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Generative models based on flow matching have attracted significant attention for their simplicity and superior performance in high-resolution image synthesis. By leveraging the instantaneous change-of-variables formula, one can directly compute image likelihoods from a learned flow, making them enticing candidates as priors for downstream tasks such as inverse problems. In particular, a natural approach would be to incorporate such image probabilities in a maximum-a-posteriori (MAP) estimation problem. A major obstacle, however, lies in the slow computation of the log-likelihood, as it requires backpropagating through an ODE solver, which can be prohibitively slow for high-dimensional problems. In this work, we propose an iterative algorithm to approximate the MAP estimator efficiently to solve a variety of linear inverse problems. Our algorithm is mathematically justified by the observation that the MAP objective can be approximated by a sum of $N$ ``local MAP'' objectives, where $N$ is the number of function evaluations. By leveraging Tweedie's formula, we show that we can perform gradient steps to sequentially optimize these objectives. We validate our approach for various linear inverse problems, such as super-resolution, deblurring, inpainting, and compressed sensing, and demonstrate that we can outperform other methods based on flow matching.

Feature extraction is a critical technology to realize the automatic transmission of feature information throughout product life cycles. As CAD models primarily capture the 3D geometry of products, feature extraction heavily relies on geometric information. However, existing feature extraction methods often yield inaccurate outcomes due to the diverse interpretations of geometric information. This report presents a set-based feature extraction approach to address this uncertainty issue. Unlike existing methods that seek accurate feature results, our approach aims to transform the uncertainty of geometric information into a set of feature subgraphs. First, we define the convexity of basic geometric entities and introduce the concept of two-level attributed adjacency graphs. Second, a feature extraction workflow is designed to determine feature boundaries and identify feature subgraphs from CAD models. This set of feature subgraphs can be used for further feature recognition. A feature extraction system is programmed using C++ and UG/Open to demonstrate the feasibility of our proposed approach., Comment: 13 pages

Text-to-image diffusion models have shown great success in generating high-quality text-guided images. Yet, these models may still fail to semantically align generated images with the provided text prompts, leading to problems like incorrect attribute binding and/or catastrophic object neglect. Given the pervasive object-oriented structure underlying text prompts, we introduce a novel object-conditioned Energy-Based Attention Map Alignment (EBAMA) method to address the aforementioned problems. We show that an object-centric attribute binding loss naturally emerges by approximately maximizing the log-likelihood of a $z$-parameterized energy-based model with the help of the negative sampling technique. We further propose an object-centric intensity regularizer to prevent excessive shifts of objects attention towards their attributes. Extensive qualitative and quantitative experiments, including human evaluation, on several challenging benchmarks demonstrate the superior performance of our method over previous strong counterparts. With better aligned attention maps, our approach shows great promise in further enhancing the text-controlled image editing ability of diffusion models.

Autonomous vehicle (AV) systems rely on robust perception models as a cornerstone of safety assurance. However, objects encountered on the road exhibit a long-tailed distribution, with rare or unseen categories posing challenges to a deployed perception model. This necessitates an expensive process of continuously curating and annotating data with significant human effort. We propose to leverage recent advances in vision-language and large language models to design an Automatic Data Engine (AIDE) that automatically identifies issues, efficiently curates data, improves the model through auto-labeling, and verifies the model through generation of diverse scenarios. This process operates iteratively, allowing for continuous self-improvement of the model. We further establish a benchmark for open-world detection on AV datasets to comprehensively evaluate various learning paradigms, demonstrating our method's superior performance at a reduced cost., Comment: Accepted by CVPR-2024

We introduce the novel Diffusion Visual Programmer (DVP), a neuro-symbolic image translation framework. Our proposed DVP seamlessly embeds a condition-flexible diffusion model within the GPT architecture, orchestrating a coherent sequence of visual programs (i.e., computer vision models) for various pro-symbolic steps, which span RoI identification, style transfer, and position manipulation, facilitating transparent and controllable image translation processes. Extensive experiments demonstrate DVP's remarkable performance, surpassing concurrent arts. This success can be attributed to several key features of DVP: First, DVP achieves condition-flexible translation via instance normalization, enabling the model to eliminate sensitivity caused by the manual guidance and optimally focus on textual descriptions for high-quality content generation. Second, the framework enhances in-context reasoning by deciphering intricate high-dimensional concepts in feature spaces into more accessible low-dimensional symbols (e.g., [Prompt], [RoI object]), allowing for localized, context-free editing while maintaining overall coherence. Last but not least, DVP improves systemic controllability and explainability by offering explicit symbolic representations at each programming stage, empowering users to intuitively interpret and modify results. Our research marks a substantial step towards harmonizing artificial image translation processes with cognitive intelligence, promising broader applications., Comment: 25 pages, 20 figures

Active recognition enables robots to intelligently explore novel observations, thereby acquiring more information while circumventing undesired viewing conditions. Recent approaches favor learning policies from simulated or collected data, wherein appropriate actions are more frequently selected when the recognition is accurate. However, most recognition modules are developed under the closed-world assumption, which makes them ill-equipped to handle unexpected inputs, such as the absence of the target object in the current observation. To address this issue, we propose treating active recognition as a sequential evidence-gathering process, providing by-step uncertainty quantification and reliable prediction under the evidence combination theory. Additionally, the reward function developed in this paper effectively characterizes the merit of actions when operating in open-world environments. To evaluate the performance, we collect a dataset from an indoor simulator, encompassing various recognition challenges such as distance, occlusion levels, and visibility. Through a series of experiments on recognition and robustness analysis, we demonstrate the necessity of introducing uncertainties to active recognition and the superior performance of the proposed method.

This paper studies the fundamental problem of multi-layer generator models in learning hierarchical representations. The multi-layer generator model that consists of multiple layers of latent variables organized in a top-down architecture tends to learn multiple levels of data abstraction. However, such multi-layer latent variables are typically parameterized to be Gaussian, which can be less informative in capturing complex abstractions, resulting in limited success in hierarchical representation learning. On the other hand, the energy-based (EBM) prior is known to be expressive in capturing the data regularities, but it often lacks the hierarchical structure to capture different levels of hierarchical representations. In this paper, we propose a joint latent space EBM prior model with multi-layer latent variables for effective hierarchical representation learning. We develop a variational joint learning scheme that seamlessly integrates an inference model for efficient inference. Our experiments demonstrate that the proposed joint EBM prior is effective and expressive in capturing hierarchical representations and modelling data distribution.

