Machine learning model predicts DFT total energy to complete basis set limit.
problem Finding a model to extrapolate DFT calculations to complete basis set limit.
method Quantile-random-forest model trained on binary solids data.
result Random-forest model achieves <25% symmetric MAPE for both DFT codes.
Optimizes basis for density-based atomic representations to enhance compactness and accuracy.
problem Improving the efficiency and accuracy of machine learning models for atomic properties.
method An unsupervised approach to determine the optimal basis set for atom density representations using splines.
result Optimal basis sets that encode structural information more compactly and accurately.
A new kernel improves statistical surrogates for stochastic manifolds with diverse data.
problem Handling statistical surrogates for stochastic manifolds with heterogeneous data.
method A transient anisotropic kernel is introduced to improve statistical surrogates for stochastic manifolds with heterogeneous data.
result The transient anisotropic kernel provides a better representation of statistical dependencies in the learned probability measure.
BASIS improves LLM reasoning by sharing batchwise rollout info, reducing MSE by 69%.
problem Improving large language model reasoning with limited rollouts and batch information.
method BASIS samples only one rollout per prompt but uses batch information to improve value function estimation.
result BASIS reduces MSE in value function estimation by 69% compared to REINFORCE++.
Optimizes basis functions for learning dynamical systems from data.
problem Learning suitable basis functions for dynamical systems from data.
method Gradient-based optimization framework for learning basis functions.
result Efficacy demonstrated on various benchmark problems.
Several multiscale methods account for sub-grid scale features using coarse scale basis functions. For example, in the Multiscale Finite Volume method the coarse scale basis functions are obtained by solving a set of local problems over dual-grid cells. We introduce a data-driven approach for the estimation of these co…
RI-DeepONet learns neural operators from arbitrary sensor data.
problem Discretization of input functions limits practical applications of DeepONet.
method Introduces RI-DeepONet and two dictionary learning algorithms for INRs.
result RINO handles arbitrary sensor data robustly and applies to various problems.
We propose a new method for learning deep neural network models that is based on a greedy learning approach: we add one basis function at a time, and a new basis function is generated as a non-linear activation function applied to a linear combination of the previous basis functions. Such a method (growing deep neural …
Adaptive neural networks learn functional data bases for improved performance.
problem Applying deep learning to functional data is challenging due to high dimensionality.
method Proposes adaptive neural networks with Basis Layers that learn relevant basis functions.
result Empirically outperforms other neural network approaches across various tasks.
New basis for permutation equivariant layers reduces computation costs.
problem Efficiently computing permutation equivariant layers in neural networks.
method Generalized partition algebra basis with low-rank tensors.
result Low-rank tensors enable faster computation compared to orbit basis.
A new method for learning manifolds efficiently using canonical basis functions.
problem Learning manifolds in high-dimensional data with efficient and distinct latent dimensions.
method Proposes a novel optimization objective to enforce a transformation matrix with a few prominent and non-degenerate basis functions.
result Demonstrates that minimizing the off-diagonal manifold metric elements ℓ1-norm results in a more efficient latent space representation. New model explains how concepts grow based on experience.
problem Existing models assume fixed representation; new model allows for growth.
method Geometric framework with MDL criterion for basis extension.
result Conceptual growth is selective and conservative, exposing or amplifying residual error.
Ordinal Regression (OR) aims to model the ordering information between different data categories, which is a crucial topic in multi-label learning. An important class of approaches to OR models the problem as a linear combination of basis functions that map features to a high dimensional non-linear space. However, most…
A new density model using Fourier basis achieves better approximations and compression.
problem Approximating multi-modal 1D densities.
method Constrained Fourier basis model for end-to-end training.
result Lower cross entropy compared to deep factorized models.
