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In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the restricted isometry property (RIP) of the problem local search methods can find the ground truth with a small error. By analyzing the landscape of the non-convex problem, we first propose a global guarantee on the maximum distance between an arbitrary local minimizer and the ground truth under the assumption that the RIP constant is smaller than 1/2. We show that this distance shrinks to zero as the intensity of the noise reduces. Our new guarantee is sharp in terms of the RIP constant and is much stronger than the existing results. We then present a local guarantee for problems with an arbitrary RIP constant, which states that any local minimizer is either considerably close to the ground truth or far away from it. Next, we prove the strict saddle property, which guarantees the global convergence of the perturbed gradient descent method in polynomial time. The developed results demonstrate how the noise intensity and the RIP constant of the problem affect the landscape of the problem.

AAAI 2022

Sharp Restricted Isometry Property Bounds for Low-Rank Matrix Recovery Problems with Corrupted Measurements

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

technical paper

Transformers have become one of the dominant architectures in deep learning, particularly as a powerful alternative to convolutional neural networks (CNNs) in computer vision. However, Transformer training and inference in previous works can be prohibitively expensive due to the quadratic complexity of self-attention over a long sequence of representations, especially for high-resolution dense prediction tasks. To this end, we present a novel Less attention vIsion Transformer (LIT), building upon the fact that the early self-attention layers in Transformers still focus on local patterns and bring minor benefits in recent hierarchical vision Transformers. Specifically, we propose a hierarchical Transformer where we use pure multi-layer perceptrons (MLPs) to encode rich local patterns in the early stages while applying self-attention modules to capture longer dependencies in deeper layers. Moreover, we further propose a learned deformable token merging module to adaptively fuse informative patches in a non-uniform manner. The proposed LIT achieves promising performance on image recognition tasks, including image classification, object detection and instance segmentation, serving as a strong backbone for many vision tasks. Code is available at https://github.com/zip-group/LIT.

Less is More: Pay Less Attention in Vision Transformers

Text revision refers to a family of natural language generation tasks, where the source and target sequences share moderate resemblance in surface form but differentiate in attributes, such as text formality and simplicity. Current state-of-the-art methods formulate these tasks as sequence-to-sequence learning problems, which rely on large-scale parallel training corpus. In this paper, we present an iterative in-place editing approach for text revision, which requires no parallel data. In this approach, we simply fine-tune a pre-trained Transformer with masked language modeling and attribute classification. During inference, the editing at each iteration is realized by two-step span replacement. At the first step, the distributed representation of the text optimizes on the fly towards an attribute function. At the second step, a text span is masked and another new one is proposed conditioned on the optimized representation. The empirical experiments on two typical and important text revision tasks, text formalization and text simplification, show the effectiveness of our approach. It achieves competitive and even better performance than state-of-the-art supervised methods on text simplification, and gains better performance than strong unsupervised methods on text formalization. Our code and model are released at https://github.com/jingjingli01/OREO.

Text Revision by On-the-Fly Representation Optimization

Algorithmic fairness is typically studied from the perspective of predictions. Instead, here we investigate fairness from the perspective of recourse actions suggested to individuals to remedy an unfavourable classification. We propose two new fair-ness criteria at the group and individual level, whichâ€”unlike prior work on equalising the average group-wise distance from the decision boundaryâ€”explicitly account for causal relationships between features, thereby capturing downstream effects of recourse actions performed in the physical world. We explore how our criteria relate to others, such as counterfactual fairness, and show that fairness of recourse is complementary to fairness of prediction. We study theoretically and empirically how to enforce fair causal recourse by altering the classifier and perform a case study on the Adult dataset. Finally, we discuss whether fairness violations in the data generating process revealed by our criteria may be better addressed by societal interventions as opposed to constraints on the classifier.

On the Fairness of Causal Algorithmic Recourse

Anomaly detection attempts to find examples in a dataset that do not conform to the expected behavior. Algorithms for this task assign an anomaly score to each example representing its degree of anomalousness. Setting a threshold on the anomaly scores enables converting these scores into a discrete prediction for each example. Setting an appropriate threshold is challenging in practice since anomaly detection is often treated as an unsupervised problem. A common approach is to set the threshold based on the dataset's contamination factor, i.e., the proportion of anomalous examples in the data. While the contamination factor may be known based on domain knowledge, it is often necessary to estimate it by labeling data. However, many anomaly detection problems involve monitoring multiple related, yet slightly different entities (e.g., a fleet of machines). Then, estimating the contamination factor for each dataset separately by labeling data would be extremely time-consuming. Therefore, this paper introduces a method for transferring the known contamination factor from one dataset (the source domain) to a related dataset where it is unknown (the target domain). Our approach does not require labeled target data and is based on modeling the shape of the distribution of the anomaly scores in both domains. We theoretically analyze how our method behaves when the (biased) target domain anomaly score distribution converges to its true one. Empirically, our method outperforms several baselines on real-world datasets.

