Zhuofeng Li, Yi Lu, Dongfu Jiang, Haoxiang Zhang, Yuyang Bai, Chuan Li, Yu Wang, Shuiwang Ji, Jianwen Xie, Yu Zhang. Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers). 2026.

We present a central-peripheral vision-inspired framework (CVP), a simple yet effective multimodal model for spatial reasoning that draws inspiration from the two types of human visual fields – central vision and peripheral vision. Existing approaches primarily rely on unstructured representations, such as point clouds, voxels, or patch features, and inject scene context implicitly via coordinate embeddings. However, this often results in limited spatial reasoning capabilities due to the lack of explicit, high-level structural understanding. To address this limitation, we introduce two complementary components into a Large Multimodal Model-based architecture: target-affinity token, analogous to central vision, that guides the model’s attention toward query-relevant objects; and allocentric grid, akin to peripheral vision, that captures global scene context and spatial arrangements. These components work in tandem to enable structured, context-aware understanding of complex 3D environments. Experiments show that CVP achieves state-of-the-art performance across a range of 3D scene understanding benchmarks.

Theory-of-Mind (ToM) tasks pose a unique challenge for large language models (LLMs), which often lack the capability for dynamic logical reasoning.In this work, we propose DEL-ToM, a framework that improves verifiable ToM reasoning through inference-time scaling rather than architectural changes.Our approach decomposes ToM tasks into a sequence of belief updates grounded in Dynamic Epistemic Logic (DEL), enabling structured and verifiable dynamic logical reasoning.We use data generated automatically via a DEL simulator to train a verifier, which we call the Process Belief Model (PBM), to score each belief update step.During inference, the PBM evaluates candidate belief traces from the LLM and selects the highest-scoring one.This allows LLMs to allocate extra inference-time compute to yield more transparent reasoning.Experiments across model scales and benchmarks show that DEL-ToM consistently improves performance, demonstrating that verifiable belief supervision significantly enhances LLMs' ToM capabilities without retraining.

Large Reasoning Models (LRMs) are often bottlenecked by the high cost of output tokens.We show that a significant portion of these tokens are useless self-repetitions -what we call "word salad" -that exhaust the decoding budget without adding value.Interestingly, we observe that LRMs are self-aware when trapped in these loops: the hidden states of <\n\n> tokens trailing each reasoning chunk exhibit patterns that allow us to detect word salad behavior onthe-fly via a single-layer linear classifier.Once detected, a simple chop appended by a straightforward regeneration prompt yields substantial length savings with minimal quality loss.Our work offers WordSaladChopper (WSC) -a lightweight, turnkey component for LRM that is minimally invasive to its reasoning trajectory by only removing semantically redundant tokens.Given its low overhead, strong savings, and the lack of semantic value of word salad tokens, we believe it is not too far-fetched to argue that WSC -or a similar component -is a must-have for all LRM applications with user experience in mind.

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.

Despite steady progress in layout-to-image generation, current methods still struggle with layouts containing significant overlap between bounding boxes. We identify two primary challenges: (1) large overlapping regions and (2) overlapping instances with minimal semantic distinction. Through both qualitative examples and quantitative analysis, we demonstrate how these factors degrade generation quality. To systematically assess this issue, we introduce OverLayScore, a novel metric that quantifies the complexity of overlapping bounding boxes. Our analysis reveals that existing benchmarks are biased toward simpler cases with low OverLayScore values, limiting their effectiveness in evaluating models under more challenging conditions. To reduce this gap, we present OverLayBench, a new benchmark featuring balanced OverLayScore distributions and high-quality annotations. As an initial step toward improved performance on complex overlaps, we also propose CreatiLayout-AM, a model trained on a curated amodal mask dataset. Together, our contributions establish a foundation for more robust layout-to-image generation under realistic and challenging scenarios.

