The paper addresses rigid alignment of noisy patches, providing a polynomial time algorithm and convergence conditions.
problem Finding a rigid alignment of overlapping local views (patches) that minimizes alignment error in a noisy setting.
method Characterizes non-degeneracy based on kernel and positivity of a matrix, provides polynomial time algorithm for testing non-degeneracy, and uses Riemannian gradient descent for alignment.
result The algorithm converges locally linearly to a non-degenerate perfect alignment under certain conditions.
Algorithm aligns 3D density maps using Wasserstein distance.
problem Aligning 3D density maps in cryogenic electron microscopy.
method Minimizing 1-Wasserstein distance after rigid transformation using Bayesian optimization.
result Improved accuracy and efficiency in protein molecule alignment.
A new FFT-based method for fast rigid alignment of 2D closed curves.
problem Rigid alignment of 2D closed curves with application to shape analysis.
method FFT-based algorithm for optimal rigid alignment of closed curves with O(N log N) complexity.
result Order of magnitude speed-up in curve alignment compared to previous methods.
Study rigidity on CR Yamabe equation on Sasakian manifolds.
problem Proving rigidity on CR Yamabe equation on Sasakian manifolds.
method Using Jerison-Lee's differential identity and integral estimates.
result Prove that the manifold is CR isometric to Heisenberg group \(\mathbb{H}^n\).
New Gromov-Wasserstein metric controls rigidity and incorporates prior knowledge.
problem Inflexible Gromov-Wasserstein distance and lack of feature alignment.
method Augmented Gromov-Wasserstein distance with feature alignments and prior knowledge.
result Improved performance in single-cell multi-omic alignment and transfer learning.
Arbitrary style transfer is an important problem in computer vision that aims to transfer style patterns from an arbitrary style image to a given content image. However, current methods either rely on slow iterative optimization or fast pre-determined feature transformation, but at the cost of compromised visual qualit…
The paper improves alignment methods for deep neural networks using geometric and spectral analysis.
problem Improving alignment methods for deep neural networks.
method Geometric and spectral analysis of residual Jacobian chains.
result Deterministic and margin-verified results on the transport of dominant singular subspaces across layers.
We tackle here the problem of multimodal image non-rigid registration, which is of prime importance in remote sensing and medical imaging. The difficulties encountered by classical registration approaches include feature design and slow optimization by gradient descent. By analyzing these methods, we note the significa…
Diagnostic stroke imaging with C-arm cone-beam computed tomography (CBCT) enables reduction of time-to-therapy for endovascular procedures. However, the prolonged acquisition time compared to helical CT increases the likelihood of rigid patient motion. Rigid motion corrupts the geometry alignment assumed during reconst…
Paper solves a new Minkowski problem for a specific type of rigidity.
problem Solving a new Minkowski problem for a specific type of rigidity.
method Developed a nonlinear partial differential equation and used a curvature flow method.
result Existence of smooth non-even solutions to the p-th dual Minkowski problem for p < n-2.
New model simplifies symmetry handling in generative AI.
problem Symmetry handling in generative models for scientific tasks.
method Quotient-space diffusion models, viewing symmetry as quotient space.
result Improves performance over existing methods for molecular structure generation.
A new method for computing shape barycenters from point clouds using Procrustes-Wasserstein distance.
problem Computing representative shapes from point clouds with precise alignment and shape preservation.
method Developed a new distance metric (Procrustes-Wasserstein) and algorithms for computing barycenters.
result Superior performance in precise alignment and shape preservation compared to existing OT approaches.
A new method matches similar regions in non-rigid shapes using spectra of differential operators.
problem Evaluating similarity of non-rigid shapes with partiality.
method Alignment of spectra of differential operators (SI-LBO and regular LBO) on a manifold with multiple metrics.
result Matching spectra outperforms competing methods on standard benchmarks.
This paper concerns rigidity results to Serrin's overdetermined problem in an epigraph {Δu+f(u)=0, in Ω={(x′,xn):xn>φ(x′)},u>0, in Ω,u=0, on ∂Ω,∣∇u∣=const.on∂Ω.. We prove that up to isometry the ep…
GWIL uses Gromov-Wasserstein distance to align expert and imitation agent states.
problem Cross-domain imitation learning challenges due to different system dimensions and stationary distributions.
method Gromov-Wasserstein Imitation Learning (GWIL) using Gromov-Wasserstein distance.
result GWIL effectively aligns expert and imitation agent states in various continuous control domains.