Visual planning simulates how humans make decisions to achieve desired goals in the form of searching for visual causal transitions between an initial visual state and a final visual goal state. It has become increasingly important in egocentric vision with its advantages in guiding agents to perform daily tasks in complex environments. In this paper, we propose an interpretable and generalizable visual planning framework consisting of i) a novel Substitution-based Concept Learner (SCL) that abstracts visual inputs into disentangled concept representations, ii) symbol abstraction and reasoning that performs task planning via the self-learned symbols, and iii) a Visual Causal Transition model (ViCT) that grounds visual causal transitions to semantically similar real-world actions. Given an initial state, we perform goal-conditioned visual planning with a symbolic reasoning method fueled by the learned representations and causal transitions to reach the goal state. To verify the effectiveness of the proposed model, we collect a large-scale visual planning dataset based on AI2-THOR, dubbed as CCTP. Extensive experiments on this challenging dataset demonstrate the superior performance of our method in visual task planning. Empirically, we show that our framework can generalize to unseen task trajectories, unseen object categories, and real-world data. Further details of this work are provided at https://fqyqc.github.io/ConTranPlan/.

Analysis of human actions in videos demands understanding complex human dynamics, as well as the interaction between actors and context. However, these interaction relationships usually exhibit large intra-class variations from diverse human poses or object manipulations, and fine-grained inter-class differences between similar actions. Thus the performance of existing methods is severely limited. Motivated by the observation that interactive actions can be decomposed into actor dynamics and participating objects or humans, we propose to investigate the composite property of them. In this paper, we present a novel Grammatical Compositional Model (GCM) for action detection based on typical And-Or graphs. Our model exploits the intrinsic structures and latent relationships of actions in a hierarchical manner to harness both the compositionality of grammar models and the capability of expressing rich features of DNNs. The proposed model can be readily embodied into a neural network module for efficient optimization in an end-to-end manner. Extensive experiments are conducted on the AVA dataset and the Something-Else task to demonstrate the superiority of our model, meanwhile the interpretability is enhanced through an inference parsing procedure.

In real-world scenarios, typical visual recognition systems could fail under two major causes, i.e., the misclassification between known classes and the excusable misbehavior on unknown-class images. To tackle these deficiencies, flexible visual recognition should dynamically predict multiple classes when they are unconfident between choices and reject making predictions when the input is entirely out of the training distribution. Two challenges emerge along with this novel task. First, prediction uncertainty should be separately quantified as confusion depicting inter-class uncertainties and ignorance identifying out-of-distribution samples. Second, both confusion and ignorance should be comparable between samples to enable effective decision-making. In this paper, we propose to model these two sources of uncertainty explicitly with the theory of Subjective Logic. Regarding recognition as an evidence-collecting process, confusion is then defined as conflicting evidence, while ignorance is the absence of evidence. By predicting Dirichlet concentration parameters for singletons, comprehensive subjective opinions, including confusion and ignorance, could be achieved via further evidence combinations. Through a series of experiments on synthetic data analysis, visual recognition, and open-set detection, we demonstrate the effectiveness of our methods in quantifying two sources of uncertainties and dealing with flexible recognition., Comment: Accepted by ICCV23

Existing losses used in deep metric learning (DML) for image retrieval often lead to highly non-uniform intra-class and inter-class representation structures across test classes and data distributions. When combined with the common practice of using a fixed threshold to declare a match, this gives rise to significant performance variations in terms of false accept rate (FAR) and false reject rate (FRR) across test classes and data distributions. We define this issue in DML as threshold inconsistency. In real-world applications, such inconsistency often complicates the threshold selection process when deploying commercial image retrieval systems. To measure this inconsistency, we propose a novel variance-based metric called Operating-Point-Inconsistency-Score (OPIS) that quantifies the variance in the operating characteristics across classes. Using the OPIS metric, we find that achieving high accuracy levels in a DML model does not automatically guarantee threshold consistency. In fact, our investigation reveals a Pareto frontier in the high-accuracy regime, where existing methods to improve accuracy often lead to degradation in threshold consistency. To address this trade-off, we introduce the Threshold-Consistent Margin (TCM) loss, a simple yet effective regularization technique that promotes uniformity in representation structures across classes by selectively penalizing hard sample pairs. Extensive experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings., Comment: Accepted to ICLR'24

This paper studies the fundamental problem of learning multi-layer generator models. The multi-layer generator model builds multiple layers of latent variables as a prior model on top of the generator, which benefits learning complex data distribution and hierarchical representations. However, such a prior model usually focuses on modeling inter-layer relations between latent variables by assuming non-informative (conditional) Gaussian distributions, which can be limited in model expressivity. To tackle this issue and learn more expressive prior models, we propose an energy-based model (EBM) on the joint latent space over all layers of latent variables with the multi-layer generator as its backbone. Such joint latent space EBM prior model captures the intra-layer contextual relations at each layer through layer-wise energy terms, and latent variables across different layers are jointly corrected. We develop a joint training scheme via maximum likelihood estimation (MLE), which involves Markov Chain Monte Carlo (MCMC) sampling for both prior and posterior distributions of the latent variables from different layers. To ensure efficient inference and learning, we further propose a variational training scheme where an inference model is used to amortize the costly posterior MCMC sampling. Our experiments demonstrate that the learned model can be expressive in generating high-quality images and capturing hierarchical features for better outlier detection.

In deep metric learning for visual recognition, the calibration of distance thresholds is crucial for achieving desired model performance in the true positive rates (TPR) or true negative rates (TNR). However, calibrating this threshold presents challenges in open-world scenarios, where the test classes can be entirely disjoint from those encountered during training. We define the problem of finding distance thresholds for a trained embedding model to achieve target performance metrics over unseen open-world test classes as open-world threshold calibration. Existing posthoc threshold calibration methods, reliant on inductive inference and requiring a calibration dataset with a similar distance distribution as the test data, often prove ineffective in open-world scenarios. To address this, we introduce OpenGCN, a Graph Neural Network-based transductive threshold calibration method with enhanced adaptability and robustness. OpenGCN learns to predict pairwise connectivity for the unlabeled test instances embedded in a graph to determine its TPR and TNR at various distance thresholds, allowing for transductive inference of the distance thresholds which also incorporates test-time information. Extensive experiments across open-world visual recognition benchmarks validate OpenGCN's superiority over existing posthoc calibration methods for open-world threshold calibration.

