Artificial neural nets can represent and classify many types of high-dimensional data but are often tailored to particular applications -- e.g., for fair'' orhierarchical'' classification. Once an architecture has been selected, it is often difficult for humans to adjust models for a new task; for example, a hierarchical classifier cannot be easily transformed into a fair classifier that shields a protected field. Our contribution in this work is a new neural network architecture, the concept subspace network (CSN), which generalizes existing specialized classifiers to produce a unified model capable of learning a spectrum of multi-concept relationships. We demonstrate that CSNs reproduce state-of-the-art results in fair classification when enforcing concept independence, may be transformed into hierarchical classifiers, or may even reconcile fairness and hierarchy within a single classifier. The CSN is inspired by and matches the performance of existing prototype-based classifiers that promote interpretability.

Answering complex first-order logic (FOL) queries on knowledge graphs is a fundamental task for multi-hop reasoning. Traditional symbolic methods traverse a complete knowledge graph to extract the answers, which provides good interpretation for each step. Recent neural methods learn geometric embeddings for complex queries. These methods can generalize to incomplete knowledge graphs, but their reasoning process is hard to interpret. In this paper, we propose Graph Neural Network Query Executor (GNN-QE), a neural-symbolic model that enjoys the advantages of both worlds. GNN-QE decomposes a complex FOL query into relation projections and logical operations over fuzzy sets, which provides interpretability for intermediate variables. To reason about the missing links, GNN-QE adapts a graph neural network from knowledge graph completion to execute the relation projections, and models the logical operations with product fuzzy logic. Experiments on 3 datasets show that GNN-QE significantly improves over previous state-of-the-art models in answering FOL queries. Meanwhile, GNN-QE can predict the number of answers without explicit supervision, and provide visualizations for intermediate variables.

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or whether a patient has died or not), because the ground-truth probabilities of the events of interest are typically unknown. The problem is therefore analogous to binary classification, with the difference that the objective is to estimate probabilities rather than predicting the specific outcome. This work investigates probability estimation from high-dimensional data using deep neural networks. There exist several methods to improve the probabilities generated by these models but they mostly focus on model (epistemic) uncertainty. For problems with inherent uncertainty, it is challenging to evaluate performance without access to ground-truth probabilities. To address this, we build a synthetic dataset to study and compare different computable metrics. We evaluate existing methods on the synthetic data as well as on three real-world probability estimation tasks, all of which involve inherent uncertainty: precipitation forecasting from radar images, predicting cancer patient survival from histopathology images, and predicting car crashes from dashcam videos. We also give a theoretical analysis of a model for high-dimensional probability estimation which reproduces several of the phenomena evinced in our experiments. Finally, we propose a new method for probability estimation using neural networks, which modifies the training process to promote output probabilities that are consistent with empirical probabilities computed from the data. The method outperforms existing approaches on most metrics on the simulated as well as real-world data.

Compressed sensing (CS) aims to recover a high-dimensional signal with structural priors from its low-dimensional linear measurements. Inspired by the huge success of deep neural networks in modeling the priors of natural signals, generative neural networks have been recently used to replace the hand-crafted structural priors in CS. However, the reconstruction capability of the generative model is fundamentally limited by the range of its generator, typically a small subset of the signal space of interest. To break this bottleneck and thus reconstruct those out-of-range signals, this paper presents a novel method called CS-BGM that can effectively expands the range of generator. Specifically, CS-BGM introduces uncertainties to the latent variable and parameters of the generator, while adopting the variational inference (VI) and maximum a posteriori (MAP) to infer them. Theoretical analysis demonstrates that expanding the range of generators is necessary for reducing the reconstruction error in generative CS. Extensive experiments show a consistent improvement of CS-BGM over the baselines.

The invariance to permutations of the adjacency matrix, i.e., graph isomorphism, is an overarching requirement for Graph Neural Networks (GNNs). Conventionally, this prerequisite can be satisfied by the invariant operations over node permutations when aggregating messages. However, such an invariant manner may ignore the relationships among neighboring nodes, thereby hindering the expressivity of GNNs. In this work, we devise an efficient permutation-sensitive aggregation mechanism via permutation groups, capturing pairwise correlations between neighboring nodes. We prove that our approach is strictly more powerful than the 2-dimensional Weisfeiler-Lehman (2-WL) graph isomorphism test and not less powerful than the 3-WL test. Moreover, we prove that our approach achieves the linear sampling complexity. Comprehensive experiments on multiple synthetic and real-world datasets demonstrate the superiority of our model.

