques (Matrix Product States).
result Linear scaling with parameters and reduced computational complexity.
The paper tackles high-dimensional function approximation using tree-based tensor formats.
problem Approximating high-dimensional functions in statistical learning.
method Empirical risk minimization over tree-based tensor formats, exploiting multilinear models and sparsity.
result Numerical stability and reliability of the proposed algorithms for learning.
The main goal of this paper is to study the geometric structures associated with the representation of tensors in subspace based formats. To do this we use a property of the so-called minimal subspaces which allows us to describe the tensor representation by means of a rooted tree. By using the tree structure and the d…
New algorithm speeds up knot polynomial calculations.
problem Computing Reshetikhin--Turaev knot polynomials efficiently.
method Fixed-parameter tractable computation via tensor networks.
result Knot polynomial computations are fixed-parameter tractable.
Tensor networks improve b-jet classification in high-energy physics.
problem Classifying jets from b-quarks in proton-proton collisions.
method Quantum-inspired machine learning using tensor networks.
result Optimized classification of b-jets with improved precision and speed.
We propose a new statistical model suitable for machine learning of systems with long distance correlations such as natural languages. The model is based on directed acyclic graph decorated by multi-linear tensor maps in the vertices and vector spaces in the edges, called tensor network. Such tensor networks have been …
Bayesian tensor factorization approximates a complex tree model.
problem Intractable size of state-transition matrix in Hidden Tree Markov Models.
method Tucker factorization of tensors for probabilistic interpretation.
result New model outperforms existing approximations on tree-structured data tasks.
Alternative to convolutions using decision trees for neural networks.
problem Replacing complex convolutions with simpler decision-based layers.
method Binary decisions as indices to conditional distributions, trained using backpropagation.
result Performance similar to conventional neural networks, with runtime improvements.
Interactive platform for knot invariant computation and identification.
problem Efficient computation and identification of knot invariants.
method Unified web platform using Feynman ribbon diagrams and tensor networks.
result First platform combining construction, evaluation, computation, and identification.
New framework constructs holographic tensor networks using hyperbolic buildings.
problem Building holographic tensor networks for non-integer dimensions and fractal spaces.
method Introducing a unifying framework based on hyperbolic buildings and dualities.
result Constructs a family of bulk regions satisfying complementary recovery and Ryu-Takayanagi formula.
Inspired by coarse-graining approaches used in physics, we show how similar algorithms can be adapted for data. The resulting algorithms are based on layered tree tensor networks and scale linearly with both the dimension of the input and the training set size. Computing most of the layers with an unsupervised algorith…
The paper introduces a tensor-based approach to improve neural models' aggregation of structural context.
problem Sub-optimal use of simple aggregation functions in neural models for structured data.
method Tensor-based formulation and Tucker tensor decomposition to control parameter space size.
result Effective regulation of trade-off between expressivity, computational complexity, and generalisation.
Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies predominantly on local search heuristics such as Expectation Maximization. Using te…
Flexible tree ensemble learning framework supports arbitrary loss functions and multi-task learning.
problem Limited modeling capabilities of existing tree ensemble learning toolkits.
method Differentiable tree ensembles with tensor-based formulation for efficient training.
result Our framework leads to 100x more compact and 23% more expressive tree ensembles.
The resemblance between the methods used in quantum-many body physics and in machine learning has drawn considerable attention. In particular, tensor networks (TNs) and deep learning architectures bear striking similarities to the extent that TNs can be used for machine learning. Previous results used one-dimensional T…
Machine learning predicts Kronecker coefficients with high accuracy.
problem Predicting Kronecker coefficients from tensor products of symmetric group representations.
method Training machine learning models (NN, CNN, GBDT) to classify Kronecker coefficients as zero or non-zero.
result Trained models achieve high accuracy (≈0.98) in classifying Kronecker coefficients. We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges onto a global solution. The structure learning involves combinatorial operations…
Neural models can realize decision trees with parameter sharing and improved performance.
problem Training and optimizing oblique decision trees.
method Locally constant networks based on ReLU gradients, parameter sharing, and neural tools.
result Locally constant networks can implicitly model oblique decision trees with fewer neurons.