Large language models (LLMs) have achieved remarkable progress in solving various natural language processing tasks due to emergent reasoning abilities. However, LLMs have inherent limitations as they are incapable of accessing up-to-date information (stored on the Web or in task-specific knowledge bases), using external tools, and performing precise mathematical and logical reasoning. In this paper, we present Chameleon, an AI system that mitigates these limitations by augmenting LLMs with plug-and-play modules for compositional reasoning. Chameleon synthesizes programs by composing various tools (e.g., LLMs, off-the-shelf vision models, web search engines, Python functions, and heuristic-based modules) for accomplishing complex reasoning tasks. At the heart of Chameleon is an LLM-based planner that assembles a sequence of tools to execute to generate the final response. We showcase the effectiveness of Chameleon on two multi-modal knowledge-intensive reasoning tasks: ScienceQA and TabMWP. Chameleon, powered by GPT-4, achieves an 86.54% overall accuracy on ScienceQA, improving the best published few-shot result by 11.37%. On TabMWP, GPT-4-powered Chameleon improves the accuracy by 17.0%, lifting the state of the art to 98.78%. Our analysis also shows that the GPT-4-powered planner exhibits more consistent and rational tool selection via inferring potential constraints from instructions, compared to a ChatGPT-powered planner. The project is available at https://chameleon-llm.github.io., Comment: 32 pages, 10 figures, 24 tables. Accepted to NeurIPS 2023

It is critical that the models pay attention not only to accuracy but also to the certainty of prediction. Uncertain predictions of deep models caused by noisy data raise significant concerns in trustworthy AI areas. To explore and handle uncertainty due to intrinsic data noise, we propose a novel method called ALUM to simultaneously handle the model uncertainty and data uncertainty in a unified scheme. Rather than solely modeling data uncertainty in the ultimate layer of a deep model based on randomly selected training data, we propose to explore mined adversarial triplets to facilitate data uncertainty modeling and non-parametric uncertainty estimations to compensate for the insufficiently trained latent model layers. Thus, the critical data uncertainty and model uncertainty caused by noisy data can be readily quantified for improving model robustness. Our proposed ALUM is model-agnostic which can be easily implemented into any existing deep model with little extra computation overhead. Extensive experiments on various noisy learning tasks validate the superior robustness and generalization ability of our method. The code is released at https://github.com/wwzjer/ALUM., Comment: 10 pages, 5 figures

It is broadly known that deep neural networks are susceptible to being fooled by adversarial examples with perturbations imperceptible by humans. Various defenses have been proposed to improve adversarial robustness, among which adversarial training methods are most effective. However, most of these methods treat the training samples independently and demand a tremendous amount of samples to train a robust network, while ignoring the latent structural information among these samples. In this work, we propose a novel Local Structure Preserving (LSP) regularization, which aims to preserve the local structure of the input space in the learned embedding space. In this manner, the attacking effect of adversarial samples lying in the vicinity of clean samples can be alleviated. We show strong empirical evidence that with or without adversarial training, our method consistently improves the performance of adversarial robustness on several image classification datasets compared to the baselines and some state-of-the-art approaches, thus providing promising direction for future research., Comment: 13 pages, 4 figures

We consider concept generalization at a large scale in the diverse and natural visual spectrum. Established computational modes (i.e., rule-based or similarity-based) are primarily studied isolated and focus on confined and abstract problem spaces. In this work, we study these two modes when the problem space scales up, and the $complexity$ of concepts becomes diverse. Specifically, at the $representational \ level$, we seek to answer how the complexity varies when a visual concept is mapped to the representation space. Prior psychology literature has shown that two types of complexities (i.e., subjective complexity and visual complexity) (Griffiths and Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun and Firestone, 2021). Leveraging Representativeness of Attribute (RoA), we computationally confirm the following observation: Models use attributes with high RoA to describe visual concepts, and the description length falls in an inverted-U relation with the increment in visual complexity. At the $computational \ level$, we aim to answer how the complexity of representation affects the shift between the rule- and similarity-based generalization. We hypothesize that category-conditioned visual modeling estimates the co-occurrence frequency between visual and categorical attributes, thus potentially serving as the prior for the natural visual world. Experimental results show that representations with relatively high subjective complexity outperform those with relatively low subjective complexity in the rule-based generalization, while the trend is the opposite in the similarity-based generalization.

Current learning models often struggle with human-like systematic generalization, particularly in learning compositional rules from limited data and extrapolating them to novel combinations. We introduce the Neural-Symbolic Recursive Machine (NSR), whose core is a Grounded Symbol System (GSS), allowing for the emergence of combinatorial syntax and semantics directly from training data. The NSR employs a modular design that integrates neural perception, syntactic parsing, and semantic reasoning. These components are synergistically trained through a novel deduction-abduction algorithm. Our findings demonstrate that NSR's design, imbued with the inductive biases of equivariance and compositionality, grants it the expressiveness to adeptly handle diverse sequence-to-sequence tasks and achieve unparalleled systematic generalization. We evaluate NSR's efficacy across four challenging benchmarks designed to probe systematic generalization capabilities: SCAN for semantic parsing, PCFG for string manipulation, HINT for arithmetic reasoning, and a compositional machine translation task. The results affirm NSR's superiority over contemporary neural and hybrid models in terms of generalization and transferability., Comment: ICLR 2024. Project website: https://liqing-ustc.github.io/NSR/

Mathematical reasoning, a core ability of human intelligence, presents unique challenges for machines in abstract thinking and logical reasoning. Recent large pre-trained language models such as GPT-3 have achieved remarkable progress on mathematical reasoning tasks written in text form, such as math word problems (MWP). However, it is unknown if the models can handle more complex problems that involve math reasoning over heterogeneous information, such as tabular data. To fill the gap, we present Tabular Math Word Problems (TabMWP), a new dataset containing 38,431 open-domain grade-level problems that require mathematical reasoning on both textual and tabular data. Each question in TabMWP is aligned with a tabular context, which is presented as an image, semi-structured text, and a structured table. There are two types of questions: free-text and multi-choice, and each problem is annotated with gold solutions to reveal the multi-step reasoning process. We evaluate different pre-trained models on TabMWP, including the GPT-3 model in a few-shot setting. As earlier studies suggest, since few-shot GPT-3 relies on the selection of in-context examples, its performance is unstable and can degrade to near chance. The unstable issue is more severe when handling complex problems like TabMWP. To mitigate this, we further propose a novel approach, PromptPG, which utilizes policy gradient to learn to select in-context examples from a small amount of training data and then constructs the corresponding prompt for the test example. Experimental results show that our method outperforms the best baseline by 5.31% on the accuracy metric and reduces the prediction variance significantly compared to random selection, which verifies its effectiveness in selecting in-context examples., Comment: ICLR 2023. 26 pages and 18 figures. The data and code are available at https://promptpg.github.io

