Study on ground states of semilinear elliptic equations with various potential wells.
problem Characterizing ground states of semilinear elliptic equations with arbitrary potential wells.
method Analyzing solutions in convex domains and manifolds with non-negative Ricci curvature, using Morse theory and min-max methods.
result Ground states are mountain-pass type with Morse index 1 in convex domains and manifolds with non-negative Ricci curvature.
The paper identifies magnetic ground states and their role in determining the conformal class of a surface.
problem Understanding the magnetic ground states and their relation to the conformal class of a surface.
method Analyzing the magnetic Laplacian and its eigenvalues on a Riemannian surface.
result The ground state spectrum uniquely determines the volume and conformal class of the metric.
New method uses adiabatic principles to improve ground-state preparation in quantum computing.
problem Challenges in variational training of complex energy landscapes.
method Iterative Hamiltonian deformation complemented with adiabatic principles.
result Consistent convergence to target ground state through sequence of intermediate problems.
Classification of ground state solutions to critical Dirac equation on spheres.
problem Classifying ground state solutions of the critical Dirac equation.
method Exploiting conformal covariance and relating to the Yamabe equation.
result Ground state solutions are given by Killing spinors up to conformal diffeomorphisms.
We provide some new results of the ground state of quantum layers.
New method uses kernel methods to approximate ground states of quantum Hamiltonians efficiently.
problem Approximating ground states of quantum Hamiltonians using neural networks is computationally expensive.
method Introduces a statistical learning approach using kernel methods to make optimization trivial.
result Ground state properties of arbitrary gapped quantum Hamiltonians can be reached with polynomial resources.
In this paper, we consider the generalized lambda constant and the existence of ground states of the generalized Perelman's W-functional from a variational formulation. One result is concerned with the estimation of the generalized λ constant. The other results are about the existence of ground states of generalized …
Study on existence of ground states for free energy on hyperbolic space.
problem Existence of ground states for a free energy functional on hyperbolic space.
method Derived HLS-type inequalities on Cartan-Hadamard manifolds to prove existence.
result Established conditions for the existence of ground states on hyperbolic space.
CLuP achieves near optimal ground state energies for positive and negative Hopfield models.
problem Finding near optimal ground state energies for positive and negative Hopfield models.
method Controlled Loosening-up (CLuP) algorithm with fully lifted random duality theory (fl RDT).
result Achieves ground state free energies of 1.77 and 0.33 for positive and negative Hopfield models respectively. Study on existence of ground states on curved spaces with conditions on potential growth.
problem Existence of ground states for aggregation-diffusion models on Cartan-Hadamard manifolds.
method Investigation of a free energy functional on Cartan-Hadamard manifolds, considering entropy and interaction energies.
result Necessary and sufficient conditions for existence of ground states are found, depending on the growth of the attractive potential.
Study heat profiles and eigenfunctions using Brownian motion.
problem Investigate heat profiles and eigenfunctions of Laplace equations.
method Probabilistic tools based on Brownian motion and Feynman-Kac formulae.
result Supremum norm bounds for ground state Dirichlet eigenfunctions and comparison of maximum temperatures.
New pseudo-Hermitian models from non-semisimple TQFTs.
problem Constructing exactly solvable pseudo-Hermitian spin Hamiltonians.
method Identifying ground states on surfaces using non-semisimple TQFTs.
result Ground states depend only on spatial topology and can be assigned by non-semisimple TQFTs.
New algorithm nearly achieves ground state free energy of SK model.
problem Determining the ground state free energy of the SK model.
method Controlled Loosening-up (CLuP) algorithm applied to SK models.
result Achieves ground state free energy of ~0.76 for n in the thousands.
The excited states of polyatomic systems are rather complex, and often exhibit meta-stable dynamical behaviors. Static analysis of reaction pathway often fails to sufficiently characterize excited state motions due to their highly non-equilibrium nature. Here, we proposed a time series guided clustering algorithm to ge…
Parts of Texas, Oklahoma, and Kansas have experienced increased rates of seismicity in recent years, providing new datasets of earthquake recordings to develop ground motion prediction models for this particular region of the Central and Eastern North America (CENA). This paper outlines a framework for using Artificial…
The paper analyzes neural networks for solving high-dimensional Schrödinger eigenvalue problems.
problem Analyzing generalization error of neural networks for high-dimensional Schrödinger eigenvalue problems.
method Proves convergence rate of generalization error independent of dimension d under spectral Barron space assumption. Verifies assumption by proving regularity estimate. result Generalization error rate is independent of dimension d under spectral Barron space assumption. Paper introduces untangling number to quantify 3-periodic tangle complexity.
problem Quantifying the complexity of 3-periodic tangles in biological, chemical, and physical systems.
method Introduces untangling number, a measure of minimum distance to ground state through diagrammatic operations.
result For infinite open curves, generic ground states are crystallographic rod packings.
