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Proximal gradient algorithms (PGA), while foundational for inverse problems like image reconstruction, often yield unstable convergence and suboptimal solutions by violating the critical non-negativity constraint. We identify the gradient…
This work investigates Source-Free Domain Adaptation (SFDA), where a model adapts to a target domain without access to source data. A new augmentation technique, Shuffle PatchMix (SPM), and a novel reweighting strategy are introduced to…
Although Simultaneous Localization and Mapping (SLAM) has been an active research topic for decades, current state-of-the-art methods still suffer from instability or inaccuracy due to feature insufficiency or its inherent estimation drift,…
Optimization on Hadamard manifolds -- the natural Riemannian setting for globally geodesically convex problems -- relies on exponential maps to retract tangent vectors and parallel transport to connect tangent spaces across the manifold.…
Direct alignment methods typically train large language models (LLMs) by contrasting the likelihoods of preferred and dispreferred responses. While effective at capturing relative preferences, these methods are widely observed to suppress…
Inferring 3D structures from sparse, unposed observations is challenging due to its unconstrained nature. Recent methods propose to predict implicit representations directly from unposed inputs in a data-driven manner, achieving promising…
We consider a generic empirical composition optimization problem, where there are empirical averages present both outside and inside nonlinear loss functions. Such a problem is of interest in various machine learning applications, and…
Models that perform well on a training domain often fail to generalize to out-of-domain (OOD) examples. Data augmentation is a common method used to prevent overfitting and improve OOD generalization. However, in natural language, it is…
Stochastic optimization finds a wide range of applications in operations research and management science. However, existing stochastic optimization techniques usually require the information of random samples (e.g., demands in the…
In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data…
We study the problem of supervised learning for both binary and multiclass classification from a unified geometric perspective. In particular, we propose a geometric regularization technique to find the submanifold corresponding to a robust…
This work presents a geometric refinement of the classical Cram\'er--Rao bound (CRB) in the non-asymptotic regime by incorporating curvature-aware corrections based on the second fundamental form associated with the statistical model…
Recent efforts on image restoration have focused on developing "all-in-one" models that can handle different degradation types and levels within single model. However, most of mainstream Transformer-based ones confronted with dilemma…
In this paper, we propose a new primal-dual algorithmic framework for a class of convex-concave saddle point problems frequently arising from image processing and machine learning. Our algorithmic framework updates the primal variable…
Probability density models based on deep networks have achieved remarkable success in modeling complex high-dimensional datasets. However, unlike kernel density estimators, modern neural models do not yield marginals or conditionals in…
Inverse problems arise in many applications, especially tomographic imaging. We develop a Learned Alternating Minimization Algorithm (LAMA) to solve such problems via two-block optimization by synergizing data-driven and classical…
This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…
Structure-from-Motion (SfM), a task aiming at jointly recovering camera poses and 3D geometry of a scene given a set of images, remains a hard problem with still many open challenges despite decades of significant progress. The traditional…
Two-view structure from motion (SfM) is the cornerstone of 3D reconstruction and visual SLAM (vSLAM). Many existing end-to-end learning-based methods usually formulate it as a brute regression problem. However, the inadequate utilization of…
We propose a Regularized Adaptive Momentum Dual Averaging (RAMDA) algorithm for training structured neural networks. Similar to existing regularized adaptive methods, the subproblem for computing the update direction of RAMDA involves a…