Visual Question Answering (VQA) attracts much attention from both industry and academia. As a multi-modality task, it is challenging since it requires not only visual and textual understanding, but also the ability to align cross-modality representations. Previous approaches extensively employ entity-level alignments, such as the correlations between the visual regions and their semantic labels, or the interactions across question words and object features. These attempts aim to improve the cross-modality representations, while ignoring their internal relations. Instead, we propose to apply structured alignments, which work with graph representation of visual and textual content, aiming to capture the deep connections between the visual and textual modalities. Nevertheless, it is nontrivial to represent and integrate graphs for structured alignments. In this work, we attempt to solve this issue by first converting different modality entities into sequential nodes and the adjacency graph, then incorporating them for structured alignments. As demonstrated in our experimental results, such a structured alignment improves reasoning performance. In addition, our model also exhibits better interpretability for each generated answer. The proposed model, without any pretraining, outperforms the state-of-the-art methods on GQA dataset, and beats the non-pretrained state-of-the-art methods on VQA-v2 dataset.

Outside-knowledge visual question answering (OK-VQA) requires the agent to comprehend the image, make use of relevant knowledge from the entire web, and digest all the information to answer the question. Most previous works address the problem by first fusing the image and question in the multi-modal space, which is inflexible for further fusion with a vast amount of external knowledge. In this paper, we call for a paradigm shift for the OK-VQA task, which transforms the image into plain text, so that we can enable knowledge passage retrieval, and generative question-answering in the natural language space. This paradigm takes advantage of the sheer volume of gigantic knowledge bases and the richness of pre-trained language models. A Transform-Retrieve-Generate framework (TRiG) framework is proposed, which can be plug-and-played with alternative image-to-text models and textual knowledge bases. Experimental results show that our TRiG framework outperforms all state-of-the-art supervised methods by at least 11.1% absolute margin.

Is intelligence realized by connectionist or classicist? While connectionist approaches have achieved superhuman performance, there has been growing evidence that such task-specific superiority is particularly fragile in systematic generalization. This observation lies in the central debate between connectionist and classicist, wherein the latter continually advocates an algebraic treatment in cognitive architectures. In this work, we follow the classicist's call and propose a hybrid approach to improve systematic generalization in reasoning. Specifically, we showcase a prototype with algebraic representation for the abstract spatial-temporal reasoning task of Raven's Progressive Matrices (RPM) and present the ALgebra-Aware Neuro-Semi-Symbolic (ALANS) learner. The ALANS learner is motivated by abstract algebra and the representation theory. It consists of a neural visual perception frontend and an algebraic abstract reasoning backend: the frontend summarizes the visual information from object-based representation, while the backend transforms it into an algebraic structure and induces the hidden operator on the fly. The induced operator is later executed to predict the answer's representation, and the choice most similar to the prediction is selected as the solution. Extensive experiments show that by incorporating an algebraic treatment, the ALANS learner outperforms various pure connectionist models in domains requiring systematic generalization. We further show the generative nature of the learned algebraic representation; it can be decoded by isomorphism to generate an answer., Comment: ECCV 2022 paper. Supplementary: http://wellyzhang.github.io/attach/eccv22zhang_alans_supp.pdf Project: http://wellyzhang.github.io/project/alans.html

We present Deep Region Competition (DRC), an algorithm designed to extract foreground objects from images in a fully unsupervised manner. Foreground extraction can be viewed as a special case of generic image segmentation that focuses on identifying and disentangling objects from the background. In this work, we rethink the foreground extraction by reconciling energy-based prior with generative image modeling in the form of Mixture of Experts (MoE), where we further introduce the learned pixel re-assignment as the essential inductive bias to capture the regularities of background regions. With this modeling, the foreground-background partition can be naturally found through Expectation-Maximization (EM). We show that the proposed method effectively exploits the interaction between the mixture components during the partitioning process, which closely connects to region competition, a seminal approach for generic image segmentation. Experiments demonstrate that DRC exhibits more competitive performances on complex real-world data and challenging multi-object scenes compared with prior methods. Moreover, we show empirically that DRC can potentially generalize to novel foreground objects even from categories unseen during training., Comment: NeurIPS 2021

Many emerging applications of intelligent robots need to explore and understand new environments, where it is desirable to detect objects of novel classes on the fly with minimum online efforts. This is an object detection on demand (ODOD) task. It is challenging, because it is impossible to annotate a large number of data on the fly, and the embedded systems are usually unable to perform back-propagation which is essential for training. Most existing few-shot detection methods are confronted here as they need extra training. We propose a novel morphable detector (MD), that simply "morphs" some of its changeable parameters online estimated from the few samples, so as to detect novel classes without any extra training. The MD has two sets of parameters, one for the feature embedding and the other for class representation (called "prototypes"). Each class is associated with a hidden prototype to be learned by integrating the visual and semantic embeddings. The learning of the MD is based on the alternate learning of the feature embedding and the prototypes in an EM-like approach which allows the recovery of an unknown prototype from a few samples of a novel class. Once an MD is learned, it is able to use a few samples of a novel class to directly compute its prototype to fulfill the online morphing process. We have shown the superiority of the MD in Pascal, COCO and FSOD datasets. The code is available https://github.com/Zhaoxiangyun/Morphable-Detector., Comment: ICCV 2021

Existing popular unsupervised embedding learning methods focus on enhancing the instance-level local discrimination of the given unlabeled images by exploring various negative data. However, the existed sample outliers which exhibit large intra-class divergences or small inter-class variations severely limit their learning performance. We justify that the performance limitation is caused by the gradient vanishing on these sample outliers. Moreover, the shortage of positive data and disregard for global discrimination consideration also pose critical issues for unsupervised learning but are always ignored by existing methods. To handle these issues, we propose a novel solution to explicitly model and directly explore the uncertainty of the given unlabeled learning samples. Instead of learning a deterministic feature point for each sample in the embedding space, we propose to represent a sample by a stochastic Gaussian with the mean vector depicting its space localization and covariance vector representing the sample uncertainty. We leverage such uncertainty modeling as momentum to the learning which is helpful to tackle the outliers. Furthermore, abundant positive candidates can be readily drawn from the learned instance-specific distributions which are further adopted to mitigate the aforementioned issues. Thorough rationale analyses and extensive experiments are presented to verify our superiority., Comment: 14 pages, in submission

