Double Permutation Equivariance for Knowledge Graph Completion

This work provides a formalization of Knowledge Graphs (KGs) as a new class of graphs that we denote doubly exchangeable attributed graphs, where node and pairwise (joint 2-node) representations must be equivariant to permutations of both node ids and edge (& node) attributes (relations & node features). Double-permutation equivariant KG representations open a new research direction in KGs. We show that this equivariance imposes a structural representation of relations that allows neural networks to perform complex logical reasoning tasks in KGs. Finally, we introduce a general blueprint for such equivariant representations and test a simple GNN-based double-permutation equivariant neural architecture that achieve 100% Hits@10 test accuracy in both the WN18RRv1 and NELL995v1 inductive KG completion tasks, and can accurately perform logical reasoning tasks that no existing methods can perform, to the best of our knowledge.

PKD: General Distillation Framework for Object Detectors via Pearson Correlation Coefficient

Knowledge distillation(KD) is a widely-used technique to train compact models in object detection. However, there is still a lack of study on how to distill between heterogeneous detectors. In this paper, we empirically find that better FPN features from a heterogeneous teacher detector can help the student although their detection heads and label assignments are different. However, directly aligning the feature maps to distill detectors suffers from two problems. First, the difference in feature magnitude between the teacher and the student could enforce overly strict constraints on the student. Second, the FPN stages and channels with large feature magnitude from the teacher model could dominate the gradient of distillation loss, which will overwhelm the effects of other features in KD and introduce much noise. To address the above issues, we propose to imitate features with Pearson Correlation Coefficient to focus on the relational information from the teacher and relax constraints on the magnitude of the features. Our method consistently outperforms the existing detection KD methods and works for both homogeneous and heterogeneous student-teacher pairs. Furthermore, it converges faster. With a powerful MaskRCNN-Swin detector as the teacher, ResNet-50 based RetinaNet and FCOS achieve 41.5% and 43.9% mAP on COCO2017, which are 4.1\% and 4.8\% higher than the baseline, respectively.

On the Equivalence Between Temporal and Static Graph Representations for Observational Predictions

In this work we formalize the (pure observational) task of predicting node attribute evolution in temporal graphs. We show that node representations of temporal graphs can be cast into two distinct frameworks: (a) The de-facto standard approach, which we denote {\em time-and-graph}, where equivariant graph (e.g., GNN) and sequence (e.g., RNN) representations are intertwined to represent the temporal evolution of the graph; and (b) an approach that we denote {\em time-then-graph}, where the sequences describing the node and edge dynamics are represented first (e.g., RNN), then fed as node and edge attributes into a (static) equivariant graph representation that comes after (e.g., GNN). In real-world datasets, we show that our {\em time-then-graph} framework achieves the same prediction performance as state-of-the-art {\em time-and-graph} methods. Interestingly, {\em time-then-graph} representations have an expressiveness advantage over {\em time-and-graph} representations when both use component GNNs that are not most-expressive (e.g., 1-Weisfeiler-Lehman GNNs). We introduce a task where this expressiveness advantage allows {\em time-then-graph} methods to succeed while state-of-the-art {\em time-and-graph} methods fail.

Channel-wise Distillation for Semantic Segmentation

Knowledge distillation (KD) has been proven to be a simple and effective tool for training compact models. Almost all KD variants for semantic segmentation align the student and teacher networks' feature maps in the spatial domain, typically by minimizing point-wise and/or pair-wise discrepancy. Observing that in semantic segmentation, some layers' feature activations of each channel tend to encode saliency of scene categories (analogue to class activation mapping), we propose to align features channel-wise between the student and teacher networks. To this end, we first transform the feature map of each channel into a distribution using softmax normalization, and then minimize the Kullback-Leibler (KL) divergence of the corresponding channels of the two networks. By doing so, our method focuses on mimicking the soft distributions of channels between networks. In particular, the KL divergence enables learning to pay more attention to the most salient regions of the channel-wise maps, presumably corresponding to the most useful signals for semantic segmentation. Experiments demonstrate that our channel-wise distillation outperforms almost all existing spatial distillation methods for semantic segmentation considerably, and requires less computational cost during training. We consistently achieve superior performance on three benchmarks with various network structures. Code is available at: https://git.io/ChannelDis

Infinity Learning: Learning Markov Chains from Aggregate Steady-State Observations

We consider the task of learning a parametric Continuous Time Markov Chain (CTMC) sequence model without examples of sequences, where the training data consists entirely of aggregate steady-state statistics. Making the problem harder, we assume that the states we wish to predict are unobserved in the training data. Specifically, given a parametric model over the transition rates of a CTMC and some known transition rates, we wish to extrapolate its steady state distribution to states that are unobserved. A technical roadblock to learn a CTMC from its steady state has been that the chain rule to compute gradients will not work over the arbitrarily long sequences necessary to reach steady state ---from where the aggregate statistics are sampled. To overcome this optimization challenge, we propose $\infty$-SGD, a principled stochastic gradient descent method that uses randomly-stopped estimators to avoid infinite sums required by the steady state computation, while learning even when only a subset of the CTMC states can be observed. We apply $\infty$-SGD to a real-world testbed and synthetic experiments showcasing its accuracy, ability to extrapolate the steady state distribution to unobserved states under unobserved conditions (heavy loads, when training under light loads), and succeeding in difficult scenarios where even a tailor-made extension of existing methods fails.