Distributed model training suffers from communication overheads due to frequent gradient updates transmitted between compute nodes. To mitigate these overheads, several studies propose the use of sparsified stochastic gradients. We argue that these are facets of a general sparsification method that can operate on any p…
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48 results for “atomic decompositions”
Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincaré inequality, the space $\Mone$, defined by Hajłasz, is identified with a Hardy-Sobolev space defined in terms of atoms. Decomposition results are proved for both the homoge…
In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the orthogonality condition of the atoms, yielding overcomplete dictionaries with an exten…
Efficiently decomposes tensors with Boolean factors using BMP.
problem Tensor decomposition with Boolean factors is challenging due to non-convexity and combinatorial constraints.
method Binary Matching Pursuit (BMP) iteratively searches for atoms in a greedy fashion, solving the greedy atom search step via MAXCUT-like boolean quadratic program.
result BMP converges sublinearly to the optimal solution and recovers factors under mild conditions.
We develop a theory of `non-uniformly local' tent spaces on metric measure spaces. As our main result, we give a remarkably simple proof of the atomic decomposition.
Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has proven to be very effective in many image processing tasks. Traditionally, the di…
Let be a complete connected Riemannian manifold. Assuming that the Riemannian measure is doubling, we define Hardy spaces of differential forms on and give various characterizations of them, including an atomic decomposition. As a consequence, we derive the -boundedness for Riesz transforms on , g…
The paper analyzes deep neural networks using rectified linear units.
problem Understanding the individual affine linear representations of deep neural networks.
method Signal processing perspective, atomic decompositions, Lipschitz regularity estimation.
result Conditions for stabilizing learning in deep neural networks without network depth constraints.
A multi-way factor analysis model is introduced for tensor-variate data of any order. Each data item is represented as a (sparse) sum of Kruskal decompositions, a Kruskal-factor analysis (KFA). KFA is nonparametric and can infer both the tensor-rank of each dictionary atom and the number of dictionary atoms. The model …
Suppose that is the open region in above a Lipschitz graph and let denote the exterior derivative on . We construct a convolution operator which preserves support in $\bar{Ω$}, is smoothing of order 1 on the homogeneous function spaces, and is a potential map in the sense that …
This paper studies periodic and free periodic knots in alternating projections.
problem Understanding periodic and free periodic knots in alternating projections.
method Analyzing the essential Conway decomposition and Murasugi decomposition of alternating knots.
result Conditions for an alternating knot to be freely periodic are identified.
Ancient grain boundaries resemble atoms in their formation and properties.
problem Understanding the formation and properties of ancient grain boundaries.
method Analyzing ancient grain boundaries as analogous to atoms and using geometric flow techniques.
result New examples of convex ancient and translating solutions to mean curvature flow.
This paper proposes a subspace decomposition method based on an over-complete dictionary in sparse representation, called "Sparse Signal Subspace Decomposition" (or 3SD) method. This method makes use of a novel criterion based on the occurrence frequency of atoms of the dictionary over the data set. This criterion, wel…
A new CNN architecture tackles domain shifts with a dictionary approach.
problem Handling domain shifts in deep learning models.
method Decompose CNN layers into domain-specific and shared parts using a dictionary of atoms.
result The approach promotes shared semantics across domains with minimal additional parameters.
The paper proposes a new method for online image decomposition using auto-encoders.
problem Building a part-based representation of image datasets for interpretation and online computation.
method Sparse, non-negative auto-encoder with deep encoder and shallow decoder for online computation.
result The method outperforms state-of-the-art online methods on MNIST and Fashion MNIST datasets.
Graph-neural-network predictions of solid-state NMR parameters from spherical tensor decompositioncond-mat.mtrl-sci
Graph neural networks predict solid-state NMR parameters from atomic structures.
problem Efficiently predicting NMR parameters from atomic structures for complex materials.
method Graph neural networks applied to tensor quantities for anisotropic magnetic shielding and electric field gradient.
result Improved accuracy in predicting NMR properties from diverse and complex materials.
Learning the electronic density of states in condensed mattercond-mat.mtrl-sci
Machine learning predicts electronic density of states for condensed matter.
problem Predicting the electronic density of states (DOS) in complex condensed matter systems.
method Developed a machine learning framework to predict DOS from density functional theory data, considering geometric configurations of atoms.
result Demonstrated the model's effectiveness in predicting DOS and its components for various silicon configurations.
