Boyan Duan, Xiao Liang, Shuai Lu, Yaoxiang Wang, Yelong Shen, Kai-Wei Chang, Ying Nian Wu, Mao Yang, Weizhu Chen, Yeyun Gong. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Eric Hanchen Jiang, Levina Li, Frank Wan, Xiao Liang, Sophia Yin, Yuchen Wu, Xinfeng Li, Yizhou Sun, Wei Wang, Kai-Wei Chang, Ying Nian Wu. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Eric Hanchen Jiang, Weixuan Ou, Run Liu, Shengyuan Pang, Guancheng Wan, Ranjie Duan, Wei Dong, Kai-Wei Chang, XiaoFeng Wang, Ying Nian Wu, Xinfeng Li. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Xiao Liang, Zhong-Zhi Li, Zhenghao Lin, Eric Hanchen Jiang, Hengyuan Zhang, Yelong Shen, Kai-Wei Chang, Ying Nian Wu, Yeyun Gong, Weizhu Chen. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

Zhou Ziheng, Huacong Tang, Mingjie Bi, Wanying He, Fang Sun, Yizhou Sun, Ying Nian Wu, Demetri Terzopoulos, Yipeng Kang, Fangwei Zhong. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

As long-context language modeling becomes increasingly important, the cost of maintaining and attending to large Key/Value (KV) caches grows rapidly, becoming a major bottleneck in both training and inference. While prior works such as Multi-Query Attention (MQA) and Multi-Latent Attention (MLA) reduce memory by sharing or compressing KV features, they often trade off representation quality or incur runtime overhead. We propose Memory-Keyed Attention (MKA), a hierarchical attention mechanism that integrates multi-level KV caches—local, session, and long-term—and learns to route attention across them dynamically. We further introduce Route-Fused MKA (FastMKA), a broadcast-routed variant that fuses memory sources before attention computation for enhanced efficiency. Experiments on different sequence lengths show that FastMKA achieves a favorable accuracy-efficiency trade-off: comparable perplexity to MLA while achieving up to 5 × faster training throughput and 1.8 × lower evaluation latency. These results highlight MKA as a practical and extensible framework for efficient long-context attention.

This paper focuses on the newly emerged research topic, i.e., whether the complex decision-making logic of a DNN can be mathematically summarized into a few simple logics. Beyond the explanation of a static DNN, in this paper, we hope to show that the seemingly complex learning dynamics of a DNN can be faithfully represented as the change of a few primitive interaction patterns encoded by the DNN. Therefore, we redefine the interaction of principal feature components in intermediate-layer features, which enables us to concisely summarize the highly complex dynamics of interactions throughout the learning of the DNN. The mathematical faithfulness of the new interaction is experimentally verified. From the perspective of learning efficiency, we find that the interactions naturally belong to five groups (reliable, withdrawn, forgotten, betraying, and fluctuating interactions), each representing a distinct type of dynamics of an interaction being learned and/or being forgotten. This provides deep insights into the learning process of a DNN.

The recent progress in Vision-Language Models (VLMs) has broadened the scope of multimodal applications. However, evaluations often remain limited to functional tasks, neglecting abstract dimensions such as personality traits and human values. To address this gap, we introduce Value-Spectrum, a novel Visual Question Answering (VQA) benchmark aimed at assessing VLMs based on Schwartz’s value dimensions that capture core human values guiding people’s preferences and actions. We design a VLM agent pipeline to simulate video browsing and construct a vector database comprising over 50,000 short videos from TikTok, YouTube Shorts, and Instagram Reels. These videos span multiple months and cover diverse topics, including family, health, hobbies, society, technology, etc. Benchmarking on Value-Spectrum highlights notable variations in how VLMs handle value-oriented content. Beyond identifying VLMs’ intrinsic preferences, we also explore the ability of VLM agents to adopt specific personas when explicitly prompted, revealing insights into the adaptability of the model in role-playing scenarios. These findings highlight the potential of Value-Spectrum as a comprehensive evaluation set for tracking VLM preferences in value-based tasks and abilities to simulate diverse personas. The complete code and data are available at https://github.com/Jeremyyny/Value-Spectrum.

The rapid development of AI highlights the pressing need for sustainable energy, a critical global challenge for decades. Nuclear fusion, generally seen as a promising solution, has been the focus of intensive research for nearly a century, with investments reaching hundreds of billions of dollars. Recent advancements in Inertial Confinement Fusion (ICF) have drawn significant attention to fusion research, in which Laser-Plasma Interaction (LPI) is critical for ensuring fusion stability and efficiency. However, the complexity of LPI makes analytical approaches impractical, leaving researchers dependent on extremely computationally intensive Particle-in-Cell (PIC) simulations to generate data, posing a significant bottleneck to the advancement of fusion research. In response, this work introduces Diff-PIC, a novel framework that leverages conditional diffusion models as a computationally efficient alternative to PIC simulations for generating high-fidelity scientific LPI data. In this work, physical patterns captured by PIC simulations are distilled into diffusion models associated with two tailored enhancements: (1) To effectively capture the complex relationships between physical parameters and their corresponding outcomes, the parameters are encoded in a physically informed manner. (2) To further enhance efficiency while maintaining physical validity, the rectified flow technique is employed to transform our model into a one-step conditional diffusion model. Experimental results show that Diff-PIC achieves a $\sim$16,200$\times$ speedup compared to traditional PIC on a 100 picosecond simulation, while delivering superior accuracy compared to other data generation approaches.

Human beings are endowed with a complementary learning system, which bridges the slow learning of general world dynamics with fast storage of episodic memory from a new experience. Previous video generation models, however, primarily focus on slow learning by pre-training on vast amounts of data, overlooking the fast learning phase crucial for episodic memory storage. This oversight leads to inconsistencies across temporally distant frames when generating longer videos, as these frames fall beyond the model's context window. To this end, we introduce SlowFast-VGen, a novel dual-speed learning system for action-driven long video generation. Our approach incorporates a masked conditional video diffusion model for the slow learning of world dynamics, alongside an inference-time fast learning strategy based on a temporal LoRA module. Specifically, the fast learning process updates its temporal LoRA parameters based on local inputs and outputs, thereby efficiently storing episodic memory in its parameters. We further propose a slow-fast learning loop algorithm that seamlessly integrates the inner fast learning loop into the outer slow learning loop, enabling the recall of prior multi-episode experiences for context-aware skill learning. To facilitate the slow learning of an approximate world model, we collect a large-scale dataset of 200k videos with language action annotations, covering a wide range of scenarios. Extensive experiments show that SlowFast-VGen outperforms baselines across various metrics for action-driven video generation, achieving an FVD score of 514 compared to 782, and maintaining consistency in longer videos, with an average of 0.37 scene cuts versus 0.89. The slow-fast learning loop algorithm significantly enhances performances on long-horizon planning tasks as well.

The training of large language models (LLMs) faces significant computational cost challenges, limiting their scalability toward artificial general intelligence (AGI) and broader adoption. With model sizes doubling approximately every 3.4 months and training costs escalating from 64 million USD for GPT-4 in 2020 to 191 million USD for Gemini Ultra in 2023, the economic burden has become unsustainable. While techniques such as quantization offer incremental improvements, they fail to address the fundamental computational bottleneck. In this work, we introduce DS-LLM, a novel framework that leverages dynamical system (DS)-based machines, which exploit Natural Annealing to rapidly converge to minimal energy states, yielding substantial efficiency gains. Unlike traditional methods, DS-LLM maps LLM components to optimization problems solvable via Hamiltonian configurations and utilizes continuous electric current flow in DS-machines for hardware-native gradient descent during training. We mathematically demonstrate the equivalence between conventional LLMs and DS-LLMs and present a method for transforming a trained LLM into a DS-LLM. Experimental evaluations across multiple model sizes demonstrate orders-of-magnitude improvements in speed and energy efficiency for both training and inference while maintaining consistent accuracy. Additionally, we provide an in-depth analysis of the challenges and potential solutions associated with this emerging computing paradigm, aiming to lay a solid foundation for future research.

Achieving human-level intelligence requires refining cognitive distinctions between \textit{System 1} and \textit{System 2} thinking. While contemporary AI, driven by large language models, demonstrates human-like traits, it falls short of genuine cognition. Transitioning from structured benchmarks to real-world scenarios presents challenges for visual agents, often leading to inaccurate and overly confident responses. To address the challenge, we introduce \textbf{\textsc{FaST}}, which incorporates the \textbf{Fa}st and \textbf{S}low \textbf{T}hinking mechanism into visual agents. \textsc{FaST} employs a switch adapter to dynamically select between \textit{System 1/2} modes, tailoring the problem-solving approach to different task complexity. It tackles uncertain and unseen objects by adjusting model confidence and integrating new contextual data. With this novel design, we advocate a \textit{flexible system}, \textit{hierarchical reasoning} capabilities, and a \textit{transparent decision-making} pipeline, all of which contribute to its ability to emulate human-like cognitive processes in visual intelligence. Empirical results demonstrate that \textsc{FaST} outperforms various well-known baselines, achieving 80.8\% accuracy over $VQA^{v2}$ for visual question answering and 48.7\% $GIoU$ score over ReasonSeg for reasoning segmentation, demonstrate \textsc{FaST}'s superior performance. Extensive testing validates the efficacy and robustness of \textsc{FaST}'s core components, showcasing its potential to advance the development of cognitive visual agents in AI systems.

This paper investigates the conformal isometry hypothesis as a potential explanation for the hexagonal periodic patterns in grid cell response maps. We posit that grid cell activities form a high-dimensional vector in neural space, encoding the agent's position in 2D physical space. As the agent moves, this vector rotates within a 2D manifold in the neural space, driven by a recurrent neural network. The conformal hypothesis proposes that this neural manifold is a conformal isometric embedding of 2D physical space, where local physical distance is preserved by the embedding up to a scaling factor (or unit of metric). Such distance-preserving position embedding is indispensable for path planning in navigation, especially planning local straight path segments. We conduct numerical experiments to show that this hypothesis leads to the hexagonal grid firing patterns by learning maximally distance-preserving position embedding, agnostic to the choice of the recurrent neural network. Furthermore, we present a theoretical explanation of why hexagon periodic patterns emerge by minimizing our loss function by showing that hexagon flat torus is maximally distance preserving.