Transferring the Contamination Factor between Anomaly Detection Domains by Shape Similarity

Deep neural networks are vulnerable to input deformations in the form of vector fields of pixel displacements and to other parameterized geometric deformations e.g. translations, rotations, etc. Current input deformation certification methods either (i) do not scale to deep networks on large input datasets, or (ii) can only certify a specific class of deformations, e.g. only rotations. We reformulate certification in randomized smoothing setting for both general vector field and parameterized deformations and propose DeformRS-VF and DeformRS-Par, respectively. Our new formulation scales to large networks on large input datasets. For instance, DeformRS-Par certifies rich deformations, covering translations, rotations, scaling, affine deformations, and other visually aligned deformations such as ones parameterized by Discrete-Cosine-Transform basis. Extensive experiments on MNIST, CIFAR10, and ImageNet show competitive performance of DeformRS-Par achieving a certified accuracy of 39\% against perturbed rotations in the set [-10 degree, 10 degree] on ImageNet.

DeformRS: Certifying Input Deformations with Randomized Smoothing

This paper proposes a new sequential model learning architecture to solve partially observable Markov decision problems. Rather than compressing sequential information at every timestep as in conventional recurrent neural network-based methods, the proposed architecture generates a latent variable in each data block with a length of multiple timesteps and passes the most relevant information to the next block for policy optimization. The proposed blockwise sequential model is implemented based on self-attention, making the model capable of detailed sequential learning in partial observable settings. The proposed model builds an additional learning network to efficiently implement gradient estimation by using self-normalized importance sampling, which does not require the complex blockwise input data reconstruction in the model learning. Numerical results show that the proposed method significantly outperforms previous methods in various partially observable environments.

Blockwise Sequential Model Learning for Partially Observable Reinforcement Learning

Self-supervised learning (SSL), especially contrastive methods, has raised attraction recently as it learns effective transferable representations without semantic annotations. A common practice for self-supervised pre-training is to use as much data as possible. For a specific downstream task, however, 
 involving irrelevant data in pre-training may degenerate the downstream performance, observed from our extensive experiments. On the other hand, for existing SSL methods, it is burdensome and infeasible to use different downstream-task-customized datasets in pre-training for different tasks.
 To address this issue, we propose a novel SSL paradigm called Scalable Dynamic Routing (SDR), which can be trained once and deployed efficiently to different downstream tasks with task-customized pre-trained models. Specifically, we construct the SDRnet with various sub-nets and train each sub-net with only one subset of the data by data-aware progressive training. When a downstream task arrives, we route among all the pre-trained sub-nets to get the best along with its corresponding weights. Experiment results show that our SDR can train 256 sub-nets on ImageNet simultaneously, which provides better transfer performance than a unified model trained on the full ImageNet, achieving state-of-the-art (SOTA) averaged accuracy over 11 downstream classification tasks and AP on PASCAL VOC detection task.

Task-Customized Self-Supervised Pre-Training with Scalable Dynamic Routing

Advantage Learning (AL) seeks to increase the action gap between the optimal action and its competitors, so as to improve the robustness to estimation errors. However, the method becomes problematic when the optimal action induced by the approximated value function does not agree with the true optimal action. In this paper, we present a novel method, named clipped Advantage Learning (clipped AL), to address this issue. The method is inspired by our observation that increasing the action gap blindly for all given samples while not taking their necessities into account could accumulate more errors in the performance loss bound, leading to a slow value convergence, and to avoid that, we should adjust the advantage value adaptively. We show that our simple clipped AL operator not only enjoys fast convergence guarantee but also retains proper action gaps, hence achieving a good balance between the large action gap and the fast convergence. The feasibility and effectiveness of the proposed method are verified empirically on several RL benchmarks with promising performance.

Robust Action Gap Increasing with Clipped Advantage Learning

We consider Reinforcement Learning (RL) problems where an agent attempts to maximize a reward signal while minimizing a cost function that models unsafe behaviors. Such formalization is addressed in the literature using constrained optimization on the cost, limiting the exploration and leading to a significant trade-off between cost and reward. In contrast, we propose a Safety-Oriented Search that complements Deep RL algorithms to bias the policy toward safety within an evolutionary cost optimization. We leverage evolutionary exploration benefits to design a novel concept of safe mutations that use visited unsafe states to explore safer actions. We further characterize the behaviors of the policies over desired specifics with a sample-based bound estimation, which makes prior verification analysis tractable in the training loop. Hence, driving the learning process towards safer regions of the policy space. Empirical evidence on the Safety Gym benchmark shows that we successfully avoid drawbacks on the return while improving the safety of the policy.

Exploring Safer Behaviors for Deep Reinforcement Learning

Random forests have long been considered as powerful model ensembles in machine learning. By training multiple decision trees, whose diversity is fostered through data and feature subsampling, the resulting random forest can lead to more stable and reliable predictions than a single decision tree. This however comes at the cost of decreased interpretability: while decision trees are often easily interpretable, the predictions made by random forests are much more difficult to understand, as they involve a majority vote over multiple decision trees. In this paper, we examine different types of reasons that explain "why" an input instance is classified as positive or negative by a Boolean random forest. Notably, as an alternative to prime-implicant explanations taking the form of subset-minimal implicants of the random forest, we introduce majoritary reasons which are subset-minimal implicants of a strict majority of decision trees. For these abductive explanations, the tractability of the generation problem (finding one reason) and the optimization problem (finding one minimum-sized reason) are investigated. Unlike prime-implicant explanations, majoritary reasons may contain redundant features. However, in practice, prime-implicant explanations - for which the identification problem is DP-complete - are slightly larger than majoritary reasons that can be generated using a simple linear-time greedy algorithm. They are also significantly larger than minimum-sized majoritary reasons which can be approached using an anytime Partial MaxSAT algorithm.

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Local and Global Linear Convergence of General Low-Rank Matrix Recovery Problems

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