Stochastic gradient descent (SGD) exhibits strong algorithmic regularization effects in practice, which has been hypothesized to play an important role in the generalization of modern machine learning approaches. In this work, we seek to understand these issues in the simpler setting of linear regression (including both underparameterized and overparameterized regimes), where our goal is to make sharp instance-based comparisons of the implicit regularization afforded by (unregularized) average SGD with the explicit regularization of ridge regression. For a broad class of least squares problem instances (that are natural in high-dimensional settings), we show: (1) for every problem instance and for every ridge parameter, (unregularized) SGD, when provided with logarithmically more samples than that provided to the ridge algorithm, generalizes no worse than the ridge solution (provided SGD uses a tuned constant stepsize); (2) conversely, there exist instances (in this wide problem class) where optimally-tuned ridge regression requires quadratically more samples than SGD in order to have the same generalization performance. Taken together, our results show that, up to the logarithmic factors, the generalization performance of SGD is always no worse than that of ridge regression in a wide range of overparameterized problems, and, in fact, could be much better for some problem instances. More generally, our results show how algorithmic regularization has important consequences even in simpler (overparameterized) convex settings.

Traditionally convolutional neural network architectures have been designed by stacking layers on top of each other to form deeper hierarchical networks. The cortex in the brain however does not just stack layers as done in standard convolution neural networks, instead different regions are organized next to each other in a large single sheet of neurons. Biological neurons self organize to form topographic maps, where neurons encoding similar stimuli group together to form logical clusters. Here we propose new self-organization principles that allow for the formation of hierarchical cortical regions (i.e.

Achieving an immersive experience enabling users to explore virtual environments with six degrees of freedom (6DoF) is essential for various applications such as virtual reality (VR). Wide-baseline panoramas are commonly used in these applications to reduce network bandwidth and storage requirements. However, synthesizing novel views from these panoramas remains a key challenge. Although existing neural radiance field methods can produce photorealistic views under narrow-baseline and dense image captures, they tend to overfit the training views when dealing with wide-baseline panoramas due to the difficulty in learning accurate geometry from sparse 360 views. To address this problem, we propose PanoGRF, Generalizable Spherical Radiance Fields for Wide-baseline Panoramas, which construct spherical radiance fields incorporating 360 scene priors. Unlike generalizable radiance fields trained on perspective images, PanoGRF avoids the information loss from panorama-to-perspective conversion and directly aggregates geometry and appearance features of 3D sample points from each panoramic view based on spherical projection. Moreover, as some regions of the panorama are only visible from one view while invisible from others under wide baseline settings, PanoGRF incorporates 360 monocular depth priors into spherical depth estimation to improve the geometry features. Experimental results on multiple panoramic datasets demonstrate that PanoGRF significantly outperforms state-of-the-art generalizable view synthesis methods for wide-baseline panoramas (e.g., OmniSyn) and perspective images (e.g., IBRNet, NeuRay).

We propose a new framework for Imitation Learning (IL) via density estimation of the expert's occupancy measure followed by Maximum Occupancy Entropy Reinforcement Learning (RL) using the density as a reward. Our approach maximizes a non-adversarial model-free RL objective that provably lower bounds reverse Kullback-Leibler divergence between occupancy measures of the expert and imitator. We present a practical IL algorithm, Neural Density Imitation (NDI), which obtains state-of-the-art demonstration efficiency on benchmark control tasks.