Function learning forms the foundation of numerous scientific and engineering tasks. While modern machine learning (ML) methods model complex functions effectively, their escalating complexity and computational demands pose challenges to efficient deployment. In contrast, natural dynamical systems exhibit remarkable computational efficiency in representing and solving complex functions. However, existing dynamical system approaches are limited by low expressivity and inefficient training. To this end, we propose EADS, an Expressive and self-Adaptive Dynamical System capable of accurately learning a wide spectrum of functions with extraordinary efficiency. Specifically, (1) drawing inspiration from biological dynamical systems, we integrate hierarchical architectures and heterogeneous dynamics into EADS, significantly enhancing its capacity to represent complex functions. (2) We propose an on-device training method that leverages intrinsic electrical signals to update parameters, making EADS self-adaptive with exceptional efficiency. Experimental results across diverse domains demonstrate that EADS achieves higher accuracy than existing works, while offering orders-of-magnitude speedups over traditional neural network solutions on GPUs for both inference and training, showcasing its broader impact in overcoming computational bottlenecks across various fields.

We propose a novel class of language models, Latent Thought Models (LTMs), which incorporate explicit latent thought vectors that follow an explicit prior model in latent space. These latent thought vectors guide the autoregressive generation of ground tokens through a Transformer decoder. Training employs a dual-rate optimization process within the classical variational Bayes framework: fast learning of local variational parameters for the posterior distribution of latent vectors (inference-time computation), and slow learning of global decoder parameters. Empirical studies reveal that LTMs possess additional scaling dimensions beyond traditional Large Language Models (LLMs), such as the number of iterations in inference-time computation and number of latent thought vectors. Higher sample efficiency can be achieved by increasing training compute per token, with further gains possible by trading model size for more inference steps. Designed based on these scaling properties, LTMs demonstrate superior sample and parameter efficiency compared to autoregressive models and discrete diffusion models. They significantly outperform these counterparts in validation perplexity and zero-shot language modeling tasks. Additionally, LTMs exhibit emergent few-shot in-context reasoning capabilities that scale with model size, and achieve competitive performance in conditional and unconditional text generation. The project page is available at https://deqiankong.github.io/blogs/ltm.

Time-Independent Differential Equations (TIDEs) are central to modeling equilibrium behavior across a wide range of scientific and engineering domains.Conventional numerical solvers offer reliable solutions but incur significant computational costs due to fine-grained discretization and iterative procedures.Machine learning-based approaches address this by replacing iterative solving with one-time inference; however, they inevitably sacrifice accuracy and incur even higher costs once the training of sophisticated models is taken into account.Consequently, designing a TIDE solver that achieves high accuracy, broad applicability, and exceptional computational efficiency remains a fundamental challenge.In this paper, we propose DS-TIDE, a novel hardware solver that is inspired by, and subsequently leverages, the intrinsic connection between Dynamical Systems (DS) and Differential Equations (DE) to efficiently and accurately solve TIDEs.DS-TIDE employs a CMOS-compatible DS-based processor, whose physical states evolve under carefully designed DE-driven dynamics and naturally converge to equilibria -the solutions of the target TIDE within ∼ 1𝜇𝑠.To enhance expressivity, DS-TIDE incorporates Heterogeneous Dynamics with Temporal Layering (HDTL), which solves TIDEs through a three-stage DS evolution -conditioning, solving, and decoding -each governed by specialized dynamics.The entire evolution process is analogous to an infinitely deep neural network temporally unrolled, offering the system the capability of representing complex equations.Furthermore, DS-TIDE is equipped

Tianyang Zhao, Kunwar Yashraj Singh, Srikar Appalaraju, Peng Tang, Ying Nian Wu, Li Erran Li. Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers). 2025.

Existing AutoML systems have advanced the automation of machine learning (ML); however, they still require substantial manual configuration and expert input, particularly when handling multimodal data. We introduce MLZero, a novel multi-agent framework powered by Large Language Models (LLMs) that enables end-to-end ML automation across diverse data modalities with minimal human intervention. A cognitive perception module is first employed, transforming raw multimodal inputs into perceptual context that effectively guides the subsequent workflow. To address key limitations of LLMs, such as hallucinated code generation and outdated API knowledge, we enhance the iterative code generation process with semantic and episodic memory. MLZero demonstrates superior performance on MLE-Bench Lite, outperforming all competitors in both success rate and solution quality, securing six gold medals. Furthermore, when evaluated on our Multimodal AutoML Agent Benchmark, which includes 25 more challenging tasks spanning diverse data modalities, MLZero outperforms the competing methods by a large margin with a success rate of 0.92 (+263.6\%) and an average rank of 2.28. Our approach maintains its robust effectiveness even with a compact 8B LLM, outperforming full-size systems from existing solutions.

AI agents today are mostly siloed — they either retrieve and reason over vast amount of digital information and knowledge obtained online; or interact with the physical world through embodied perception, planning and action — but rarely both. This separation limits their ability to solve tasks that require integrated physical and digital intelligence, such as cooking from online recipes, navigating with dynamic map data, or interpreting real-world landmarks using web knowledge. We introduce \textsc{Embodied Web Agents}, a novel paradigm for AI agents that fluidly bridge embodiment and web-scale reasoning. To operationalize this concept, we first develop the \textsc{Embodied Web Agents} task environments, a unified simulation platform that integrates realistic 3D indoor and outdoor environments with functional web interfaces. Building upon this platform, we construct and release the \textsc{Embodied Web Agents} Benchmark, which encompasses a diverse suite of tasks including cooking, navigation, shopping, tourism, and geolocation — all requiring coordinated reasoning across physical and digital realms for systematic assessment of cross-domain intelligence. Experimental results reveal significant performance gaps between state-of-the-art AI systems and human capabilities, establishing both challenges and opportunities at the intersection of embodied cognition and web-scale knowledge access.

Reinforcement Learning with Verifiable Rewards (RLVR) has proven effective for training large language models (LLMs) on complex reasoning tasks, such as mathematical problem solving. A prerequisite for the scalability of RLVR is a high-quality problem set with precise and verifiable answers. However, the scarcity of well-crafted human-labeled math problems and limited-verification answers in existing distillation-oriented synthetic datasets limit their effectiveness in RL. Additionally, most problem synthesis strategies indiscriminately expand the problem set without considering the model’s capabilities, leading to low efficiency in generating useful questions. To mitigate this issue, we introduce a Self-aware Weakness-driven problem Synthesis framework (SwS) that systematically identifies model deficiencies and leverages them for problem augmentation. Specifically, we define weaknesses as questions that the model consistently fails to learn through its iterative sampling during RL training. We then extract the core concepts from these failure cases and synthesize new problems to strengthen the model's weak areas in subsequent augmented training, enabling it to focus on and gradually overcome its weaknesses. Without relying on external knowledge distillation, our framework enables robust generalization by empowering the model to self-identify and address its weaknesses in RL, yielding average performance gains of 10% and 7.7% on 7B and 32B models across eight mainstream reasoning benchmarks. Our code and data are available at https://anonymous.4open.science/r/SwS-E6F5/

Existing Bayesian Optimization (BO) methods typically balance exploration and exploitation to optimize costly objective functions. However, these methods often suffer from a significant one-step bias, which may lead to convergence towards local optima and poor performance in complex or high-dimensional tasks. Recently, Black-Box Optimization (BBO) has achieved success across various scientific and engineering domains, particularly when function evaluations are costly and gradients are unavailable. Motivated by this, we propose the Reinforced Energy-Based Model for Bayesian Optimization (REBMBO), which integrates Gaussian Processes (GP) for local guidance with an Energy-Based Model (EBM) to capture global structural information. Notably, we define each Bayesian Optimization iteration as a Markov Decision Process (MDP) and use Proximal Policy Optimization (PPO) for adaptive multi-step lookahead, dynamically adjusting the depth and direction of exploration to effectively overcome the limitations of traditional BO methods. We conduct extensive experiments on synthetic and real-world benchmarks, confirming the superior performance of REBMBO. Additional analyses across various GP configurations further highlight its adaptability and robustness. Our code is publicly available at: https://github.com/ruiyaoMiao0809/Black-Box-Bayesian-Optimization-with-Energy-Based-Model-and-Reinforcement-Learning

The hippocampus supports spatial navigation by encoding cognitive maps through collective place cell activity. We model the place cell population as non-negative spatial embeddings derived from the spectral decomposition of multi-step random walk transition kernels. In this framework, inner product or equivalently Euclidean distance between embeddings encode similarity between locations in terms of their transition probability across multiple scales, forming a cognitive map of adjacency. The combination of non-negativity and inner-product structure naturally induces sparsity, providing a principled explanation for the localized firing fields of place cells without imposing explicit constraints. The temporal parameter that defines the diffusion scale also determines field size, aligning with the hippocampal dorsoventral hierarchy. Our approach constructs global representations efficiently through recursive composition of local transitions, enabling smooth, trap-free navigation and preplay-like trajectory generation. Moreover, theta phase arises intrinsically as the angular relation between embeddings, linking spatial and temporal coding within a single representational geometry.

Knowledge distillation aims at reducing model size without compromising much performance. Recent work has applied it to large vision-language (VL) Transformers, and has shown that attention maps in the multi-head attention modules of vision-language Transformers contain extensive intra-modal and cross-modal co-reference relations to be distilled. The standard approach is to apply a one-to-one attention map distillation loss, i.e. the Teacher's first attention head instructs the Student's first head, the second teaches the second, and so forth, but this only works when the numbers of attention heads in the Teacher and Student are the same. To remove this constraint, we propose a new Attention Map Alignment Distillation (AMAD) method for Transformers with multi-head attention, which works for a Teacher and a Student with different numbers of attention heads. Specifically, we soft-align different heads in Teacher and Student attention maps using a cosine similarity weighting. The Teacher head contributes more to the Student heads for which it has a higher similarity weight. Each Teacher head contributes to all the Student heads by minimizing the divergence between the attention activation distributions for the soft-aligned heads. No head is left behind. This distillation approach operates like cross-attention. We experiment on distilling VL-T5 and BLIP, and apply AMAD loss on their T5, BERT, and ViT sub-modules. We show, under vision-language setting, that AMAD outperforms conventional distillation methods on VQA-2.0, COCO captioning, and Multi30K translation datasets. We further show that even without VL pre-training, the distilled VL-T5 models outperform corresponding VL pre-trained VL-T5 models that are further fine-tuned by ground-truth signals, and that fine-tuning distillation can also compensate to some degree for the absence of VL pre-training for BLIP models.