Proves effective positive mass theorem for AF manifolds and singular spaces.
problem Proves positive mass theorem for AF manifolds with singularities.
method Dimension reduction techniques, bypassing N. Smale's regularity theorem.
result Effective positive mass theorem for AF manifolds of dimension n≤8 with singularities. A new method for analyzing latent space models without reference configurations.
problem Posterior summaries of latent coordinates in Euclidean latent space models are not canonical due to likelihood invariance.
method Quotient-based posterior analysis using the centered Gram map.
result Intrinsic posterior summaries of mean structure and uncertainty can be computed directly from posterior samples.
Efficient method for shape modeling invariant to rigid motion.
problem Statistical shape modeling for rigidly moving shapes.
method Non-Euclidean Lie group analysis of metric distortion and curvature.
result Outperforms state-of-the-art classifiers in sparse data.
This paper surveys scalable automated alignment methods for LLMs.
problem Scalability issues in traditional human-annotated alignment methods for LLMs.
method Categorizes and discusses various automated alignment methods.
result Emerging automated alignment methods are effective and scalable.
Inference-aware meta-alignment of LLMs reduces computational cost.
problem Aligning LLMs to diverse human preferences is challenging due to conflicting criteria.
method IAMA trains a base model to be aligned to multiple tasks via different inference-time alignment algorithms, using non-linear GRPO for optimization.
result IAMA enables effective alignment of LLMs to multiple criteria with limited computational budget.
Conformal Alignment ensures trustworthy outputs from foundation models.
problem Ensuring outputs from foundation models align with human values in high-stakes tasks.
method A framework that trains an alignment predictor using reference data to select trustworthy outputs.
result Conformal Alignment accurately identifies trustworthy outputs via lightweight training over moderate reference data.
LPL optimizes embeddings to align local neighborhoods, improving cross-lingual word alignment.
problem Aligning embeddings across different datasets and languages.
method Locality Preserving Loss (LPL) optimizes model to project embeddings while maintaining local neighborhoods and aligning them.
result LPL-based alignment leads to better and consistent accuracy, especially in small training set settings.
Extends reinforcement learning alignment to scalar rewards, improving math reasoning.
problem Designing reinforcement learning algorithms for general LLM alignment.
method Introduces f-GRPO and f-HAL, estimating f-divergences between reward-aligned and unaligned distributions.
result Improves math reasoning RLVR tasks and mitigates reward hacking.
The paper proposes a learning-theoretic perspective on representation alignment.
problem Understanding how AI models' representations become aligned as they scale.
method Reviewing and connecting different notions of alignment, focusing on stitching.
result Relating properties of stitching to kernel alignment of representations.
Survey of alignment techniques for large language models.
problem Ensuring large language models align with human values.
method Analysis of diverse alignment methods and training paradigms.
result Preference-based methods offer more flexibility for nuanced alignment.
Study connects database alignment and planted matching using Gaussian features.
problem Identify matching between correlated user features in anonymized databases.
method Derived results for database alignment and planted matching, showing connections and thresholds.
result Performance thresholds for database alignment converge to planted matching when feature dimensionality is sufficiently high.
Bayesian framework proves thresholds for multi-graph alignment feasibility.
problem Determining when multi-graph alignment is statistically possible.
method Developed a Bayesian estimation framework over metric spaces.
result Identified thresholds for Gaussian and sparse Erdős-Rényi models.
SMAI framework tests and integrates single-cell data alignability.
problem Lack of a rigorous statistical test for alignability and distortion during alignment.
method Spectral manifold alignment and inference (SMAI) framework.
result SMAI outperforms existing methods in alignability testing and integration.
New method aligns brain data across individuals for better brain decoding.
problem Inter-individual variability in brain response patterns limits decoder generalization.
method SpectralOT method that embeds cortical geometry into Laplace-Beltrami eigenmodes.
result SpectralOT strikes balance between aligning functional features and preserving anatomical structure.
Method aligns multilingual news for better stock return prediction.
problem Losing nuances in multilingual news translations.
method Optimal transport for sentence alignment.
result Aligned sentences correlate better with stock returns.
This paper studies aligning knowledge graphs from different sources or languages. Most existing methods train supervised methods for the alignment, which usually require a large number of aligned knowledge triplets. However, such a large number of aligned knowledge triplets may not be available or are expensive to obta…
Hölder-DPO aligns models robustly with noisy human feedback.
problem No existing alignment methods can handle severe label noise.
method Proposes Hölder-DPO, a principled alignment loss with provable redescending property.
result Hölder-DPO enables scalable human feedback valuation and improves model alignment.