SO(3)-equivariant networks are the dominant models for machine learning interatomic potentials (MLIPs). The key operation of such networks is the Clebsch-Gordan (CG) tensor product, which is computationally expensive. To accelerate the computation, we develop tensor decomposition networks (TDNs) as a class of approximately equivariant networks whose CG tensor products are replaced by low-rank tensor decompositions, such as the CANDECOMP/PARAFAC (CP) decomposition. With the CP decomposition, we prove (i) a uniform bound on the induced error of SO(3)-equivariance, and (ii) the universality of approximating any equivariant bilinear map. To further reduce the number of parameters, we propose path-weight sharing that ties all multiplicity-space weights across the O(L^3) CG paths into a single shared parameter set without compromising equivariance, where L is the maximum angular degree. The resulting layer acts as a plug-and-play replacement for tensor products in existing networks, and the computational complexity of tensor products is reduced from O(L^6) to O(L^4). We evaluate TDNs on PubChemQCR, a newly curated molecular relaxation dataset containing 105 million DFT-calculated snapshots. We also use existing datasets, including OC20, and OC22. Results show that TDNs achieve competitive performance with dramatic speedup in computations. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Despite recent advances on multi-modal models, 3D spatial reasoning remains a challenging task for state-of-the-art open-source and proprietary models. Recent studies explore data-driven approaches and achieve enhanced spatial reasoning performance by fine-tuning models on 3D-related visual question-answering data. However, these methods typically perform spatial reasoning in an implicit manner and often fail on questions that are trivial to humans, even with long chain-of-thought reasoning. In this work, we introduce SpatialReasoner, a novel large vision-language model (LVLM) that addresses 3D spatial reasoning with explicit 3D representations shared between multiple stages--3D perception, computation, and reasoning. Explicit 3D representations provide a coherent interface that supports advanced 3D spatial reasoning and improves the generalization ability to novel question types. Furthermore, by analyzing the explicit 3D representations in multi-step reasoning traces of SpatialReasoner, we study the factual errors and identify key shortcomings of current LVLMs. Results show that our SpatialReasoner achieves improved performance on a variety of spatial reasoning benchmarks, outperforming Gemini 2.0 by 9.2% on 3DSRBench, and generalizes better when evaluating on novel 3D spatial reasoning questions. Our study bridges the 3D parsing capabilities of prior visual foundation models with the powerful reasoning abilities of large language models, opening new directions for 3D spatial reasoning.

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.

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.

We study a normalizing flow in the latent space of a top-down generator model, in which the normalizing flow model plays the role of the informative prior model of the generator. We propose to jointly learn the latent space normalizing flow prior model and the top-down generator model by a Markov chain Monte Carlo (MCMC)-based maximum likelihood algorithm, where a short-run Langevin sampling from the intractable posterior distribution is performed to infer the latent variables for each observed example, so that the parameters of the normalizing flow prior and the generator can be updated with the inferred latent variables. We show that, under the scenario of non-convergent short-run MCMC, the finite step Langevin dynamics is a flow-like approximate inference model and the learning objective actually follows the perturbation of the maximum likelihood estimation (MLE). We further point out that the learning framework seeks to (i) match the latent space normalizing flow and the aggregated posterior produced by the short-run Langevin flow, and (ii) bias the model from MLE such that the short-run Langevin flow inference is close to the true posterior. Empirical results of extensive experiments validate the effectiveness of the proposed latent space normalizing flow model in the tasks of image generation, image reconstruction, anomaly detection, supervised image inpainting and unsupervised image recovery.

Numerous research efforts have been made to stabilize the training of the Generative Adversarial Networks (GANs), such as through regularization and architecture design. However, we identify the instability can also arise from the fragile balance at the early stage of adversarial learning. This paper proposes the CoopInit, a simple yet effective cooperative learning-based initialization strategy that can quickly learn a good starting point for GANs, with a very small computation overhead during training. The proposed algorithm consists of two learning stages: (i) Cooperative initialization stage: The discriminator of GAN is treated as an energy-based model (EBM) and is optimized via maximum likelihood estimation (MLE), with the help of the GAN's generator to provide synthetic data to approximate the learning gradients. The EBM also guides the MLE learning of the generator via MCMC teaching; (ii) Adversarial finalization stage: After a few iterations of initialization, the algorithm seamlessly transits to the regular mini-max adversarial training until convergence. The motivation is that the MLE-based initialization stage drives the model towards mode coverage, which is helpful in alleviating the issue of mode dropping during the adversarial learning stage. We demonstrate the effectiveness of the proposed approach on image generation and one-sided unpaired image-to-image translation tasks through extensive experiments.

We propose the NeRF-LEBM, a likelihoodbased top-down 3D-aware 2D image generative model that incorporates 3D representation via Neural Radiance Fields (NeRF) and 2D imaging process via differentiable volume rendering. The model represents an image as a rendering process from 3D object to 2D image and is conditioned on some latent variables that account for object characteristics and are assumed to follow informative trainable energy-based prior models. We propose two likelihood-based learning frameworks to train the NeRF-LEBM: (i) maximum likelihood estimation with Markov chain Monte Carlo-based inference and (ii) variational inference with the reparameterization trick. We study our models in the scenarios with both known and unknown camera poses. Experiments on several benchmark datasets demonstrate that the NeRF-LEBM can infer 3D object structures from 2D images, generate 2D images with novel views and objects, learn from incomplete 2D images, and learn from 2D images with known or unknown camera poses.

