However, there are three challenges.

Dynamic scene reconstruction is a long-term challenge in the field of 3D vision.

Aligning foundation models is essential for their safe and trustworthy deployment.

In this work, we explore online convex optimization (OCO) and introduce a new condition and analysis that provides fast rates by exploiting the curvature of feasible sets. In online linear optimization, it is known that if the average gradient of loss functions exceeds a certain threshold, the curvature of feasible sets can be exploited by the follow-the-leader (FTL) algorithm to achieve a logarithmic regret. This study reveals that algorithms adaptive to the curvature of loss functions can also leverage the curvature of feasible sets. In particular, we first prove that if an optimal decision is on the boundary of a feasible set and the gradient of an underlying loss function is non-zero, then the algorithm achieves a regret bound of O ( ρ ln T) in stochastic environments. Here, ρ > 0 is the radius of the smallest sphere that includes the optimal decision and encloses the feasible set. Our approach, unlike existing ones, can work directly with convex loss functions, exploiting the curvature of loss functions simultaneously, and can achieve the logarithmic regret only with a local property of feasible sets. Additionally, the algorithm achieves an O ( T) regret even in adversarial environments, in which FTL suffers an Ω( T) regret, and achieves an O ( ρ ln T + Cρ ln T) regret in corrupted stochastic environments with corruption level C .

We start from an intuition that many complex visual data, e.g., videos and 3D scenes, are represented

Implicit neural representations (INRs) have proven effective in various tasks including image, shape, audio, and video reconstruction. These INRs typically learn the implicit field from sampled input points.