Paper presents new matrix formats for deep neural networks that improve inference efficiency.
problem High computational cost of dot product operations in deep neural networks.
method Develops new matrix formats with bounded complexity by entropy of weight matrices.
result Up to x90 energy savings and x5 speed ups in dot product operations.
We present memory-efficient and scalable algorithms for kernel methods used in machine learning. Using hierarchical matrix approximations for the kernel matrix the memory requirements, the number of floating point operations, and the execution time are drastically reduced compared to standard dense linear algebra routi…
The ubiquitous proliferation of online social networks has led to the widescale emergence of relational graphs expressing unique patterns in link formation and descriptive user node features. Matrix Factorization and Completion have become popular methods for Link Prediction due to the low rank nature of mutual node fr…
Paper proposes a deep Gaussian process for predicting formation energy of inorganic compounds.
problem High computational cost of quantum chemistry calculations for material design.
method Develops a deep Gaussian process emulator for quantum calculations using a novel molecular descriptor.
result Demonstrates that the approach can be implemented using a small dataset for prediction of formation energy.
Study improves material similarity measures considering distinctiveness.
problem Improving similarity measures for materials science applications.
method Used machine learning techniques with specific descriptors and kernels.
result Minimizing loss of distinctiveness improves prediction accuracy.
A guide to AI+ML for portfolio weight formation.
problem Optimizing portfolio weights using AI and ML techniques.
method Analysis of machine learning tools and their performance in portfolio weight formation.
result Nodewise regression with Global Minimum Variance portfolio weights deliver high Sharpe Ratios and returns.
Combines Koopman theory and tensor trains for high-dimensional dynamical systems.
problem Analyzing complex, high-dimensional dynamical systems.
method Tensor train (TT) format for low-rank approximation, Koopman operator theory for dynamics.
result Efficient algorithms for low-rank representation of evolution operators.
We investigated the topological properties of stock networks through a comparison of the original stock network with the estimated stock network from the correlation matrix created by the random matrix theory (RMT). We used individual stocks traded on the market indices of Korea, Japan, Canada, the USA, Italy, and the …
Proposes CVKT to complete missing kernel matrices across multiple views.
problem Missing data in multiple views of kernel matrices.
method Cross-View Kernel Transfer (CVKT) with kernel alignment.
result Predicts missing values in kernel matrices using other views' 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.
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.
Describing the dimension reduction (DR) techniques by means of probabilistic models has recently been given special attention. Probabilistic models, in addition to a better interpretability of the DR methods, provide a framework for further extensions of such algorithms. One of the new approaches to the probabilistic D…
This paper proposes a new weight representation scheme for efficient model compression and performance enhancement.
problem Challenges in achieving performance enhancement on devices due to irregular sparse matrix representations.
method Fine-grained and unstructured pruning method combined with structured weight encryption.
result Achieved high compression ratios and performance on various deep learning models.
Develops a new causal model for path-dependent link prediction.
problem Existing causal models assume fixed node factors, but real-world links can depend on existing ones.
method Introduces causal lifting and structural pairwise embeddings for path-dependent link prediction.
result Validated on three scenarios, demonstrating improved accuracy for causal link prediction.
Model predicts majority of countries will prefer BRI over USD by 2020.
problem Predicting currency preferences in global trade networks.
method Opinion formation model based on UN Comtrade database, Monte Carlo simulations.
result By 2020, majority of countries prefer BRI over USD.
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.
SMM preserves matrix data structure for SVM classification.
problem Preserving spatial correlations in matrix data for SVM.
method SMM uses spectral elastic net combining nuclear and Frobenius norms.
result SMM improves SVM performance on matrix data.
Research tackles alliance formation in many-player zero-sum games, showing reinforcement learning fails but a contract mechanism can help.
problem Tackles the challenge of alliance formation in many-player zero-sum games.
method Demonstrates the social dilemma aspect of alliance formation, introduces a contract mechanism to augment reinforcement learning.
result Naïve reinforcement learning fails to form alliances, but a contract mechanism can help.
New pruning technique reduces index size for DNNs.
problem Irregular index form in fine-grained pruning limits parallelism and memory usage.
method Proposes a low-rank binary index matrix for efficient compression and decompression.
result Fine-grained pruning with binary matrices achieves lower memory footprint and higher parallelism.
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.
Simulating fluid flow in geological formations requires mesh generation, lithology mapping to the cells, and computing geometric properties such as normal vectors and volume of cells. The purpose of this research work is to compute and process the geometrical information required for performing numerical simulations in…
Few attempts have been proposed in order to describe the statistical features and historical evolution of the export bipartite matrix countries/products. An important standpoint is the introduction of a products network, namely a hierarchical forest of products that models the formation and the evolution of commodities…
Study singularity formation in Ricci flow solutions.
problem Understanding singularity behavior in noncompact manifolds.
method Analyzing complete Ricci flow solutions.
result Evidence for stability of generalized cylinders as singularity models.
The paper models network formation using mixed logit models.
problem Modeling network formation in various fields.
method Mixed logit models, specifically the repeated-choice (RC) model.
result The RC model outperforms the multinomial logit (MNL) model in estimating network formation.
SoccerCPD detects tactical changes in soccer matches using spatiotemporal tracking data.
problem Detecting consistent team formations in fluid sports like soccer.
method Two-step change-point detection: formation and role changes.
result Accurately detects tactical changes and estimates formation and role assignments.
New method estimates large matrices' spectra from small sub-matrices.
problem Estimating large matrices' spectra when full matrix-vector products are not available.
method Free decompression based on free probability theory.
result Estimates eigenspectrum of impalpable matrices from small sub-matrices.