Optimizes angular velocity transfers for rigid bodies under deadline constraints.
problem Stochastic guidance of spin states of rigid bodies over a hard deadline.
method Structural analysis of Kantorovich optimal coupling formulation for nonlinear dynamics.
result Derives the ground cost for optimal transport of angular velocity.
Paper defines untangling number to measure entanglement complexity in 3-periodic networks.
problem Measuring the complexity of entanglement in 3-periodic networks.
method Defining ground states through knot-theoretic crossing diagrams and measuring untangling number.
result Introduced untangling number as a measure of entanglement complexity.
Existence of Q-processes for Brownian motion on hyperbolic spaces with Poissonian potentials shown.
problem Existence of path limits (Q-processes) for Brownian motion on hyperbolic spaces with Poissonian potentials.
method Analysis of stationary random potentials with spectral and sup norm bounds, and use of foliated space defined by the point process.
result Existence of Q-processes for Brownian motion on hyperbolic spaces with Poissonian potentials shown.
Statistical learning theory provides bounds of the generalization gap, using in particular the Vapnik-Chervonenkis dimension and the Rademacher complexity. An alternative approach, mainly studied in the statistical physics literature, is the study of generalization in simple synthetic-data models. Here we discuss the c…
New framework for AI to learn causal models through experience.
problem Lack of guidance for variable choice and interventions in causal models for AI.
method Defines actions as state space transformations, introduces causal variables, and identifies interventions.
result Clarifies the concept of interventions and makes causal representation learning clearer.
QUACKIE creates a new benchmark for NLP interpretability.
problem Evaluating NLP interpretability methods is challenging due to biased ground truths.
method Formulated a custom classification task from question-answering datasets, generating unbiased ground truths.
result Demonstrated the effectiveness of current interpretability methods on the new benchmark.
Study uses supervised learning to classify quantum phases with limited measurements.
problem Classifying quantum phases of matter with incomplete phase diagrams.
method Combines classical and quantum techniques, including tensor networks, kernel methods, and quantum algorithms.
result Certification of new ground states can be achieved with polynomial measurements.
Smooth solutions and classification of Dirac-Einstein equations on 3-manifolds.
problem Analyzing solutions of Dirac-Einstein equations on R3. method Proving smoothness and asymptotic behavior, classifying ground state solutions.
result Scalar part is given by Aubin-Talenti functions, spinorial part is conformal image of −21-Killing spinors on S3. Quantum annealing improves VB inference, avoiding local minima.
problem Variational Bayes inference stuck in local minima.
method Quantum annealing approach to VB inference.
result Quantum annealing variational Bayes (QAVB) outperforms classical VB.
Neural model predicts object states and physical parameters from visual observations.
problem Computational models struggle with physical reasoning and adapting to new environments.
method Visual prior predicts particle-based system from visual observations; inference module refines estimates subject to dynamics constraints.
result Model can infer physical properties within a few observations and adapt to unseen scenarios.
Paper proposes a method to recover accurate labels from partially valid data in multi-label learning.
problem Tackles noisy supervision in multi-label learning with partially valid labels.
method Develops a two-stage method that estimates label enrichment and ground-truth confidences.
result Demonstrates improved performance over state-of-the-art PML methods.
Study of unoriented SL(4) foams in 3-manifolds.
problem Understanding unoriented SL(4) foams in 3-manifolds.
method Combinatorial evaluation and state space study of unoriented SL(4) foams.
result State space of any web is free of rank given by the number of its 4-colorings over a localized ground ring.
Sketch Tomography improves quantum state estimation accuracy.
problem Efficiently estimating quantum states, especially MPS states.
method Hybridizes classical shadow protocol with tensor train ansatz.
result Proven convergence with quadratic sample complexity.
