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Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze trained neural networks using an operator theoretic approach which is rooted in Koopman theory, the Koopman Analysis of Neural Networks (KANN). Key to our method is the Koopman operator, which is a linear object that globally represents the dominant behavior of the network dynamics. The linearity of the Koopman operator facilitates analysis via its eigenvectors and eigenvalues. Our method reveals that the latter eigendecomposition holds semantic information related to the neural network inner workings. For instance,  the eigenvectors highlight positive and negative n-grams in the sentiments analysis task; similarly, the eigenvectors capture the salient features of healthy heart beat signals in the ECG classification problem.

AAAI 2023

An Operator Theoretic Approach for Analyzing Sequence Neural Networks

koopman theory

understanding

time-series

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-23 is the Thirty-Seventh AAAI Conference on Artificial Intelligence. The theme of this conference is to create collaborative bridges within and beyond AI. Like previous AAAI conferences, AAAI-23 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and two new activities: a Bridge Program and a Lab Program. Many of these activities are tailored to the theme of bridges and all are selected according to the highest standards, with additional programs for students and young researchers. 
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The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines.

poster

ImageNet pre-training has enabled state-of-the-art results on many tasks. In spite of its recognized contribution to generalization, we observed in this study that ImageNet pre-training also transfers adversarial non-robustness from pre-trained model into fine-tuned model in the downstream classification tasks. We first conducted experiments on various datasets and network backbones to uncover the adversarial non-robustness in fine-tuned model. Further analysis was conducted on examining the learned knowledge of fine-tuned model and standard model, and revealed that the reason leading to the non-robustness is the non-robust features transferred from ImageNet pre-trained model. Finally, we analyzed the preference for feature learning of the pre-trained model, explored the factors influencing robustness, and introduced a simple robust ImageNet pre-training solution. Our code is available at https://github.com/jiamingzhang94/ImageNet-Pretraining-transfers-non-robustness.

ImageNet Pre-training also Transfers Non-robustness

Doubly stochastic matrix plays an essential role in several areas such as statistics and machine learning. In this paper we consider the optimal approximation of an $n \times n$ matrix $A$ in the set of doubly stochastic matrices. A structured BFGS method is proposed to solve the dual of the primal problem. The resulting algorithm builds curvature information into the diagonal components of the true Hessian, so that it takes only additional $O(n)$ cost to obtain the descent direction based on the gradient information without having to explicitly store the inverse Hessian approximation. The cost is substantially fewer than $O(n^2)$ arithmetic operations of the classical BFGS algorithm. Meanwhile, a Newton-based line search method is presented for finding a suitable step size, which in practice uses the existing knowledge and takes only one iteration. The global convergence of our algorithm is established. We verify the advantages of our approach on both synthetic data and real data sets. The experimental results demonstrate that our algorithm outperforms the state-of-the-art solvers and enjoys outstanding scalability.

Structured BFGS Method for Optimal Doubly Stochastic Matrix Approximation

We study the problem of synthesizing immersive 3D indoor scenes from one or a few images. Our aim is to generate high-resolution images and videos from novel viewpoints, including viewpoints that extrapolate far beyond the input images while maintaining 3D consistency. Existing approaches are highly complex, with many separately trained stages and components. We propose a simple alternative: an image-to-image GAN that maps directly from reprojections of incomplete point clouds to full high-resolution RGB-D images. On the Matterport3D and RealEstate10K datasets, our approach significantly outperforms prior work when evaluated by humans, as well as on FID scores. Further, we show that our model is useful for generative data augmentation. A vision-and-language navigation (VLN) agent trained with trajectories spatially-perturbed by our model improves success rate by up to 1.5% over a state of the art baseline on the mature R2R benchmark. Our code will be made available to facilitate generative data augmentation and applications to downstream robotics and embodied AI tasks.

Simple and Effective Synthesis of Indoor 3D Scenes

An agent's ability to distinguish between sensory effects that are self-caused, and those that are not, is instrumental in the achievement of its goals. This ability is thought to be central to a variety of functions in biological organisms, from perceptual stabilisation and accurate motor control, to higher level cognitive functions such as planning, mirroring and the sense of agency. Although many of these functions are well studied in AI, this important distinction is rarely made explicit and the focus tends to be on the associational relationship between action and sensory effect or success. Toward the development of more general agents, we develop a framework that enables agents to disentangle self caused and externally caused sensory effects. Informed by relevant models and experiments in robotics, and in the biological and cognitive sciences, we demonstrate the general applicability of this framework through an extensive experimental evaluation over three different environments.

Disentangling Reafferent Effects by Doing Nothing

Meta-learning owns unique effectiveness and swiftness in tackling emerging tasks with limited data. Its broad applicability is revealed by viewing it as a bi-level optimization problem. The resultant algorithmic viewpoint however, faces scalability issues when the inner-level optimization relies on gradient-based iterations. Implicit differentiation has been considered to alleviate this challenge, but it is restricted to an isotropic Gaussian prior, and only favors deterministic meta-learning approaches. This work markedly mitigates the scalability bottleneck by cross-fertilizing the benefits of implicit differentiation to probabilistic Bayesian meta-learning. The novel implicit Bayesian meta-learning (iBaML) method not only broadens the scope of learnable priors, but also quantifies the associated uncertainty. Furthermore, the ultimate complexity is well controlled regardless of the inner-level optimization trajectory. Analytical error bounds are established to demonstrate the precision and efficiency of the generalized implicit gradient over the explicit one. Extensive numerical tests are also carried out to empirically validate the performance of the proposed method.

