Study uses machine learning to predict optimal bridge types based on NBI data.
problem Improving bridge design selection through machine learning.
method Supervised learning on modified NBI dataset, feature selection, cross-validation, state-specific models.
result Supervised learning models predict optimal bridge types with high accuracy.
New algorithm solves complex mean-field Schrödinger bridge problem.
problem Designing a controller for diffusion processes with nonlocal interaction.
method Generalized Hopf-Cole transform and Sinkhorn-type algorithm.
result Convergence guarantees for the proposed algorithm under mild assumptions.
New methods optimize transport and sampling for neural networks.
problem Designing effective training losses for neural networks.
method Optimal transport and stochastic optimal control through Schrödinger bridge problem.
result Valid training losses can be designed with numerical advantages.
The paper bridges spectral and spatial graph convolutions, improving model capacity and transferability.
problem Improving graph neural networks by bridging spectral and spatial design.
method Theoretical demonstration and general framework for spectral analysis, new spectral convolutions, and depthwise separable convolutions.
result General framework allows spectral analysis of ConvGNNs, showing their performance and limits, and proposing new spectral convolutions.
Neural approach enhances AI trustworthiness, generalization, and robustness.
problem Challenges in explaining, generalizing, and adapting AI models to uncertain environments.
method Customized trustworthy networks, flexible learning regularizers, open-world recognition losses.
result Significant performance improvements across various open-world multimedia recognition scenarios.
Unified framework for robust, stable, and efficient density ratio estimation.
problem Density-chasm and support-chasm problems in density ratio estimation.
method Dequantified diffusion-Schrödinger bridge (D3RE) framework with DDBI and DSBI.
result Offers uniform approximation and bounded time scores in theory and empirical performance.
New algorithm solves Schrödinger bridge problem with mismatched channels.
problem Solving Schrödinger bridge problem with input and noise channel mismatch.
method Design of a Sinkhorn recursion with memory for nonlinear PDEs.
result Demonstrates solving control-affine Schrödinger bridge problem.
Extends diffusion-based Schrödinger bridge models to handle time-dependent potentials.
problem Approximating optimal transport dynamics between two boundary distributions with a twisted Brownian motion reference.
method Introduces Twisted Schrödinger Bridge Matching (TSBM) using the Iterative Markovian Fitting (IMF) paradigm, incorporating a gradient-dependent bridge-matching loss.
result Improves trajectory inference across high-dimensional settings, including crowd navigation and single-cell data.
This research categorizes AMM designs for secure token exchanges.
problem Designing AMMs for cryptoeconomic systems can lead to financial risks and inefficiencies.
method Developed an AMM taxonomy and proposed three archetypes.
result AMM archetypes meet key requirements for token issuance and exchange.
This paper classifies stablecoin designs to mitigate volatility risks.
problem Mitigating the volatility of stablecoins.
method Systematic design classification, component analysis, and future direction identification.
result Identified strengths and drawbacks of existing stablecoin designs.
Model trains passing events on a bridge using multilevel Gaussian process.
problem Represent aggregate train-passing events from a bridge monitoring system.
method Formulate a combined model with low-rank approximation hierarchical Gaussian process, incorporating domain expertise as constraints.
result Allow for simulation of previously unobserved train types.
Deep learning predicts bridge load capacity from images.
problem Lack of data on aging bridges in post-disaster zones.
method Crowd-sourced images trained on a new CNN for multiclass classification.
result Improved prediction accuracy and practical optimisation.
BRIDGE improves decentralized learning resilience against Byzantine failures.
problem Decentralized learning in distributed systems is vulnerable to Byzantine failures.
method Introduces BRIDGE, a scalable Byzantine-resilient decentralized gradient descent algorithm.
result Proves algorithmic and statistical convergence guarantees for BRIDGE.
New framework bridges climate science and ML for easier climate model emulation.
problem High computational costs and mistrust of ML methods in climate models.
method Integrating climate science and machine learning perspectives to design easy-to-adopt emulators.
result Demonstrated reliability of emulators designed to address specific tasks.
MSBM extends SB for multi-marginal trajectory inference.
problem Trajectory inference from multiple discrete snapshots.
method Multi-Marginal Schrödinger Bridge Matching (MSBM) using iterative Markovian fitting (IMF).
result MSBM effectively captures complex trajectories and respects intermediate distributions.
