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We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our technique is complete (i.e., it always computes finite size bounds) for a subclass of loops, possibly with non-linear arithmetic. Moreover, we present a novel approach to combine and integrate this complete technique into an incomplete approach to infer size and runtime bounds of general integer programs. We prove completeness of our integration for an important subclass of integer programs. We implemented our new algorithm in the automated complexity analysis tool KoAT to evaluate its power, in particular on programs with non-linear arithmetic.

Existing approaches to modeling associations between visual stimuli and brain responses are facing difficulties in handling between-subject variance and model generalization. Inspired by the recent progress in modeling speech-brain response, we propose in this work a ``match-vs-mismatch'' deep learning model to classify whether a video clip induces excitatory responses in recorded EEG signals and learn associations between the visual content and corresponding neural recordings. Using an exclusive experimental dataset, we demonstrate that the proposed model is able to achieve the highest accuracy on unseen subjects as compared to other baseline models. Furthermore, we analyze the inter-subject noise using a subject-level silhouette score in the embedding space and show that the developed model is able to mitigate inter-subject noise and significantly reduce the silhouette score. Moreover, we examine the Grad-CAM activation score and show that the brain regions associated with language processing contribute most to the model predictions, followed by regions associated with visual processing. These results have the potential to facilitate the development of neural recording-based video reconstruction and its related applications.

Diffusion models have revolted the field of text-to-image generation recently. The unique way of fusing text and image information contributes to their remarkable capability of generating highly text-related images. From another perspective, these generative models imply clues about the precise correlation between words and pixels. In this work, a simple but effective method is proposed to utilize the attention mechanism in the denoising network of text-to-image diffusion models. Without re-training nor inference-time optimization, the semantic grounding of phrases can be attained directly. We evaluate our method on Pascal VOC 2012 and Microsoft COCO 2014 under weakly-supervised semantic segmentation setting and our method achieves superior performance to prior methods. In addition, the acquired word-pixel correlation is found to be generalizable for the learned text embedding of customized generation methods, requiring only a few modifications. To validate our discovery, we introduce a new practical task called "personalized referring image segmentation" with a new dataset. Experiments in various situations demonstrate the advantages of our method compared to strong baselines on this task. In summary, our work reveals a novel way to extract the rich multi-modal knowledge hidden in diffusion models for segmentation.

Patch robustness certification ensures no patch within a given bound on a sample can manipulate a deep learning model to predict a different label. However, existing techniques cannot certify samples that cannot meet their strict bars at the classifier or patch region levels. This paper proposes MajorCert. MajorCert firstly finds all possible label sets manipulatable by the same patch region on the same sample across the underlying classifiers, then enumerates their combinations element-wise, and finally checks whether the majority invariant of all these combinations is intact to certify samples.

Recent advances in diffusion models such as ControlNet have enabled geometrically controllable, high-fidelity text-to-image generation. However, none of them addresses the question of adding such controllability to text-to-3D generation. In response, we propose Text2Control3D, a controllable text-to-3D avatar generation method whose facial expression is controllable given a monocular video casually captured with hand-held camera. Our main strategy is to construct the 3D avatar in Neural Radiance Fields (NeRF) optimized with a set of controlled viewpoint-aware images that we generate from ControlNet, whose condition input is the depth map extracted from the input video. When generating the viewpoint-aware images, we utilize cross-reference attention to inject well-controlled, referential facial expression and appearance via cross attention. We also conduct low-pass filtering of Gaussian latent of the diffusion model in order to ameliorate the viewpoint-agnostic texture problem we observed from our empirical analysis, where the viewpoint-aware images contain identical textures on identical pixel positions that are incomprehensible in 3D. Finally, to train NeRF with the images that are viewpoint-aware yet are not strictly consistent in geometry, our approach considers per-image geometric variation as a view of deformation from a shared 3D canonical space. Consequently, we construct the 3D avatar in a canonical space of deformable NeRF by learning a set of per-image deformation via deformation field table. We demonstrate the empirical results and discuss the effectiveness of our method.

We propose personalized Tucker decomposition (perTucker) to address the limitations of traditional tensor decomposition methods in capturing heterogeneity across different datasets. perTucker decomposes tensor data into shared global components and personalized local components. We introduce a mode orthogonality assumption and develop a proximal gradient regularized block coordinate descent algorithm that is guaranteed to converge to a stationary point. By learning unique and common representations across datasets, we demonstrate perTucker's effectiveness in anomaly detection, client classification, and clustering through a simulation study and two case studies on solar flare detection and tonnage signal classification.

We study stochastic Cubic Newton methods for solving general possibly non-convex minimization problems. We propose a new framework, which we call the helper framework, that provides a unified view of the stochastic and variance-reduced second-order algorithms equipped with global complexity guarantees. It can also be applied to learning with auxiliary information. Our helper framework offers the algorithm designer high flexibility for constructing and analyzing the stochastic Cubic Newton methods, allowing arbitrary size batches, and the use of noisy and possibly biased estimates of the gradients and Hessians, incorporating both the variance reduction and the lazy Hessian updates. We recover the best-known complexities for the stochastic and variance-reduced Cubic Newton, under weak assumptions on the noise. A direct consequence of our theory is the new lazy stochastic second-order method, which significantly improves the arithmetic complexity for large dimension problems. We also establish complexity bounds for the classes of gradient-dominated objectives, that include convex and strongly convex problems. For Auxiliary Learning, we show that using a helper (auxiliary function) can outperform training alone if a given similarity measure is small.

Spoken language evolves constrained by the economy of speech, which depends on factors such as the structure of the human mouth. This gives rise to local phonetic correlations in spoken words. Here we demonstrate that these local correlations facilitate the learning of spoken words by reducing their information content. We do this by constructing a locally-connected tensor-network model, inspired by similar variational models used for many-body physics, which exploits these local phonetic correlations to facilitate the learning of spoken words. The model is therefore a minimal model of phonetic memory, where "learning to pronounce" and "learning a word" are one and the same. A consequence of which is the learned ability to produce new words which are phonetically reasonable for the target language; as well as providing a hierarchy of the most likely errors that could be produced during the action of speech. We test our model against Latin and Turkish words. (The code is available on GitHub.)

Graph Neural Networks (GNNs) have gained momentum in graph representation learning and boosted the state of the art in a variety of areas, such as data mining (\emph{e.g.,} social network analysis and recommender systems), computer vision (\emph{e.g.,} object detection and point cloud learning), and natural language processing (\emph{e.g.,} relation extraction and sequence learning), to name a few. With the emergence of Transformers in natural language processing and computer vision, graph Transformers embed a graph structure into the Transformer architecture to overcome the limitations of local neighborhood aggregation while avoiding strict structural inductive biases. In this paper, we present a comprehensive review of GNNs and graph Transformers in computer vision from a task-oriented perspective. Specifically, we divide their applications in computer vision into five categories according to the modality of input data, \emph{i.e.,} 2D natural images, videos, 3D data, vision + language, and medical images. In each category, we further divide the applications according to a set of vision tasks. Such a task-oriented taxonomy allows us to examine how each task is tackled by different GNN-based approaches and how well these approaches perform. Based on the necessary preliminaries, we provide the definitions and challenges of the tasks, in-depth coverage of the representative approaches, as well as discussions regarding insights, limitations, and future directions.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.