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Understanding the black-box prediction for neural networks is challenging. To achieve this, early studies have designed influence function (IF) to measure the effect of removing a single training point on neural networks. However, the classic implicit Hessian-vector product (IHVP) method for calculating IF is fragile, and theoretical analysis of IF in the context of neural networks is still lacking. To this end, we utilize the neural tangent kernel (NTK) theory to calculate IF for the neural network trained with regularized mean-square loss, and prove that the approximation error can be arbitrarily small when the width is sufficiently large for two-layer ReLU networks. We analyze the error bound for the classic IHVP method in the over-parameterized regime to understand when and why it fails or not. In detail, our theoretical analysis reveals that (1) the accuracy of IHVP depends on the regularization term, and is pretty low under weak regularization; (2) the accuracy of IHVP has a significant correlation with the probability density of corresponding training points. We further borrow the theory from NTK to understand the IFs better, including quantifying the complexity for influential samples and depicting the variation of IFs during the training dynamics. Numerical experiments on real-world data confirm our theoretical results and demonstrate our findings.

AAAI 2022

Rethinking Influence Functions of Neural Networks in the Over-Parameterized Regime

technical paper

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. 

Knowledge Distillation (KD) is a widely-used technology to inherit information from cumbersome teacher models to compact student models, consequently realizing model compression and acceleration. Compared with image classification, object detection is a more complex task, and designing specific KD methods for object detection is non-trivial. In this work, we elaborately study the behaviour difference between the teacher and student detection models, and obtain two intriguing observations: First, the teacher and student rank their detected candidate boxes quite differently, which results in their precision discrepancy. Second, there is a considerable gap between the feature response differences and prediction differences between teacher and student, indicating that equally imitating all the feature maps of the teacher is the sub-optimal choice for improving the student's accuracy. Based on the two observations, we propose Rank Mimicking (RM) and Prediction-guided Feature Imitation (PFI) for distilling one-stage detectors, respectively. RM takes the rank of candidate boxes from teachers as a new form of knowledge to distill, which consistently outperforms the traditional soft label distillation. PFI attempts to correlate feature differences with prediction differences, making feature imitation directly help to improve the student's accuracy. On MS COCO and PASCAL VOC benchmarks, extensive experiments are conducted on various detectors with different backbones to validate the effectiveness of our method. Specifically, RetinaNet with ResNet50 achieves 40.4% mAP on MS COCO, which is 3.5% higher than its baseline, and also outperforms previous KD methods.

Knowledge Distillation for Object Detection via Rank Mimicking and Prediction-Guided Feature Imitation

k-means and k-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta, Rashtchian, and  Frost  proposed an elegant model of explainable k-means and k-median clustering  in ICML 2020. In this model, a  decision tree with k leaves provides a straightforward characterization of the data set into clusters. 
 
 
 We study two natural algorithmic questions about explainable clustering.  (1) For a given clustering, how to find the ``best explanation'' by using a decision tree with k leaves?  (2) For a given set of points, how to find a decision tree with k leaves minimizing the k-means/median objective of the resulting explainable clustering?
To address the first question, we introduce a new model of explainable clustering. Our model, inspired by the notion of outliers in robust statistics, is the following. We are seeking a small number of points (outliers) whose removal makes the existing clustering well-explainable. For addressing the second question, we initiate the study of the model of Moshkovitz et al. from the perspective of multivariate complexity. Our rigorous algorithmic analysis sheds some light on the influence of parameters like the input size, dimension of the data, the number of outliers, the number of clusters, and the approximation ratio,  on the computational complexity of explainable clustering.

How to Find a Good Explanation for Clustering?