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.

As embodied agents learn to interact, it is crucial for them to understand when, what, and to whom they should respond. While advances in natrual language processing and speech technologies have enabled conversational agents to focus on what to respond, they still struggle to determine when and to whom they should respond. In this paper, we address the addressee detection (Talking-To-Me, TTM) problem under the egocentric view. Instead of relying solely on short-term audio and video data, we propose a simple architecture SICNet with self/cross-modality attention that leverages long-term social interaction context. By leveraging long-term information, our approach has achieved a mean Average Precision (mAP) of 68.98% on the Ego4D TTM task, surpassing the previous state-of-the-art single-task model by 10.07%. We also conducted a detailed ablation study to demonstrate the effectiveness of each component in the long-term social interaction context.

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 Ma- chine ( 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.

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 frame work 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.

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 large-scale 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. Large-scale experiments demonstrate TCM's effectiveness in enhancing threshold consistency while preserving accuracy, simplifying the threshold selection process in practical DML settings.

Training energy-based models (EBMs) on high-dimensional data can be both challenging and time-consuming, and there exists a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the two models are jointly estimated within a cooperative training framework: Samples from the initializer serve as starting points that are refined by a few MCMC sampling steps from the EBM. The EBM is then optimized by maximizing recovery likelihood, while the initializer model is optimized by learning from the difference between the refined samples and the initial samples. In addition, we made several practical designs for EBM training to further improve the sample quality. Combining these advances, we significantly boost the generation performance compared to existing EBM methods on CIFAR-10 and ImageNet 32x32. And we have shown that CDRL has great potential to largely reduce the sampling time. We also demonstrate the effectiveness of our models for several downstream tasks, including classifier-free guided generation, compositional generation, image inpainting and out-of-distribution detection.

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 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 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/.

Conventional Task and Motion Planning (TAMP) approaches rely on manually designed interfaces connecting symbolic task planning with continuous motion generation. These domain-specific and labor-intensive modules are limited in addressing emerging tasks in real-world settings. Here, we present LLM3, a novel Large Language Model (LLM)-based TAMP framework featuring a domain-independent interface. Specifically, we leverage the powerful reasoning and planning capabilities of pre-trained LLMs to propose symbolic action sequences and select continuous action parameters for motion planning. Crucially, LLM3incorporates motion planning feedback through prompting, allowing the LLM to iteratively refine its proposals by reasoning about motion failure. Consequently, LLM3interfaces between task planning and motion planning, alleviating the intricate design process of handling domain-specific messages between them. Through a series of simulations in a box-packing domain, we quantitatively demonstrate the effectiveness of LLM3in solving TAMP problems and the efficiency in selecting action parameters. Ablation studies underscore the significant contribution of motion failure reasoning to the success of LLM3. Furthermore, we conduct qualitative experiments on a physical manipulator, demonstrating the practical applicability of our approach in real-world settings.

Existing diffusion-based text-to-3D generation methods primarily focus on producing visually realistic shapes and appearances, often neglecting the physical constraints necessary for downstream tasks. Generated models frequently fail to maintain balance when placed in physics-based simulations or 3D printed. This balance is crucial for satisfying user design intentions in interactive gaming, embodied AI, and robotics, where stable models are needed for reliable interaction. Additionally, stable models ensure that 3D-printed objects, such as figurines for home decoration, can stand on their own without requiring additional supports. To fill this gap, we introduce Atlas3D, an automatic and easy-to-implement method that enhances existing Score Distillation Sampling (SDS)-based text-to-3D tools. Atlas3D ensures the generation of self-supporting 3D models that adhere to physical laws of stability under gravity, contact, and friction. Our approach combines a novel differentiable simulation-based loss function with physically inspired regularization, serving as either a refinement or a post-processing module for existing frameworks. We verify Atlas3D's efficacy through extensive generation tasks and validate the resulting 3D models in both simulated and real-world environments.

This work explores the challenging problem of molecule design by framing it as a conditional generative modeling task, where target biological properties or desired chemical constraints serve as conditioning variables. We propose the Latent Prompt Transformer (LPT), a novel generative model comprising three components: (1) a latent vector with a learnable prior distribution modeled by a neural transformation of Gaussian white noise; (2) a molecule generation model based on a causal Transformer, which uses the latent vector as a prompt; and (3) a property prediction model that predicts a molecule's target properties and/or constraint values using the latent prompt. LPT can be learned by maximum likelihood estimation on molecule-property pairs. During property optimization, the latent prompt is inferred from target properties and constraints through posterior sampling and then used to guide the autoregressive molecule generation. After initial training on existing molecules and their properties, we adopt an online learning algorithm to progressively shift the model distribution towards regions that support desired target properties. Experiments demonstrate that LPT not only effectively discovers useful molecules across single-objective, multi-objective, and structure-constrained optimization tasks, but also exhibits strong sample efficiency.

In tasks aiming for long-term returns, planning becomes essential. We study generative modeling for planning with datasets repurposed from offline reinforcement learning. Specifically, we identify temporal consistency in the absence of step-wise rewards as one key technical challenge. We introduce the Latent Plan Transformer (LPT), a novel model that leverages a latent variable to connect a Transformer- based trajectory generator and the final return. LPT can be learned with maximum likelihood estimation on trajectory-return pairs. In learning, posterior sampling of the latent variable naturally integrates sub-trajectories to form a consistent abstrac- tion despite the finite context. At test time, the latent variable is inferred from an expected return before policy execution, realizing the idea of planning as inference. Our experiments demonstrate that LPT can discover improved decisions from sub- optimal trajectories, achieving competitive performance across several benchmarks, including Gym-Mujoco, Franka Kitchen, Maze2D, and Connect Four. It exhibits capabilities in nuanced credit assignments, trajectory stitching, and adaptation to environmental contingencies. These results validate that latent variable inference can be a strong alternative to step-wise reward prompting.

While diffusion models can learn complex distributions, sampling requires a computationally expensive iterative process. Existing distillation methods enable efficient sampling, but have notable limitations, such as performance degradation with very few sampling steps, reliance on training data access, or mode-seeking optimization that may fail to capture the full distribution. We propose EM Distillation (EMD), a maximum likelihood-based approach that distills a diffusion model to a one-step generator model with minimal loss of perceptual quality. Our approach is derived through the lens of Expectation-Maximization (EM), where the generator parameters are updated using samples from the joint distribution of the diffusion teacher prior and inferred generator latents. We develop a reparametrized sampling scheme and a noise cancellation technique that together stabilizes the distillation process. We further reveal an interesting connection of our method with existing methods that minimize mode-seeking KL. EMD outperforms existing one-step generative methods in terms of FID scores on ImageNet-64 and ImageNet-128, and compares favorably with prior work on distilling text-to-image diffusion models.

With the scale of vision Transformer-based models continuing to grow, finetuning these large-scale pretrained models for new tasks has become increasingly parameter-intensive. Visual prompt tuning is introduced as a parameter-efficient finetuning (PEFT) method to this trend. Despite its successes, a notable research challenge persists within almost all PEFT approaches: significant performance degradation is observed when there is a substantial disparity between the datasets applied in pretraining and finetuning phases. To address this challenge, we draw inspiration from human visual cognition, and propose the Visual Fourier Prompt Tuning (VFPT) method as a general and effective solution for adapting large-scale transformer-based models. Our approach innovatively incorporates the Fast Fourier Transform into prompt embeddings and harmoniously considers both spatial and frequency domain information. Apart from its inherent simplicity and intuitiveness, VFPT exhibits superior performance across all datasets, offering a general solution to dataset challenges, irrespective of data disparities. Empirical results demonstrate that our approach outperforms current state-of-the-art baselines on two benchmarks, with low parameter usage (e.g., 0.57% of model parameters on VTAB-1k) and notable performance enhancements (e.g., 73.20% of mean accuracy on VTAB-1k). Our code is avaliable at https://github.com/runtsang/VFPT.

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. Code is available at \url{https://github.com/YasminZhang/ICTM}.

The information processing in the brain and embodied agents form a sensory-action loop to interact with the world. An important step in the loop is motion planning which selects motor actions based on the current world state and task need. In goal-directed navigation, the brain chooses and generates motor actions to bring the current state into the goal state. It is unclear about the neural circuit mechanism of motor action selection, nor its underlying theory. The present study formulates the motion planning as a Lie group operator search problem, and uses the 1D rotation group as an example to provide insight into general operator search in neural circuits. We found the abstract group operator search can be implemented by a two-layer feedforward circuit utilizing circuit motifs of connection phase shift, nonlinear activation function, and pooling, similar to Drosophila's goal-directed navigation neural circuits. And the computational complexity of the feedforward circuit can be even lower than common signal processing algorithms in certain conditions. We also provide geometric interpretations of circuit computation in the group representation space. The feedforward motion planning circuit is further combined with sensory and motor circuit modules into a full circuit of the sensory-action loop implementing goal-directed navigation. Our work for the first time links the abstract operator search with biological neural circuits.

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.

This paper studies the fundamental problem of multilayer 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.

We examine concept generalization at a large scale in the natural visual spectrum. Established computational modes (*i.e.*, rule-based or similarity-based) are primarily studied isolated, focusing on confined and abstract problem spaces. In this work, we study these two modes when the *problem space* scales up and when the *complexity* of concepts becomes diverse. At the **representational level**, we investigate how the complexity varies when a visual concept is mapped to the representation space. Prior literature has shown that two types of complexities (Griffiths & Tenenbaum, 2003) build an inverted-U relation (Donderi, 2006; Sun & Firestone, 2021). Leveraging *Representativeness of Attribute* (RoA), we computationally confirm: 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 examine 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 rule-based generalization, while the trend is the opposite in similarity-based generalization.