We propose a novel generative saliency prediction framework that adopts an informative energy-based model as a prior distribution. The energy-based prior model is defined on the latent space of a saliency generator network that generates the saliency map based on a continuous latent variables and an observed image. Both the parameters of saliency generator and the energy-based prior are jointly trained via Markov chain Monte Carlo-based maximum likelihood estimation, in which the sampling from the intractable posterior and prior distributions of the latent variables are performed by Langevin dynamics. With the generative saliency model, we can obtain a pixel-wise uncertainty map from an image, indicating model confidence in the saliency prediction. Different from existing generative models, which define the prior distribution of the latent variables as a simple isotropic Gaussian distribution, our model uses an energy-based informative prior which can be more expressive in capturing the latent space of the data. With the informative energy-based prior, we extend the Gaussian distribution assumption of generative models to achieve a more representative distribution of the latent space, leading to more reliable uncertainty estimation. We apply the proposed frameworks to both RGB and RGB-D salient object detection tasks with both transformer and convolutional neural network backbones. We further propose an adversarial learning algorithm and a variational inference algorithm as alternatives to train the proposed generative framework. Experimental results show that our generative saliency model with an energy-based prior can achieve not only accurate saliency predictions but also reliable uncertainty maps that are consistent with human perception.

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.

Conventional saliency prediction models typically learn a deterministic mapping from an image to its saliency map, and thus fail to explain the subjective nature of human attention. In this paper, to model the uncertainty of visual saliency, we study the saliency prediction problem from the perspective of generative models by learning a conditional probability distribution over the saliency map given an input image, and treating the saliency prediction as a sampling process from the learned distribution. Specifically, we propose a generative cooperative saliency prediction framework, where a conditional latent variable model~(LVM) and a conditional energy-based model~(EBM) are jointly trained to predict salient objects in a cooperative manner. The LVM serves as a fast but coarse predictor to efficiently produce an initial saliency map, which is then refined by the iterative Langevin revision of the EBM that serves as a slow but fine predictor. Such a coarse-to-fine cooperative saliency prediction strategy offers the best of both worlds. Moreover, we propose a ``cooperative learning while recovering" strategy and apply it to weakly supervised saliency prediction, where saliency annotations of training images are partially observed. Lastly, we find that the learned energy function in the EBM can serve as a refinement module that can refine the results of other pre-trained saliency prediction models. Experimental results show that our model can produce a set of diverse and plausible saliency maps of an image, and obtain state-of-the-art performance in both fully supervised and weakly supervised saliency prediction tasks.

While researches on model-based blind single image super-resolution (SISR) have achieved tremendous successes recently, most of them do not consider the image degradation sufficiently. Firstly, they always assume image noise obeys an independent and identically distributed (i.i.d.) Gaussian or Laplacian distribution, which largely underestimates the complexity of real noise. Secondly, previous commonly-used kernel priors (e.g., normalization, sparsity) are not effective enough to guarantee a rational kernel solution, and thus degenerates the performance of subsequent SISR task. To address the above issues, this paper proposes a model-based blind SISR method under the probabilistic framework, which elaborately models image degradation from the perspectives of noise and blur kernel. Specifically, instead of the traditional i.i.d. noise assumption, a patch-based non-i.i.d. noise model is proposed to tackle the complicated real noise, expecting to increase the degrees of freedom of the model for noise representation. As for the blur kernel, we novelly construct a concise yet effective kernel generator, and plug it into the proposed blind SISR method as an explicit kernel prior (EKP). To solve the proposed model, a theoretically grounded Monte Carlo EM algorithm is specifically designed. Comprehensive experiments demonstrate the superiority of our method over current state-of-the-arts on synthetic and real datasets. The source code is available at https://github.com/zsyOAOA/BSRDM.

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.

