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Understanding the capability of Generative Adversarial Networks (GANs) in learning the full spectrum of spatial frequencies, that is, beyond the low-frequency dominant spectrum of natural images, is critical for assessing the reliability of GAN-generated data in any detail-sensitive application. In this work, we show that the ability of convolutional GANs to learn an image distribution depends on the spatial frequency of the underlying carrier signal, that is, they have a bias against learning high spatial frequencies. Our findings are consistent with the recent observations of high-frequency artifacts in GAN-generated images, but further suggest that such artifacts are the consequence of an underlying bias. We also provide a theoretical explanation for this bias as the manifestation of linear dependencies present in the spectrum of filters of a typical generative Convolutional Neural Network (CNN). Finally, by proposing a proof-of-concept method that can effectively manipulate this bias towards other spatial frequencies, we show that the bias is not fixed and can be exploited to explicitly direct computational resources towards any specific spatial frequency of interest in a dataset, with minimal computational overhead.

AAAI 2022

Spatial Frequency Bias in Convolutional Generative Adversarial Networks

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

We develop a new method of online inference for a vector of parameters estimated by the Polyak-Ruppert averaging procedure of stochastic gradient descent (SGD) algorithms. We leverage insights from time series regression in econometrics and construct asymptotically pivotal statistics via random scaling. Our approach is fully operational with online data and is rigorously underpinned by a functional central limit theorem. Our proposed inference method has a couple of key advantages over the existing methods. First, the test statistic is computed in an online fashion with only SGD iterates and the critical values can be obtained without any resampling methods, thereby allowing for efficient implementation suitable for massive online data. Second, there is no need to estimate the asymptotic variance and our inference method is shown to be robust to changes in the tuning parameters for SGD algorithms in simulation experiments with synthetic data.

Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling

Hyperparameter optimization is a ubiquitous challenge in machine learning, and the performance of a trained model depends crucially upon their effective selection. While a rich set of tools exist for this purpose, there are currently no practical hyperparameter selection methods under the constraint of differential privacy (DP). We study honest hyperparameter selection for differentially private machine learning, in which the process of hyperparameter tuning is accounted for in the overall privacy budget. To this end, we i) show that standard composition tools outperform more advanced techniques in many settings, ii) empirically and theoretically demonstrate an intrinsic connection between the learning rate and clipping norm hyperparameters, iii) show that adaptive optimizers like DPAdam enjoy a significant advantage in the process of honest hyperparameter tuning, and iv) draw upon novel limiting behaviour of Adam in the DP setting to design a new and more efficient optimizer.

The Role of Adaptive Optimizers for Honest Private Hyperparameter Selection

Given the incomplete knowledge of classes that exist in the world, Open-set Recognition (OSR) enables networks to identify and reject the unseen classes after training. This problem of breaking the common closed-set assumption is far from being solved. Recent studies focus on designing new losses, neural network encoding structures, and calibration methods to optimize a feature space for OSR relevant tasks. In this work, we make the first attempt to tackle OSR by searching the architecture of a Neural Network (NN) under the open-set assumption. In contrast to the prior arts, we develop a mechanism to both search the architecture of the network and train a network suitable for tackling OSR. Inspired by the compact abating probability (CAP) model, which is theoretically proven to reduce the open space risk, we regularize the searching space by VAE contrastive learning. To discover a more robust structure for OSR, we propose Pseudo Auxiliary Searching (PAS), in which we split a pretended set of know-unknown classes from the original training set in the searching phase, hence enabling the super-net to explore an effective architecture that can handle unseen classes in advance. We demonstrate the benefits of this learning pipeline on 5 OSR datasets, including MNIST, SVHN, CIFAR10, CIFARAdd10, and CIFARAdd50, where our approach outperforms prior state-of-the-art networks designed by humans. To spark research in this field, our code is available at https://github.com/zxl101/NAS OSR.

Learning Network Architecture for Open-Set Recognition

Optimizing a machine learning (ML) pipeline has been an important topic of AI and ML. Despite recent progress, pipeline optimization remains a challenging problem, due to potentially many combinations to consider as well as slow training and validation. We present the BLDS algorithm for optimized algorithm selection (ML operations) in a fixed ML pipeline structure. BLDS performs multi-fidelity optimization for selecting ML algorithms trained with smaller computational overhead, while controlling its pipeline search based on multi-armed bandit and limited discrepancy search. Our experiments on well-known classification benchmarks show that BLDS is superior to competing algorithms. We also combine BLDS with hyperparameter optimization, empirically showing the advantage of BLDS.

Bandit Limited Discrepancy Search and Application to Machine Learning Pipeline Optimization

Central to active learning (AL) is what data should be selected for annotation. Existing works attempt to select highly uncertain or informative data for annotation. Nevertheless, it remains unclear how selected data impacts the test performance of the task model used in AL. In this work, we explore such an impact by theoretically proving that selecting unlabeled data of higher gradient norm leads to a lower upper-bound of test loss, resulting in a better test performance.  However, due to the lack of label information, directly computing gradient norm for unlabeled data is infeasible. To address this challenge, we propose two schemes, namely expected-gradnorm and entropy-gradnorm. The former computes the gradient norm by constructing an expected empirical loss while the latter constructs an unsupervised loss with entropy. Furthermore, we integrate the two schemes in a universal AL framework. We evaluate our method on classical image classification and semantic segmentation tasks. To demonstrate its competency in domain applications and its robustness to noise, we also validate our method on a cellular imaging analysis task, namely cryo-Electron Tomography subtomogram classification. Results demonstrate that our method achieves superior performance against the state of the art. We refer readers to https://arxiv.org/pdf/2112.05683.pdf for the full version of this paper which includes the appendix and source code link.

