SGD updates align with a low-rank subspace but do not lead to further loss reduction.
problem Understanding the training dynamics of deep neural networks, particularly the role of the dominant subspace.
method Exploring whether neural networks can be trained within the dominant subspace of the loss Hessian.
result SGD updates, when projected onto the dominant subspace, do not decrease the training loss further, suggesting spurious alignment.
Unsupervised domain adaptation aims to transfer and adapt knowledge learned from a labeled source domain to an unlabeled target domain. Key components of unsupervised domain adaptation include: (a) maximizing performance on the target, and (b) aligning the source and target domains. Traditionally, these tasks have eith…
BO method identifies sparse subspaces for efficient high-dimensional optimization.
problem Efficient optimization of high-dimensional black-box functions.
method Sparse Gaussian process surrogate models on axis-aligned subspaces with Hamiltonian Monte Carlo inference.
result SAASBO achieves excellent performance on synthetic and real-world problems.
GTBO uses group testing to optimize high-dimensional functions efficiently.
problem Optimizing expensive, high-dimensional functions with limited data.
method Group testing to identify active dimensions, then guide optimization.
result GTBO outperforms state-of-the-art methods on high-dimensional benchmarks.
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two kernels, data kernel and class indicator kernel. The problem is to find a subspace to …
Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local n…
We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces ass…
High-dimensional models pose both safety benefits and risks.
problem Emergent problems in safety alignment due to high-dimensional representations.
method Detailed visualizations and lower-dimensional subspace projections.
result Dimensional reduction preserves safety alignment while avoiding linear jailbreaking.
Method generates intermediate domains to align source and target domains.
problem Challenges of domain adaptation with significant domain divergence.
method Progressive domain augmentation via domain interpolation and multiple subspace alignment.
result Achieves state-of-the-art performance on multiple domain adaptation tasks.
Paper proposes CLAIR for efficient LLM fine-tuning across clients.
problem Fine-tuning large language models (LLMs) efficiently and collaboratively.
method Federated LoRA fine-tuning with Collaborative Low-rank Alignment and Identifiable Recovery (CLAIR).
result CLAIR achieves better performance and contamination detection compared to local fine-tuning.
This paper extends neural collapse to regression problems, revealing key features and structures.
problem Understanding the structure learned by deep neural networks in regression tasks.
method Established Neural Regression Collapse (NRC) across different models, analyzing feature and weight alignments.
result Deep neural regression models exhibit a collapsed feature space, aligning with target dimensions and covariances.
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
LoRA-One uses one-step full gradient to align adapters for efficient large model fine-tuning.
problem Fine-tuning large language models efficiently and accurately.
method Properly initializing LoRA adapters using the one-step full gradient and incorporating preconditioners.
result LoRA-One achieves significant empirical improvements over existing methods.
SIG model identifies invariant variables for MSDA with fewer domain constraints.
problem Challenges in enforcing minimal changes across domains for MSDA.
method Subspace identification theory and variational inference.
result SIG model outperforms existing techniques on various benchmark datasets.
EAGC boosts GCD by regulating gradient entanglement, improving known and novel category separability.
problem Gradient entanglement distorts supervised gradients and overlaps known and novel class representations.
method EAGC uses AGA and EEP to align and project gradients, reducing entanglement and overlap.
result EAGC consistently boosts GCD performance, setting new state-of-the-art results.
Emergent misalignment is influenced by training dynamics, model priors, and data.
problem Emergent misalignment in models
method Exploring training dynamics, model priors, and data
result Activation deltas before and after narrow fine-tuning correlate with their similarities when measured with the last prompt-token activations.
New framework assesses neural sensitivity to small perturbations.
problem Comparing neural representations' sensitivity to small changes.
method Local decodable information, Fisher information, and projected pullback/Fisher metric.
result Reveals differences in neural sensitivity not captured by activation alignment.
Robust high-dimensional data processing has witnessed an exciting development in recent years, as theoretical results have shown that it is possible using convex programming to optimize data fit to a low-rank component plus a sparse outlier component. This problem is also known as Robust PCA, and it has found applicati…
A new protocol corrects confounding effects to measure alignment-induced activation shifts accurately.
problem Confounding effects in measuring alignment-induced activation shifts using naive methods.
method Introduces a four-variant decomposition to separate alignment shift from template effects.
result Correctly measures alignment-induced activation shifts, recovering behaviorally active subspace.