Learning to predict missing links is important for many graph-based applications. Existing methods were designed to learn the association between observed graph structure and existence of link between a pair of nodes. However, the causal relationship between the two variables was largely ignored for learning to predict links on a graph. In this work, we visit this factor by asking a counterfactual question: "would the link still exist if the graph structure became different from observation?" Its answer, counterfactual links, will be able to augment the graph data for representation learning. To create these links, we employ causal models that consider the information (i.e., learned representations) of node pairs as context, global graph structural properties as treatment, and link existence as outcome. We propose a novel data augmentation-based link prediction method that creates counterfactual links and learns representations from both the observed and counterfactual links. Experiments on benchmark data show that our graph learning method achieves state-of-the-art performance on the task of link prediction.

While deep generative models have succeeded in image processing, natural language processing, and reinforcement learning, training that involves discrete random variables remains challenging due to the high variance of its gradient estimation process. Monte Carlo is a common solution used in most variance reduction approaches. However, this involves time-consuming resampling and multiple function evaluations. We propose a Gapped Straight-Through (GST) estimator to reduce the variance without incurring resampling overhead. This estimator is inspired by the essential properties of Straight-Through Gumbel-Softmax. We determine these properties and show via an ablation study that they are essential. Experiments demonstrate that the proposed GST estimator enjoys better performance compared to strong baselines on two discrete deep generative modeling tasks, MNIST-VAE and ListOps.

Spurious correlations pose a major challenge for robust machine learning. Models trained with empirical risk minimization (ERM) may learn to rely on correlations between class labels and spurious attributes, leading to poor performance on data groups without these correlations. This is challenging to address when the spurious attribute labels are unavailable. To improve worst-group performance on spuriously correlated data without training attribute labels, we propose Correct-N-Contrast (CNC), a contrastive approach to directly learn representations robust to spurious correlations. As ERM models can be good spurious attribute predictors, CNC works by (1) using a trained ERM model’s outputs to identify samples with the same class but dissimilar spurious features, and (2) training a robust model with contrastive learning to learn similar representations for these samples. To support CNC, we introduce new connections between worst-group error and a representation alignment loss that CNC aims to minimize. We empirically observe that worst-group error closely tracks with alignment loss, and prove that the alignment loss over a class helps upper-bound the class's worst-group vs. average error gap. On popular benchmarks, CNC reduces alignment loss drastically, and achieves state-of-the-art worst-group accuracy by 3.6% average absolute lift. CNC is also competitive with oracle methods that require group labels.

Normalizing flows map an independent set of latent variables to their samples using a bijective transformation. Despite the exact correspondence between samples and latent variables, their high level relationship is not well understood. In this paper we characterize the geometric structure of flows using principal manifolds and understand the relationship between latent variables and samples using contours. We introduce a novel class of normalizing flows, called principal component flows (PCF), whose contours are its principal manifolds, and a variant for injective flows (iPCF) that is more efficient to train than regular injective flows. PCFs can be constructed using any flow architecture, are trained with a regularized maximum likelihood objective and can perform density estimation on all of their principal manifolds. In our experiments we show that PCFs and iPCFs are able to learn the principal manifolds over a variety of datasets. Additionally, we show that PCFs can perform density estimation on data that lie on a manifold with variable dimensionality, which is not possible with existing normalizing flows.

The hierarchical variational autoencoder (HVAE) is a popular generative model used for many representation learning tasks. However, its application to image synthesis often yields models with poor sample quality. In this work, we treat image synthesis itself as a hierarchical representation learning problem and regularize an HVAE toward representations that improve the model's image synthesis performance. We do so by leveraging the progressive coding hypothesis, which claims hierarchical latent variable models that are good at progressive lossy compression will generate high-quality samples. To test this hypothesis, we first show empirically that conventionally-trained HVAEs are not good progressive coders. We then propose a simple method that constrains the hierarchical representations to prioritize the encoding of information beneficial for lossy compression, and show that this modification leads to improved sample quality. Our work lends further support to the progressive coding hypothesis and demonstrates that this hypothesis should be exploited when designing variational autoencoders.