Scalable Bayesian Meta-Learning through Generalized Implicit Gradients

Simulations that produce three-dimensional data are ubiquitous in science, ranging from fluid flows to plasma physics. We propose a similarity model based on entropy, which allows for the creation of physically meaningful ground truth distances for the similarity assessment of scalar and vectorial data, produced from transport and motion-based simulations. Utilizing two data acquisition methods derived from this model, we create collections of fields from numerical PDE solvers and existing simulation data repositories. Furthermore, a multiscale CNN architecture that computes a volumetric similarity metric (VolSiM) is proposed. To the best of our knowledge this is the first learning method inherently designed to address the challenges arising for the similarity assessment of high-dimensional simulation data. Additionally, the tradeoff between a large batch size and an accurate correlation computation for correlation-based loss functions is investigated, and the metric's invariance with respect to rotation and scale operations is analyzed. Finally, the robustness and generalization of VolSiM is evaluated on a large range of test data, as well as a particularly challenging turbulence case study, that is close to potential real-world applications.

Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs

Vehicle ReID has been an active topic in computer vision, with a substantial number of deep neural models proposed as end-to-end solutions. In this paper, we solve the problem from a new perspective and present an interesting variant called human-in-the-loop vehicle ReID to leverage interactive (and possibly wrong) human feedback signal for performance enhancement. Such human-machine cooperation mode is orthogonal to existing ReID models. To avoid incremental training overhead, we propose an Interaction ReID Network (IRIN) that can directly accept the feedback signal as an input and adjust the embedding of query image in an online fashion. IRIN is offline trained by simulating the human interaction process, with multiple optimization strategies to fully exploit the feedback signal. Experimental results show that even by interacting  with flawed feedback generated by non-experts, IRIN still outperforms state-of-the-art ReID models by a considerable margin. If the feedback contains no false positive, IRIN boosts the mAP in Veri776 from 81.6% to 95.2% with only 5 rounds of interaction per query image.

Human-in-the-Loop Vehicle ReID

Predicting personality traits based on online posts has emerged as an important task in many fields such as social network analysis. One of the challenges of this task is assembling information from various posts into an overall profile for each user. While many previous solutions simply concatenate the posts into a long text and then encode the text by sequential or hierarchical models, they introduce unwarranted orders for the posts, which may mislead the models. In this paper, we propose a dynamic deep graph convolutional network (D-DGCN) to overcome the above limitation. Specifically, we design a learn-to-connect approach that adopts a dynamic multi-hop structure instead of a deterministic structure, and combine it with the DGCN module to automatically learn the connections between posts. The modules of post encoder, learn-to-connect, and DGCN are jointly trained in an end-to-end manner. Experimental results on the Kaggle and Pandora datasets show the superior performance of D-DGCN to state-of-the-art baselines. Our code is available at https://github.com/djz233/D-DGCN.

Orders Are Unwanted: Dynamic Deep Graph Convolutional Network for Personality Detection

Gate functions in recurrent models, such as an LSTM and GRU, play a central role in learning various time scales in modeling time series data by using a bounded activation function. However, it is difficult to train gates to capture extremely long time scales due to gradient vanishing of the bounded function for large inputs, which is known as the saturation problem. We closely analyze the relation between saturation of the gate function and efficiency of the training. We prove that the gradient vanishing of the gate function can be mitigated by accelerating the convergence of the saturating function, i.e., making the output of the function converge to 0 or 1 faster. Based on the analysis results, we propose a gate function called fast gate that has a doubly exponential convergence rate with respect to inputs by simple function composition. We empirically show that our method outperforms previous methods in accuracy and computational efficiency on benchmark tasks involving extremely long time scales.

Fast Saturating Gate for Learning Long Time Scales with Recurrent Neural Networks

We propose a novel solution for unpaired image-to-image (I2I) translation. To translate complex images with a wide range of objects to a different domain, recent approaches often use the object annotations to perform per-class source-to-target style mapping. However, there remains a point for us to exploit in the I2I. An object in each class consists of multiple components, and all the sub-object components have different characteristics. For example, a car in CAR class consists of a car body, tires, windows and head and tail lamps, etc., and they should be handled separately for realistic I2I translation. The simplest solution to the problem will be to use more detailed annotations with sub-object component annotations than the simple object annotations, but it is not possible. The key idea of this paper is to bypass the sub-object component annotations by leveraging the original style of the input image because the original style will include the information about the characteristics of the sub-object components. Specifically, for each pixel, we use not only the per-class style gap between the source and target domains but also the pixel’s original style to determine the target style of a pixel. To this end, we present Style Harmonization for unpaired I2I translation (SHUNIT). Our SHUNIT generates a new style by harmonizing the target domain style retrieved from a class memory and an original source image style. Instead of direct source-to-target style mapping, we aim for source and target styles harmonization. We validate our method with extensive experiments and achieve state-of-the-art performance on the latest benchmark sets. The source code and model will be available online. We included the code of our model in the supplementary material.

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An Operator Theoretic Approach for Analyzing Sequence Neural Networks

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ImageNet Pre-training also Transfers Non-robustness

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