SGD's training dynamics align with Hessian and gradient spectra in high-dimensional classification tasks.
problem Understanding the spectra of Hessian and gradient matrices in high-dimensional classification tasks.
method Rigorous analysis of SGD dynamics and spectra of Hessian and gradient matrices.
result SGD trajectory and emergent outlier eigenspaces align with a common low-dimensional subspace in multi-class high-dimensional mixtures and neural networks.
The paper develops methods to reduce deployment risk under dynamic covariate shifts.
problem Reduction of deployment risk under dynamic covariate shifts.
method Time-domain Poincare inequality and Jacobian-velocity theorem to identify and control directional tangent energy.
result Drift-aligned tangent regularization (DTR) reduces risk volatility and directional gain in low-rank drift regimes.
New method accelerates neural network training by focusing on flat directions.
problem Improving neural network training speed and stability.
method Bulk-SGD, interpolated gradient methods.
result Updates along the Dominant subspace can accelerate convergence but compromise stability.
A new method routes EEG covariance matrices across domains using adaptive subspace selection.
problem Challenges in cross-domain EEG decoding due to distinct SPD manifold regions.
method Dynamic Stiefel routing with expert filters and cross-attention for adaptive subspace projection.
result Consistent gains across three datasets: balanced accuracy improves from 0.773 to 0.823, 0.757 to 0.809, and 0.801 to 0.839.
GTBO uses group testing to optimize high-dimensional functions efficiently.
problem Challenges in optimizing high-dimensional, expensive functions due to the curse of dimensionality.
method GTBO combines testing and optimization phases to identify active variables and guide efficient optimization.
result GTBO outperforms state-of-the-art methods on high-dimensional optimization tasks.
In this paper, we address the Online Unsupervised Domain Adaptation (OUDA) problem, where the target data are unlabelled and arriving sequentially. The traditional methods on the OUDA problem mainly focus on transforming each arriving target data to the source domain, and they do not sufficiently consider the temporal …
Paper introduces a new metric to select optimal Graph Shift Operator for GNNs.
problem Empirical selection of Graph Shift Operator remains challenging.
method Introduces a novel alignment gain metric connecting geometric distortion to generalization bounds via spectral proxy.
result Provides a principled, computation-efficient criterion to rank and select optimal GSO.
New method aligns diffusion models for inference-time properties without retraining.
problem Aligning pre-trained diffusion models for desired inference-time properties.
method Variationally stable Doob's matching for provable guidance estimation.
result Consistent estimator of guidance with non-asymptotic convergence guarantees.
Paper analyzes singular subspace estimation in noisy matrix models.
problem Estimating low-rank signals in noisy matrix data.
method Asymptotic distributional theory, extreme value theory, saddle point approximation, random matrix theory.
result Plug-in test statistic based on two-to-infinity norm has higher power for detecting structured alternatives.
A framework for federated learning with heterogeneous data.
problem Federated learning with data from clients using different data representations.
method FLIC framework that maps client data into a common feature space via local embedding functions, learned federally using Wasserstein barycenters and trained locally via distribution alignment.
result FLIC outperforms FL benchmarks with heterogeneous input feature spaces.
We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of init…
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.
The paper analyzes how noise geometry influences the performance of SGD in machine learning.
problem Understanding how noise geometry affects the performance of stochastic gradient descent.
method Developed two metrics to quantify noise alignment strength and analyzed their effects on loss and subspace projection dynamics.
result Noise geometry can be used to guarantee alignment under certain conditions, aiding SGD's ability to escape from sharp minima.
Diffusion models' sampling paths lie in a low-dimensional subspace, resembling boomerangs.
problem Understanding the geometric structure of diffusion-based generative models.
method Characterization of deterministic sampling trajectories using low-dimensional subspace and kernel-estimated data modeling.
result Sampling trajectories in diffusion models are confined to a low-dimensional subspace and exhibit a boomerang shape.
Study on low-dimensional adversarial perturbations in classification models.
problem Understanding and quantifying the effectiveness of low-dimensional adversarial perturbations.
method Analytical lower-bounds for fooling rate, considering binary classifiers under generic regularity conditions.
result Rigorous explanation for the success of heuristic methods in generating low-dimensional adversarial perturbations.