Deep QMC method accurately computes electronic excited states.
problem Accurate calculation of electronic excited states in large systems.
method Extends variational QMC with deep neural networks for excited states.
result Consistently achieves high accuracy for low-lying excited states.
Recently developed deep-learning-based denoisers often outperform state-of-the-art conventional denoisers such as the BM3D. They are typically trained to minimize the mean squared error (MSE) between the output image of a deep neural network (DNN) and a ground truth image. Thus, it is important for deep-learning-based …
In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this process "grounding"). The approach is particularly well-suited for extracting large nu…
Solve Painleve VI to relate instanton bundles.
problem Relate instanton bundles to Painleve VI solutions.
method Generalize Hitchin's logarithmic connection to vector bundles with SL2 action.
result Identify Okamoto transformations as creation operators.
In this note we make an attempt to compare a cohomological theory of Hilbert spaces of ground states in the N=(2,2) 2d Landau-Ginzburg theory in models describing link embeddings in R3 to Khovanov and Khovanov-Rozansky homologies. To confirm the equivalence we exploit the invariance of Hilbert sp…
Combining insights from machine learning and quantum Monte Carlo, the stochastic reconfiguration method with neural network Ansatz states is a promising new direction for high-precision ground state estimation of quantum many-body problems. Even though this method works well in practice, little is known about the learn…
In this paper, we proved the quantum layer over a surface which is ruled outside a compact set, asymptotically flat but not totally geodesic admits ground states.
We design, conduct and present the results of a highly personalized baseline emotion recognition experiment, which aims to set reliable ground-truth estimates for the subject's emotional state for real-life prediction under similar conditions using a small number of physiological sensors. We also propose an adaptive st…
FedSpace optimizes ML training on satellites and ground stations.
problem Training machine learning models on satellites with limited bandwidth.
method Federated Learning framework that dynamically schedules model aggregation based on satellite orbits.
result Reduces training time by 1.7 days over state-of-the-art algorithms.
Study of Dirac equation with non-local nonlinearity on spheres.
problem Conformally invariant Dirac equation with non-local nonlinearity.
method Investigation of compactness, bubbling, and energy quantization of energy functional; characterization of ground state solutions; proof of Aubin-type inequality and Brezis-Nirenberg type result.
result Existence of solutions to the conformal Einstein-Dirac problem in dimension 4.
We prove sharp pointwise decay estimates for critical Dirac equations on Rn with n≥2. They appear for instance in the study of critical Dirac equations on compact spin manifolds, describing blow-up profiles, and as effective equations in honeycomb structures. For the latter case, we find excited state…
Proposes a method to align language and image data.
problem Aligning language and image data for better understanding.
method Uses triplet loss to learn consistent embeddings of language and images.
result Outperforms four baselines across multiple metrics.
The theorems we proved describe the structure of economic equilibrium in the exchange economy model. We have studied the structure of property vectors under given structure of demand vectors at which given price vector is equilibrium one. On this ground, we describe the general structure of the equilibrium state and gi…
We consider a bounded domain Ω of RN, N≥3, and h a continuous function on Ω. Let Γ be a closed curve contained in Ω. We study existence of positive solutions u∈H01(Ω) to the equation −Δu+hu=ρΓ−σu2σ∗−1 in Ω where 2σ∗:=N−22(N−σ), $σ\in (0,2)…
New method learns high-quality Laplacian representations for reinforcement learning.
problem Lack of accurate Laplacian representations in large or continuous state spaces.
method Reformulated spectral graph drawing objective to have eigenvectors as unique global minimizer.
result Learned Laplacian representations more faithfully approximate the ground truth.
Separating an audio scene such as a cocktail party into constituent, meaningful components is a core task in computer audition. Deep networks are the state-of-the-art approach. They are trained on synthetic mixtures of audio made from isolated sound source recordings so that ground truth for the separation is known. Ho…
New method uses quantum computing to process classical data efficiently.
problem Inefficient quantum machine learning due to data loading and trainability issues.
method Linear Hamiltonian-based machine learning with ground state problems for k-local Hamiltonians.
result Demonstrated the effectiveness and scalability of the method on up to 50 qubits.
Multimodalities provide promising performance than unimodality in most tasks. However, learning the semantic of the representations from multimodalities efficiently is extremely challenging. To tackle this, we propose the Transformer based Cross-modal Translator (TCT) to learn unimodal sequence representations by trans…