The capability to generate responses with diversity and faithfulness using factual knowledge is paramount for creating a human-like, trustworthy dialogue system. Common strategies either adopt a two-step paradigm, which optimizes knowledge selection and response generation separately, and may overlook the inherent correlation between these two tasks, or leverage conditional variational method to jointly optimize knowledge selection and response generation by employing an inference network. In this paper, we present an end-to-end learning framework, termed Sequential Posterior Inference (SPI), capable of selecting knowledge and generating dialogues by approximately sampling from the posterior distribution. Unlike other methods, SPI does not require the inference network or assume a simple geometry of the posterior distribution. This straightforward and intuitive inference procedure of SPI directly queries the response generation model, allowing for accurate knowledge selection and generation of faithful responses. In addition to modeling contributions, our experimental results on two common dialogue datasets (Wizard of Wikipedia and Holl-E) demonstrate that SPI outperforms previous strong baselines according to both automatic and human evaluation metrics.

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.

Latent space EBMs, also known as energy-based priors, have drawn growing interests in the field of generative modeling due to its flexibility in the formulation and strong modeling power of the latent space. However, the common practice of learning latent space EBMs with non-convergent short-run MCMC for prior and posterior sampling is hindering the model from further progress; the degenerate MCMC sampling quality in practice often leads to degraded generation quality and instability in training, especially with highly multi-modal and/or high-dimensional target distributions. To remedy this sampling issue, in this paper we introduce a simple but effective diffusion-based amortization method for long-run MCMC sampling and develop a novel learning algorithm for the latent space EBM based on it. We provide theoretical evidence that the learned amortization of MCMC is a valid long-run MCMC sampler. Experiments on several image modeling benchmark datasets demonstrate the superior performance of our method compared with strong counterparts.

Time perception is critical in our daily life. An important feature of time perception is temporal scaling (TS): the ability to generate temporal sequences (e.g., motor actions) at different speeds. However, it is largely unknown about the math principle underlying temporal scaling in recurrent circuits in the brain. To shed insight, the present study investigates the temporal scaling from the Lie group point of view. We propose a canonical nonlinear recurrent circuit dynamics, modeled as a continuous attractor network, whose neuronal population responses embed a temporal sequence that is TS equivariant. Furthermore, we found the TS group operators can be explicitly represented by a control input fed into the recurrent circuit, where the input gain determines the temporal scaling factor (group parameter), and the spatial offset between the control input and network state emerges the generator. The neuronal responses in the recurrent circuit are also consistent with experimental findings. We illustrated that the recurrent circuit can drive a feedforward circuit to generate complex temporal sequences with different time scales, even in the case of negative time scaling (''time reversal''). Our work for the first time analytically links the abstract temporal scaling group and concrete neural circuit dynamics.

Generation of molecules with desired chemical and biological properties such as high drug-likeness, high binding affinity to target proteins, is critical for drug discovery. In this paper, we propose a probabilistic generative model to capture the joint distribution of molecules and their properties. Our model assumes an energy-based model (EBM) in the latent space. Conditional on the latent vector, the molecule and its properties are modeled by a molecule generation model and a property regression model respectively. To search for molecules with desired properties, we propose a sampling with gradual distribution shifting (SGDS) algorithm, so that after learning the model initially on the training data of existing molecules and their properties, the proposed algorithm gradually shifts the model distribution towards the region supported by molecules with desired values of properties. Our experiments show that our method achieves very strong performances on various molecule design tasks.

The problem of continuous inverse optimal control (over finite time horizon) is to learn the unknown cost function over the sequence of continuous control variables from expert demonstrations. In this article, we study this fundamental problem in the framework of energy-based model (EBM), where the observed expert trajectories are assumed to be random samples from a probability density function defined as the exponential of the negative cost function up to a normalizing constant. The parameters of the cost function are learned by maximum likelihood via an "analysis by synthesis" scheme, which iterates: 1) synthesis step: sample the synthesized trajectories from the current probability density using the Langevin dynamics via backpropagation through time and 2) analysis step: update the model parameters based on the statistical difference between the synthesized trajectories and the observed trajectories. Given the fact that an efficient optimization algorithm is usually available for an optimal control problem, we also consider a convenient approximation of the above learning method, where we replace the sampling in the synthesis step by optimization. Moreover, to make the sampling or optimization more efficient, we propose to train the EBM simultaneously with a top-down trajectory generator via cooperative learning, where the trajectory generator is used to fast initialize the synthesis step of the EBM. We demonstrate the proposed methods on autonomous driving tasks and show that they can learn suitable cost functions for optimal control.

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.

The core of self-supervised learning for pre-training language models includes pre-training task design as well as appropriate data augmentation. Most data augmentations in language model pre-training are context-independent. A seminal contextualized augmentation was recently proposed in ELECTRA and achieved state-of-the-art performance by introducing an auxiliary generation network (generator) to produce contextualized data augmentation for the training of a main discrimination network (discriminator). This design, however, introduces extra computation cost of the generator and a need to adjust the relative capability between the generator and the discriminator. In this paper, we propose a self-augmentation strategy (SAS) where a single network is utilized for both regular pre-training and contextualized data augmentation for the training in later epochs. Essentially, this strategy eliminates a separate generator and uses the single network to jointly conduct two pre-training tasks with MLM (Masked Language Modeling) and RTD (Replaced Token Detection) heads. It avoids the challenge to search for an appropriate size of the generator, which is critical to the performance as evidenced in ELECTRA and its subsequent variant models. In addition, SAS is a general strategy that can be seamlessly combined with many new techniques emerging recently or in the future, such as the disentangled attention mechanism from DeBERTa. Our experiments show that SAS is able to outperform ELECTRA and other state-of-the-art models in the GLUE tasks with similar or less computation cost.

Multivariate time series anomaly detection has become an active area of research in recent years, with Deep Learning models outperforming previous approaches on benchmark datasets. Among reconstruction-based models, most previous work has focused on Variational Autoencoders and Generative Adversarial Networks. This work presents DGHL, a new family of generative models for time series anomaly detection, trained by maximizing the observed likelihood by posterior sampling and alternating back-propagation. A top-down Convolution Network maps a novel hierarchical latent space to time series windows, exploiting temporal dynamics to encode information efficiently. Despite relying on posterior sampling, it is computationally more efficient than current approaches, with up to 10x shorter training times than RNN based models. Our method outperformed current state-of-the-art models on four popular benchmark datasets. Finally, DGHL is robust to variable features between entities and accurate even with large proportions of missing values, settings with increasing relevance with the advent of IoT. We demonstrate the superior robustness of DGHL with novel occlusion experiments in this literature. Our code is available at https://github.com/cchallu/dghl.

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 an alternative paradigm 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 pretrained language models. A Transform-Retrieve-Generate framework (TRiG) framework is proposed11The code of this work will be made public., 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.

Latent space Energy-Based Models (EBMs), also known as energy-based priors, have drawn growing interests in generative modeling. Fueled by its flexibility in the formulation and strong modeling power of the latent space, recent works built upon it have made interesting attempts aiming at the interpretability of text modeling. However, latent space EBMs also inherit some flaws from EBMs in data space; the degenerate MCMC sampling quality in practice can lead to poor generation quality and instability in training, especially on data with complex latent structures. Inspired by the recent efforts that leverage diffusion recovery likelihood learning as a cure for the sampling issue, we introduce a novel symbiosis between the diffusion models and latent space EBMs in a variational learning framework, coined as the latent diffusion energy-based model. We develop a geometric clustering-based regularization jointly with the information bottleneck to further improve the quality of the learned latent space. Experiments on several challenging tasks demonstrate the superior performance of our model on interpretable text modeling over strong counterparts.

Equivariant representation is necessary for the brain and artificial perceptual systems to faithfully represent the stimulus under some (Lie) group transformations. However, it remains unknown how recurrent neural circuits in the brain represent the stimulus equivariantly, nor the neural representation of abstract group operators. The present study uses a one-dimensional (1D) translation group as an example to explore the general recurrent neural circuit mechanism of the equivariant stimulus representation. We found that a continuous attractor network (CAN), a canonical neural circuit model, self-consistently generates a continuous family of stationary population responses (attractors) that represents the stimulus equivariantly. Inspired by the Drosophila's compass circuit, we found that the 1D translation operators can be represented by extra speed neurons besides the CAN, where speed neurons' responses represent the moving speed (1D translation group parameter), and their feedback connections to the CAN represent the translation generator (Lie algebra). We demonstrated that the network responses are consistent with experimental data. Our model for the first time demonstrates how recurrent neural circuitry in the brain achieves equivariant stimulus representation.

This paper studies the problem of learning the conditional distribution of a high-dimensional output given an input, where the output and input may belong to two different domains, e.g., the output is a photo image and the input is a sketch image. We solve this problem by cooperative training of a fast thinking initializer and slow thinking solver. The initializer generates the output directly by a non-linear transformation of the input as well as a noise vector that accounts for latent variability in the output. The slow thinking solver learns an objective function in the form of a conditional energy function, so that the output can be generated by optimizing the objective function, or more rigorously by sampling from the conditional energy-based model. We propose to learn the two models jointly, where the fast thinking initializer serves to initialize the sampling of the slow thinking solver, and the solver refines the initial output by an iterative algorithm. The solver learns from the difference between the refined output and the observed output, while the initializer learns from how the solver refines its initial output. We demonstrate the effectiveness of the proposed method on various conditional learning tasks, e.g., class-to-image generation, image-to-image translation, and image recovery. The advantage of our method over GAN-based methods is that our method is equipped with a slow thinking process that refines the solution guided by a learned objective function.

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.

We present a deformable generator model to disentangle the appearance and geometric information for both image and video data in a purely unsupervised manner. The appearance generator network models the information related to appearance, including color, illumination, identity or category, while the geometric generator performs geometric warping, such as rotation and stretching, through generating deformation field which is used to warp the generated appearance to obtain the final image or video sequences. Two generators take independent latent vectors as input to disentangle the appearance and geometric information from image or video sequences. For video data, a nonlinear transition model is introduced to both the appearance and geometric generators to capture the dynamics over time. The proposed scheme is general and can be easily integrated into different generative models. An extensive set of qualitative and quantitative experiments shows that the appearance and geometric information can be well disentangled, and the learned geometric generator can be conveniently transferred to other image datasets that share similar structure regularity to facilitate knowledge transfer tasks.