This paper improves cross-domain learning using random forests for manifold alignment.
problem Improving cross-domain learning and feature integration.
method Semi-supervised manifold alignment using random forest proximities.
result Random forest proximities enhance downstream classification accuracy.
Detecting correlated trees helps align sparse graphs.
problem Detecting correlation between trees for sparse random graphs.
method MPAlign message-passing algorithm for graph alignment.
result MPAlign succeeds in polynomial time for partial alignment.
We study alignment in linear neural networks and its relation to gradient descent.
problem Understanding alignment in linear neural networks and its impact on training.
method Defined alignment for fully connected networks, analyzed alignment under gradient descent, and compared gradient descent to projected gradient descent for layer-constrained networks.
result Gradient descent can converge linearly to a global minimum when alignment is invariant, and alignment is impossible with large datasets in layer-constrained networks.
Proposes ACCA for better alignment of multiple data perspectives.
problem Unclear alignment between multiple data perspectives.
method Iteratively solves alignment and multi-view embedding.
result Improved alignment and embedding of multiple data perspectives.
Unified framework for aligning and composing diffusion models to satisfy multiple constraints.
problem Improving quality and compliance of generated samples from diffusion models.
method Constrained optimization framework that unifies alignment and composition of diffusion models.
result Proposed framework effectively satisfies multiple constraints in image generation.
Study improves understanding and performance of FA learning rules in neural networks.
problem Lack of theoretical understanding and limited applications of Feedback Alignment (FA) methods.
method Introduces a unified framework linking synaptic weight changes to implicit regularization, providing convergence conditions and empirical evidence.
result Better alignment can enhance FA performance on complex multi-class tasks.
DFA trains deep networks by aligning weights then memorizing data.
problem Understanding why DFA works for some networks but not others.
method Two-step learning process: alignment followed by memorization.
result DFA aligns weights to maximize gradient alignment, breaking degeneracy.
The study explains how neural networks align their kernels to target functions during training.
problem Understanding how neural networks align their kernels to target functions during training.
method Theoretical analysis of kernel evolution in toy models and deep networks.
result Kernel alignment naturally emerges during training to accelerate convergence and improve generalization.
We consider the problem of aligning a pair of databases with jointly Gaussian features. We consider two algorithms, complete database alignment via MAP estimation among all possible database alignments, and partial alignment via a thresholding approach of log likelihood ratios. We derive conditions on mutual informatio…
Soft geometric bias improves physical dynamics predictions.
problem Learning physical dynamics with exact group equivariance can degrade performance.
method Object-centric world models using geometric algebra neural networks.
result Soft geometric inductive bias leads to better physical fidelity predictions.
We present Manifold Alignment Determination (MAD), an algorithm for learning alignments between data points from multiple views or modalities. The approach is capable of learning correspondences between views as well as correspondences between individual data-points. The proposed method requires only a few aligned exam…
LLM safety alignment explained as divergence estimation.
problem Aligning large language models to avoid harmful outputs.
method Presented a theoretical framework showing alignment methods as divergence estimators.
result KLDO method improves safety alignment using compliance-refusal datasets.
This study presents the results of a series of simulation experiments that evaluate and compare four different manifold alignment methods under the influence of noise. The data was created by simulating the dynamics of two slightly different double pendulums in three-dimensional space. The method of semi-supervised fea…
Align-RUDDER improves reinforcement learning with few demonstrations by redistributing rewards.
problem Learning complex tasks with sparse and delayed rewards using few demonstrations.
method Align-RUDDER uses a profile model for reward redistribution based on multiple sequence alignment of demonstrations.
result Align-RUDDER outperforms competitors on complex tasks with few demonstrations.
New model optimizes feature alignment, improving statistical and computational efficiency.
problem Statistical and computational challenges in feature alignment.
method Covariance alignment model, Gromov-Wasserstein algorithm.
result Gromov-Wasserstein algorithm is minimax optimal and practical for covariance alignment.
Alignment of neural network representations is influenced by SNR and sample size.
problem Understanding how neural network representations align across different conditions.
method Controlled training of neural networks on perturbed datasets, analyzing alignment and generalization.
result Alignment varies monotonically with SNR but non-monotonically with sample size, with minimal alignment near the interpolation threshold.