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Test-Time-Training (TTT) is an approach to cope with out-of-distribution (OOD) data by adapting a trained model to distribution shifts occurring at test-time. We propose to perform this adaptation via Activation Matching (ActMAD): We analyze activations of the model and align activation statistics of the OOD test data to those of the training data. In contrast to existing methods, which model the distribution of entire channels in the ultimate layer of the feature extractor, we model the distribution of each feature in multiple layers across the network. This results in a more fine-grained supervision and makes ActMAD attain state of the art performance on CIFAR-100C and Imagenet-C. ActMAD is also architecture- and task-agnostic, which lets us go beyond image classification, and score 15.4% improvement over previous approaches when evaluating a KITTI-trained object detector on KITTI-Fog. Our experiments highlight that ActMAD can be applied to online adaptation in realistic scenarios, requiring little data to attain its full performance.

In many automation tasks involving manipulation of rigid objects, the poses of the objects must be acquired. Vision-based pose estimation using a single RGB or RGB-D sensor is especially popular due to its broad applicability. However, single-view pose estimation is inherently limited by depth ambiguity and ambiguities imposed by various phenomena like occlusion, self-occlusion, reflections, etc. Aggregation of information from multiple views can potentially resolve these ambiguities, but the current state-of-the-art multi-view pose estimation method only uses multiple views to aggregate single-view pose estimates, and thus rely on obtaining good single-view estimates. We present a multi-view pose estimation method which aggregates learned 2D-3D distributions from multiple views for both the initial estimate and optional refinement. Our method performs probabilistic sampling of 3D-3D correspondences under epipolar constraints using learned 2D-3D correspondence distributions which are implicitly trained to respect visual ambiguities such as symmetry. Evaluation on the T-LESS dataset shows that our method reduces pose estimation errors by 80-91% compared to the best single-view method, and we present state-of-the-art results on T-LESS with four views, even compared with methods using five and eight views.

Representing complex objects with basic geometric primitives has long been a topic in computer vision. Primitive-based representations have the merits of compactness and computational efficiency in higher-level tasks such as physics simulation, collision checking, and robotic manipulation. Unlike previous works which extract polygonal meshes from a signed distance function (SDF), in this paper, we present a novel method, named Marching-Primitives, to obtain a primitive-based abstraction directly from an SDF. Our method grows geometric primitives (such as superquadrics) iteratively by analyzing the connectivity of voxels while marching at different levels of signed distance. For each valid connected volume of interest, we march on the scope of voxels from which a primitive is able to be extracted in a probabilistic sense and simultaneously solve for the parameters of the primitive to capture the underlying local geometry. We evaluate the performance of our method on both synthetic and real-world datasets. The results show that the proposed method outperforms the state-of-the-art in terms of accuracy, and is directly generalizable among different categories and scales. The code is open-sourced at //github.com/ChirikjianLab/Marching-Primitives.git.

Most recent 6D object pose estimation methods first use object detection to obtain 2D bounding boxes before actually regressing the pose. However, the general object detection methods they use are ill-suited to handle cluttered scenes, thus producing poor initialization to the subsequent pose network. To address this, we propose a rigidity-aware detection method exploiting the fact that, in 6D pose estimation, the target objects are rigid. This lets us introduce an approach to sampling positive object regions from the entire visible object area during training, instead of naively drawing samples from the bounding box center where the object might be occluded. As such, every visible object part can contribute to the final bounding box prediction, yielding better detection robustness. Key to the success of our approach is a visibility map, which we propose to build using a minimum barrier distance between every pixel in the bounding box and the box boundary. Our results on seven challenging 6D pose estimation datasets evidence that our method outperforms general detection frameworks by a large margin. Furthermore, combined with a pose regression network, we obtain state-of-the-art pose estimation results on the challenging BOP benchmark.

In this paper, we introduce a new methodology to solve the orthogonal nonnegative matrix factorization (ONMF) problem, where the objective is to approximate an input data matrix by a product of two nonnegative matrices, the features matrix and the mixing matrix, where one of them is orthogonal. We show how the ONMF can be interpreted as a specific facility-location problem (FLP), and adapt a maximum-entropy-principle based solution for FLP to the ONMF problem. The proposed approach guarantees orthogonality and sparsity of the features or the mixing matrix, while ensuring nonnegativity of both. Additionally, our methodology develops a quantitative characterization of ``true" number of underlying features - a hyperparameter required for the ONMF. An evaluation of the proposed method conducted on synthetic datasets, as well as a standard genetic microarray dataset indicates significantly better sparsity, orthogonality, and performance speed compared to similar methods in the literature, with comparable or improved reconstruction errors.