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.

Inferring social relations from dialogues is vital for building emotionally intelligent robots to interpret human language better and act accordingly. We model the social network as an And-or Graph, named SocAoG, for the consistency of relations among a group and leveraging attributes as inference cues. Moreover, we formulate a sequential structure prediction task, and propose an $\alpha$-$\beta$-$\gamma$ strategy to incrementally parse SocAoG for the dynamic inference upon any incoming utterance: (i) an $\alpha$ process predicting attributes and relations conditioned on the semantics of dialogues, (ii) a $\beta$ process updating the social relations based on related attributes, and (iii) a $\gamma$ process updating individual's attributes based on interpersonal social relations. Empirical results on DialogRE and MovieGraph show that our model infers social relations more accurately than the state-of-the-art methods. Moreover, the ablation study shows the three processes complement each other, and the case study demonstrates the dynamic relational inference.

Human trajectory prediction is critical for autonomous platforms like self-driving cars or social robots. We present a latent belief energy-based model (LB-EBM) for diverse human trajectory forecast. LB-EBM is a probabilistic model with cost function defined in the latent space to account for the movement history and social context. The low-dimensionality of the latent space and the high expressivity of the EBM make it easy for the model to capture the multi-modality of pedestrian trajectory distributions. LB-EBM is learned from expert demonstrations (i.e., human trajectories) projected into the latent space. Sampling from or optimizing the learned LB-EBM yields a belief vector which is used to make a path plan, which then in turn helps to predict a long-range trajectory. The effectiveness of LB-EBM and the two-step approach are supported by strong empirical results. Our model is able to make accurate, multi-modal, and social compliant trajectory predictions and improves over prior state-of-the-arts performance on the Stanford Drone trajectory prediction benchmark by 10.9% and on the ETH-UCY benchmark by 27.6%.

We propose a generative model of unordered point sets, such as point clouds, in the forms 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.

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.

Latent variable models for text, when trained successfully, accurately model the data distribution and capture global semantic and syntactic features of sentences.The prominent approach to train such models is variational autoencoders (VAE).It is nevertheless challenging to train and often results in a trivial local optimum where the latent variable is ignored and its posterior collapses into the prior, an issue known as posterior collapse.Various techniques have been proposed to mitigate this issue.Most of them focus on improving the inference model to yield latent codes of higher quality.The present work proposes a short run dynamics for inference.It is initialized from the prior distribution of the latent variable and then runs a small number (e.g., 20) of Langevin dynamics steps guided by its posterior distribution.The major advantage of our method is that it does not require a separate inference model or assume simple geometry of the posterior distribution, thus rendering an automatic, natural and flexible inference engine.We show that the models trained with short run dynamics more accurately model the data, compared to strong language model and VAE baselines, and exhibit no sign of posterior collapse.Analyses of the latent space show that interpolation in the latent space is able to generate coherent sentences with smooth transition and demonstrate improved classification over strong baselines with latent features from unsupervised pretraining.These results together expose a well-structured latent space of our generative model.

We propose a latent space energy-based prior model for text generation and classification. The model stands on a generator network that generates the text sequence based on a continuous latent vector. The energy term of the prior model couples a continuous latent vector and a symbolic one-hot vector, so that discrete category can be inferred from the observed example based on the continuous latent vector. Such a latent space coupling naturally enables incorporation of information bottleneck regularization to encourage the continuous latent vector to extract information from the observed example that is informative of the underlying category. In our learning method, the symbol-vector coupling, the generator network and the inference network are learned jointly. Our model can be learned in an unsupervised setting where no category labels are provided. It can also be learned in semi-supervised setting where category labels are provided for a subset of training examples. Our experiments demonstrate that the proposed model learns well-structured and meaningful latent space, which (1) guides the generator to generate text with high quality, diversity, and interpretability, and (2) effectively classifies text.

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. Source code and dataset tools can be accessed via Github.

Planning in environments with other agents whose future actions are uncertain often requires compromise between safety and performance. Here our goal is to design efficient planning algorithms with guaranteed bounds on the probability of safety violation, which nonetheless achieve non-conservative performance. To quantify a system’s risk, we define a natural criterion called interval risk bounds (IRBs), which provide a parametric upper bound on the probability of safety violation over a given time interval or task. We present a novel receding horizon algorithm, and prove that it can satisfy a desired IRB. Our algorithm maintains a dynamic risk budget which constrains the allowable risk at each iteration, and guarantees recursive feasibility by requiring a safe set to be reachable by a contingency plan within the budget. We empirically demonstrate that our algorithm is both safer and less conservative than strong baselines in two simulated autonomous driving experiments in scenarios involving collision avoidance with other vehicles, and additionally demonstrate our algorithm running on an autonomous class 8 truck.

In many fields such as bioinformatics, high energy physics, power distribution, etc., it is desirable to learn non-linear models where a small number of variables are selected and the interaction between them is explicitly modeled to predict the response. In principle, neural networks (NNs) could accomplish this task since they can model non-linear feature interactions very well. However, NNs require large amounts of training data to have a good generalization. In this paper we study feature selection in the data-starved regime where a NN is trained on a relatively small amount of training data. Feature selection is known to improve generalization for linear models. As an extreme case of data with feature selection and feature interactions we study the XOR-like data with irrelevant variables. We experimentally observed that the cross-entropy loss function on XOR-like data has many non-equivalent local minima, and the number of local minima grows exponentially with the number of irrelevant variables. To deal with the local minima and for feature selection we propose a node pruning and feature selection algorithm that improves the capability of NNs to find better local minima even when there are irrelevant variables. Finally, we show that the performance of a NN on real datasets can be improved using pruning, obtaining compact networks on a small number of features, with good prediction and interpretability.

Erik Nijkamp, Bo Pang, Ying Nian Wu, Caiming Xiong. Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies. 2021.

Understanding how grid cells perform path integration calculations remains a fundamental problem. In this paper, we conduct theoretical analysis of a general representation model of path integration by grid cells, where the 2D self-position is encoded as a higher dimensional vector, and the 2D self-motion is represented by a general transformation of the vector. We identify two conditions on the transformation. One is a group representation condition that is necessary for path integration. The other is an isotropic scaling condition that ensures locally conformal embedding, so that the error in the vector representation translates conformally to the error in the 2D self-position. Then we investigate the simplest transformation, i.e., the linear transformation, uncover its explicit algebraic and geometric structure as matrix Lie group of rotation, and explore the connection between the isotropic scaling condition and a special class of hexagon grid patterns. Finally, with our optimization-based approach, we manage to learn hexagon grid patterns that share similar properties of the grid cells in the rodent brain. The learned model is capable of accurate long distance path integration. Code is available at https://github.com/ruiqigao/grid-cell-path.

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.

In human pedagogy, teachers and students can interact adaptively to maximize communication efficiency. The teacher adjusts her teaching method for different students, and the student, after getting familiar with the teacher’s instruction mechanism, can infer the teacher’s intention to learn faster. Recently, the benefits of integrating this cooperative pedagogy into machine concept learning in discrete spaces have been proved by multiple works. However, how cooperative pedagogy can facilitate machine parameter learning hasn’t been thoroughly studied. In this paper, we propose a gradient optimization based teacher-aware learner who can incorporate teacher’s cooperative intention into the likelihood function and learn provably faster compared with the naive learning algorithms used in previous machine teaching works. We give theoretical proof that the iterative teacher-aware learning (ITAL) process leads to local and global improvements. We then validate our algorithms with extensive experiments on various tasks including regression, classification, and inverse reinforcement learning using synthetic and real data. We also show the advantage of modeling teacher-awareness when agents are learning from human teachers.

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.

In this paper, we present a method to mine object-part patterns from conv-layers of a pre-trained convolutional neural network (CNN). The mined object-part patterns are organized by an And-Or graph (AOG). This interpretable AOG representation consists of a four-layer semantic hierarchy, i.e., semantic parts, part templates, latent patterns, and neural units. The AOG associates each object part with certain neural units in feature maps of conv-layers. The AOG is constructed with very few annotations (e.g., 3-20) of object parts. We develop a question-answering (QA) method that uses active human-computer communications to mine patterns from a pre-trained CNN, in order to explain features in conv-layers incrementally. During the learning process, our QA method uses the current AOG for part localization. The QA method actively identifies objects, whose feature maps cannot be explained by the AOG. Then, our method asks people to annotate parts on the unexplained objects, and uses answers to discover CNN patterns corresponding to newly labeled parts. In this way, our method gradually grows new branches and refines existing branches on the AOG to semanticize CNN representations. In experiments, our method exhibited a high learning efficiency. Our method used about 1/6- 1/3 of the part annotations for training, but achieved similar or better part-localization performance than fast-RCNN methods.

in a conv-layer usually represents a mixture of object parts. We develop a simple yet effective method to learn an explanatory graph, which automatically disentangles object parts from each filter without any part annotations. Specifically, given the feature map of a filter, we mine neural activations from the feature map, which correspond to different object parts. The explanatory graph is constructed to organize each mined part as a graph node. Each edge connects two nodes, whose corresponding object parts usually co-activate and keep a stable spatial relationship. Experiments show that each graph node consistently represented the same object part through different images, which boosted the transferability of CNN features. The explanatory graph transferred features of object parts to the task of part localization, and our method significantly outperformed other approaches.

This paper proposes a generic method to learn interpretable convolutional filters in a deep convolutional neural network (CNN) for object classification, where each interpretable filter encodes features of a specific object part. Our method does not require additional annotations of object parts or textures for supervision. Instead, we use the same training data as traditional CNNs. Our method automatically assigns each interpretable filter in a high conv-layer with an object part of a certain category during the learning process. Such explicit knowledge representations in conv-layers of the CNN help people clarify the logic encoded in the CNN, i.e., answering what patterns the CNN extracts from an input image and uses for prediction. We have tested our method using different benchmark CNNs with various architectures to demonstrate the broad applicability of our method. Experiments have shown that our interpretable filters are much more semantically meaningful than traditional filters.

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.