In this paper, we propose a pose grammar to tackle the problem of 3D human pose estimation from a monocular RGB image. Our model takes estimated 2D pose as the input and learns a generalized 2D-3D mapping function to leverage into 3D pose. The proposed model consists of a base network which efficiently captures pose-aligned features and a hierarchy of Bi-directional RNNs (BRNNs) on the top to explicitly incorporate a set of knowledge regarding human body configuration (i.e., kinematics, symmetry, motor coordination). The proposed model thus enforces high-level constraints over human poses. In learning, we develop a data augmentation algorithm to further improve model robustness against appearance variations and cross-view generalization ability. We validate our method on public 3D human pose benchmarks and propose a new evaluation protocol working on cross-view setting to verify the generalization capability of different methods. We empirically observe that most state-of-the-art methods encounter difficulty under such setting while our method can well handle such challenges.

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.

Due to the intractable partition function, training energy-based models (EBMs) by maximum likelihood requires Markov chain Monte Carlo (MCMC) sampling to approximate the gradient of the Kullback-Leibler divergence between data and model distributions. However, it is non-trivial to sample from an EBM because of the difficulty of mixing between modes. In this paper, we propose to learn a variational auto-encoder (VAE) to initialize the finite-step MCMC, such as Langevin dynamics that is derived from the energy function, for efficient amortized sampling of the EBM. With these amortized MCMC samples, the EBM can be trained by maximum likelihood, which follows an "analysis by synthesis" scheme; while the VAE learns from these MCMC samples via variational Bayes. We call this joint training algorithm the variational MCMC teaching, in which the VAE chases the EBM toward data distribution. We interpret the learning algorithm as a dynamic alternating projection in the context of information geometry. Our proposed models can generate samples comparable to GANs and EBMs. Additionally, we demonstrate that our model can learn effective probabilistic distribution toward supervised conditional learning tasks.

For a good advertising effect, images in the ad should be highly relevant with the ad title. The images in an ad are normally selected from the gallery based on their relevance scores with the ad's title. To ensure the selected images are relevant with the title, a reliable text-image matching model is necessary. The state-of-the-art text- image matching model, cross-modal BERT, only understands the visual content in the image, which is sub-optimal when the image description is available. In this work, we present MixBERT, an adimage relevance scoring model. It models the ad-image relevance by matching the ad title with the image description and visual content. MixBERT adopts a two-stream architecture. It adaptively selects the useful information from noisy image description and suppresses the noise impeding effective matching. To effectively describe the details in visual content of the image, a set of local convolutional features is used as the initial representation of the image. Moreover, to enhance the perceptual capability of our model in key entities which are important to advertising, we upgrade masked language modeling in vanilla BERT to masked key entity modeling. Offline and online experiments demonstrate its effectiveness.

Learning latent variable models with deep top-down architectures typically requires inferring the latent variables for each training example based on the posterior distribution of these latent variables. The inference step typically relies on either time-consuming long-run Markov chain Monte Carlo (MCMC) sampling or a separate inference model for variational learning. In this paper, we propose to use a shortrun MCMC, such as a short-run Langevin dynamics, as an approximate flow-based inference engine. The bias existing in the output distribution of the non-convergent short-run Langevin dynamics is corrected by the optimal transport (OT), which aims at transforming the biased distribution produced by the finite-step MCMC to the prior distribution with a minimum transport cost. Our experiments not only verify the effectiveness of the OT correction for the short-run MCMC, but also demonstrate that the latent variable model trained by the proposed strategy performs better than the variational auto-encoder (VAE) in terms of image reconstruction/generation and anomaly detection.

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.

While deep learning (DL)-based video deraining methods have achieved significant successes in recent years, they still have two major drawbacks. Firstly, most of them are insufficient to model the characteristics of rain layers contained in rainy videos. In fact, the rain layers exhibit strong visual properties (e.g., direction, scale, and thickness) in spatial dimension and causal properties (e.g., velocity and acceleration) in temporal dimension, and thus can be modeled by the spatial-temporal process in statistics. Secondly, current DL-based methods rely heavily on the labeled training data, whose rain layers are synthetic, thus leading to a deviation from real data. Such a gap between synthetic and real data sets results in poor performance when applying them to real scenarios. To address these issues, this paper proposes a new semi-supervised video deraining method, in which a dynamical rain generator is employed to fit the rain layer for the sake of better depicting its intrinsic characteristics. Specifically, the dynamical generator consists of one emission model and one transition model to simultaneously encode the spatial appearance and temporal dynamics of rain streaks, respectively, both of which are parameterized by deep neural networks (DNNs). Furthermore, different prior formats are designed for the labeled synthetic and unlabeled real data so as to fully exploit their underlying common knowledge. Last but not least, we design a Monte Carlo-based EM algorithm to learn the model. Extensive experiments are conducted to verify the superiority of the proposed semi-supervised deraining model.