How to effectively represent camera pose is an essential problem in 3D computer vision, especially in tasks such as camera pose regression and novel view synthesis. Traditionally, 3D position of the camera is represented by Cartesian coordinate and the orientation is represented by Euler angle or quaternions. These representations are manually designed, which may not be the most effective representation for downstream tasks. In this work, we propose an approach to learn neural representations of camera poses and 3D scenes, coupled with neural representations of local camera movements. Specifically, the camera pose and 3D scene are represented as vectors and the local camera movement is represented as a matrix operating on the vector of the camera pose. We demonstrate that the camera movement can further be parametrized by a matrix Lie algebra that underlies a rotation system in the neural space. The vector representations are then concatenated and generate the posed 2D image through a decoder network. The model is learned from only posed 2D images and corresponding camera poses, without access to depths or shapes. We conduct extensive experiments on synthetic and real datasets. The results show that compared with other camera pose representations, our learned representation is more robust to noise in novel view synthesis and more effective in camera pose regression.

Predicting agents' future trajectories plays a crucial role in modern AI systems, yet it is challenging due to intricate interactions exhibited in multi-agent systems, especially when it comes to collision avoidance. To address this challenge, we propose to learn congestion patterns as contextual cues explicitly and devise a novel "Sense--Learn--Reason--Predict" framework by exploiting advantages of three different doctrines of thought, which yields the following desirable benefits: (i) Representing congestion as contextual cues via latent factors subsumes the concept of social force commonly used in physics-based approaches and implicitly encodes the distance as a cost, similar to the way a planning-based method models the environment. (ii) By decomposing the learning phases into two stages, a "student" can learn contextual cues from a "teacher" while generating collision-free trajectories. To make the framework computationally tractable, we formulate it as an optimization problem and derive an upper bound by leveraging the variational parametrization. In experiments, we demonstrate that the proposed model is able to generate collision-free trajectory predictions in a synthetic dataset designed for collision avoidance evaluation and remains competitive on the commonly used NGSIM US-101 highway dataset., Comment: ICRA 2021 paper. Project: https://xuxie1031.github.io/projects/GTA/GTAProj.html

HDR reconstruction is an important task in computer vision with many industrial needs. The traditional approaches merge multiple exposure shots to generate HDRs that correspond to the physical quantity of illuminance of the scene. However, the tedious capturing process makes such multi-shot approaches inconvenient in practice. In contrast, recent single-shot methods predict a visually appealing HDR from a single LDR image through deep learning. But it is not clear whether the previously mentioned physical properties would still hold, without training the network to explicitly model them. In this paper, we introduce the physical illuminance constraints to our single-shot HDR reconstruction framework, with a focus on spherical panoramas. By the proposed physical regularization, our method can generate HDRs which are not only visually appealing but also physically plausible. For evaluation, we collect a large dataset of LDR and HDR images with ground truth illuminance measures. Extensive experiments show that our HDR images not only maintain high visual quality but also top all baseline methods in illuminance prediction accuracy.

This paper studies the unsupervised cross-domain translation problem by proposing a generative framework, in which the probability distribution of each domain is represented by a generative cooperative network that consists of an energy-based model and a latent variable model. The use of generative cooperative network enables maximum likelihood learning of the domain model by MCMC teaching, where the energy-based model seeks to fit the data distribution of domain and distills its knowledge to the latent variable model via MCMC. Specifically, in the MCMC teaching process, the latent variable model parameterized by an encoder-decoder maps examples from the source domain to the target domain, while the energy-based model further refines the mapped results by Langevin revision such that the revised results match to the examples in the target domain in terms of the statistical properties, which are defined by the learned energy function. For the purpose of building up a correspondence between two unpaired domains, the proposed framework simultaneously learns a pair of cooperative networks with cycle consistency, accounting for a two-way translation between two domains, by alternating MCMC teaching. Experiments show that the proposed framework is useful for unsupervised image-to-image translation and unpaired image sequence translation., Comment: The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI) 2021

Inspired by humans' exceptional ability to master arithmetic and generalize to new problems, we present a new dataset, Handwritten arithmetic with INTegers (HINT), to examine machines' capability of learning generalizable concepts at three levels: perception, syntax, and semantics. In HINT, machines are tasked with learning how concepts are perceived from raw signals such as images (i.e., perception), how multiple concepts are structurally combined to form a valid expression (i.e., syntax), and how concepts are realized to afford various reasoning tasks (i.e., semantics), all in a weakly supervised manner. Focusing on systematic generalization, we carefully design a five-fold test set to evaluate both the interpolation and the extrapolation of learned concepts w.r.t. the three levels. Further, we design a few-shot learning split to determine whether or not models can rapidly learn new concepts and generalize them to more complex scenarios. To comprehend existing models' limitations, we undertake extensive experiments with various sequence-to-sequence models, including RNNs, Transformers, and GPT-3 (with the chain of thought prompting). The results indicate that current models struggle to extrapolate to long-range syntactic dependency and semantics. Models exhibit a considerable gap toward human-level generalization when evaluated with new concepts in a few-shot setting. Moreover, we discover that it is infeasible to solve HINT by merely scaling up the dataset and the model size; this strategy contributes little to the extrapolation of syntax and semantics. Finally, in zero-shot GPT-3 experiments, the chain of thought prompting exhibits impressive results and significantly boosts the test accuracy. We believe the HINT dataset and the experimental findings are of great interest to the learning community on systematic generalization., Comment: ICLR 2023. website: https://liqing-ustc.github.io/HINT

3D data that contains rich geometry information of objects and scenes is valuable for understanding 3D physical world. With the recent emergence of large-scale 3D datasets, it becomes increasingly crucial to have a powerful 3D generative model for 3D shape synthesis and analysis. This paper proposes a deep 3D energy-based model to represent volumetric shapes. The maximum likelihood training of the model follows an "analysis by synthesis" scheme. The benefits of the proposed model are six-fold: first, unlike GANs and VAEs, the model training does not rely on any auxiliary models; second, the model can synthesize realistic 3D shapes by Markov chain Monte Carlo (MCMC); third, the conditional model can be applied to 3D object recovery and super resolution; fourth, the model can serve as a building block in a multi-grid modeling and sampling framework for high resolution 3D shape synthesis; fifth, the model can be used to train a 3D generator via MCMC teaching; sixth, the unsupervisedly trained model provides a powerful feature extractor for 3D data, which is useful for 3D object classification. Experiments demonstrate that the proposed model can generate high-quality 3D shape patterns and can be useful for a wide variety of 3D shape analysis., Comment: 16 pages. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI) 2020. arXiv admin note: substantial text overlap with arXiv:1804.00586