We take a random matrix theory approach to random sketching and show an asymptotic first-order equivalence of the regularized sketched pseudoinverse of a positive semidefinite matrix to a certain evaluation of the resolvent of the same matrix. We focus on real-valued regularization and extend previous results on an asymptotic equivalence of random matrices to the real setting, providing a precise characterization of the equivalence even under negative regularization, including a precise characterization of the smallest nonzero eigenvalue of the sketched matrix, which may be of independent interest. We then further characterize the second-order equivalence of the sketched pseudoinverse. We also apply our results to the analysis of the sketch-and-project method and to sketched ridge regression. Lastly, we propose a conjecture that these results generalize to asymptotically free sketching matrices, obtaining the resulting equivalence for orthogonal sketching matrices and comparing our results to several common sketches used in practice.

The aim of this work is to study the dual and the algebraic dual of an evaluation code using standard monomials and indicator functions. We show that the dual of an evaluation code is the evaluation code of the algebraic dual. We develop an algorithm for computing a basis for the algebraic dual. Let $C_1$ and $C_2$ be linear codes spanned by standard monomials. We give a combinatorial condition for the monomial equivalence of $C_1$ and the dual $C_2^\perp$. Moreover, we give an explicit description of a generator matrix of $C_2^\perp$ in terms of that of $C_1$ and coefficients of indicator functions. For Reed--Muller-type codes we give a duality criterion in terms of the v-number and the Hilbert function of a vanishing ideal. As an application, we provide an explicit duality for Reed--Muller-type codes corresponding to Gorenstein ideals. In addition, when the evaluation code is monomial and the set of evaluation points is a degenerate affine space, we classify when the dual is a monomial code.

Pairwise metrics are often employed to estimate statistical dependencies between brain regions, however they do not capture higher-order information interactions. It is critical to explore higher-order interactions that go beyond paired brain areas in order to better understand information processing in the human brain. To address this problem, we applied multivariate mutual information, specifically, Total Correlation and Dual Total Correlation to reveal higher-order information in the brain. In this paper, we estimate these metrics using matrix-based R\'enyi's entropy, which offers a direct and easily interpretable approach that is not limited by direct assumptions about probability distribution functions of multivariate time series. We applied these metrics to resting-state fMRI data in order to examine higher-order interactions in the brain. Our results showed that the higher-order information interactions captured increase gradually as the interaction order increases. Furthermore, we observed a gradual increase in the correlation between the Total Correlation and Dual Total Correlation as the interaction order increased. In addition, the significance of Dual Total Correlation values compared to Total Correlation values also indicate that the human brain exhibits synergy dominance during the resting state.

We present a method for selecting valuable projections in computed tomography (CT) scans to enhance image reconstruction and diagnosis. The approach integrates two important factors, projection-based detectability and data completeness, into a single feed-forward neural network. The network evaluates the value of projections, processes them through a differentiable ranking function and makes the final selection using a straight-through estimator. Data completeness is ensured through the label provided during training. The approach eliminates the need for heuristically enforcing data completeness, which may exclude valuable projections. The method is evaluated on simulated data in a non-destructive testing scenario, where the aim is to maximize the reconstruction quality within a specified region of interest. We achieve comparable results to previous methods, laying the foundation for using reconstruction-based loss functions to learn the selection of projections.

A mainstream type of current self-supervised learning methods pursues a general-purpose representation that can be well transferred to downstream tasks, typically by optimizing on a given pretext task such as instance discrimination. In this work, we argue that existing pretext tasks inevitably introduce biases into the learned representation, which in turn leads to biased transfer performance on various downstream tasks. To cope with this issue, we propose Maximum Entropy Coding (MEC), a more principled objective that explicitly optimizes on the structure of the representation, so that the learned representation is less biased and thus generalizes better to unseen downstream tasks. Inspired by the principle of maximum entropy in information theory, we hypothesize that a generalizable representation should be the one that admits the maximum entropy among all plausible representations. To make the objective end-to-end trainable, we propose to leverage the minimal coding length in lossy data coding as a computationally tractable surrogate for the entropy, and further derive a scalable reformulation of the objective that allows fast computation. Extensive experiments demonstrate that MEC learns a more generalizable representation than previous methods based on specific pretext tasks. It achieves state-of-the-art performance consistently on various downstream tasks, including not only ImageNet linear probe, but also semi-supervised classification, object detection, instance segmentation, and object tracking. Interestingly, we show that existing batch-wise and feature-wise self-supervised objectives could be seen equivalent to low-order approximations of MEC. Code and pre-trained models are available at //github.com/xinliu20/MEC.