From an engineering perspective, a design should not only perform well in an ideal condition, but should also resist noises. Such a design methodology, namely robust design, has been widely implemented in the industry for product quality control. However, classic robust design requires a lot of evaluations for a single design target, while the results of these evaluations could not be reused for a new target. To achieve data-efficient robust design, we propose Robust Inverse Design under Noise (RID-Noise), which can utilize existing data to train a conditional invertible neural network. Specifically, we estimate the robustness of a design parameter by its predictability, measured by the prediction error of a forward neural network. We also define a sample-wise weight, which can be used in the maximum weighted likelihood estimation of an inverse model based on a conditional invertible neural network. With the visual results from experiments, we clearly justify how RID-Noise works by learning the distribution and robustness from data. Further experiments on several real-world benchmark tasks with noises confirm that our method is more effective than other state-of-the-art inverse design methods. Code and supplementary is publicly available at https://github.com/ThyrixYang/rid-noise-aaai22

RID-Noise: Towards Robust Inverse Design under Noisy Environments

In many games, moves consist of several decisions made by the player. These decisions can be viewed as separate moves, which is already a common practice in multi-action games for efficiency reasons. Such division of a player move into a sequence of simpler / lower level moves is called splitting. So far, split moves have been applied only in forementioned straightforward cases, and furthermore, there was almost no study revealing its impact on agents' playing strength. Taking the knowledge-free perspective, we aim to answer how to effectively use split moves within Monte-Carlo Tree Search (MCTS) and what is the practical impact of split design on agents' strength. This paper proposes a generalization of MCTS that works with arbitrarily split moves. We design several variations of the algorithm and try to measure the impact of split moves separately on efficiency, quality of MCTS, simulations, and action-based heuristics. The tests are carried out on a set of board games and performed using the Regular Boardgames General Game Playing formalism, where split strategies of different granularity can be automatically derived based on an abstract description of the game. The results give an overview of the behavior of agents using split design in different ways. We conclude that split design can be greatly beneficial for single- as well as multi-action games.

Split Moves for Monte-Carlo Tree Search

Accurate protein contact map prediction (PCMP) is essential for precise protein structure estimation and further biological studies. Recent works achieve significant performance on this task with high quality multiple sequence alignment (MSA). However, the PCMP accuracy drops dramatically while only poor MSA (e.g., absolute MSA count less than 10) is available. Therefore, in this paper, we propose the Contact-Distil to improve the low homologous PCMP accuracy through knowledge distillation on a self-supervised model. Particularly, two pre-trained transformers are exploited to learn the high quality and low quality MSA representation in parallel for the teacher and student model correspondingly. Besides, the co-evolution information is further extracted from pure sequence through a pretrained ESM-1b model, which provides auxiliary knowledge to improve student performance. Extensive experiments show Contact-Distil outperforms previous state-of-the-arts by large margins on CAMEO-L dataset for low homologous PCMP, i.e., around 13.3% and 9.5% improvements against Alphafold2 and MSA Transformer respectively when MSA count less than 10.

Contact-Distil: Boosting Low Homologous Protein Contact Map Prediction by Self-Supervised Distillation

Recent years have witnessed a flurry of research activity in graph matching, which aims at finding the correspondence of nodes across two graphs and lies at the heart of many artificial intelligence applications. However, matching heterogeneous graphs with partial overlap remains a challenging problem in real-world applications. This paper proposes the first practical learning-to-match method to meet this challenge. The proposed unsupervised method adopts a novel partial optimal transport paradigm to learn a transport plan and node embeddings simultaneously. In a from-one-to-all manner, the entire learning procedure is decomposed into a series of easy-to-solve sub-procedures, each of which only handles the alignment of a single type of nodes. A mechanism for searching the transport mass is also proposed. Experimental results demonstrate that the proposed method outperforms state-of-the-art graph matching methods.

From One to All: Learning to Match Heterogeneous and Partially Overlapped Graphs

Participatory budgeting (PB) is a democratic process where citizens jointly decide on how to allocate public funds to indivisible projects. In this work, we focus on PB processes where citizens may provide additional money to projects they want to see funded. We introduce a formal framework for this kind of PB with donations. Our framework also allows for diversity constraints, meaning that each project belongs to one or more types, and there are lower and upper bounds on the number of projects of the same type that can be funded. We propose three general classes of methods for aggregating the citizens' preferences in the presence of donations and analyze their axiomatic properties. Furthermore, we investigate the computational complexity of determining the outcome of a PB process with donations and of finding a citizen's optimal donation strategy.