Unified theory linking atom-centered and message-passing models for molecular properties.
problem Combining atom-centered and message-passing models for accurate molecular property prediction.
method Generalizing ACDC framework to include multi-centered information, providing a complete linear basis for regression.
result Unified understanding of atom-centered and message-passing models, providing a coherent foundation.
The atomic swap protocol allows for the exchange of cryptocurrencies on different blockchains without the need to trust a third-party. However, market participants who desire to hold derivative assets such as options or futures would also benefit from trustless exchange. In this paper I propose the atomic swaption, whi…
New method interprets ranked data on permutahedron graph.
problem Interpreting and exploiting structure in ranked data sets.
method Combining combinatorial representation theory and signal processing on graphs.
result Developed scalable transform method using Parseval frames.
Researchers use manifold learning to analyze 4D-STEM data of graphene, revealing atomic structure details.
problem Challenges in processing and interpreting large 4D-STEM datasets, especially for light materials.
method Data-driven manifold learning approaches for visualization and exploration of 4D-STEM datasets.
result Extracted patterns relate to individual atom sites and sublattice structures, effectively discriminating single dopant anomalies.
Machine Learning Prediction of Accurate Atomization Energies of Organic Molecules from Low-Fidelity Quantum Chemical Calculationsphysics.comp-ph
Machine learning predicts atomization energies accurately from low-fidelity calculations.
problem Predicting accurate atomization energies of organic molecules efficiently.
method Machine learning models trained on low-fidelity B3LYP energies to predict high-fidelity G4MP2 energies.
result Predicted G4MP2 atomization energies within 0.012 eV for molecules with 10-14 heavy atoms.
Cormorant: Covariant Molecular Neural Networksphysics.comp-ph
Cormorant learns molecular properties via rotationally covariant neural networks.
problem Learning molecular potential energy surfaces and properties.
method Rotationally covariant neural network architecture with tensor products and Clebsch-Gordan decomposition.
result Significantly outperforms competing algorithms in learning molecular Potential Energy Surfaces.
Equivariant representations for molecular Hamiltonians and N-center atomic-scale propertiesphysics.chem-ph
New features for quantum calculations learn N-center Hamiltonian matrix elements.
problem Quantum calculations need features for N-center Hamiltonians, not just atom-centered ones.
method Developed fully equivariant N-center features for machine learning.
result Learned matrix elements of N-center Hamiltonians efficiently.
Neural network learns atomic coordinates from Patterson maps in a simplified case.
problem Training a neural network to infer atomic coordinates from Patterson maps.
method Synthetic data training, centering output maps, removing centrosymmetric inversion, and adding empty space.
result The network can generalize to infer atom positions from Patterson maps not in the training set.
Comparison of Atom Representations in Graph Neural Networks for Molecular Property Predictionphysics.chem-ph
Study compares atom representations in graph neural networks for molecular properties.
problem Incorrect attribution of results in molecular property prediction due to varying atom features.
method Evaluated multiple atom representations on free energy, solubility, and metabolic stability predictions.
result Different atom representations can lead to varying predictive performance in graph neural networks.
We introduce a machine learning model to predict atomization energies of a diverse set of organic molecules, based on nuclear charges and atomic positions only. The problem of solving the molecular Schrödinger equation is mapped onto a non-linear statistical regression problem of reduced complexity. Regression models a…
We revisit Merton's portfolio optimization problem under boun-ded state-dependent utility functions, in a market driven by a Lévy process extending results by Karatzas et. al. (1991) and Kunita (2003). The problem is solved using a dual variational problem as it is customarily done for non-Markovian models. One of …
We prove that the introduction of the class of geometrically atomic bundle maps by Harvey and Lawson in their theory of singular connections is not necessary because an arbitrary map satisfies the conditions of geometric atomicity.
We introduce a novel class of localized atomic environment representations, based upon the Coulomb matrix. By combining these functions with the Gaussian approximation potential approach, we present LC-GAP, a new system for generating atomic potentials through machine learning (ML). Tests on the QM7, QM7b and GDB9 biom…
Atomistic structure learningcond-mat.mtrl-sci
ASLA learns atomic structures using neural networks and reinforcement learning.
problem Designing materials and drugs with desired properties.
method Atomistic structure learning algorithm (ASLA) using a convolutional neural network and reinforcement learning.
result ASLA can predict optimal structural arrangements of atoms for various target properties.