PrototypeML simplifies neural network design and development.
problem Error-prone code and time-consuming model design.
method Visual interface for neural networks, abstracting PyTorch.
result Reduces model design and development time, easier debugging.
We propose the Bayesian bridge estimator for regularized regression and classification. Two key mixture representations for the Bayesian bridge model are developed: (1) a scale mixture of normals with respect to an alpha-stable random variable; and (2) a mixture of Bartlett--Fejer kernels (or triangle densities) with r…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate constraints or objective functions for optimization. Ensemble methods, like bagging, sm…
Differentiable optimization bridges arbitrary metrics to tree metrics.
problem Designing algorithms to convert arbitrary metrics to tree metrics with guarantees.
method DeltaZero framework, leveraging differentiable Gromov hyperbolicity.
result DeltaZero consistently achieves state-of-the-art distortion on synthetic and real-world datasets.
Paper bridges theory and algorithm for domain adaptation.
problem Domain adaptation from theory to algorithm gap.
method Extended domain adaptation theories, introduced Margin Disparity Discrepancy, and transformed into adversarial learning algorithm.
result Empirical studies show state-of-the-art accuracies on domain adaptation tasks.
We bridge statistical and worst-case approaches to experimental design for linear regression.
problem Designing efficient experiments for linear regression models with arbitrary responses.
method Propose a new experimental design framework for arbitrary response distributions, combining statistical and worst-case approaches.
result Develop efficient randomized design procedures achieving strong variance bounds for unbiased estimators using few responses.
Paper bridges ResNet and Feynman path integral for mathematical understanding.
problem Gradient vanishing issue in ResNet.
method Proves equivalence between ResNet and Feynman path integral, using partial differential equations.
result ResNet's advantage in gradient vanishing issue is mathematically explained.
Researchers dissect Neural ODEs to understand their dynamics.
problem Understanding the inner workings of Neural ODEs.
method Developing continuous-depth formulation to clarify design choices.
result Clarified the influence of design choices on Neural ODE dynamics.
ASBS improves sampling from Boltzmann distributions without importance weighting.
problem Sampling from Boltzmann distributions with known energies but unknown samples.
method Adjoint Schrödinger Bridge Sampler using kinetic-optimal transportation.
result ASBS achieves scalable and efficient sampling without importance weighting.
Smooth Contextual Bandits bridge two previously studied extremes of non-differentiable and parametric-response bandits.
problem Nonparametric contextual bandits with Hölder smoothness.
method Developed a novel algorithm that optimally balances between non-differentiable and parametric-response bandits.
result Proved the algorithm achieves rate-optimal regret for all smoothness settings.
BOED improves SBI by optimizing experimental designs and inference functions.
problem Efficiently use experimental resources for better inference on complex models.
method Link mutual information bounds between SBI and BOED, optimizing both design and inference.
result BOED improves inference in real-world simulators in epidemiology and biology.
Study bridge spectra of 2-bridge knots and their cables.
problem Computing bridge spectra for 2-bridge knots and their cables.
method Computed bridge spectra of cables of 2-bridge knots.
result Results on bridge spectra and distance of Montesinos knots.
A new framework uses text descriptions to improve protein design.
problem Lack of effective methods to incorporate textual descriptions in protein design.
method ProteinDT framework that combines text and protein structural information.
result ProteinDT significantly improves protein design accuracy and performance.
New method for flexible tubes and structures, enabling rigid-foldability.
problem Creating flexible tubes with rigid-foldability.
method Discrete, semi-discrete, and smooth construction of surfaces (T-hedra and profile-affine surfaces).
result Unified treatment of continuous flexible structures composed of tubes.
Alternative proof for 2-bridge knots' bridge positions.
problem Proving genus one 1-bridge positions for 2-bridge knots.
method Alternative proof using disk complexes.
result Every genus one 1-bridge position is a stabilization.
For every bridge number, critical spheres exist for links.
problem Finding critical bridge spheres for links with arbitrary bridge numbers.
method Constructing infinite families of links with square bridge spheres.
result Existence of critical bridge spheres for links with arbitrary bridge numbers.
Study on knot diagrams showing bridge number can differ from crossing number.
problem Incompatibility between crossing number and bridge number for knot diagrams.
method Defined and compared various bridge number computations for knot diagrams, studied minimizing diagrams, and constructed families of minimal crossing diagrams.
result Found examples where bridge number differs from crossing number, and demonstrated this difference can grow infinitely.
