Extends knot invariant to filtered grid complexes.
problem Knot invariants and grid complexes.
method Combining Ozsváth-Szabó-Stipsicz crossing-change maps with Alishahi-Eftekhary l(K) invariant.
result Combinatorial formulation of knot invariant.
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48 results for “filtered maps”
We analyze errors in filtering algorithms using optimal transport.
problem Estimation errors in optimal transport-based filtering algorithms.
method Systematic analysis of estimation errors for conditional Brenier maps.
result Demonstrates effectiveness and practical potential of the optimal transport filtering algorithm.
Visualizes deep neural networks for speech recognition using learned topographic filter maps.
problem Unintuitive internal structure of deep neural networks complicates activation visualization.
method Trains a convolutional speech recognition model with filters arranged in a 2D grid, highlighting similar filters.
result Topographic filter maps visualize artificial neuron activations more intuitively.
A new method improves Bayesian filtering in nonlinear systems.
problem Bayesian filtering in nonlinear dynamical systems with non-Gaussian posteriors.
method Transport maps with block-triangular structure and gradient flows for MMD minimization.
result Accurate approximation of non-Gaussian posteriors without particle collapse.
A method for optimal Bayesian filtering using progressive particle flow and optimal transport maps.
problem Optimizing Bayesian filtering with deterministic particles to avoid degeneration.
method Progressive flow of particles through a sequence of sub-steps, each using an optimal transport map to replace non-equally weighted particles with equally weighted ones.
result The method avoids particle degeneration and simplifies the filtering process by not requiring inversions or monotonicity constraints.
Formula calculates knot Floer complexes for specific cable knots.
problem Computing knot Floer complexes for -cable knots.
method Filtered mapping cone formula generalizing previous results.
result Existence of knots with arbitrary concordance homomorphisms values.
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
Convergence of the Kalman filter is best analyzed by studying the contraction of the Riccati map in the space of positive definite (covariance) matrices. In this paper, we explore how this contraction property relates to a more fundamental non-expansiveness property of filtering maps in the space of probability distrib…
Study uses SAR data to map defoliation and regrowth in tundra-forest areas.
problem Mapping defoliation and regrowth in tundra-forest areas using SAR data.
method Novel guided nonlocal means speckle filtering of polarimetric covariance matrix.
result Over 99.7% classification accuracy in defoliation and regrowth mapping.
In this article, we reformulate the cobordism map of embedded contact homology, which is induced by exact symplectic cobordism and defined as direct limit of homomorphisms called filtered ECH cobordism map. The filtered ECH cobordism map is defined by counting embedded holomorphic curves with zero ECH index and we prov…
We introduce filtered cohomologies of differential forms on symplectic manifolds. They generalize and include the cohomologies discussed in Paper I and II as a subset. The filtered cohomologies are finite-dimensional and can be associated with differential elliptic complexes. Algebraically, we show that the filtered co…
Paper uses optimal transport for Bayesian filtering, deriving new EnKF and FPF formulations.
problem Bayesian filtering for nonlinear systems with non-Gaussian observations.
method Optimal transport theory applied to Bayes' law, constructing Brenier maps.
result New variational formulations of EnKF and FPF for non-Gaussian settings.
We construct Hodge filtered cohomology groups for complex manifolds that combine the topological information of generalized cohomology theories with geometric data of Hodge filtered holomorphic forms. This theory provides a natural generalization of Deligne cohomology. For smooth complex algebraic varieties, we show th…
Increasing availability of vehicle GPS data has created potentially transformative opportunities for traffic management, route planning and other location-based services. Critical to the utility of the data is their accuracy. Map-matching is the process of improving the accuracy by aligning GPS data with the road netwo…
Kernel embedding of maps for sequential Bayesian inference: The variational mapping particle filterstat.ML
In this work, a novel sequential Monte Carlo filter is introduced which aims at efficient sampling of high-dimensional state spaces with a limited number of particles. Particles are pushed forward from the prior to the posterior density using a sequence of mappings that minimizes the Kullback-Leibler divergence between…
NBF combines deep learning with classical filtering for better belief tracking.
problem Maintaining distributions over hidden states in partially observable systems.
method Trains neural networks to map beliefs to fixed-length vectors, updating them with incoming observations and dynamics.
result NBF efficiently tracks shifting, multimodal beliefs without particle impoverishment.