Collecting labeled data for the task of semantic segmentation is expensive and time-consuming, as it requires dense pixel-level annotations. While recent Convolutional Neural Network (CNN) based semantic segmentation approaches have achieved impressive results by using large amounts of labeled training data, their performance drops significantly as the amount of labeled data decreases. This happens because deep CNNs trained with the de facto cross-entropy loss can easily overfit to small amounts of labeled data. To address this issue, we propose a simple and effective contrastive learning-based training strategy in which we first pretrain the network using a pixel-wise, label-based contrastive loss, and then fine-tune it using the cross-entropy loss. This approach increases intra-class compactness and inter-class separability, thereby resulting in a better pixel classifier. We demonstrate the effectiveness of the proposed training strategy using the Cityscapes and PASCAL VOC 2012 segmentation datasets. Our results show that pretraining with the proposed contrastive loss results in large performance gains (more than 20% absolute improvement in some settings) when the amount of labeled data is limited. In many settings, the proposed contrastive pretraining strategy, which does not use any additional data, is able to match or outperform the widely-used ImageNet pretraining strategy that uses more than a million additional labeled images., Comment: International Conference on Computer Vision (ICCV), 2021

Given multiple datasets with different label spaces, the goal of this work is to train a single object detector predicting over the union of all the label spaces. The practical benefits of such an object detector are obvious and significant application-relevant categories can be picked and merged form arbitrary existing datasets. However, naive merging of datasets is not possible in this case, due to inconsistent object annotations. Consider an object category like faces that is annotated in one dataset, but is not annotated in another dataset, although the object itself appears in the latter images. Some categories, like face here, would thus be considered foreground in one dataset, but background in another. To address this challenge, we design a framework which works with such partial annotations, and we exploit a pseudo labeling approach that we adapt for our specific case. We propose loss functions that carefully integrate partial but correct annotations with complementary but noisy pseudo labels. Evaluation in the proposed novel setting requires full annotation on the test set. We collect the required annotations and define a new challenging experimental setup for this task based one existing public datasets. We show improved performances compared to competitive baselines and appropriate adaptations of existing work., Comment: To appear in ECCV 2020, project page http://www.nec-labs.com/~mas/UniDet/

Recent deep learning based video synthesis approaches, in particular with applications that can forge identities such as "DeepFake", have raised great security concerns. Therefore, corresponding deep forensic methods are proposed to tackle this problem. However, existing methods are either based on unexplainable deep networks which greatly degrades the principal interpretability factor to media forensic, or rely on fragile image statistics such as noise pattern, which in real-world scenarios can be easily deteriorated by data compression. In this paper, we propose an fully-interpretable video forensic method that is designed specifically to expose deep-faked videos. To enhance generalizability on videos with various content, we model the temporal motion of multiple specific spatial locations in the videos to extract a robust and reliable representation, called Co-Motion Pattern. Such kind of conjoint pattern is mined across local motion features which is independent of the video contents so that the instance-wise variation can also be largely alleviated. More importantly, our proposed co-motion pattern possesses both superior interpretability and sufficient robustness against data compression for deep-faked videos. We conduct extensive experiments to empirically demonstrate the superiority and effectiveness of our approach under both classification and anomaly detection evaluation settings against the state-of-the-art deep forensic methods.

Assessing action quality from videos has attracted growing attention in recent years. Most existing approaches usually tackle this problem based on regression algorithms, which ignore the intrinsic ambiguity in the score labels caused by multiple judges or their subjective appraisals. To address this issue, we propose an uncertainty-aware score distribution learning (USDL) approach for action quality assessment (AQA). Specifically, we regard an action as an instance associated with a score distribution, which describes the probability of different evaluated scores. Moreover, under the circumstance where fine-grained score labels are available (e.g., difficulty degree of an action or multiple scores from different judges), we further devise a multi-path uncertainty-aware score distributions learning (MUSDL) method to explore the disentangled components of a score. We conduct experiments on three AQA datasets containing various Olympic actions and surgical activities, where our approaches set new state-of-the-arts under the Spearman's Rank Correlation., Comment: CVPR2020

The goal of neural-symbolic computation is to integrate the connectionist and symbolist paradigms. Prior methods learn the neural-symbolic models using reinforcement learning (RL) approaches, which ignore the error propagation in the symbolic reasoning module and thus converge slowly with sparse rewards. In this paper, we address these issues and close the loop of neural-symbolic learning by (1) introducing the \textbf{grammar} model as a \textit{symbolic prior} to bridge neural perception and symbolic reasoning, and (2) proposing a novel \textbf{back-search} algorithm which mimics the top-down human-like learning procedure to propagate the error through the symbolic reasoning module efficiently. We further interpret the proposed learning framework as maximum likelihood estimation using Markov chain Monte Carlo sampling and the back-search algorithm as a Metropolis-Hastings sampler. The experiments are conducted on two weakly-supervised neural-symbolic tasks: (1) handwritten formula recognition on the newly introduced HWF dataset; (2) visual question answering on the CLEVR dataset. The results show that our approach significantly outperforms the RL methods in terms of performance, converging speed, and data efficiency. Our code and data are released at \url{https://liqing-ustc.github.io/NGS}., Comment: ICML 2020. Project page: https://liqing-ustc.github.io/NGS

This paper proposes a joint training method to learn both the variational auto-encoder (VAE) and the latent energy-based model (EBM). The joint training of VAE and latent EBM are based on an objective function that consists of three Kullback-Leibler divergences between three joint distributions on the latent vector and the image, and the objective function is of an elegant symmetric and anti-symmetric form of divergence triangle that seamlessly integrates variational and adversarial learning. In this joint training scheme, the latent EBM serves as a critic of the generator model, while the generator model and the inference model in VAE serve as the approximate synthesis sampler and inference sampler of the latent EBM. Our experiments show that the joint training greatly improves the synthesis quality of the VAE. It also enables learning of an energy function that is capable of detecting out of sample examples for anomaly detection.