PAM models generate dependent random distributions across groups with overlapping clusters.
problem Generating dependent random distributions across multiple groups.
method Atom skipping in an infinite mixture model.
result Interpretable posterior inference of cluster exclusivity and sharing.
Non-atomic arbitrage exploits price differences on Ethereum and other blockchains, accounting for over 10% of Ethereum's block value.
problem Price differences on decentralized exchanges and centralized exchanges lead to MEV.
method Analyzed non-atomic arbitrage on Ethereum's largest DEXes, identifying its prevalence and impact.
result More than 10% of Ethereum's block value is attributed to non-atomic arbitrage, involving over $132 billion.
Site-specific graph neural network for predicting protonation energy of oxygenate moleculesphysics.chem-ph
Graph neural network predicts protonation energies of oxygen atoms in bio-oil molecules.
problem Predicting protonation energies of oxygen atoms in bio-oil molecules for chemical upgrading.
method Site-specific graph neural network approach using iterative local nonlinear embedding.
result Effective prediction of protonation energies of individual oxygen atoms in bio-oil molecules.
Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks…
This paper studies the effect of discretizing the parametrization of a dictionary used for Matching Pursuit decompositions of signals. Our approach relies on viewing the continuously parametrized dictionary as an embedded manifold in the signal space on which the tools of differential (Riemannian) geometry can be appli…
The crushing operation of Jaco and Rubinstein is a powerful technique in algorithmic 3-manifold topology: it enabled the first practical implementations of 3-sphere recognition and prime decomposition of orientable manifolds, and it plays a prominent role in state-of-the-art algorithms for unknot recognition and testin…
Improved chemical predictions through compressed atomic species representations.
problem Intractable chemical space of molecules and materials.
method Introducing elemental modes for compressed representation of atomic species.
result Elemental modes enable improvements in machine learning tasks for chemical predictions.
Atoms meet symbolsmath.AG
Unified approach to invariants in equivariant geometry.
problem Constructing invariants in -equivariant birational geometry.
method Combining atom theory and modular symbols.
result Developed new geometric invariants for orbifolds and surfaces.
Improves molecular activity prediction using graph convolutional neural networks considering graph distances.
problem Predicting molecular activity using graph convolutional neural networks with improved distance representation.
method Proposed three improvements: modified graph distances, distance-dependent weight matrices, and weighted sum conversion.
result The proposed method slightly outperforms the original weave module in compound activity prediction.
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learningstat.ML
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such at…
Develops conformal Bayes for two-sided censored Gaussian regression under label shift.
problem Prediction under label shift with censored responses.
method Combines posterior predictive tilting with weighted conformal calibration.
result Restores marginal coverage with smaller prediction sets.
In many signal processing applications, the aim is to reconstruct a signal that has a simple representation with respect to a certain basis or frame. Fundamental elements of the basis known as "atoms" allow us to define "atomic norms" that can be used to formulate convex regularizations for the reconstruction problem. …
Geometric GNNs model 3D atomic systems with rotations and translations.
problem Modeling 3D atomic systems with geometric graphs and machine learning.
method Invariant, equivariant, and unconstrained GNN architectures.
result Geometric GNNs leverage physical symmetries and chemical properties.
Proposes an algorithm for infinite-dimensional sparse learning in system identification.
problem System identification without known model structures.
method Atomic norm regularization and greedy algorithm for solving an infinite-dimensional group lasso problem.
result The proposed algorithm outperforms benchmark methods in impulse response fitting and pole location estimation.
Generative models encode and decode 3D crystal structures from a large dataset.
problem Challenges in encoding and decoding 3D crystal structures from large datasets.
method Training two neural networks on a dataset of over 120,000 crystal structures to encode and decode 3D atom positions.
result Ability to generate compressed, continuous latent space representations and decode molecules accurately.
Learning molecular energies using localized graph kernelsphysics.comp-ph
Recent machine learning methods make it possible to model potential energy of atomic configurations with chemical-level accuracy (as calculated from ab-initio calculations) and at speeds suitable for molecular dynam- ics simulation. Best performance is achieved when the known physical constraints are encoded in the mac…
Robust method for finding sparse solutions to linear inverse problems using an L2 regularizationmath.NA
We analyzed the performance of a biologically inspired algorithm called the Corrected Projections Algorithm (CPA) when a sparseness constraint is required to unambiguously reconstruct an observed signal using atoms from an overcomplete dictionary. By changing the geometry of the estimation problem, CPA gives an analyti…