Participatory Budgeting with Donations and Diversity Constraints

Partial Differential Equations (PDEs) are notoriously difficult to solve. In general, closed form solutions are not available and numerical approximation schemes are computationally expensive. In this paper, we propose to approach the solution of PDEs based on a novel technique that combines the advantages of two recently emerging machine learning based approaches.
 First, physics-informed neural networks (PINNs) learn continuous solutions of PDEs and can be trained with little to no ground truth data. However, PINNs do not generalize well to unseen domains. Second, convolutional neural networks provide fast inference and generalize but either require large amounts of training data or a physics-constrained loss based on finite differences that can lead to inaccuracies and discretization artifacts.
 We leverage the advantages of both of these approaches by using Hermite spline kernels in order to continuously interpolate a grid-based state representation that can be handled by a CNN. This allows for training without any precomputed training data using a physics-informed loss function only and provides fast, continuous solutions that generalize to unseen domains.
 We demonstrate the potential of our method at the examples of the incompressible Navier-Stokes equation and the damped wave equation. Our models are able to learn several intriguing phenomena such as Karman vortex streets, the Magnus effect, Doppler effect, interference patterns and wave reflections. Our quantitative assessment and an interactive real-time demo show that we are narrowing the gap in accuracy of unsupervised ML based methods to industrial solvers for computational fluid dynamics (CFD) while being orders of magnitude faster.

Spline-PINN: Approaching PDEs without Data Using Fast, Physics-Informed Hermite-Spline CNNs

We study the theoretical properties of random Fourier features classification with Lipschitz continuous loss functions such as support vector machine and logistic regression. Utilizing the regularity condition, we show for the first time that random Fourier features classification can achieve O(1/n^0.5) learning rate with only O(n^0.5) features, as opposed to O(n) features suggested by previous results. Our study covers the standard feature sampling method for which we reduce the number of features required, as well as a problem-dependent sampling method which further reduces the number of features while still keeping the optimal generalization property. Moreover, we prove that the random Fourier features classification can obtain a fast O(1/n) learning rate for both sampling schemes under Massart's low noise assumption. Our results demonstrate the potential effectiveness of random Fourier features approximation in reducing the computational complexity (roughly from O(n^3) in time and O(n^2) in space to O(n^2) and O(n^1.5) respectively) without having to trade-off the statistical prediction accuracy. In addition, the achieved trade-off in our analysis is at least the same as the optimal results in the literature under the worst case scenario and significantly improves the optimal results under benign regularity conditions.

Sharp Analysis of Random Fourier Features in Classification

RGB-NIR fusion is a promising method for low-light imaging. However, high-intensity noise in low-light images amplifies the effect of structure inconsistency between RGB-NIR images, which fails existing algorithms. To handle this, we propose a new RGB-NIR fusion algorithm called Dark Vision Net (DVN) with two technical novelties: Deep Structure and Deep Inconsistency Prior (DIP). The Deep Structure extracts clear structure details in deep multiscale feature space rather than raw input space, which is more robust to noisy inputs. Based on the deep structures from both RGB and NIR domains, we introduce the DIP to leverage the structure inconsistency to guide the fusion of RGB-NIR. Benefits from this, the proposed DVN obtains high-quality low-light images without the visual artifacts. We also propose a new dataset called Dark Vision Dataset (DVD), consisting of aligned RGB-NIR image pairs, as the first public RGB-NIR fusion benchmark. Quantitative and qualitative results on the proposed benchmark show that DVN significantly outperforms other comparison algorithms in PSNR and SSIM, especially in extremely low light conditions.

Rethinking Influence Functions of Neural Networks in the Over-Parameterized Regime

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Rethinking Influence Functions of Neural Networks in the Over-Parameterized Regime

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Knowledge Distillation for Object Detection via Rank Mimicking and Prediction-Guided Feature Imitation

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