Recent progress in deep learning is essentially based on a "big data for small tasks" paradigm, under which massive amounts of data are used to train a classifier for a single narrow task. In this paper, we call for a shift that flips this paradigm upside down. Specifically, we propose a "small data for big tasks" paradigm, wherein a single artificial intelligence (AI) system is challenged to develop "common sense", enabling it to solve a wide range of tasks with little training data. We illustrate the potential power of this new paradigm by reviewing models of common sense that synthesize recent breakthroughs in both machine and human vision. We identify functionality, physics, intent, causality, and utility (FPICU) as the five core domains of cognitive AI with humanlike common sense. When taken as a unified concept, FPICU is concerned with the questions of "why" and "how", beyond the dominant "what" and "where" framework for understanding vision. They are invisible in terms of pixels but nevertheless drive the creation, maintenance, and development of visual scenes. We therefore coin them the "dark matter" of vision. Just as our universe cannot be understood by merely studying observable matter, we argue that vision cannot be understood without studying FPICU. We demonstrate the power of this perspective to develop cognitive AI systems with humanlike common sense by showing how to observe and apply FPICU with little training data to solve a wide range of challenging tasks, including tool use, planning, utility inference, and social learning. In summary, we argue that the next generation of AI must embrace "dark" humanlike common sense for solving novel tasks., Comment: For high quality figures, please refer to http://wellyzhang.github.io/attach/dark.pdf

We propose a generative model of unordered point sets, such as point clouds, in the form of an energy-based model, where the energy function is parameterized by an input-permutation-invariant bottom-up neural network. The energy function learns a coordinate encoding of each point and then aggregates all individual point features into an energy for the whole point cloud. We call our model the Generative PointNet because it can be derived from the discriminative PointNet. Our model can be trained by MCMC-based maximum likelihood learning (as well as its variants), without the help of any assisting networks like those in GANs and VAEs. Unlike most point cloud generators that rely on hand-crafted distance metrics, our model does not require any hand-crafted distance metric for the point cloud generation, because it synthesizes point clouds by matching observed examples in terms of statistical properties defined by the energy function. Furthermore, we can learn a short-run MCMC toward the energy-based model as a flow-like generator for point cloud reconstruction and interpolation. The learned point cloud representation can be useful for point cloud classification. Experiments demonstrate the advantages of the proposed generative model of point clouds.

This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the following traits. (1) The update of the energy-based model is based on noise contrastive estimation, with the flow model serving as a strong noise distribution. (2) The update of the flow model approximately minimizes the Jensen-Shannon divergence between the flow model and the data distribution. (3) Unlike generative adversarial networks (GAN) which estimates an implicit probability distribution defined by a generator model, our method estimates two explicit probabilistic distributions on the data. Using the proposed method we demonstrate a significant improvement on the synthesis quality of the flow model, and show the effectiveness of unsupervised feature learning by the learned energy-based model. Furthermore, the proposed training method can be easily adapted to semi-supervised learning. We achieve competitive results to the state-of-the-art semi-supervised learning methods.

Dynamic patterns are characterized by complex spatial and motion patterns. Understanding dynamic patterns requires a disentangled representational model that separates the factorial components. A commonly used model for dynamic patterns is the state space model, where the state evolves over time according to a transition model and the state generates the observed image frames according to an emission model. To model the motions explicitly, it is natural for the model to be based on the motions or the displacement fields of the pixels. Thus in the emission model, we let the hidden state generate the displacement field, which warps the trackable component in the previous image frame to generate the next frame while adding a simultaneously emitted residual image to account for the change that cannot be explained by the deformation. The warping of the previous image is about the trackable part of the change of image frame, while the residual image is about the intrackable part of the image. We use a maximum likelihood algorithm to learn the model that iterates between inferring latent noise vectors that drive the transition model and updating the parameters given the inferred latent vectors. Meanwhile we adopt a regularization term to penalize the norms of the residual images to encourage the model to explain the change of image frames by trackable motion. Unlike existing methods on dynamic patterns, we learn our model in unsupervised setting without ground truth displacement fields. In addition, our model defines a notion of intrackability by the separation of warped component and residual component in each image frame. We show that our method can synthesize realistic dynamic pattern, and disentangling appearance, trackable and intrackable motions. The learned models are useful for motion transfer, and it is natural to adopt it to define and measure intrackability of a dynamic pattern.

Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are non-stationary in either spatial or temporal domain. We show that an energy-based spatial-temporal generative ConvNet can be used to model and synthesize dynamic patterns. The model defines a probability distribution on the video sequence, and the log probability is defined by a spatial-temporal ConvNet that consists of multiple layers of spatial-temporal filters to capture spatial-temporal patterns of different scales. The model can be learned from the training video sequences by an "analysis by synthesis" learning algorithm that iterates the following two steps. Step 1 synthesizes video sequences from the currently learned model. Step 2 then updates the model parameters based on the difference between the synthesized video sequences and the observed training sequences. We show that the learning algorithm can synthesize realistic dynamic patterns. We also show that it is possible to learn the model from incomplete training sequences with either occluded pixels or missing frames, so that model learning and pattern completion can be accomplished simultaneously.

This paper proposes to learn hierarchical compositional AND-OR model for interpretable image synthesis by sparsifying the generator network. The proposed method adopts the scene-objects-parts-subparts-primitives hierarchy in image representation. A scene has different types (i.e., OR) each of which consists of a number of objects (i.e., AND). This can be recursively formulated across the scene-objects-parts-subparts hierarchy and is terminated at the primitive level (e.g., wavelets-like basis). To realize this AND-OR hierarchy in image synthesis, we learn a generator network that consists of the following two components: (i) Each layer of the hierarchy is represented by an over-complete set of convolutional basis functions. Off-the-shelf convolutional neural architectures are exploited to implement the hierarchy. (ii) Sparsity-inducing constraints are introduced in end-to-end training, which induces a sparsely activated and sparsely connected AND-OR model from the initially densely connected generator network. A straightforward sparsity-inducing constraint is utilized, that is to only allow the top-$k$ basis functions to be activated at each layer (where $k$ is a hyper-parameter). The learned basis functions are also capable of image reconstruction to explain the input images. In experiments, the proposed method is tested on four benchmark datasets. The results show that meaningful and interpretable hierarchical representations are learned with better qualities of image synthesis and reconstruction obtained than baselines., Comment: This is the CVPR version