Exploiting internal statistics of a single natural image has long been recognized as a significant research paradigm where the goal is to learn the internal distribution of patches within the image without relying on external training data. Different from prior works that model such a distribution implicitly with a top-down latent variable model (e.g., generator), this paper proposes to explicitly represent the statistical distribution within a single natural image by using an energy-based generative framework, where a pyramid of energy functions, each parameterized by a bottom-up deep neural network, are used to capture the distributions of patches at different resolutions. Meanwhile, a coarse-to-fine sequential training and sampling strategy is presented to train the model efficiently. Besides learning to generate random samples from white noise, the model can learn in parallel with a self-supervised task (e.g., recover the input image from its corrupted version), which can further improve the descriptive power of the learned model. The proposed model is simple and natural in that it does not require an auxiliary model (e.g., discriminator) to assist the training. Besides, it also unifies internal statistics learning and image generation in a single framework. Experimental results presented on various image generation and manipulation tasks, including super-resolution, image editing, harmonization, style transfer, etc, have demonstrated the effectiveness of our model for internal learning.

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.

Vision transformer networks have shown superiority in many computer vision tasks. In this paper, we take a step further by proposing a novel generative vision transformer with latent variables following an informative energy-based prior for salient object detection. Both the vision transformer network and the energy-based prior model are jointly trained via Markov chain Monte Carlo-based maximum likelihood estimation, in which the sampling from the intractable posterior and prior distributions of the latent variables are performed by Langevin dynamics. Further, with the generative vision transformer, we can easily obtain a pixel-wise uncertainty map from an image, which indicates the model confidence in predicting saliency from the image. Different from the existing generative models which define the prior distribution of the latent variables as a simple isotropic Gaussian distribution, our model uses an energy-based informative prior which can be more expressive to capture the latent space of the data. We apply the proposed framework to both RGB and RGB-D salient object detection tasks. Extensive experimental results show that our framework can achieve not only accurate saliency predictions but also meaningful uncertainty maps that are consistent with the human perception.

Predicting where people look in static scenes, a.k.a visual saliency, has received significant research interest recently. However, relatively less effort has been spent in understanding and modeling visual attention over dynamic scenes. This work makes three contributions to video saliency research. First, we introduce a new benchmark, called DHF1K (Dynamic Human Fixation 1K), for predicting fixations during dynamic scene free-viewing, which is a long-time need in this field. DHF1K consists of 1K high-quality elaborately-selected video sequences annotated by 17 observers using an eye tracker device. The videos span a wide range of scenes, motions, object types and backgrounds. Second, we propose a novel video saliency model, called ACLNet (Attentive CNN-LSTM Network), that augments the CNN-LSTM architecture with a supervised attention mechanism to enable fast end-to-end saliency learning. The attention mechanism explicitly encodes static saliency information, thus allowing LSTM to focus on learning a more flexible temporal saliency representation across successive frames. Such a design fully leverages existing large-scale static fixation datasets, avoids overfitting, and significantly improves training efficiency and testing performance. Third, we perform an extensive evaluation of the state-of-the-art saliency models on three datasets : DHF1K, Hollywood-2, and UCF sports. An attribute-based analysis of previous saliency models and cross-dataset generalization are also presented. Experimental results over more than 1.2K testing videos containing 400K frames demonstrate that ACLNet outperforms other contenders and has a fast processing speed (40 fps using a single GPU). Our code and all the results are available at https://github.com/wenguanwang/DHF1K.

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.

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 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 a segregated temporal assembly recurrent (STAR) network for weakly-supervised multiple action detection. The model learns from untrimmed videos with only supervision of video-level labels and makes prediction of intervals of multiple actions. Specifically, we first assemble video clips according to class labels by an attention mechanism that learns class-variable attention weights and thus helps the noise relieving from background or other actions. Secondly, we build temporal relationship between actions by feeding the assembled features into an enhanced recurrent neural network. Finally, we transform the output of recurrent neural network into the corresponding action distribution. In order to generate more precise temporal proposals, we design a score term called segregated temporal gradient-weighted class activation mapping (ST-GradCAM) fused with attention weights. Experiments on THUMOS’14 and ActivityNet1.3 datasets show that our approach outperforms the state-of-theart weakly-supervised method, and performs at par with the fully-supervised counterparts.