Spatially scalable recursive estimation of Gaussian process terrain maps using local basis functionscs.LG
New algorithm speeds up online mapping of unknown terrains.
problem Increasing computational demands of GP mapping as area expands.
method Recursive GP mapping using local basis functions in an information filter.
result Reduces overall computational complexity and speeds up mapping.
Paper learns to rotate filters for group convolutions.
problem Difficult to rotate 3x3 filters on pixel grids.
method Learn filter basis and rotation-invariant coefficients; switch basis for rotation.
result Produces feature maps insensitive to input rotations.
BlurNet defends against adversarial attacks by filtering feature maps.
problem Adversarial attacks on deep neural networks, especially for image classification.
method BlurNet introduces a depthwise convolution layer with standard blur kernels after the first layer to filter high frequency noise.
result The defense reduces the success rate of adversarial attacks from 90% to 20% with total variation regularization.
A new framework for efficient sequence maps using Bayesian filtering and covariance.
problem Designing efficient recurrent sequence maps from explicit memory assumptions.
method Design-model framework, exact Bayesian filtering, query-dependent readout, linear-Gaussian instantiation.
result Improved robustness and retrieval performance across various benchmarks.
Enhanced ensemble filters use machine learning to improve accuracy in filtering models.
problem Accuracy limitations of traditional ensemble Kalman filters.
method Introduces a measure neural mapping (MNM) to map joint predicted state and observation to updated state estimates.
result Superior root-mean-square-error performance compared to leading methods in filtering models.
Improving Bayesian filtering with strictly proper scoring rules
problem Bayesian filtering of partially and noisily observed dynamical systems
method Proper scoring ensemble filter (PSEF)
result Accurate approximation of challenging filtering distributions
Constructs a cyclic, filtered, strictly unital curved category for Lagrangian submanifolds and develops Floer theory.
problem Proving that any Lagrangian submanifold equipped with a weak bounding cochain lies in the category split-generated by a given collection of Lagrangian submanifolds.
method Develops a cyclic, filtered, strictly unital curved category and uses it to prove the above statement.
result Any Lagrangian submanifold equipped with a weak bounding cochain lies in the category split-generated by a given collection of Lagrangian submanifolds.
Net2Vec: Quantifying and Explaining how Concepts are Encoded by Filters in Deep Neural Networkscs.CV
In an effort to understand the meaning of the intermediate representations captured by deep networks, recent papers have tried to associate specific semantic concepts to individual neural network filter responses, where interesting correlations are often found, largely by focusing on extremal filter responses. In this …
DeepLocalization uses neural networks to localize vehicles from landmarks.
problem Vehicle self-localization from multi-modal sensor data and a reference map.
method Deep neural network that regresses vehicle pose from unordered landmarks.
result DeepLocalization achieves state-of-the-art accuracy and is faster than related work.
Improved action detection for multi-person videos using attention filtering.
problem Difficulty in distinguishing relevant parts of multi-person videos for action detection.
method Fovea attention filtering and generalized binary loss function.
result 20% relative improvement in mAP over baseline in AVA dataset.
A Bloom filter approach combined with Transformer models improves accuracy for machine learning tasks on opaque IDs.
problem Improving accuracy for machine learning tasks on opaque IDs with large vocabulary sizes.
method Applying hash functions to map opaque IDs to multiple hash tokens, similar to a Bloom filter, and using a multi-layer Transformer to process these digests.
result Models outperform those without hashing and sampled softmax, achieving high accuracy with a smaller computational budget.
Compressing convolutional neural networks (CNNs) is essential for transferring the success of CNNs to a wide variety of applications to mobile devices. In contrast to directly recognizing subtle weights or filters as redundant in a given CNN, this paper presents an evolutionary method to automatically eliminate redunda…
This study uses neural networks to approximate Bayesian filtering problems.
problem Estimating latent time-series signal statistics from observation sequences.
method Formulated a generic recurrent neural network framework to learn recursive mappings directly.
result Approximation error bounds for filtering in non-compact domains and strong time-uniform bounds.