Proposes a simple neural network model similar to gradient boosted decision trees.
problem Building a neural network equivalent to gradient boosted decision trees.
method Converts an ensemble of decision trees to a neural network, relaxes properties, and trains a simple neural network model.
result The proposed Hammock model achieves similar performance to gradient boosted decision trees.
The purpose of this paper is twofold. On one hand, we introduce a modification of the dual canonical basis for invariant tensors of the 3-dimensional irreducible representation of Uq(sl2), given in terms of Jacobi diagrams, a central tool in quantum topology. On the other hand, we use this modified basis to study t…
This work automates decision tree construction from neural networks.
problem Creating optimal decision tree architectures from neural networks.
method Automatic induction of non-greedy decision trees using weights transfer from neural networks.
result Improved model performance over fixed hyperparameters.
We introduce the concept of community trees that summarizes topological structures within a network. A community tree is a tree structure representing clique communities from the clique percolation method (CPM). The community tree also generates a persistent diagram. Community trees and persistent diagrams reveal topol…
Discovering the latent structure from many observed variables is an important yet challenging learning task. Existing approaches for discovering latent structures often require the unknown number of hidden states as an input. In this paper, we propose a quartet based approach which is \emph{agnostic} to this number. Th…
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.
New spectral tensor network algorithms solve continuous tensor problems.
problem Continuous tensor decomposition and orbit recovery problems over infinite groups.
method Leverage tensor networks to design spectral algorithms.
result Solve continuous multi-reference alignment over infinite SO(2) group.
Converts GBDT trees to neural networks for online updates.
problem Performance loss in converting GBDT trees to neural networks.
method Converts existing GBDT implementations to neural network architectures, allowing online updates of decision splits.
result Learning bounds for neural network architecture with updated splits.
In this article we show the duality between tensor networks and undirected graphical models with discrete variables. We study tensor networks on hypergraphs, which we call tensor hypernetworks. We show that the tensor hypernetwork on a hypergraph exactly corresponds to the graphical model given by the dual hypergraph. …
Automated medical protocol uses neural networks and decision trees.
problem Improving healthcare delivery through automated decision-making.
method Hybrid model combining neural networks and decision trees.
result Effective early decisions for patient care.
Tree-SMU enables strong compositional generalization in neural networks.
problem Zero-shot generalization to novel compositions of concepts.
method Tree Stack Memory Units (Tree-SMU) with Stack Memory Units (SMU).
result Tree-SMU achieves strong empirical results on mathematical reasoning benchmarks.
TRNN combines tensor geometry with neural network nonlinearity for HD data.
problem Modeling high-dimensional data with preserved tensor geometry and nonlinear interactions.
method Introduces TRNN that integrates tensor geometry and neural network nonlinearity.
result TRNN preserves tensor geometry while offering nonlinearity.
T-Basis represents neural network tensors with fewer parameters.
problem Efficiently representing neural network tensors with fewer parameters.
method T-Basis uses Tensor Rings to represent tensors in a neural network, parameterizing them with a small number of coefficients.
result T-Basis achieves high compression rates with minimal performance loss.
Tensor networks improve integration accuracy for high-dimensional problems.
problem Integration of high-dimensional functions with exponential convergence.
method Regression-free tensor network representations for integration.
result Exponential convergence achieved for non-analytic integrands.
This paper finds efficient algorithms for approximating Markov networks with k-tree topologies.
problem Efficiently approximating Markov networks with complex topologies.
method Developed O(n^{k+1})-time algorithms for finding maximum spanning k-trees (MSkT) that retain certain subgraphs.
result Optimal approximation of Markov networks with k-tree topology is achieved in polynomial time.
Generative Adversarial Network creates realistic halo merger trees.
problem Comparing galaxy formation theories with observations using halo merger trees.
method Treated halo merger tree construction as a matrix generation problem, using Generative Adversarial Network.
result Generated halo merger trees are of high quality and realistic.
New algorithms learn simple staged trees from data, improving model fit.
problem Complex conditional independences in categorical data vectors.
method Structural learning algorithms for simple staged trees, coalescing the underlying tree.
result Data-learned simple staged trees often outperform Bayesian networks in model fit.
This paper proposes a method to automatically compress neural networks using Bayesian tensor decomposition.
problem Challenges in directly applying tensor compression in neural network training.
method Bayesian tensorized neural network with automatic rank selection.
result Produces significantly more compact neural networks (7.4x to 137x) directly from training.