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A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs.

Tracking and segmenting multiple similar objects with complex or separate parts in long-term videos is inherently challenging due to the ambiguity of target parts and identity confusion caused by occlusion, background clutter, and long-term variations. In this paper, we propose a robust video object segmentation framework equipped with spatial-semantic features and discriminative object queries to address the above issues. Specifically, we construct a spatial-semantic network comprising a semantic embedding block and spatial dependencies modeling block to associate the pretrained ViT features with global semantic features and local spatial features, providing a comprehensive target representation. In addition, we develop a masked cross-attention module to generate object queries that focus on the most discriminative parts of target objects during query propagation, alleviating noise accumulation and ensuring effective long-term query propagation. The experimental results show that the proposed method set a new state-of-the-art performance on multiple datasets, including the DAVIS2017 test (89.1%), YoutubeVOS 2019 (88.5%), MOSE (75.1%), LVOS test (73.0%), and LVOS val (75.1%), which demonstrate the effectiveness and generalization capacity of the proposed method. We will make all source code and trained models publicly available.

Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would allow for gradient-based parameter optimization, the nonlinear dynamics of ODEs often lead to many local minima and extreme sensitivity to initial conditions. We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which improves convergence of gradient-based parameter optimization in ODEs. By iteratively reducing a noise parameter of the probabilistic integrator, the proposed method converges more reliably to the true parameters. We demonstrate that our method is effective for dynamical systems of different complexity and show that it obtains reliable parameter estimates for a Hodgkin-Huxley model with a practically relevant number of parameters.

Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space, by adding the fine-tuned weights of different tasks. The performance has been further improved by a linear property which is illustrated by weight disentanglement. Yet, conventional linearization methods (e.g., NTK linearization) not only double the time and training cost but also have a disadvantage on single-task performance. We propose a simple yet effective and efficient method that only fine-tunes linear layers, which improves weight disentanglement and efficiency simultaneously. Specifically, our study reveals that only fine-tuning the linear layers in the attention modules makes the whole model occur in a linear regime, significantly improving weight disentanglement. To further understand how our method improves the disentanglement of task arithmetic, we present a comprehensive study of task arithmetic by differentiating the role of representation model and task-specific model. In particular, we find that the representation model plays an important role in improving weight disentanglement whereas the task-specific models such as the classification heads can degenerate the weight disentanglement performance. Overall, our work uncovers novel insights into the fundamental mechanisms of task arithmetic and offers a more reliable and effective approach to editing pre-trained models.

Knowing the effect of an intervention is critical for human decision-making, but current approaches for causal effect estimation rely on manual data collection and structuring, regardless of the causal assumptions. This increases both the cost and time-to-completion for studies. We show how large, diverse observational text data can be mined with large language models (LLMs) to produce inexpensive causal effect estimates under appropriate causal assumptions. We introduce NATURAL, a novel family of causal effect estimators built with LLMs that operate over datasets of unstructured text. Our estimators use LLM conditional distributions (over variables of interest, given the text data) to assist in the computation of classical estimators of causal effect. We overcome a number of technical challenges to realize this idea, such as automating data curation and using LLMs to impute missing information. We prepare six (two synthetic and four real) observational datasets, paired with corresponding ground truth in the form of randomized trials, which we used to systematically evaluate each step of our pipeline. NATURAL estimators demonstrate remarkable performance, yielding causal effect estimates that fall within 3 percentage points of their ground truth counterparts, including on real-world Phase 3/4 clinical trials. Our results suggest that unstructured text data is a rich source of causal effect information, and NATURAL is a first step towards an automated pipeline to tap this resource.