A new method extends GLRAM for matrices, preserving feature relationships and reducing overfitting.
problem Overfitting and loss of feature relationships in matrix data.
method Generalized Low-Rank Approximation of Matrices (GLRAM) extension with multiple-pairs of transformations.
result The proposed method reduces overfitting and preserves feature relationships.
Extends ONNX for quantized neural networks with new formats and operators.
problem Handling arbitrary-precision quantization in neural networks.
method Introduces new formats and operators in ONNX to represent quantized neural networks.
result Enabled representation of uniform quantization in neural networks.
In the age of globalization, it is natural that the stock market of each country is not independent form the other markets. In this case, collective behavior could be emerged form their dependency together. This article studies the collective behavior of a set of forty influential markets in the world economy with the …
Proves finite step termination of Kähler-Einstein metric singularity formation.
problem Singularity formation of Kähler-Einstein metrics.
method Finite step termination of bubble trees for singularity formation.
result Finite step termination of Kähler-Einstein metric singularity formation proved in non-collapsing situation.
We develop a theory of bid and ask price dynamics where the two prices form due to interaction of buy and sell orders. In this model the two prices are represented by eigenvalues of a 2x2 price operator corresponding to "bid" and "ask" eigenstates. Matrix elements of price operator fluctuate in time which results in ph…
Deep neural networks are commonly developed and trained in 32-bit floating point format. Significant gains in performance and energy efficiency could be realized by training and inference in numerical formats optimized for deep learning. Despite advances in limited precision inference in recent years, training of neura…
Study shows formation of Kerr black holes with complete apparent horizons and proves Penrose inequalities.
problem Formation of Kerr black holes and Penrose inequalities.
method Combining gravitational-collapse and Kerr stability results with new coordinate changes and elliptic arguments.
result Proves dynamical and spacetime Penrose inequalities in black hole formation spacetimes.
Optimizes neural network training by dynamically updating Tucker decomposition ranks.
problem Redundant parameters in neural network architectures.
method Geometry-aware training of factorized layers in tensor Tucker format.
result Optimal locally approximating the original dynamics without initial rank knowledge.
Paper proves trapped surface formation for EMCSF system without symmetry assumptions.
problem Formation of trapped surfaces for the Einstein--Maxwell--charged scalar field system.
method Scale-critical trapped surface formation result established from past null infinity.
result Focusing of gravitational waves, concentration of electromagnetic fields, or condensation of scalar fields can lead to trapped surface formation.
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…
Study on Kähler-Ricci flow and conformal submersion singularity formation.
problem Singularity formation of Kähler-Ricci flow on manifolds with conformal submersion.
method Derive conditions for the preservation of conformal submersion and analyze singularity formation.
result Formation of type I singularity and standard splitting of Cheeger-Gromov limit.
Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.
problem Challenges in fitting regression models with multivariate responses and covariates.
method Low-rank tensor formats on regression coefficients and tensor-variate normal distribution for errors.
result Maximum likelihood estimators for tensor-on-tensor regression via block-relaxation algorithms.
Research connects topological changes to black hole formation and wormholes.
problem Understanding topological changes in mathematical three-space.
method Direct connection via surgery to black hole and wormhole formation.
result New platform for exploring geometrical physics.
DKLM learns adaptive kernels for robust nonlinear subspace clustering.
problem Nonlinear structures in data and challenges with kernel-based clustering.
method Data-driven kernel learning with adaptive weighting and optimal block-diagonal affinity matrix.
result DKLM enhances robustness and preserves manifold structure in nonlinear space.
Study equilibrium consumption habits in a large population using mean field games.
problem Equilibrium consumption under external habit formation in a large population.
method Formulated and solved mean field games for linear and multiplicative habit formation preferences, constructed approximate Nash equilibria for large n-player games.
result Characterized mean field equilibrium strategies and derived financial implications.
GraphOpt learns the formation mechanism of graphs from observed structures.
problem Learning formation mechanisms from observed graphs with complex structural properties.
method GraphOpt uses maximum entropy inverse reinforcement learning to solve the link formation problem in a sequential decision-making process.
result GraphOpt discovers a latent objective function that can explain and transfer across different graphs.
Analyzes how order flow affects price formation in financial markets.
problem Understanding how prices are formed by order flow in financial markets.
method Critical discussion of modeling approaches and empirical observations, focusing on market impact and transaction costs.
result Algorithmic trading impacts the quality and cost of trading.
MiFID II impacts European stock liquidity and price formation.
problem Impact of MiFID II on European stock liquidity and price formation.
method Analyzed effects of MiFID II on European stock markets, focusing on intraday and closing auction liquidity and tick size changes.
result Closing auction volumes increased and price formation became more efficient after MiFID II.
We seek to utilize the nonextensive statistics to the microscopic modeling of the interacting many-investor dynamics that drive the price changes in a market. The statistics of price changes are known to be fit well by the Students-T and power-law distributions of the nonextensive statistics. We therefore derive models…
System predicts ice formation to improve road safety.
problem Improving road safety through accurate ice formation prediction.
method Combining physical models and machine learning for data correction.
result Machine learning effectively corrects incorrect data in forecasts.
Model asset pricing with habit formation in a large market.
problem Understanding asset pricing in large heterogeneous markets with habit formation.
method Mean field game theory and quadratic-growth mean field BSDEs.
result Derives a semi-analytic solution for asset pricing model.
The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of consumption at any given time depends only on the amount consumed at that time.…