For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? While this could potentially guide practitioners to improve classification and mixture proportion estimation in applications where negative unlabeled data is not available but unlabeled data is abundant, we do not believe that it will fundamentally impact how machine learning is used in a way that could conceivably be socially salient. If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? The proof primarily involves using DKW inequality [15] on pqupcqand pqppcqto show convergence to their respective means qupcqand qppcq. The main idea of the proof is to use the confidence bound derived in Lemma 1 at pcand use the fact that pcminimizes the upper confidence bound. The proof is split into two parts.

We analyze the dynamics of finite width effects in wide but finite feature learning neural networks. Starting from a dynamical mean field theory description of infinite width deep neural network kernel and prediction dynamics, we provide a characterization of the O(1/ width) fluctuations of the DMFT order parameters over random initializations of the network weights. Our results, while perturbative in width, unlike prior analyses, are non-perturbative in the strength of feature learning. In the lazy limit of network training, all kernels are random but static in time and the prediction variance has a universal form. However, in the rich, feature learning regime, the fluctuations of the kernels and predictions are dynamically coupled with a variance that can be computed self-consistently.

Based on the feedback from the reviewers, we perform the following additional experiments which 0 explore the robustness of the choice of buffer size in SGD RER, choice of step sizes for GLMtron 10 and the behavior of the said algorithms with heavy tailed noise with a similar setup as in Section 7. We first perform an experimental study about the robustness of SGD RER to the choice of buffer size in Figure 3a. Notice that the performance remains the same for a large range of buffer sizes ( 100 from to 2000). However the performance degrades when the buffer size is too large ( 10000). We believe this is the case since the number of buffers decreases as the buffer size increases and the output is averaged over too few number of iterates (In the case of B = 10000, the final output is just an average of 10 iterates). Theoretically, this largest step-size is L where Lis the largest eigenvalue of -1 the Hessian. In the case of GLMtron, it was experimentally observed that if the step size was chosen 10 to be about 1.5 times the step size reported in Section 7, the iterates diverged. Quasi Newton method essentially normalizes the gradient with the inverse of the Hessian (or rather an approximation of the Hessian) in order to let it converge faster with large step sizes. In Figure 4, we consider the same system as in Section 7 but with heavy tailed noise given by the student t distribution (scale ν = 4.1) so that the 4-th moment exists but higher moments do not. The typical behavior of Forward SGD, SGD-ER, SGD-RER and Quasi Newton methods seems to be similar to that observed in the Sub-Gaussian noise case. However, GLMtron requires much smaller step sizes to ensure convergence and hence it takes much longer.

It is well-known that modern computer vision systems often exhibit behaviors misaligned with those of humans: from adversarial attacks to image corruptions, deep learning vision models suffer in a variety of settings that humans capably handle. In light of these phenomena, here we introduce another, orthogonal perspective studying the human-machine vision gap. We revisit the task of recovering images under degradation, first introduced over 30 years ago in the Recognition-by-Components theory of human vision. Specifically, we study the performance and behavior of neural networks on the seemingly simple task of classifying regular polygons at varying orders of degradation along their perimeters. To this end, we implement the Automated Shape Recoverability Test1 for rapidly generating large-scale datasets of perimeter-degraded regular polygons, modernizing the historically manual creation of image recoverability experiments. We then investigate the capacity of neural networks to recognize and recover such degraded shapes when initialized with different priors. Ultimately, we find that neural networks' behavior on this simple task conflicts with human behavior, raising a fundamental question of the robustness and learning capabilities of modern computer vision models.

In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR) graphs. On the other hand, ensemble methods combine predictions from multiple models to create a new one that is more robust and accurate than individual predictions. In the literature, there are many ensembling techniques proposed for classification or regression problems, however, ensemble graph prediction has not been studied thoroughly. In this work, we formalize this problem as mining the largest graph that is the most supported by a collection of graph predictions. As the problem is NP-Hard, we propose an efficient heuristic algorithm to approximate the optimal solution. To validate our approach, we carried out experiments in AMR parsing problems. The experimental results demonstrate that the proposed approach can combine the strength of state-of-the-art AMR parsers to create new predictions that are more accurate than any individual models in five standard benchmark datasets.

In many machine learning tasks, models are trained to predict structure data such as graphs. For example, in natural language processing, it is very common to parse texts into dependency trees or abstract meaning representation (AMR) graphs. On the other hand, ensemble methods combine predictions from multiple models to create a new one that is more robust and accurate than individual predictions. In the literature, there are many ensembling techniques proposed for classification or regression problems, however, ensemble graph prediction has not been studied thoroughly. In this work, we formalize this problem as mining the largest graph that is the most supported by a collection of graph predictions. As the problem is NP-Hard, we propose an efficient heuristic algorithm to approximate the optimal solution. To validate our approach, we carried out experiments in AMR parsing problems. The experimental results demonstrate that the proposed approach can combine the strength of state-of-the-art AMR parsers to create new predictions that are more accurate than any individual models in five standard benchmark datasets.