For nonconvex optimization in machine learning, this article proves that every local minimum achieves the globally optimal value of the perturbable gradient basis model at any differentiable point. As a result, nonconvex machine learning is theoretically as supported as convex machine learning with a handcrafted basis …
Option discovery and skill acquisition frameworks are integral to the functioning of a Hierarchically organized Reinforcement learning agent. However, such techniques often yield a large number of options or skills, which can potentially be represented succinctly by filtering out any redundant information. Such a reduc…
A method to select validation data from a dataset using statistical criteria.
problem Selecting a validation basis from a full dataset for machine learning model validation.
method Adopting a 'design of experiments' point of view and using statistical criteria, particularly Maximum Mean Discrepancy criteria.
result The 'support points' concept is particularly relevant for selecting validation data.
New neural architectures invariant to sign flips and basis symmetries for graph representation learning.
problem Learning invariant graph representations from eigenvectors.
method SignNet and BasisNet neural architectures that are invariant to sign flips and basis symmetries.
result Proven to be universal, approximating any continuous function of eigenvectors with desired invariances.
A new method integrates Fourier basis expansion and mapping for improved time series forecasting.
problem Inconsistent starting cycles and series length issues in Fourier-based methods.
method Fourier Basis Mapping (FBM) method that integrates time-frequency features through Fourier basis expansion and mapping.
result FBM addresses inconsistencies and preserves temporal characteristics, achieving SOTA performance.
Deep neural network predicts molecular wave functions in minimal basis.
problem Improving accuracy and efficiency in quantum chemistry calculations.
method Adapted SchNet for Orbitals (SchNOrb) model in quasi-atomic minimal basis.
result Model accurately predicts molecular orbital energies and wavefunctions for large molecules.
Gradient-based training and pruning for radial basis function networks in materials physics.
problem Interpretable and robust machine learning for materials physics problems.
method Gradient-based training and pruning of radial basis function networks with closed-form optimization criteria.
result Pruned models provide compact and interpretable versions of larger models, offering insights into atom-level migration processes.
We prove Transformers can learn diverse Gröbner bases.
problem Training Transformers for Gröbner basis computation.
method Prove generality of dataset generation algorithm; propose extended algorithm.
result Datasets are sufficiently general for diverse Gröbner bases learning.
Proposes a new method to learn entire solution paths without discretization.
problem Optimizing a family of problems indexed by hyperparameters.
method Parameterizes the solution path with basis functions and solves a single stochastic optimization problem.
result Uniform error of learned path converges linearly to a constant related to basis expressiveness.
Derives representations invariant under crystallographic groups for functions.
problem Representing and learning functions invariant under crystallographic groups.
method Derives linear and nonlinear representations of functions invariant under crystallographic groups.
result Derives orthonormal crystallographically invariant basis functions and embedding maps.
Recent work (Cohen & Welling, 2016) has shown that generalizations of convolutions, based on group theory, provide powerful inductive biases for learning. In these generalizations, filters are not only translated but can also be rotated, flipped, etc. However, coming up with exact models of how to rotate a 3 x 3 filter…
Ensembles dynamic models using random feature approximations.
problem Online scalable Bayesian learning with dynamic models and ensembling.
method Random feature approximations and dynamic models using random walks.
result Better performance with alternative basis expansions like Hilbert space Gaussian processes.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, we considered the definition of orthonormal basis in Minkows…
Introduces tunable basis functions for Gaussian processes.
problem Reduces computational complexity in Gaussian process approximations.
method Introduces tunable, local, and bounded basis functions for kernel approximation.
result Demonstrates superior performance compared to state-of-the-art methods, especially with poorly chosen kernel functions.
We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibi…
New model uses financial news to predict stock returns.
problem Predicting stock returns based on financial news.
method Derive company embedding vectors from news, select basis assets, and use statistical methods.
result NEUS model outperforms Fama-French 5-factor model.