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 parameters 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 or optical flows. 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 can be useful for motion transfer, and it is natural to adopt it to define and measure intrackability of a dynamic pattern.

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.

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.

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.

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 grammar model as a symbolic prior to bridge neural perception and symbolic reasoning, and (2) proposing a novel 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 https://liqing-ustc.github.io/NGS.

We propose an energy-based model (EBM) in the latent space of a generator model, so that the EBM serves as a prior model that stands on the top-down network of the generator model. Both the latent space EBM and the top-down network can be learned jointly by maximum likelihood, which involves short-run MCMC sampling from both the prior and posterior distributions of the latent vector. Due to the low dimensionality of the latent space and the expressiveness of the top-down network, a simple EBM in latent space can capture regularities in the data effectively, and MCMC sampling in latent space is efficient and mixes well. We show that the learned model exhibits strong performances in terms of image and text generation and anomaly detection. The one-page code can be found in supplementary materials.

This paper studies the cooperative training of two generative models for image modeling and synthesis. Both models are parametrized by convolutional neural networks (ConvNets). The first model is a deep energy-based model, whose energy function is defined by a bottom-up ConvNet, which maps the observed image to the energy. We call it the descriptor network. The second model is a generator network, which is a non-linear version of factor analysis. It is defined by a top-down ConvNet, which maps the latent factors to the observed image. The maximum likelihood learning algorithms of both models involve MCMC sampling such as Langevin dynamics. We observe that the two learning algorithms can be seamlessly interwoven into a cooperative learning algorithm that can train both models simultaneously. Specifically, within each iteration of the cooperative learning algorithm, the generator model generates initial synthesized examples to initialize a finite-step MCMC that samples and trains the energy-based descriptor model. After that, the generator model learns from how the MCMC changes its synthesized examples. That is, the descriptor model teaches the generator model by MCMC, so that the generator model accumulates the MCMC transitions and reproduces them by direct ancestral sampling. We call this scheme MCMC teaching. We show that the cooperative algorithm can learn highly realistic generative models.

This paper studies the dynamic generator model for spatialtemporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a non-linear transformation of a latent state vector, where the non-linear transformation is parametrized by a top-down neural network. The sequence of latent state vectors follows a non-linear auto-regressive model, where the state vector of the next frame is a non-linear transformation of the state vector of the current frame as well as an independent noise vector that provides randomness in the transition. The non-linear transformation of this transition model can be parametrized by a feedforward neural network. We show that this model can be learned by an alternating back-propagation through time algorithm that iteratively samples the noise vectors and updates the parameters in the transition model and the generator model. We show that our training method can learn realistic models for dynamic textures and action patterns.

This paper proposes the divergence triangle as a framework for joint training of a generator model, energy-based model and inference model. The divergence triangle is a compact and symmetric (anti-symmetric) objective function that seamlessly integrates variational learning, adversarial learning, wake-sleep algorithm, and contrastive divergence in a unified probabilistic formulation. This unification makes the processes of sampling, inference, and energy evaluation readily available without the need for costly Markov chain Monte Carlo methods. Our experiments demonstrate that the divergence triangle is capable of learning (1) an energy-based model with well-formed energy landscape, (2) direct sampling in the form of a generator network, and (3) feed-forward inference that faithfully reconstructs observed as well as synthesized data.

We present a deformable generator model to disentangle the appearance and geometric information in purely unsupervised manner. The appearance generator models the appearance related information, including color, illumination, identity or category, of an image, while the geometric generator performs geometric related warping, such as rotation and stretching, through generating displacement of the coordinates of each pixel to obtain the final image. Two generators act upon independent latent factors to extract disentangled appearance and geometric information from image. The proposed scheme is general and can be easily integrated into different generative models. An extensive set of qualitative and quantitative experiments show that the appearance and geometric information can be well disentangled, and the learned geometric generator can be conveniently transferred to the other image datasets to facilitate knowledge transfer tasks.

This paper aims to quantitatively explain the rationales of each prediction that is made by a pre-trained convolutional neural network (CNN). We propose to learn a decision tree, which clarifies the specific reason for each prediction made by the CNN at the semantic level. I.e., the decision tree decomposes feature representations in high conv-layers of the CNN into elementary concepts of object parts. In this way, the decision tree tells people which object parts activate which filters for the prediction and how much each object part contributes to the prediction score. Such semantic and quantitative explanations for CNN predictions have specific values beyond the traditional pixel-level analysis of CNNs. More specifically, our method mines all potential decision modes of the CNN, where each mode represents a typical case of how the CNN uses object parts for prediction. The decision tree organizes all potential decision modes in a coarse-to-fine manner to explain CNN predictions at different fine-grained levels. Experiments have demonstrated the effectiveness of the proposed method.

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.

This paper studies a curious phenomenon in learning energy-based model (EBM) using MCMC. In each learning iteration, we generate synthesized examples by running a non-convergent, non-mixing, and non-persistent short-run MCMC toward the current model, always starting from the same initial distribution such as uniform noise distribution, and always running a fixed number of MCMC steps. After generating synthesized examples, we then update the model parameters according to the maximum likelihood learning gradient, as if the synthesized examples are fair samples from the current model. We treat this non-convergent short-run MCMC as a learned generator model or a flow model. We provide arguments for treating the learned non-convergent short-run MCMC as a valid model. We show that the learned short-run MCMC is capable of generating realistic images. More interestingly, unlike traditional EBM or MCMC, the learned short-run MCMC is capable of reconstructing observed images and interpolating between images, like generator or flow models. The code can be found in the Appendix.

We address the problem of learning dynamic patterns from unlabeled video sequences, either in the form of generating new video sequences, or recovering incomplete video sequences. This problem is challenging because the appearances and motions in the video sequences can be very complex. We propose to use the alternating back-propagation algorithm to learn the generator network with the spatial-temporal convolutional architecture. The proposed method is efficient and flexible. It can not only generate realistic video sequences, but can also recover the incomplete video sequences in the testing stage or even in the learning stage. The proposed algorithm can be further improved by using learned initialization which is useful for the recovery tasks. Further, the proposed algorithm can naturally help to learn the shared representation between different modalities. Our experiments show that our method is competitive with the existing state of the art methods both qualitatively and quantitatively.

paper (Chang & Tsao, 2017) reports an interesting discovery. For the face stimuli generated by a pretrained active appearance model (AAM), the responses of neurons in the areas of the primate brain that are responsible for face recognition exhibit a strong linear relationship with the shape variables and appearance variables of the AAM that generates the face stimuli. In this letter, we show that this behavior can be replicated by a deep generative model, the generator network, that assumes that the observed signals are generated by latent random variables via a top-down convolutional neural network. Specifically, we learn the generator network from the face images generated by a pretrained AAM model using a variational autoencoder, and we show that the inferred latent variables of the learned generator network have a strong linear relationship with the shape and appearance variables of the AAM model that generates the face images. Unlike the AAM model, which has an explicit shape model where the shape variables generate the control points or landmarks, the generator network has no such shape model and shape variables. Yet it can learn the shape knowledge in the sense that some of the latent variables of the learned generator network capture the shape variations in the face images generated by AAM.

This paper proposes a cooperative learning algorithm to train both the undirected energy-based model and the directed latent variable model jointly. The learning algorithm interweaves the maximum likelihood algorithms for learning the two models, and each iteration consists of the following two steps: (1) Modified contrastive divergence for energy-based model: The learning of the energy-based model is based on the contrastive divergence, but the finite-step MCMC sampling of the model is initialized from the synthesized examples generated by the latent variable model instead of being initialized from the observed examples. (2) MCMC teaching of the latent variable model: The learning of the latent variable model is based on how the MCMC in (1) changes the initial synthesized examples generated by the latent variable model, where the latent variables that generate the initial synthesized examples are known so that the learning is essentially supervised. Our experiments show that the cooperative learning algorithm can learn realistic models of images.

This paper learns a graphical model, namely an explanatory graph, which reveals the knowledge hierarchy hidden inside a pre-trained CNN. Considering that each filter in a conv-layer of a pre-trained CNN usually represents a mixture of object parts, we propose a simple yet efficient method to automatically disentangles different part patterns from each filter, and construct an explanatory graph. In the explanatory graph, each node represents a part pattern, and each edge encodes co-activation relationships and spatial relationships between patterns. More importantly, we learn the explanatory graph for a pre-trained CNN in an unsupervised manner, i.e., without a need of annotating object parts. Experiments show that each graph node consistently represents the same object part through different images. We transfer part patterns in the explanatory graph to the task of part localization, and our method significantly outperforms other approaches.

This paper proposes a multi-grid method for learning energy-based generative ConvNet models of images. For each grid, we learn an energy-based probabilistic model where the energy function is defined by a bottom-up convolutional neural network (ConvNet or CNN). Learning such a model requires generating synthesized examples from the model. Within each iteration of our learning algorithm, for each observed training image, we generate synthesized images at multiple grids by initializing the finite-step MCMC sampling from a minimal 1 Ã- 1 version of the training image. The synthesized image at each subsequent grid is obtained by a finite-step MCMC initialized from the synthesized image generated at the previous coarser grid. After obtaining the synthesized examples, the parameters of the models at multiple grids are updated separately and simultaneously based on the differences between synthesized and observed examples. We show that this multi-grid method can learn realistic energy-based generative ConvNet models, and it outperforms the original contrastive divergence (CD) and persistent CD.

This paper proposes a 3D shape descriptor network, which is a deep convolutional energy-based model, for modeling volumetric shape patterns. The maximum likelihood training of the model follows an "analysis by synthesis" scheme and can be interpreted as a mode seeking and mode shifting process. The model can synthesize 3D shape patterns by sampling from the probability distribution via MCMC such as Langevin dynamics. The model can be used to train a 3D generator network via MCMC teaching. The conditional version of the 3D shape descriptor net can be used for 3D object recovery and 3D object super-resolution. Experiments demonstrate that the proposed model can generate realistic 3D shape patterns and can be useful for 3D shape analysis.

