Neural networks can separate non-separable data using feature maps.
problem Non-separable data in neural networks.
method Characterization of feedforward neural networks and use of feature maps.
result ReLU neural networks can separate concentric data.
Riemannian Neural OT maps improve scalability on manifolds.
problem Challenges in extending neural OT to high-dimensional Riemannian manifolds.
method Introduces Riemannian Neural OT (RNOT) maps that avoid discretization and incorporate geometric structure.
result RNOT maps approximate Riemannian OT maps with sub-exponential complexity in the dimension.
Equivariant neural networks use symmetry to interpret complex data.
problem Interpreting and understanding the behavior of equivariant neural networks.
method Decompose layers into simple representations and analyze nonlinear activation functions.
result Equivariant neural networks can be interpreted using a filtration generalizing Fourier series.
A neural network method tackles high-dimensional diffeomorphic mapping problems.
problem High-dimensional diffeomorphic mapping struggles with the curse of dimensionality.
method Combines variational principles with quasi-conformal theory for accurate, bijective mappings.
result Validated accuracy, robustness, and effectiveness in complex registration scenarios.
Neural Shadow-Mapping uncovers causal links in dynamic systems.
problem Discovering causal structures in dynamic systems with mirage correlations.
method Neural network based method embedding high-dimensional data into a shadow representation for causal link estimation.
result Demonstrates performance in discovering causal links from video-representations of dynamic systems.
The study reveals simplicity bias in neural networks leading to better compositional mappings.
problem Understanding when and how to encourage neural networks to learn compositional mappings.
method Examined compositional mappings through coding length and gradient descent dynamics.
result Neural networks tend to learn the simplest bijections, explaining their good generalization.
A novel solve-training framework is proposed to train neural network in representing low dimensional solution maps of physical models. Solve-training framework uses the neural network as the ansatz of the solution map and train the network variationally via loss functions from the underlying physical models. Solve-trai…
Graph neural network predicts optimal coarse-grained mapping operators.
problem Optimal coarse-grained mapping operators selection for molecular dynamics simulations.
method Graph Neural Network (DSGPM) trained on expert-annotated data.
result DSGPM outperforms state-of-the-art methods in graph segmentation.
Neural network outperforms traditional methods in chaotic dynamics classification.
problem Classifying chaotic and regular dynamics of the Chirikov standard map.
method Trained a convolutional neural network on finite-length trajectories compared to traditional Lyapunov exponent computation.
result Neural network outperforms traditional methods for short periods, converging faster and more robustly.
The feature map obtained from the denoising autoencoder (DAE) is investigated by determining transportation dynamics of the DAE, which is a cornerstone for deep learning. Despite the rapid development in its application, deep neural networks remain analytically unexplained, because the feature maps are nested and param…
A new Gaussian process framework uses neural feature maps for scalable, accurate inference.
problem Efficient and accurate Gaussian process inference for diverse data types.
method Neural feature maps to construct expressive kernels, with theoretical guarantees and practical scalability.
result The approach outperforms existing methods in accuracy and efficiency across various data modalities.
New method uses neural maps to efficiently sample lattice QCD distributions.
problem Challenges in sampling Boltzmann distributions of lattice field theories.
method Sparse triangular transport maps exploiting conditional independence structure of lattice graphs.
result Sparse triangular maps achieve efficient sampling with linear time complexity in lattice size.
Paper introduces a neural network for consistent estimation of optimal transport maps.
problem Statistically consistent estimation of optimal transport maps between probability distributions.
method Lipschitz-constrained GAN penalized by quadratic transportation cost.
result The generator converges uniformly to the optimal transport map as sample size increases.
In this paper, we present a novel and principled approach to learn the optimal transport between two distributions, from samples. Guided by the optimal transport theory, we learn the optimal Kantorovich potential which induces the optimal transport map. This involves learning two convex functions, by solving a novel mi…
New nonlinear saliency maps improve deep neural network interpretability.
problem Lack of understanding why and how deep neural networks make decisions.
method Developed novel nonlinear saliency maps to better interpret deep neural networks.
result Nonlinear saliency maps provide more specific drivers of classification on complex examples.