A core operation in reinforcement learning (RL) is finding an action that is optimal with respect to a learned value function. This operation is often challenging when the learned value function takes continuous actions as input. We introduce deep radial-basis value functions (RBVFs): value functions learned using a de…
New basis confirms Thurston's conjecture and reveals knot configurations.
problem Understanding cluster algebras and their bases from surfaces.
method Topological construction of band basis and comparison with Kazhdan-Lusztig type basis.
result Common triangular basis matches band basis in quantum cluster algebras.
s-RBFN integrates multiple hypotheses for efficient and diverse prediction.
problem Integrating multiple hypotheses into learning models for regression.
method Structured Radial Basis Function Network (s-RBFN) using Voronoi tessellations and least-squares training.
result s-RBFN achieves superior generalization and efficiency compared to other models.
Finsler space is differentiable manifold for which Minkowski space is the fiber of the tangent bundle. To understand structure of the reference frame in Finsler space, we need to understand the structure of orthonormal basis in Minkowski space. In this paper, I considered the definition of orthonormal basis in Minkowsk…
Dual Bayesian Affine Estimators for Wiener-type state-space models
problem Estimating parameters in Wiener-type state-space models
method Fixed-point architecture combining two affine estimators
result Dual basis-parameter estimator achieves comparable parameter MSE to purely affine estimator
This paper proposes a new method to adapt ROMs for new parameter settings.
problem ROMs lack robustness when applied to new parameter settings.
method Regression trees on Grassmann Manifold to learn the mapping between parameters and POD bases.
result The proposed method is capable of establishing the mapping between parameters and POD bases, thus adapting ROMs for new parameters.
We study a novel spline-like basis, which we name the "falling factorial basis", bearing many similarities to the classic truncated power basis. The advantage of the falling factorial basis is that it enables rapid, linear-time computations in basis matrix multiplication and basis matrix inversion. The falling factoria…
DBKs enable scalable GPs with tractable inference for large datasets.
problem Scaling Gaussian processes to large and complex datasets while maintaining tractable inference.
method DBKs constructed from neural-network-parameterized basis functions with explicit low-rank structure, enabling linear-complexity inference.
result DBKs provide a unified perspective and improve predictive accuracy, uncertainty quantification, and computational efficiency.
New ODE-Block handles stateful layers with continuous-in-depth functions using basis functions.
problem Handling stateful layers in ODE-Nets.
method Formulate ODE-Block using continuous-in-depth functions with basis function expansions.
result Enables state-of-the-art performance and reduces memory footprint.
Paper proposes a method to recover point configurations from noisy distance data.
problem Recovering point configurations from noisy distance data.
method Robust Euclidean Distance Geometry via Dual Basis (RoDEoDB) algorithm.
result Exact recovery guarantees for point configuration and Gram matrix under mild conditions.
Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate GP methods have been proposed that essentially map the large dataset into a sma…
We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.
Data-aware methods for dimensionality reduction and matrix decomposition aim to find low-dimensional structure in a collection of data. Classical approaches discover such structure by learning a basis that can efficiently express the collection. Recently, "self expression", the idea of using a small subset of data vect…
Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a family of fast, flexible, lightly parametrized and general purpose kernel learning …
New framework models complex spatial data with basis functions and graphical vectors.
problem Modeling highly-multivariate spatial processes with varying resolutions.
method Extends graphical lasso to multivariate Gaussian processes with independent graphical vectors at different resolutions, using an orthogonal basis and fusion penalty.
result Linear complexity and parsimonious conditional independence structure in multilevel graphical model.
This paper proposes to learn hierarchical compositional AND-OR model for interpretable image synthesis by sparsifying the generator network. The proposed method adopts the scene-objects-parts-subparts-primitives hierarchy in image representation. A scene has different types (i.e., OR) each of which consists of a number…
The paper shows how to stabilize off-policy reinforcement learning using specific state representations.
problem Stability issues in reinforcement learning with function approximation and off-policy learning.
method Formal analysis of representation learning schemes based on the transition matrix of a policy.
result Schur and orthogonal bases of the Krylov subspace provide stable representations for TD learning.
In this paper, we propose a generic framework for devising an adaptive approximation scheme for value function approximation in reinforcement learning, which introduces multiscale approximation. The two basic ingredients are multiresolution analysis as well as tree approximation. Starting from simple refinable function…