Diffusion models are widely used for image editing tasks. Existing editing methods often design a representation manipulation procedure by curating an edit direction in the text embedding or score space. However, such a procedure faces a key challenge: overestimating the edit strength harms visual consistency while underestimating it fails the editing task. Notably, each source image may require a different editing strength, and it is costly to search for an appropriate strength via trial-and-error. To address this challenge, we propose ${\boldsymbol{Co}}{\text{ncept}}\,{\boldsymbol{Lan}}{\text{cet}}$ (CoLan), a zero-shot plug-and-play framework for principled representation manipulation in diffusion-based image editing. At inference time, we decompose the source input in the latent (text embedding or diffusion score) space as a sparse linear combination of the representations of the collected visual concepts. This allows us to accurately estimate the presence of concepts in each image, which informs the edit. Based on the editing task (replace/add/remove), we perform a customized concept transplant process to impose the corresponding editing direction. To sufficiently model the concept space, we curate a conceptual representation dataset, CoLan-150K, which contains diverse descriptions and scenarios of visual terms and phrases for the latent dictionary. Experiments on multiple diffusion-based image editing baselines show that methods equipped with CoLan achieve state-of-the-art performance in editing effectiveness and consistency preservation.

The problem of generating a perpetual dynamic scene from a single view is an important problem with widespread applications in augmented and virtual reality, and robotics. However, since dynamic scenes regularly change over time, a key challenge is to ensure that different generated views be consistent with the underlying 3D motions. Prior work learns such consistency by training on multiple views, but the generated scene regions often interpolate between training views and fail to generate perpetual views. To address this issue, we propose DynamicVoyager, which reformulates dynamic scene generation as a scene outpainting problem with new dynamic content. As 2D outpainting models struggle at generating 3D consistent motions from a single 2D view, we enrich 2D pixels with information from their 3D rays that facilitates learning of 3D motion consistency. More specifically, we first map the single-view video input to a dynamic point cloud using the estimated video depths. We then render a partial video of the point cloud from a novel view and outpaint the missing regions using ray information (e.g., the distance from a ray to the point cloud) to generate 3D consistent motions. Next, we use the outpainted video to update the point cloud, which is used for outpainting the scene from future novel views. Moreover, we can control the generated content with the input text prompt. Experiments show that our model can generate perpetual scenes with consistent motions along fly-through cameras. Project page: https://tianfr.github.io/DynamicVoyager.

The attention operator is arguably the key distinguishing factor of transformer architectures, which have demonstrated state-of-the-art performance on a variety of tasks. However, transformer attention operators often impose a significant computational burden, with the computational complexity scaling quadratically with the number of tokens. In this work, we propose a novel transformer attention operator whose computational complexity scales linearly with the number of tokens. We derive our network architecture by extending prior work which has shown that a transformer style architecture naturally arises by "white-box" architecture design, where each layer of the network is designed to implement an incremental optimization step of a maximal coding rate reduction objective (MCR$^2$). Specifically, we derive a novel variational form of the MCR$^2$ objective and show that the architecture that results from unrolled gradient descent of this variational objective leads to a new attention module called Token Statistics Self-Attention ($\texttt{TSSA}$). $\texttt{TSSA}$ has $\textit{linear computational and memory complexity}$ and radically departs from the typical attention architecture that computes pairwise similarities between tokens. Experiments on vision, language, and long sequence tasks show that simply swapping $\texttt{TSSA}$ for standard self-attention, which we refer to as the Token Statistics Transformer ($\texttt{ToST}$), achieves competitive performance with conventional transformers while being significantly more computationally efficient and interpretable. Our results also somewhat call into question the conventional wisdom that pairwise similarity style attention mechanisms are critical to the success of transformer architectures.