New algorithm reduces communication in distributed eigenspace estimation.
problem Efficiently estimating eigenspaces in distributed settings without excessive communication.
method Communication-efficient distributed algorithm using Procrustean alignment.
result Achieves similar error rate to centralized estimator for PCA.
Paper tackles distribution shifts in prediction models with unobserved confounding.
problem Distribution shifts in prediction models with unobserved confounding.
method Linear structural causal model, invariant covariate representations, data-driven representation learning method.
result Optimizes for a lower-dimensional linear subspace and a prediction model confined to that subspace, achieving nearly ideal gap between target and source risk.
DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.
problem DG algorithms fail to consistently outperform ERM in limited domains.
method Examined necessary and sufficient conditions for DG, proposing a subspace alignment method.
result DG methods focus on sufficient conditions, often neglecting necessary conditions, leading to generalization failures.
GOPO optimizes large models in Hilbert space, avoiding Kullback-Leibler's curvature.
problem Optimizing large language models with Kullback-Leibler divergence's curvature issues.
method GOPO uses Hilbert space L2(pi_k) with orthogonality constraints and a work-dissipation functional.
result GOPO achieves competitive generalization with stable gradient dynamics and entropy preservation.
The paper explains spikes in training loss as catapults, improving feature learning and generalization.
problem Understanding and improving the training process of neural networks.
method Analysis of training loss spikes in SGD, empirical evidence of catapults, and demonstration of AGOP alignment.
result Catapults in training loss promote feature learning and better generalization.
Test-time training adapts a pretrained model to each prompt via parameter updates, improving accuracy under pretraining-to-test distribution shifts.
problem Improving accuracy of pretrained models under distribution shifts.
method Explaining TTT behavior through a decision-theoretic lens.
result TTT reduces prediction error when updates are spectrally matched to the prompt's signal-to-noise ratio and aligned with query-relevant eigen-directions.
Heterogeneous domain adaptation (HDA) aims to facilitate the learning task in a target domain by borrowing knowledge from a heterogeneous source domain. In this paper, we propose a Soft Transfer Network (STN), which jointly learns a domain-shared classifier and a domain-invariant subspace in an end-to-end manner, for a…
LoCo-RLHF models diverse human feedback with contextual information.
problem Heterogeneous human feedback from diverse contexts and preferences.
method Low-rank contextual preference model, PRS policy.
result LoCo-RLHF achieves tighter sub-optimality gap than existing methods.
Study SGD dynamics in sequence models, revealing training phases and influence of sequence length.
problem Understanding SGD in sequence models like attention networks.
method Derived closed-form population loss and analyzed SGD dynamics for SSI models.
result Two distinct training phases: escape from uninformative initialization and alignment with target subspace.
Effective Gram matrix predicts deep network generalization.
problem Understanding and predicting deep network generalization.
method Derived a differential equation governing generalization gap, analyzed with effective Gram matrix.
result Effective Gram matrix accurately predicts test loss during training.
CDSPP learns domain-specific projections for heterogeneous domain adaptation.
problem Heterogeneous domain adaptation problems where source and target domains have different modalities or feature dimensions.
method Cross-Domain Structure Preserving Projection (CDSPP) algorithm that learns domain-specific projections to map features into a common subspace.
result CDSPP achieves superior performance in both supervised and semi-supervised HDA compared to state-of-the-art methods.
Enhancing spectral embedding for low-dimensional embeddings in rare disease cohorts
problem Representing clinical concepts and patients in electronic health records
method Spectral-based unsupervised learning with flexible knowledge transfer
result Outperforms competing approaches in challenging scenarios
PCA++ improves robustness to background noise in contrastive learning.
problem Recovering shared signal subspaces from positive pairs in high-dimensional data with structured background noise.
method PCA++ uses hard uniformity-constrained contrastive learning to enforce identity covariance on projected features.
result PCA++ outperforms standard PCA and alignment-only PCA+ in simulations and real-world datasets.
The paper analyzes PLS-SVD in high-dimensional data integration, revealing its strengths and limitations.
problem Understanding the behavior of PLS-SVD in high-dimensional data integration.
method Analysis using random matrix theory and singular value decomposition.
result PLS-SVD exhibits counter-intuitive or limiting behavior in certain regimes and outperforms PCA when detecting common latent subspace.