Proposes a new method to prevent overfitting in deep neural networks.
problem Overfitting in deep neural networks with many trainable parameters.
method Randomly replaces elements in feature maps with specific values during training.
result Improves the testing performance of deep neural networks on benchmark datasets.
Fixed points of nonnegative neural networks are analyzed using fixed point theory.
problem Analyzing fixed points in nonnegative neural networks.
method Fixed point theory, nonlinear Perron-Frobenius theory, monotonic and scalable mappings.
result Conditions for the existence of fixed points in nonnegative neural networks are provided.
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.
Deep neural networks improve free energy calculations for peptide conformations.
problem Challenges in developing suitable mappings for free energy perturbation.
method Adapted machine learning approach to train deep neural networks for mapping between Boltzmann distributions.
result Accurate free energy differences calculated between thermodynamic states with spring centers separated by 1 Å and sometimes 2 Å.
Synaptic strength can be seen as probability to propagate impulse, and according to synaptic plasticity, function could exist from propagation activity to synaptic strength. If the function satisfies constraints such as continuity and monotonicity, neural network under external stimulus will always go to fixed point, a…
Maps are an important medium that enable people to comprehensively understand the configuration of cultural activities and natural elements over different times and places. Although massive maps are available in the digital era, how to effectively and accurately access the required map remains a challenge today. Previo…
We introduce a new unsupervised representation learning and visualization using deep convolutional networks and self organizing maps called Deep Neural Maps (DNM). DNM jointly learns an embedding of the input data and a mapping from the embedding space to a two-dimensional lattice. We compare visualizations of DNM with…
Visualizes DNNs using topographic maps for better understanding.
problem Difficulty in understanding how DNNs solve tasks.
method Adapting neuroscience methods to visualize DNN activations.
result Improved transparency and interpretability of DNN-based systems.
Study neural networks by mapping correlations, revealing essential statistics.
problem Understanding information processing in trained neural networks.
method Characterize neural network as distribution transformations, focusing on correlation functions.
result Higher-order correlations are crucial for internal layers, while input layer captures more.
Neural framework for conditional OT maps learns from categorical and continuous variables.
problem Learning conditional optimal transport maps between complex distributions.
method Hypernetwork generates adaptive transport layer parameters based on conditioning variables.
result Our method outperforms simpler conditioning methods in comprehensive ablation studies.
In image-based camera localization systems, information about the environment is usually stored in some representation, which can be referred to as a map. Conventionally, most maps are built upon hand-crafted features. Recently, neural networks have attracted attention as a data-driven map representation, and have show…
Improved saliency maps for deep neural networks with reduced noise.
problem Noisy explanations in Integrated Gradients for deep neural networks.
method SmoothTaylor, adaptive noising, and SmoothGrad techniques.
result SmoothTaylor and adaptive noising generate better quality saliency maps.
New theory maps neural network weights to optimize faster and scale.
problem Optimizing neural networks for speed and scalability.
method Constructing a duality map using layer-wise operator norms.
result Derived GPU-friendly algorithms for various layers.
Estimates optimal transport maps with known cost functions.
problem Ensuring optimal transport maps correspond to real-world usefulness.
method Differentiable neural ground costs with known Monge map forms.
result General approach for incorporating prior information.
SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.
problem High-dimensional and incomplete tensor completion.
method Spectra-Guided Neural Tucker Factorization (SG-NTF) with Spatio-Temporal Co-Gating (STCG).
result Maintains competitive completion accuracy with parameter efficiency.
Sparse neural encoding can store more memories as targets become sparser.
problem Storing sparse input-target associations in neural networks.
method Mathematical proofs using properties of random polytopes and sub-gaussian random vector variables.
result The capacity of neural maps increases with sparsity in target layers.
Generalizes neural networks for infinite-dimensional mappings, including PDE solutions.
problem Learning mappings between infinite-dimensional spaces and finite-dimensional approximations.
method Graph kernel network architecture with message passing for kernel integration.
result Competitive performance compared to state-of-the-art solvers for PDEs.
New method calibrates neural network predictions for better reliability.
problem Improper probability estimates from deep networks leading to unreliable predictions.
method Proposes a constrained optimization approach for a monotonic calibration map.
result Achieves state-of-the-art performance across various datasets and models.