We investigate learning feature-to-feature translator networks by alternating back-propagation as a general-purpose solution to zero-shot learning (ZSL) problems. It is a generative model-based ZSL framework. In contrast to models based on generative adversarial networks (GAN) or variational autoencoders (VAE) that require auxiliary networks to assist the training, our model consists of a single conditional generator that maps class-level semantic features and Gaussian white noise vectors accounting for instance-level latent factors to visual features, and is trained by maximum likelihood estimation. The training process is a simple yet effective alternating back-propagation process that iterates the following two steps: (i) the inferential back-propagation to infer the latent noise vector of each observed example, and (ii) the learning back-propagation to update the model parameters. We show that, with slight modifications, our model is capable of learning from incomplete visual features for ZSL. We conduct extensive comparisons with existing generative ZSL methods on five benchmarks, demonstrating the superiority of our method in not only ZSL performance but also convergence speed and computational cost. Specifically, our model outperforms the existing state-of-the-art methods by a remarkable margin up to 3.1% and 4.0% in ZSL and generalized ZSL settings, respectively.

Zero-shot learning extends the conventional object classification to the unseen class recognition by introducing semantic representations of classes. Existing approaches predominantly focus on learning the proper mapping function for visual-semantic embedding, while neglecting the effect of learning discriminative visual features. In this paper, we study the significance of the discriminative region localization. We propose a semantic-guided multi-attention localization model, which automatically discovers the most discriminative parts of objects for zero-shot learning without any human annotations. Our model jointly learns cooperative global and local features from the whole object as well as the detected parts to categorize objects based on semantic descriptions. Moreover, with the joint supervision of embedding softmax loss and class-center triplet loss, the model is encouraged to learn features with high inter-class dispersion and intra-class compactness. Through comprehensive experiments on three widely used zero-shot learning benchmarks, we show the efficacy of the multi-attention localization and our proposed approach improves the state-of-the-art results by a considerable margin.

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.

Human body part parsing, or human semantic part segmentation, is fundamental to many computer vision tasks. In conventional semantic segmentation methods, the ground truth segmentations are provided, and fully convolutional networks (FCN) are trained in an end-to-end scheme. Although these methods have demonstrated impressive results, their performance highly depends on the quantity and quality of training data. In this paper, we present a novel method to generate synthetic human part segmentation data using easily-obtained human keypoint annotations. Our key idea is to exploit the anatomical similarity among human to transfer the parsing results of a person to another person with similar pose. Using these estimated results as additional training data, our semi-supervised model outperforms its strong-supervised counterpart by 6 mIOU on the PASCAL-Person-Part dataset [6], and we achieve state-of-the-art human parsing results. Our approach is general and can be readily extended to other object/animal parsing task assuming that their anatomical similarity can be annotated by keypoints. The proposed model and accompanying source code will be made publicly available.

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.

Tracking humans that are interacting with the other subjects or environment remains unsolved in visual tracking, because the visibility of the human of interests in videos is unknown and might vary over time. In particular, it is still difficult for state-of-the-art human trackers to recover complete human trajectories in crowded scenes with frequent human interactions. In this work, we consider the visibility status of a subject as a fluent variable, whose change is mostly attributed to the subject's interaction with the surrounding, e.g., crossing behind another object, entering a building, or getting into a vehicle, etc. We introduce a Causal And-Or Graph (C-AOG) to represent the causal-effect relations between an object's visibility fluent and its activities, and develop a probabilistic graph model to jointly reason the visibility fluent change (e.g., from visible to invisible) and track humans in videos. We formulate this joint task as an iterative search of a feasible causal graph structure that enables fast search algorithm, e.g., dynamic programming method. We apply the proposed method on challenging video sequences to evaluate its capabilities of estimating visibility fluent changes of subjects and tracking subjects of interests over time. Results with comparisons demonstrate that our method outperforms the alternative trackers and can recover complete trajectories of humans in complicated scenarios with frequent human interactions.

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.

We introduce a novel semi-supervised video segmentation approach based on an efficient video representation, called as “super-trajectory”. Each super-trajectory corresponds to a group of compact trajectories that exhibit consistent motion patterns, similar appearance and close spatiotemporal relationships. We generate trajectories using a probabilistic model, which handles occlusions and drifts in a robust and natural way. To reliably group trajectories, we adopt a modified version of the density peaks based clustering algorithm that allows capturing rich spatiotemporal relations among trajectories in the clustering process. The presented video representation is discriminative enough to accurately propagate the initial annotations in the first frame onto the remaining video frames. Extensive experimental analysis on challenging benchmarks demonstrate our method is capable of distinguishing the target objects from complex backgrounds and even reidentifying them after occlusions.

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.

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.