Improved model-based estimation through tempered Bayes filter.
problem Improving predictive accuracy in partially-observable stochastic systems.
method Developed tempered Bayes filter combining likelihood and full posterior tempering.
result Tempered Bayes filter achieves improved predictive performance over the Bayes filter baseline.
Let f:A-->B be a covering map. We say A has e filtered ends with respect to f (or B) if for some filtration {K_n} of B by compact subsets, A - f^{-1}(K_n) "eventually" has e components. The main theorem states that if Y is a (suitable) free H-space, if K < H has infinite index, and if Y has a positive finite number of …
Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly…
Bayesian method learns optimal momentum for landmark matching.
problem Finding a diffeomorphism between two sets of landmarks.
method Ensemble Kalman filter for derivative-free Bayesian inverse method.
result Efficient algorithm for various target shapes.
Particle filtering is a powerful approach to sequential state estimation and finds application in many domains, including robot localization, object tracking, etc. To apply particle filtering in practice, a critical challenge is to construct probabilistic system models, especially for systems with complex dynamics or r…
The main goal of this paper is to prove that a connected bounded geometry complete Kahler manifold which has at least 3 filtered ends admits a proper holomorphic mapping onto a Riemann surface. This also provides a different proof of the theorem of Gromov and Schoen that, for a connected compact Kahler manifold whose f…
Formula for knot concordance invariant derived from surgery on knots.
problem Defining knot concordance invariant via surgery on knots.
method Computation of knot Floer filtration induced by cable of meridian, formula in terms of original knot Floer complex.
result Knot concordance invariant defined equivalently via filtered maps on Heegaard Floer homology.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
New subgroup found in knot homology concordance group.
problem Understanding the structure of knot homology concordance groups.
method Applying filtered mapping cone formula to L-space knots and using connected knot complex.
result Contains a subgroup.
Paper proposes a DNN-driven AF framework for improved generalization.
problem Generalization challenge in adaptive filtering.
method Structural embedding of DNN into AF system, using maximum likelihood as implicit cost function.
result Demonstrates improved generalization capability through extensive experiments.
Kalman filters are routinely used for many data fusion applications including navigation, tracking, and simultaneous localization and mapping problems. However, significant time and effort is frequently required to tune various Kalman filter model parameters, e.g. process noise covariance, pre-whitening filter models f…
Proposes Gaussian Processes for more accurate time-correlated measurement noise in robotics.
problem Time-correlated measurement noise in robotics applications.
method Gaussian Processes as a non-parametric model for correlated measurement noise.
result Improved performance of Kalman filtering with Gaussian Processes.
Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how fast the energy contained in the propagated signals (a.k.a. feature maps) decays across laye…
Defines cobordism maps connecting Khovanov and instanton homologies.
problem No direct correspondence between Khovanov and instanton homology cobordism maps.
method Defines a cobordism map on the instanton cube complex as a filtered chain map.
result Proves the cobordism map recovers both Khovanov and instanton homology cobordism maps.
Algorithm learns dynamics from past observations.
problem Learning a nonlinear dynamical system.
method Spectral filtering, online convex optimization.
result Vanishing prediction error for marginally stable systems.
This paper improves collaborative filtering by integrating user and item embeddings with attention.
problem Sparse ratings and limited robustness of Bayesian methods in collaborative filtering.
method Proposes a VAE-based Bayesian MF framework that leverages both data and embedding information.
result The proposed method enhances robustness and accuracy of collaborative filtering models.
No-trick kernel adaptive filtering uses deterministic features for scalability and robustness.
problem Scalability issues in kernel methods for large datasets.
method Deterministic feature-map construction using polynomial-exact solutions.
result Deterministic features outperform random Fourier features in performance and scalability.
New method improves portfolio selection by filtering noisy covariance matrices.
problem Noisy covariance matrices in financial datasets affect portfolio performance evaluation.
method Combinatorial Optimization approach using Mixed Integer Quadratic Programming.
result Our method outperforms existing filtering strategies for real financial datasets.
ROAD-EnKFs use learned low-dimensional models to improve state reconstruction and forecasting.
problem Reconstructing and forecasting states of unknown or expensive systems.
method Learned low-dimensional surrogate models and ensemble Kalman filter integration.
result ROAD-EnKFs achieve higher accuracy at lower computational cost than existing methods.