Boosting Active Learning via Improving Test Performance

We address the overlooked unbiasedness in existing long-tailed classification methods: we find that their overall improvement is mostly attributed to the biased preference of "tail" over "head", as the test distribution is assumed to be balanced; however, when the test is as imbalanced as the long-tailed training data---let the test respect Zipf's law of nature---the "tail" bias is no longer beneficial overall because it hurts the "head" majorities. In this paper, we propose Cross-Domain Empirical Risk Minimization (xERM) for training an unbiased test-agnostic model to achieve strong performances on both test distributions, which empirically demonstrates that xERM fundamentally improves the classification by learning better feature representation rather than the "head vs. tail" game. Based on causality, we further theoretically explain why xERM achieves unbiasedness: the bias caused by the domain selection is removed by adjusting the empirical risks on the imbalanced domain and the balanced but unseen domain.

Cross-Domain Empirical Risk Minimization for Unbiased Long-Tailed Classification

Training scene graph classification models requires a large amount of annotated image data. Meanwhile, scene graphs represent relational knowledge that can be modeled with symbolic data from texts or knowledge graphs. While image annotation demands extensive labor, collecting textual descriptions of natural scenes requires less effort. In this work, we investigate whether textual scene descriptions can substitute for annotated image data. To this end, we employ a scene graph classification framework that is trained not only from annotated images but also from symbolic data. In our architecture, the symbolic entities are first mapped to their correspondent image-grounded representations and then fed into the relational reasoning pipeline. Even though a structured form of knowledge, such as the form in knowledge graphs, is not always available, we can generate it from unstructured texts using a transformer-based language model. We show that by fine-tuning the classification pipeline with the extracted knowledge from texts, we can achieve ~8x more accurate results in scene graph classification, ~3x in object classification, and ~1.5x in predicate classification, compared to the supervised baselines with only 1% of the annotated images.

Improving Scene Graph Classification by Exploiting Knowledge from Texts

Reinforcement learning typically assumes that agents observe feedback for their actions immediately, but in many real-world applications (like recommendation systems) feedback is observed in delay. This paper studies online learning in episodic Markov decision processes (MDPs) with unknown transitions, adversarially changing costs and unrestricted delayed feedback. That is, the costs and trajectory of episode k are revealed to the learner only in the end of episode k+dáµ, where the delays dáµ are neither identical nor bounded, and are chosen by an oblivious adversary. We present novel algorithms based on policy optimization that achieve near-optimal high-probability regret of (K+D)Â¹áŸÂ² under full-information feedback, where K is the number of episodes and D=âˆ‘â‚– dáµ is the total delay. Under bandit feedback, we prove similar (K+D)Â¹áŸÂ² regret assuming the costs are stochastic, and (K+D)Â²áŸÂ³ regret in the general case. We are the first to consider regret minimization in the important setting of MDPs with delayed feedback.

Learning Adversarial Markov Decision Processes with Delayed Feedback

Given a data set of size n in d'-dimensional Euclidean space, the k-means problem asks for a set of k points (called centers) such that the sum of the l_2^2-distances between the data points and the set of centers is minimized. Previous work on this problem in the local differential privacy setting shows how to achieve multiplicative approximation factors arbitrarily close to optimal, but suffers high additive error. The additive error has also been seen to be an issue in implementations of differentially private k-means clustering algorithms in both the central and local settings. In this work, we introduce a new locally private k-means clustering algorithm that achieves near-optimal additive error whilst retaining constant multiplicative approximation factors and round complexity. Concretely, given any c>âˆš2, our algorithm achieves O(k^(1 + O(1/(2c^2-1))) âˆš(d' n) log d' poly log n) additive error with an O(c^2) multiplicative approximation factor.

Locally Private $k$-Means Clustering with Constant Multiplicative Approximation and Near-Optimal Additive Error

The mathematical formalization of a neurological mechanism in the fruit-fly olfactory circuit as a locality sensitive hash (Flyhash) and bloom filter (FBF) has been recently proposed and "reprogrammed" for various learning tasks such as similarity search, outlier detection and text embeddings. We propose a novel reprogramming of this hash and bloom filter to emulate the canonical nearest neighbor classifier (NNC) in the challenging Federated Learning (FL) setup where training and test data are spread across parties and no data can leave their respective parties. Specifically, we utilize Flyhash and FBF to create the FlyNN classifier, and theoretically establish conditions where FlyNN matches NNC. We show how FlyNN is trained exactly in a FL setup with low communication overhead to produce FlyNNFL, and how it can be differentially private. Empirically, we demonstrate that (i) FlyNN matches NNC accuracy across 70 OpenML datasets, (ii) FlyNNFL training is highly scalable with low communication overhead, providing up to 8x speedup with 16 parties.

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Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling

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A Computable Definition of the Spectral Bias

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