This paper proposes a method to modify a traditional convolutional neural network (CNN) into an interpretable CNN, in order to clarify knowledge representations in high conv-layers of the CNN. In an interpretable CNN, each filter in a high conv-layer represents a specific object part. Our interpretable CNNs use the same training data as ordinary CNNs without a need for any annotations of object parts or textures for supervision. The interpretable CNN automatically assigns each filter in a high conv-layer with an object part during the learning process. We can apply our method to different types of CNNs with various structures. The explicit knowledge representation in an interpretable CNN can help people understand the logic inside a CNN, i.e. what patterns are memorized by the CNN for prediction. Experiments have shown that filters in an interpretable CNN are more semantically meaningful than those in a traditional CNN. The code is available at https://github.com/zqs1022/interpretableCNN.

Multi-view representation learning is challenging because different views contain both the common structure and the complex view specific information. The traditional generative models may not be effective in such situation, since view-specific and common information cannot be well separated, which may cause problems for downstream vision tasks. In this paper, we introduce a multi-view generator model to solve the problem of multi-view generation and recognition in a unified framework. We propose a multi-view alternating back-propagation algorithm to learn multi-view generator networks by allowing them to share common latent factors. Our experiments show that the proposed method is effective for both image generation and recognition. Specifically, we first qualitatively demonstrate that our model can rotate and complete faces accurately. Then we show that our model can achieve state-of-art or competitive recognition performances through quantitative comparisons.

A recent Cell paper [Chang and Tsao, 2017] reports an interesting discovery. For the face stimuli generated by a pre-trained active appearance model (AAM), the responses of neurons in the areas of the primate brain that are responsible for face recognition exhibit strong linear relationship with the shape variables and appearance variables of the AAM that generates the face stimuli. In this paper, we show that this behavior can be replicated by a deep generative model called the generator network, which assumes that the observed signals are generated by latent random variables via a top-down convolutional neural network. Specifically, we learn the generator network from the face images generated by a pre-trained AAM model using variational auto-encoder, and we show that the inferred latent variables of the learned generator network have strong linear relationship with the shape and appearance variables of the AAM model that generates the face images. Unlike the AAM model that has an explicit shape model where the shape variables generate the control points or landmarks, the generator network has no such shape model and shape variables. Yet the generator network can learn the shape knowledge in the sense that some of the latent variables of the learned generator network capture the shape variations in the face images generated by AAM.

Holistic 3D indoor scene understanding refers to jointly recovering the i) object bounding boxes, ii) room layout, and iii) camera pose, all in 3D. The existing methods either are ineffective or only tackle the problem partially. In this paper, we propose an end-to-end model that simultaneously solves all three tasks in real-time given only a single RGB image. The essence of the proposed method is to improve the prediction by i) parametrizing the targets (e.g., 3D boxes) instead of directly estimating the targets, and ii) cooperative training across different modules in contrast to training these modules individually. Specifically, we parametrize the 3D object bounding boxes by the predictions from several modules, i.e., 3D camera pose and object attributes. The proposed method provides two major advantages: i) The parametrization helps maintain the consistency between the 2D image and the 3D world, thus largely reducing the prediction variances in 3D coordinates. ii) Constraints can be imposed on the parametrization to train different modules simultaneously. We call these constraints "cooperative losses" as they enable the joint training and inference. We employ three cooperative losses for 3D bounding boxes, 2D projections, and physical constraints to estimate a geometrically consistent and physically plausible 3D scene. Experiments on the SUN RGB-D dataset shows that the proposed method significantly outperforms prior approaches on 3D layout estimation, 3D object detection, 3D camera pose estimation, and holistic scene understanding.

This paper proposes an alternating back-propagation algorithm for learning the generator network model. The model is a non-linear generalization of factor analysis. In this model, the mapping from the continuous latent factors to the observed signal is parametrized by a convolutional neural network. The alternating back-propagation algorithm iterates the following two steps: (1) Inferential back-propagation, which infers the latent factors by Langevin dynamics or gradient descent. (2) Learning back-propagation, which updates the parameters given the inferred latent factors by gradient descent. The gradient computations in both steps are powered by back-propagation, and they share most of their code in common. We show that the alternating back-propagation algorithm can learn realistic generator models of natural images, video sequences, and sounds. Moreover, it can also be used to learn from incomplete or indirect training data.

This paper proposes a learning strategy that embeds object-part concepts into a pre-trained convolutional neural network (CNN), in an attempt to 1) explore explicit semantics hidden in CNN units and 2) gradually transform the pre-trained CNN into a semantically interpretable graphical model for hierarchical object understanding. Given part annotations on very few (e.g., 3-12) objects, our method mines certain latent patterns from the pre-trained CNN and associates them with different semantic parts. We use a four-layer And-Or graph to organize the CNN units, so as to clarify their internal semantic hierarchy. Our method is guided by a small number of part annotations, and it achieves superior part-localization performance (about 13%-107% improvement in part center prediction on the PASCAL VOC and ImageNet datasets)

This paper proposes a method for generative learning of hierarchical random field models. The resulting model, which we call the hierarchical sparse FRAME (Filters, Random field, And Maximum Entropy) model, is a generalization of the original sparse FRAME model by decomposing it into multiple parts that are allowed to shift their locations, scales and rotations, so that the resulting model becomes a hierarchical deformable template. The model can be trained by an EM-type algorithm that alternates the following two steps: (1) Inference: Given the current model, we match it to each training image by inferring the unknown locations, scales, and rotations of the object and its parts by recursive sum-max maps, and (2) Re-learning: Given the inferred geometric configurations of the objects and their parts, we re-learn the model parameters by maximum likelihood estimation via stochastic gradient algorithm. Experiments show that the proposed method is capable of learning meaningful and interpretable templates that can be used for object detection, classification and clustering.

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 a 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.

Given a convolutional neural network (CNN) that is pre-trained for object classification, this paper proposes to use active question-answering to semanticize neural patterns in conv-layers of the CNN and mine part concepts. For each part concept, we mine neural patterns in the pre-trained CNN, which are related to the target part, and use these patterns to construct an And-Or graph (AOG) to represent a four-layer semantic hierarchy of the part. As an interpretable model, the AOG associates different CNN units with different explicit object parts. We use an active human-computer communication to incrementally grow such an AOG on the pre-trained CNN as follows. We allow the computer to actively identify objects, whose neural patterns cannot be explained by the current AOG. Then, the computer asks human about the unexplained objects, and uses the answers to automatically discover certain CNN patterns corresponding to the missing knowledge. We incrementally grow the AOG to encode new knowledge discovered during the active-learning process. In experiments, our method exhibits high learning efficiency. Our method uses about 1/6-1/3 of the part annotations for training, but achieves similar or better part-localization performance than fast-RCNN methods.

The convolutional neural network (ConvNet or CNN) has proven to be very successful in many tasks such as those in computer vision. In this conceptual paper, we study the generative perspective of the discriminative CNN. In particular, we propose to learn the generative FRAME (Filters, Random field, And Maximum Entropy) model using the highly expressive filters pre-learned by the CNN at the convolutional layers. We show that the learning algorithm can generate realistic and rich object and texture patterns in natural scenes. We explain that each learned model corresponds to a new CNN unit at a layer above the layer of filters employed by the model. We further show that it is possible to learn a new layer of CNN units using a generative CNN model, which is a product of experts model, and the learning algorithm admits an EM interpretation with binary latent variables.

We show that a generative random field model, which we call generative ConvNet, can be derived from the commonly used discriminative ConvNet, by assuming a ConvNet for multi-category classification and assuming one of the category is a base category generated by a reference distribution. If we further assume that the non-linearity in the ConvNet is Rectified Linear Unit (ReLU) and the reference distribution is Gaussian white noise, then we obtain a generative ConvNet model that is unique among energy-based models: The model is piecewise Gaussian, and the means of the Gaussian pieces are defined by an auto-encoder, where the filters in the bottom-up encoding become the basis functions in the top-down decoding, and the binary activation variables detected by the filters in the bottom-up convolution process become the coefficients of the basis functions in the top-down deconvolution process. The Langevin dynamics for sampling the generative ConvNet is driven by the reconstruction error of this auto-encoder. The contrastive divergence learning of the generative ConvNet reconstructs the training images by the auto-encoder. The maximum likelihood learning algorithm can synthesize realistic natural image patterns.

This paper reformulates the theory of graph mining on the technical basis of graph matching, and extends its scope of applications to computer vision. Given a set of attributed relational graphs (ARGs), we propose to use a hierarchical And-Or Graph (AoG) to model the pattern of maximal-size common subgraphs embedded in the ARGs, and we develop a general method to mine the AoG model from the unlabeled ARGs. This method provides a general solution to the problem of mining hierarchical models from unannotated visual data without exhaustive search of objects. We apply our method to RGB/RGB-D images and videos to demonstrate its generality and the wide range of applicability. The code will be available at https://sites.google.com/site/quanshizhang/mining-and-or-graphs.

This paper proposes an unsupervised method for learning dictionaries of hierarchical compositional models for representing natural images. Each model is in the form of a template that consists of a small group of part templates that are allowed to shift their locations and orientations relative to each other, and each part template is in turn a composition of Gabor wavelets that are also allowed to shift their locations and orientations relative to each other. Given a set of unannotated training images, a dictionary of such hierarchical templates are learned so that each training image can be represented by a small number of templates that are spatially translated, rotated and scaled versions of the templates in the learned dictionary. The learning algorithm iterates between the following two steps: (1) Image encoding by a template matching pursuit process that involves a bottom-up template matching sub-process and a top-down template localization sub-process. (2) Dictionary re-learning by a shared matching pursuit process. Experimental results show that the proposed approach is capable of learning meaningful templates, and the learned templates are useful for tasks such as domain adaption and image cosegmentation.

We investigate an inhomogeneous version of the FRAME (Filters, Random field, And Maximum Entropy) model and apply it to modeling object patterns. The inhomogeneous FRAME is a non-stationary Markov random field model that reproduces the observed marginal distributions or statistics of filter responses at all the different locations, scales and orientations. Our experiments show that the inhomogeneous FRAME model is capable of generating a wide variety of object patterns in natural images. We then propose a sparsified version of the inhomogeneous FRAME model where the model reproduces observed statistical properties of filter responses at a small number of selected locations, scales and orientations. We propose to select these locations, scales and orientations by a shared sparse coding scheme, and we explore the connection between the sparse FRAME model and the linear additive sparse coding model. Our experiments show that it is possible to learn sparse FRAME models in unsupervised fashion and the learned models are useful for object classification.