The advent of large pre-trained models has brought about a paradigm shift in both visual representation learning and natural language processing. However, clustering unlabeled images, as a fundamental and classic machine learning problem, still lacks an effective solution, particularly for large-scale datasets. In this paper, we propose a novel image clustering pipeline that leverages the powerful feature representation of large pre-trained models such as CLIP and cluster images effectively and efficiently at scale. We first developed a novel algorithm to estimate the number of clusters in a given dataset. We then show that the pre-trained features are significantly more structured by further optimizing the rate reduction objective. The resulting features may significantly improve the clustering accuracy, e.g., from 57\% to 66\% on ImageNet-1k. Furthermore, by leveraging CLIP's multimodality bridge between image and text, we develop a simple yet effective self-labeling algorithm that produces meaningful text labels for the clusters. Through extensive experiments, we show that our pipeline works well on standard datasets such as CIFAR-10, CIFAR-100, and ImageNet-1k. It also extends to datasets without predefined labels, such as LAION-Aesthetics and WikiArts.

Large Language Models (LLMs) are being used for a wide variety of tasks. While they are capable of generating human-like responses, they can also produce undesirable output including potentially harmful information, racist or sexist language, and hallucinations. Alignment methods are designed to reduce such undesirable output, via techniques such as fine-tuning, prompt engineering, and representation engineering. However, existing methods face several challenges: some require costly fine-tuning for every alignment task; some do not adequately remove undesirable concepts, failing alignment; some remove benign concepts, lowering the linguistic capabilities of LLMs. To address these issues, we propose Parsimonious Concept Engineering (PaCE), a novel activation engineering framework for alignment. First, to sufficiently model the concepts, we construct a large-scale concept dictionary in the activation space, in which each atom corresponds to a semantic concept. Given any alignment task, we instruct a concept partitioner to efficiently annotate the concepts as benign or undesirable. Then, at inference time, we decompose the LLM activations along the concept dictionary via sparse coding, to accurately represent the activations as linear combinations of benign and undesirable components. By removing the latter ones from the activations, we reorient the behavior of the LLM towards the alignment goal. We conduct experiments on tasks such as response detoxification, faithfulness enhancement, and sentiment revising, and show that PaCE achieves state-of-the-art alignment performance while maintaining linguistic capabilities.

Manifold clustering is an important problem in motion and video segmentation, natural image clustering, and other applications where high-dimensional data lie on multiple, low-dimensional, nonlinear manifolds. While current state-of-the-art methods on large-scale datasets such as CIFAR provide good empirical performance, they do not have any proof of theoretical correctness. In this work, we propose a method that clusters data belonging to a union of nonlinear manifolds. Furthermore, for a given input data sample $y$ belonging to the $l$th manifold $\mathcal{M}_l$, we provide geometric conditions that guarantee a manifold-preserving representation of $y$ can be recovered from the solution to the proposed model. The geometric conditions require that (i) $\mathcal{M}_l$ is well-sampled in the neighborhood of $y$, with the sampling density given as a function of the curvature, and (ii) $\mathcal{M}_l$ is sufficiently separated from the other manifolds. In addition to providing proof of correctness in this setting, a numerical comparison with state-of-the-art methods on CIFAR datasets shows that our method performs competitively although marginally worse than methods without

We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are assumed to be linear subspaces, this reduces to the classical problem of subspace clustering, which has been studied extensively over the past two decades. Unfortunately, many real-world datasets such as natural images can not be well approximated by linear subspaces. On the other hand, numerous works have attempted to learn an appropriate transformation of the data, such that data is mapped from a union of general non-linear manifolds to a union of linear subspaces (with points from the same manifold being mapped to the same subspace). However, many existing works have limitations such as assuming knowledge of the membership of samples to clusters, requiring high sampling density, or being shown theoretically to learn trivial representations. In this paper, we propose to optimize the Maximal Coding Rate Reduction metric with respect to both the data representation and a novel doubly stochastic cluster membership, inspired by state-of-the-art subspace clustering results. We give a parameterization of such a representation and membership, allowing efficient mini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100, and TinyImageNet-200 datasets show that the proposed method is much more accurate and scalable than state-of-the-art deep clustering methods, and further learns a latent linear representation of the data.4