Recognizing attributes of objects and their parts is important to many computer vision applications. Although great progress has been made to apply object-level recognition, recognizing the attributes of parts remains less applicable since the training data for part attributes recognition is usually scarce especially for internet-scale applications. Furthermore, most existing part attribute recognition methods rely on the part annotation which is more expensive to obtain. To solve the data insufficiency problem and get rid of dependence on the part annotation, we introduce a novel Concept Sharing Network (CSN) for part attribute recognition. A great advantage of CSN is its capability of recognizing the part attribute (a combination of part location and appearance pattern) that has insufficient or zero training data, by learning the part location and appearance pattern respectively from the training data that usually mix them in a single label. Extensive experiments on CUB-200-2011 [51], CelebA [35] and a newly proposed human attribute dataset demonstrate the effectiveness of CSN and its advantages over other methods, especially for the attributes with few training samples. Further experiments show that CSN can also perform zero-shot part attribute recognition. The code will be made available at https://github.com/Zhaoxiangyun/Concept-Sharing-Network., Comment: To appear in ICCV 2019

Mutual calibration between color and depth cameras is a challenging topic in multi-modal data registration. In this paper, we are confronted with a "Bimodal Stereo" problem, which aims to solve camera pose from a pair of an uncalibrated color image and a depth map from different views automatically. To address this problem, an iterative Shape-from-Shading (SfS) based framework is proposed to estimate shape and pose simultaneously. In the pipeline, the estimated shape is refined by the shape prior from the given depth map under the estimated pose. Meanwhile, the estimated pose is improved by the registration of estimated shape and shape from given depth map. We also introduce a shading based refinement in the pipeline to address noisy depth map with holes. Extensive experiments showed that through our method, both the depth map, the recovered shape as well as its pose can be desirably refined and recovered., Comment: Preprinted version on May 15, 2019

Accurate prediction of others' trajectories is essential for autonomous driving. Trajectory prediction is challenging because it requires reasoning about agents' past movements, social interactions among varying numbers and kinds of agents, constraints from the scene context, and the stochasticity of human behavior. Our approach models these interactions and constraints jointly within a novel Multi-Agent Tensor Fusion (MATF) network. Specifically, the model encodes multiple agents' past trajectories and the scene context into a Multi-Agent Tensor, then applies convolutional fusion to capture multiagent interactions while retaining the spatial structure of agents and the scene context. The model decodes recurrently to multiple agents' future trajectories, using adversarial loss to learn stochastic predictions. Experiments on both highway driving and pedestrian crowd datasets show that the model achieves state-of-the-art prediction accuracy., Comment: Presented in CVPR 19: http://openaccess.thecvf.com/content_CVPR_2019/html/Zhao_Multi-Agent_Tensor_Fusion_for_Contextual_Trajectory_Prediction_CVPR_2019_paper.html ; Architecture details available: https://github.com/programmingLearner/MATF-architecture-details

This study investigates the effects of Markov chain Monte Carlo (MCMC) sampling in unsupervised Maximum Likelihood (ML) learning. Our attention is restricted to the family of unnormalized probability densities for which the negative log density (or energy function) is a ConvNet. We find that many of the techniques used to stabilize training in previous studies are not necessary. ML learning with a ConvNet potential requires only a few hyper-parameters and no regularization. Using this minimal framework, we identify a variety of ML learning outcomes that depend solely on the implementation of MCMC sampling. On one hand, we show that it is easy to train an energy-based model which can sample realistic images with short-run Langevin. ML can be effective and stable even when MCMC samples have much higher energy than true steady-state samples throughout training. Based on this insight, we introduce an ML method with purely noise-initialized MCMC, high-quality short-run synthesis, and the same budget as ML with informative MCMC initialization such as CD or PCD. Unlike previous models, our energy model can obtain realistic high-diversity samples from a noise signal after training. On the other hand, ConvNet potentials learned with non-convergent MCMC do not have a valid steady-state and cannot be considered approximate unnormalized densities of the training data because long-run MCMC samples differ greatly from observed images. We show that it is much harder to train a ConvNet potential to learn a steady-state over realistic images. To our knowledge, long-run MCMC samples of all previous models lose the realism of short-run samples. With correct tuning of Langevin noise, we train the first ConvNet potentials for which long-run and steady-state MCMC samples are realistic images., Comment: Code available at: https://github.com/point0bar1/ebm-anatomy

Visual Query Answering (VQA) is of great significance in offering people convenience: one can raise a question for details of objects, or high-level understanding about the scene, over an image. This paper proposes a novel method to address the VQA problem. In contrast to prior works, our method that targets single scene VQA, replies on graph-based techniques and involves reasoning. In a nutshell, our approach is centered on three graphs. The first graph, referred to as inference graph GI , is constructed via learning over labeled data. The other two graphs, referred to as query graph Q and entity-attribute graph GEA, are generated from natural language query Qnl and image Img, that are issued from users, respectively. As GEA often does not take sufficient information to answer Q, we develop techniques to infer missing information of GEA with GI . Based on GEA and Q, we provide techniques to find matches of Q in GEA, as the answer of Qnl in Img. Unlike commonly used VQA methods that are based on end-to-end neural networks, our graph-based method shows well-designed reasoning capability, and thus is highly interpretable. We also create a dataset on soccer match (Soccer-VQA) with rich annotations. The experimental results show that our approach outperforms the state-of-the-art method and has high potential for future investigation.

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the following two components: (1) the vector representations of local contents of images and (2) the matrix representations of local pixel displacements caused by the relative motions between the agent and the objects in the 3D scene. When the image frame undergoes changes due to local pixel displacements, the vectors are multiplied by the matrices that represent the local displacements. Thus the vector representation is equivariant as it varies according to the local displacements. Our experiments show that our model can learn Gabor-like filter pairs of quadrature phases. The profiles of the learned filters match those of simple cells in Macaque V1. Moreover, we demonstrate that the model can learn to infer local motions in either a supervised or unsupervised manner. With such a simple model, we achieve competitive results on optical flow estimation.

We introduce an explainable generative model by applying sparse operation on the feature maps of the generator network. Meaningful hierarchical representations are obtained using the proposed generative model with sparse activations. The convolutional kernels from the bottom layer to the top layer of the generator network can learn primitives such as edges and colors, object parts, and whole objects layer by layer. From the perspective of the generator network, we propose a method for inducing both sparse coding and the AND-OR grammar for images. Experiments show that our method is capable of learning meaningful and explainable hierarchical representations., Comment: In AAAI-19 Workshop on Network Interpretability for Deep Learning