Co segmentation refers to the problem of segmenting multiple images simultaneously by exploiting the similarities between the foreground and background regions in these images. The key issue in co segmentation is to align common objects between these images. To address this issue, we propose an unsupervised learning framework for co segmentation, by coupling co segmentation with what we call ``co sketch''. The goal of co sketch is to automatically discover a codebook of deformable shape templates shared by the input images. These shape templates capture distinct image patterns and each template is matched to similar image patches in different images. Thus the co sketch of the images helps to align foreground objects, thereby providing crucial information for co segmentation. We present a statistical model whose energy function couples co sketch and co segmentation. We then present an unsupervised learning algorithm that performs co sketch and co segmentation by energy minimization. Experiments show that our method outperforms state of the art methods for co segmentation on the challenging MSRC and iciest datasets. We also illustrate our method on a new dataset called Coseg-Rep where co segmentation can be performed within a single image with repetitive patterns.

This paper proposes a sparse image representation using deformable templates of simple geometric structures that are commonly observed in images of natural scenes. These deformable templates include active curve templates and active corner templates. An active curve template is a composition of Gabor wavelet elements placed with equal spacing on a straight line segment or a circular arc segment of constant curvature, where each Gabor wavelet element is allowed to locally shift its location and orientation, so that the original line and arc segment of the active curve template can be deformed to fit the observed image. An active corner or angle template is a composition of two active curve templates that share a common end point, and the active curve templates are allowed to vary their overall lengths and curvatures, so that the original corner template can deform to match the observed image. This paper then proposes a hierarchical computational architecture of summax maps that pursues a sparse representation of an image by selecting a small number of active curve and corner templates from a dictionary of all such templates. Experiments show that the proposed method is capable of finding sparse representations of natural images. It is also shown that object templates can be learned by selecting and composing active curve and corner templates.

This article proposes an active basis model, a shared sketch algorithm, and a computational architecture of sum-max maps for representing, learning, and recognizing deformable templates. In our generative model, a deformable template is in the form of an active basis, which consists of a small number of Gabor wavelet elements at selected locations and orientations. These elements are allowed to slightly perturb their locations and orientations before they are linearly combined to generate the observed image. The active basis model, in particular, the locations and the orientations of the basis elements, can be learned from training images by the shared sketch algorithm. The algorithm selects the elements of the active basis sequentially from a dictionary of Gabor wavelets. When an element is selected at each step, the element is shared by all the training images, and the element is perturbed to encode or sketch a nearby edge segment in each training image. The recognition of the deformable template from an image can be accomplished by a computational architecture that alternates the sum maps and the max maps. The computation of the max maps deforms the active basis to match the image data, and the computation of the sum maps scores the template matching by the log-likelihood of the deformed active basis.

This article proposes a method for learning object templates composed of local sketches and local textures, and investigates the relative importance of the sketches and textures for different object categories. Local sketches and local textures in the object templates account for shapes and appearances respectively. Both local sketches and local textures are extracted from the maps of Gabor filter responses. The local sketches are captured by the local maxima of Gabor responses, where the local maximum pooling accounts for shape deformations in objects. The local textures are captured by the local averages of Gabor filter responses, where the local average pooling extracts texture information for appearances. The selection of local sketch variables and local texture variables can be accomplished by a projection pursuit type of learning process, where both types of variables can be compared and merged within a common framework. The learning process returns a generative model for image intensities from a relatively small number of training images. The recognition or classification by template matching can then be based on log-likelihood ratio scores. We apply the learning method to a variety of object and texture categories. The results show that both the sketches and textures are useful for classification, and they complement each other.

This article proposes an active basis model and a shared pursuit algorithm for learning deformable templates from image patches of various object categories. In our generative model, a deformable template is in the form of an active basis, which consists of a small number of Gabor wavelet elements at different locations and orientations. These elements are allowed to slightly perturb their locations and orientations before they are linearly combined to generate each individual training or testing example. The active basis model can be learned from training image patches by the shared pursuit algorithm. The algorithm selects the elements of the active basis sequentially from a dictionary of Gabor wavelets. When an element is selected at each step, the element is shared by all the training examples, in the sense that a perturbed version of this element is added to improve the encoding of each example. Our model and algorithm are developed within a probabilistic framework that naturally embraces wavelet sparse coding and random field.

In this paper, we present a mathematical theory for Marr's primal sketch. We first conduct a theoretical study of the descriptive Markov random field model and the generative wavelet/sparse coding model from the perspective of entropy and complexity. The competition between the two types of models defines the concept of "sketchability", which divides image into texture and geometry. We then propose a primal sketch model that integrates the two models and, in addition, a Gestalt field model for spatial organization. We also propose a sketching pursuit process that coordinates the competition between two pursuit algorithms: the matching pursuit (Mallat and Zhang, 1993) and the filter pursuit (Zhu, et al., 1997), that seek to explain the image by bases and filters respectively. The model can be used to learn a dictionary of image primitives, or textons in Julesz's language, for natural images. The primal sketch model is not only parsimonious for image representation, but produces meaningful sketches over a large number of generic images.

Dynamic textures are sequences of images that exhibit some form of temporal stationarity, such as waves, steam, and foliage. We pose the problem of recognizing and classifying dynamic textures in the space of dynamical systems where each dynamic texture is uniquely represented. Since the space is non-linear, a distance between models must be defined We examine three different distances in the space of autoregressive models and assess their power.

Dynamic textures are sequences of images of moving scenes that exhibit certain stationarity properties in time; these include sea-waves, smoke, foliage, whirlwind but also talking faces, traffic scenes etc. We present a novel characterization of dynamic textures that poses the problems of modelling, learning, recognizing and synthesizing dynamic textures on a firm analytical footing. We borrow tools from system identification to capture the "essence" of dynamic textures; we do so by learning (i.e. identifying) models that are optimal in the sense of maximum likelihood or minimum prediction error variance. For the special case of second-order stationary processes we identify the model in closed form. Once learned, a model has predictive power and can be used for extrapolating synthetic sequences to infinite length with negligible computational cost. We present experimental evidence that, within our framework, even low dimensional models can capture very complex visual phenomena.

Many problems in vision can be formulated as Bayesian inference. It is important to determine the accuracy of these inferences and how they depend on the problem domain. In recent work, Coughlan and Yuille showed that, for a restricted class of problems, the performance of Bayesian inference could be summarized by an order parameter K which depends on the probability distributions which characterize the problem domain. In this paper we generalize the theory of order parameters so that it applies to domains for which the probability models can be obtained by Minimax Entropy learning theory. By analyzing order parameters it is possible to determine whether a target can be detected using a general purpose "generic" model or whether a more specific "high-level" model is needed. At critical values of the order parameters the problem becomes unsolvable without the addition of extra prior knowledge.

Presents a mathematical definition of texture, the Julesz ensemble /spl Omega/(h), which is the set of all images (defined on Z/sup 2/) that share identical statistics h. Then texture modeling is posed as an inverse problem: Given a set of images sampled from an unknown /spl Omega/(h/sub */), we search for the statistics h/sub */ which define the ensemble. A /spl Omega/(h) has an associated probability distribution q(I; h), which is uniform over the images in /spl Omega/(h) and has zero probability outside. The authors previously (1999) showed q(I; h) to be the limit distribution of the FRAME (filter, random field, and minimax entropy) model, as the image lattice /spl Lambda//spl rarr/Z/sup 2/. This conclusion establishes the intrinsic link between the scientific definition of texture on Z/sup 2/ and the mathematical models of texture on finite lattices. It brings two advantages: the practice of texture image synthesis by matching statistics is put on a mathematical foundation; and we need not learn the expensive FRAME model in feature pursuit, model selection and texture synthesis. An efficient Markov chain Monte Carte algorithm is proposed for sampling Julesz ensembles. It generates random texture images by moving along the directions of filter coefficients and, thus, extends the traditional single site Gibbs sampler. We compare four popular statistical measures in the literature, in terms of their descriptive abilities. Our experiments suggest that a small number of bins in marginal histograms are sufficient for capturing a variety of texture patterns.

Research on texture has been pursued along two different lines. The first line of research, pioneered by Julesz (1962), seeks the essential ingredients in terms of features and statistics in human texture perception. This leads us to a mathematical definition of texture as a Julesz ensemble. A Julesz ensemble is the maximum set of images that share the same value of some basic feature statistics as the image lattice /spl Lambda//spl rarr/Z/sup 2/, or equivalently it is a uniform distribution on this set. The second line of research studies statistical models, in particular, Markov random field (MRF) and FRAME models (Zhu et al., 1997), to characterize texture patterns locally. In this article, we bridge the two lines by the fundamental principle of equivalence of ensembles in statistical mechanics (Gibbs, 1902). We prove that 1) the conditional probability of an arbitrary image patch given its environment, under the Julesz ensemble or the uniform model, is inevitably a FRAME (MRF) model, and 2) the limit of the FRAME (MRF) model, which we called the Gibbs ensemble, is equivalent to a Julesz ensemble as /spl Lambda//spl rarr/Z/sup 2/. Thus the advantages of the two methodologies can be fully utilized.

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed; in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and an information criterion for feature pursuit is derived. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (filter, random field, and minimax entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. The relationship between our theory and the mechanisms of neural computation is also discussed.

In this paper, a minimax entropy principle is studied, based on which a novel theory, called FRAME (Filters, Random fields And Minimax Entropy) is proposed for texture modeling. FRAME combines attractive aspects of two important themes in texture modeling: multi-channel filtering and Markov random field (MRF) modeling. It incorporates the responses of a set of well selected filters into the distribution over a random field and hence has a much stronger descriptive ability than the traditional MRF models. Furthermore, it interprets and clarifies many previous concepts and methods for texture analysis and synthesis from a unified point of view. Algorithms are proposed for probability inference, stochastic simulation and filter selection. Experiments on a variety of textures are described to illustrate our theory and to show the performance of our algorithms. These experiments demonstrate that many textures previously considered as different categories can be modeled and synthesized in a common framework.