For each rule, if the left-hand side graph is an induced subgraph of a PDAGG, orient the undirected edge on it with the direction on the right-hand side.

Scene text detection remains a grand challenge due to the variation in text curvatures, orientations, and aspect ratios. One of the hardest problems in this task is how to represent text instances of arbitrary shapes. Although many methods have been proposed to model irregular texts in a flexible manner, most of them lose simplicity and robustness. Their complicated post-processings and the regression under Dirac delta distribution undermine the detection performance and the generalization ability. In this paper, we propose an efficient text instance representation named CentripetalText (CT), which decomposes text instances into the combination of text kernels and centripetal shifts. Specifically, we utilize the centripetal shifts to implement pixel aggregation, guiding the external text pixels to the internal text kernels. The relaxation operation is integrated into the dense regression for centripetal shifts, allowing the correct prediction in a range instead of a specific value.

It is well-known that given a smooth, bounded-from-below, and possibly nonconvex function, standard gradient-based methods can find -stationary points (with gradient norm less than) in O(1/ 2) iterations. However, many important nonconvex optimization problems, such as those associated with training modern neural networks, are inherently not smooth, making these results inapplicable. In this paper, we study nonsmooth nonconvex optimization from an oracle complexity viewpoint, where the algorithm is assumed to be given access only to local information about the function at various points. We provide two main results (under mild assumptions): First, we consider the problem of getting near -stationary points. This is perhaps the most natural relaxation of finding -stationary points, which is impossible in the nonsmooth nonconvex case. We prove that this relaxed goal cannot be achieved efficiently, for any distance and smaller than some constants. Our second result deals with the possibility of tackling nonsmooth nonconvex optimization by reduction to smooth optimization: Namely, applying smooth optimization methods on a smooth approximation of the objective function. For this approach, we prove an inherent trade-off between oracle complexity and smoothness: On the one hand, smoothing a nonsmooth nonconvex function can be done very efficiently (e.g., by randomized smoothing), but with dimension-dependent factors in the smoothness parameter, which can strongly affect iteration complexity when plugging into standard smooth optimization methods. On the other hand, these dimension factors can be eliminated with suitable smoothing methods, but only by making the oracle complexity of the smoothing process exponentially large.

Random forests are some of the most widely used machine learning models today, especially in domains that necessitate interpretability. We present an algorithm that accelerates the training of random forests and other popular tree-based learning methods. At the core of our algorithm is a novel node-splitting subroutine, dubbed MABSplit, used to efficiently find split points when constructing decision trees. Our algorithm borrows techniques from the multi-armed bandit literature to judiciously determine how to allocate samples and computational power across candidate split points. We provide theoretical guarantees that MABSplit improves the sample complexity of each node split from linear to logarithmic in the number of data points. In some settings, MABSplit leads to 100x faster training (an 99% reduction in training time) without any decrease in generalization performance. We demonstrate similar speedups when MABSplit is used across a variety of forest-based variants, such as Extremely Random Forests and Random Patches. We also show our algorithm can be used in both classification and regression tasks. Finally, we show that MABSplit outperforms existing methods in generalization performance and feature importance calculations under a fixed computational budget.

Negative-free contrastive learning methods have attracted a lot of attention with simplicity and impressive performances for large-scale pretraining. However, its disentanglement property remains unexplored. In this paper, we examine negative-free contrastive learning methods to study the disentanglement property empirically. We find that existing disentanglement metrics fail to make meaningful measurements for high-dimensional representation models, so we propose a new disentanglement metric based on Mutual Information between latent representations and data factors.

A.1 Relation of Inverse Covariance Matrix and Partial Correlation For a covariance matrix of joint distribution for variables X,Y, the covariance matrix is The derivation comes from the following: Lemma A.1 (Conditional independence (Adapted from [34])). Notice for arbitrary function f, E[f(X)|Y] = EL[f(X)|φy(Y)] with one-hot encoding of discrete variable Y. Therefore for any feature map we can also get that conditional independence ensures: This thus finishes the proof for Lemma D.4. A.3 Technical Facts for Matrix Concentration We include this covariance concentration result that is adapted from Claim A.2 in [18]: Claim A.2 (covariance concentration for gaussian variables). Let X = [x1,x2, xn]> Rn d where each xi N(0,ΣX). Then for any given matrix B Rd m that is of rank kand is independent of X, with probability at least 1 δ10 over X we have 0.9B>ΣXB 1 n B>X>XB 1.1B>ΣXB. Let X = [x1,x2, xn]> Rn d where each xi is ρ2-sub-gaussian. Then for any given matrix B Rd m that is of rank kand is independent of X, with probability at least 1 δ10 over X we have 0.9B>ΣXB 1 n B>X>XB 1.1B>ΣXB. Let Z Rn k be a matrix with row vectors sampled from i.i.d Gaussian distribution N(0,ΣZ). Let P Rn n be a fixed projection onto a space of dimension d.