We present energy-based generative flow networks (EB-GFN), a novel probabilistic modeling algorithm for high-dimensional discrete data. Building upon the theory of generative flow networks (GFlowNets), we model the generation process by a stochastic data construction policy and thus amortize expensive MCMC exploration into a fixed number of actions sampled from a GFlowNet. We show how GFlowNets can approximately perform large-block Gibbs sampling to mix between modes. We propose a framework to jointly train a GFlowNet with an energy function, so that the GFlowNet learns to sample from the energy distribution, while the energy learns with an approximate MLE objective with negative samples from the GFlowNet. We demonstrate EB-GFN's effectiveness on various probabilistic modeling tasks. Code is publicly available at https://github.com/zdhNarsil/EB_GFN.

Vector Quantized-Variational AutoEncoders (VQ-VAE) are generative models based on discrete latent representations of the data, where inputs are mapped to a finite set of learned embeddings.To generate new samples, an autoregressive prior distribution over the discrete states must be trained separately. This prior is generally very complex and leads to slow generation. In this work, we propose a new model to train the prior and the encoder/decoder networks simultaneously. We build a diffusion bridge between a continuous coded vector and a non-informative prior distribution. The latent discrete states are then given as random functions of these continuous vectors. We show that our model is competitive with the autoregressive prior on the mini-Imagenet and CIFAR dataset and is efficient in both optimization and sampling. Our framework also extends the standard VQ-VAE and enables end-to-end training.

A number of variational autoencoders (VAEs) have recently emerged with the aim of modeling multimodal data, e.g., to jointly model images and their corresponding captions. Still, multimodal VAEs tend to focus solely on a subset of the modalities, e.g., by fitting the image while neglecting the caption. We refer to this limitation as modality collapse. In this work, we argue that this effect is a consequence of conflicting gradients during multimodal VAE training. We show how to detect the sub-graphs in the computational graphs where gradients conflict (impartiality blocks), as well as how to leverage existing gradient-conflict solutions from multitask learning to mitigate modality collapse. That is, to ensure impartial optimization across modalities. We apply our training framework to several multimodal VAE models, losses and datasets from the literature, and empirically show that our framework significantly improves the reconstruction performance, conditional generation, and coherence of the latent space across modalities.

Recent advances in diffusion models bring state-of-the-art performance on image generation tasks. However, empirical results from previous research in diffusion models imply an inverse correlation between density estimation and sample generation performances. This paper investigates with sufficient empirical evidence that such inverse correlation happens because density estimation is significantly contributed by small diffusion time, whereas sample generation mainly depends on large diffusion time. However, training a score network well across the entire diffusion time is demanding because the loss scale is significantly imbalanced at each diffusion time. For successful training, therefore, we introduce Soft Truncation, a universally applicable training technique for diffusion models, that softens the fixed and static truncation hyperparameter into a random variable. In experiments, Soft Truncation achieves state-of-the-art performance on CIFAR-10, CelebA, CelebA-HQ $256\times 256$, and STL-10 datasets.

The AutoAttack (AA) has been the most reliable method to evaluate adversarial robustness when considerable computational resources are available. However, the high computational cost (e.g., 100 times more than that of the project gradient descent attack) makes AA infeasible for practitioners with limited computational resources, and also hinders applications of AA in the adversarial training (AT). In this paper, we propose a novel method, minimum-margin (MM) attack, to fast and reliably evaluate adversarial robustness. Compared with AA, our method achieves comparable performance but only costs 3% of the computational time in extensive experiments. The reliability of our method lies in that we evaluate the quality of adversarial examples using the margin between two targets that can precisely identify the most adversarial example. The computational efficiency of our method lies in an effective Sequential TArget Ranking Selection (STARS) method, ensuring that the cost of the MM attack is independent of the number of classes. The MM attack opens a new way for evaluating adversarial robustness and provides a feasible and reliable way to generate high-quality adversarial examples in AT.