The principle of Maximal Coding Rate Reduction (MCR2) has recently been proposed as a training objective for learning discriminative low-dimensional structures intrinsic to high-dimensional data to allow for more robust training than standard approaches, such as cross-entropy minimization. However, despite the advantages that have been shown for MCR2training, MCR2suffers from a significant computational cost due to the need to evaluate and differentiate a significant number of log-determinant terms that grows linearly with the number of classes. By taking advantage of variational forms of spectral functions of a matrix, we reformulate the MCR2objective to a form that can scale significantly without compromising training accuracy. Experiments in image classification demonstrate that our proposed formulation results in a significant speed up over optimizing the original MCR2objective directly and often results in higher quality learned representations. Further, our approach may be of independent interest in other models that require computation of log-determinant forms, such as in system identification or normalizing flow models.

The problem of projecting a matrix onto the space of doubly stochastic matrices finds several applications in machine learning. For example, in spectral clustering, it has been shown that forming the normalized Laplacian matrix from a data affinity matrix has close connections to projecting it onto the set of doubly stochastic matrices. However, the analysis of why this projection improves clustering has been limited. In this paper we present theoretical conditions on the given affinity matrix under which its doubly stochastic projection is an ideal affinity matrix (i.e., it has no false connections between clusters, and is well-connected within each cluster). In particular, we show that a necessary and sufficient condition for a projected affinity matrix to be ideal reduces to a set of conditions on the input affinity that decompose along each cluster. Further, in the subspace clustering problem, where each cluster is defined by a linear subspace, we provide geometric conditions on the underlying subspaces which guarantee correct clustering via a continuous version of the problem. This allows us to explain theoretically the remarkable performance of a recently proposed doubly stochastic subspace clustering method.

We revisit robust estimation of homographies over point correspondences between two or three views, a fundamental problem in geometric vision. The analysis serves as a platform to support a rigorous investigation of Dual Principal Component Pursuit (DPCP) as a valid and powerful alternative to RANSAC for robust model fitting in multiple-view geometry. Homography fitting is cast as a robust nullspace estimation problem over either homographic or epipolar/trifocal embeddings. We prove that the nullspace of epipolar or trifocal embeddings in the homographic scenario, of dimension 3 and 6 for two and three views respectively, is defined by unique, computable homographies. Experiments show that DPCP performs on par with USAC with local optimization, while requiring an order of magnitude less computing time, and it also outperforms a recent deep learning implementation for homography estimation.

Dual Principal Component Pursuit (DPCP) is a recently proposed non-convex optimization based method for learning subspaces of high relative dimension from noiseless datasets contaminated by as many outliers as the square of the number of inliers. Experimentally, DPCP has proved to be robust to noise and outperform the popular RANSAC on 3D vision tasks such as road plane detection and relative poses estimation from three views. This paper extends the global optimality and convergence theory of DPCP to the case of data corrupted by noise, and further demonstrates its robustness using synthetic and real data.

In this paper, we propose a learning-based approach to the task of automatically extracting a "wireframe" representation for images of cluttered man-made environments. The wireframe (see Fig. 1) contains all salient straight lines and their junctions of the scene that encode efficiently and accurately large-scale geometry and object shapes. To this end, we have built a very large new dataset of over 5,000 images with wireframes thoroughly labelled by humans. We have proposed two convolutional neural networks that are suitable for extracting junctions and lines with large spatial support, respectively. The networks trained on our dataset have achieved significantly better performance than state-of-the-art methods for junction detection and line segment detection, respectively. We have conducted extensive experiments to evaluate quantitatively and qualitatively the wireframes obtained by our method, and have convincingly shown that effectively and efficiently parsing wireframes for images of man-made environments is a feasible goal within reach. Such wireframes could benefit many important visual tasks such as feature correspondence, 3D reconstruction, vision-based mapping, localization, and navigation. The data and source code are available at https://github.com/huangkuns/wireframe.