Agent learns to navigate uncertain 3D maps using a hybrid planner.
problem Planning in 3D environments with uncertain topological maps.
method Hierarchical strategy combining graph planner and local policy, data-driven learning with neural network.
result Machine learning can overcome missing information in probabilistic topological maps.
Saliency Map, the gradient of the score function with respect to the input, is the most basic technique for interpreting deep neural network decisions. However, saliency maps are often visually noisy. Although several hypotheses were proposed to account for this phenomenon, there are few works that provide rigorous ana…
Neural Local Wasserstein Regression models distribution-on-distribution regression with flexible, localized transport maps.
problem Estimating distribution-on-distribution regression with global optimal transport maps or linearization limitations.
method Proposes Neural Local Wasserstein Regression, a flexible nonparametric framework using locally defined transport maps in Wasserstein space.
result Demonstrates effective capture of nonlinear and high-dimensional distributional relationships.
New algorithm constrains SOMs to create supervised low-dimensional mappings.
problem Creating supervised mappings in neural networks with known internal topology.
method Developed Supervised Topological Maps (STMs) by modifying SOMs to incorporate target distances.
result STMs allow for supervised generation of new data with known internal structure.
Develops neural network approximations for infinite-dimensional input-output maps.
problem Approximating input-output maps between infinite-dimensional spaces.
method Combines neural networks and model reduction techniques.
result Proves convergence of the proposed approximation methodology.
New neural networks learn mappings between probability measures and functions.
problem Learning mappings between Wasserstein space of probability measures and function spaces.
method Two types of neural networks: bin density and cylindrical approximation, are proposed and supported by universal approximation theorems.
result Accuracy and efficiency of mean-field neural networks in generalization error with various test distributions.
Deep neural-kernel models combine neural networks and kernel machines for scalable large datasets.
problem Combining neural networks and kernel machines for efficient large-scale learning.
method Hybrid neural-kernel architecture using explicit feature mapping and pooling layers.
result The deep neural-kernel models are effective and scalable on benchmark datasets.
Study validates saliency maps of GNNs using selective inference.
problem Reliability of GNN saliency maps in graph-structured data.
method Statistical testing framework with selective inference to control Type I error rate.
result Valid p-values for salient subgraphs, ensuring meaningful information. Generalizes neural network approximation to infinite-dimensional manifolds and derivatives.
problem Approximating differentiable maps on infinite-dimensional manifolds.
method Proves a weighted Nachbin theorem to establish universal approximation for differentiable maps, including derivatives.
result Linear functions of the signature can approximate path space functionals including their derivatives.
The use of artificial neural networks as models of chaotic dynamics has been rapidly expanding. Still, a theoretical understanding of how neural networks learn chaos is lacking. Here, we employ a geometric perspective to show that neural networks can efficiently model chaotic dynamics by becoming structurally chaotic t…
New method uses neural ODEs to approximate complex distributions efficiently.
problem Approximating complex probability distributions efficiently.
method Neural ODEs with minimum energy regularization for distribution approximation.
result Deep neural network representations can achieve accurate distribution approximation.
1-Lipschitz neural networks produce clearer, more focused Saliency Maps for explainable AI.
problem Noisy and limited Saliency Maps from traditional neural networks.
method Dual loss of optimal transport problem for 1-Lipschitz neural networks.
result Saliency Maps from 1-Lipschitz networks are highly concentrated and less noisy, aligning with human explanations.
Method generates time-series attribution maps with identifiability guarantees.
problem Lack of identifiability guarantees in gradient-based attribution methods.
method Regularized contrastive learning algorithm trained on time-series data.
result Empirically shows robust approximation of zero vs. non-zero entries in the ground-truth attribution map.
Renormalization in neural networks linked to quantum field theory.
problem Implementing renormalization in neural networks.
method Mapping neural networks to quantum field theory, applying renormalization techniques.
result Changing weight standard deviation corresponds to a renormalization flow.
Training shapes the geometry of neural network feature maps, revealing local area magnification.
problem Understanding how training affects the geometric structure of neural network feature maps.
method Analyzing the Riemannian geometry induced by neural network feature maps at infinite width and after training.
result Training breaks the symmetry of the geometry induced by random neural network feature maps, magnifying local areas along decision boundaries.