A new approach to PCGML uses discriminative models to improve design control.
problem Fundamental tension between detailed training examples and return on investment.
method Discriminative models trained on positive and negative examples.
result Demonstrates new mode of control for learning-based generators.
New examples of knots with special bridge positions found.
problem Understanding special types of bridge positions for knots.
method Derived examples of knots with unperturbed weakly reducible non-minimal bridge positions.
result Connected sum of unperturbed bridge positions is unperturbed (a new conjecture).
The paper provides examples of keen weakly reducible bridge spheres for links in b-bridge position.
problem Characterizing and finding examples of keen weakly reducible bridge spheres.
method Analyzing bridge spheres and their properties in terms of compressing disks and width complex.
result Infinitely many examples of keen weakly reducible bridge spheres for links in b-bridge position.
Neural networks improve structural optimization solutions.
problem Quality of structural optimization solutions depends on parameterization.
method Optimizing neural network parameters to output densities for optimization.
result Our approach produces the best design 50% more often than baselines.
Novel algorithms for entropic optimal transport from an optimisation perspective.
problem Solving the entropic-regularised optimal transport problem.
method Developed novel methods inspired by mirror descent, solving semi-dual problems or non-convex constrained problems over joint distributions.
result Non-asymptotic rates of convergence for the proposed methods under minimal assumptions.
Method generates i.i.d. samples from GT data using space-time mixing.
problem Generating synthetic i.i.d. samples from high-dimensional real-valued distributions.
method Space-time mixing strategies, diffusion bridges, and score-matching.
result Optimal transport from initial to target distribution.
Framework enhances AI explainability by aligning with human cognitive models.
problem Lack of explainability in AI models hinders trust and accountability.
method Integrates explainability techniques with Malle's five category model of behavior explanation.
result Demonstrates practical relevance in credit risk assessment and regulatory analysis.
Any 2-bridge knot in the 3-sphere has a bridge sphere from which any other bridge surface can be obtained by stabilization, meridional stabilization, perturbation and proper isotopy.
Lower bounds on knot distortion related to bridge distance and number.
problem Finding lower bounds on knot distortion in 3D space.
method Extending Pardon's techniques to relate distortion to bridge distance and number.
result Lower bound on knot distortion proportional to minimum of bridge distance and bridge number.
Equivariant trisections for group actions on 4-manifolds are introduced and studied.
problem Understanding the equivariant topology of G-manifolds and their quotients. method Introducing G-equivariant trisections and bridge trisections, and establishing their existence for G-manifolds. result Any G-manifold X admits a G-equivariant trisection such that a G-invariant surface S is in equivariant bridge trisection position. Suppose a knot in a 3-manifold is in n-bridge position. We consider a reduction of the knot along a bridge disk D and show that the result is an (n−1)-bridge position if and only if there is a bridge disk E such that (D,E) is a cancelling pair. We apply this to an unknot K, in n-bridge position with re…
Designing deterministic denominators for SGLD stabilizes large drifts.
problem Stabilizing large drifts in SGLD
method Using state-dependent envelopes and empirical quantiles for activation thresholds
result Proxy-quantile denominators are close to oracle-score behavior and improve deterministic taming choices
New method finds infinitely many surface knots with specific bridge numbers.
problem Finding numerical invariants for surface links.
method Colorings of surface links by keis to prove bridge number existence.
result Existence of infinitely many surface knots with bridge number n for n ≥ 4.
Adversarial training improves gradient interpretability, reducing misinterpretations.
problem Improving gradient interpretability in adversarially trained deep networks.
method Identified and demonstrated that adversarial training restricts gradients closer to the image manifold, making them more interpretable.
result Adversarial training leads to more meaningful loss gradients, aligning better with human perception.
New framework tightens certified robustness gaps in machine learning models.
problem Persistent gap between theoretical certified robustness and empirical accuracy.
method Leverages Lipschitz continuity and novel confidence intervals.
result Improves robust accuracy, compressing the gap between theory and practice.
Researchers found infinite links with specific bridge positions.
problem Finding links with minimal bridge positions.
method Applying Takao et al.'s criterion to create links with locally minimal n-bridge and globally minimal m-bridge positions. result Provided an infinite family of links with specific bridge positions.