Lensless imaging has emerged as a promising field within inverse imaging, offering compact, cost-effective solutions with the potential to revolutionize the computational camera market. By circumventing traditional optical components like lenses and mirrors, novel approaches like mask-based lensless imaging eliminate the need for conventional hardware. However, advancements in lensless image reconstruction, particularly those leveraging Generative Adversarial Networks (GANs), are hindered by the reliance on data-driven training processes, resulting in network specificity to the Point Spread Function (PSF) of the imaging system. This necessitates a complete retraining for minor PSF changes, limiting adaptability and generalizability across diverse imaging scenarios. In this paper, we introduce a novel approach to multi-PSF lensless imaging, employing a dual discriminator cyclic adversarial framework. We propose a unique generator architecture with a sparse convolutional PSF-aware auxiliary branch, coupled with a forward model integrated into the training loop to facilitate physics-informed learning to handle the substantial domain gap between lensless and lensed images. Comprehensive performance evaluation and ablation studies underscore the effectiveness of our model, offering robust and adaptable lensless image reconstruction capabilities. Our method achieves comparable performance to existing PSF-agnostic generative methods for single PSF cases and demonstrates resilience to PSF changes without the need for retraining.

Multimodal analysis has recently drawn much interest in affective computing, since it can improve the overall accuracy of emotion recognition over isolated uni-modal approaches. The most effective techniques for multimodal emotion recognition efficiently leverage diverse and complimentary sources of information, such as facial, vocal, and physiological modalities, to provide comprehensive feature representations. In this paper, we focus on dimensional emotion recognition based on the fusion of facial and vocal modalities extracted from videos, where complex spatiotemporal relationships may be captured. Most of the existing fusion techniques rely on recurrent networks or conventional attention mechanisms that do not effectively leverage the complimentary nature of audio-visual (A-V) modalities. We introduce a cross-attentional fusion approach to extract the salient features across A-V modalities, allowing for accurate prediction of continuous values of valence and arousal. Our new cross-attentional A-V fusion model efficiently leverages the inter-modal relationships. In particular, it computes cross-attention weights to focus on the more contributive features across individual modalities, and thereby combine contributive feature representations, which are then fed to fully connected layers for the prediction of valence and arousal. The effectiveness of the proposed approach is validated experimentally on videos from the RECOLA and Fatigue (private) data-sets. Results indicate that our cross-attentional A-V fusion model is a cost-effective approach that outperforms state-of-the-art fusion approaches. Code is available: \url{//github.com/praveena2j/Cross-Attentional-AV-Fusion}

Dynamic logic and its variations, because of their clear and expressive forms for capturing program properties, have been used as formalisms in program/system specification and verification for years and have many other applications. The program models of dynamic logics are in explicit forms. For different target program models, different dynamic logic theories have to be proposed to adapt different models' semantics. In this paper, we propose a parameterized `dynamic-logic-style' formalism, namely $DL_p$, for specifying and reasoning about general program models. In $DL_p$, program models and logical formulas are taken as `parameters', allowing arbitrary forms according to different interested domains. This characteristic allows $DL_p$ to support direct reasoning based on the operational semantics of program models, while still preserving compositional reasoning based on syntactic structures. $DL_p$ provides a flexible verification framework to encompass different dynamic logic theories. In addition, it also facilitates reasoning about program models whose semantics is not compositional, examples are neural networks, automata-based models, synchronous programming languages, etc. We mainly focus on building the theory of $DL_p$, including defining its syntax and semantics, building a proof system and constructing a cyclic preproof structure. We analyze and prove the soundness of $DL_p$. Case studies show how $DL_p$ works for reasoning about different types of program models.

Tabular synthesis models remain ineffective at capturing complex dependencies, and the quality of synthetic data is still insufficient for comprehensive downstream tasks, such as prediction under distribution shifts, automated decision-making, and cross-table understanding. A major challenge is the lack of prior knowledge about underlying structures and high-order relationships in tabular data. We argue that a systematic evaluation on high-order structural information for tabular data synthesis is the first step towards solving the problem. In this paper, we introduce high-order structural causal information as natural prior knowledge and provide a benchmark framework for the evaluation of tabular synthesis models. The framework allows us to generate benchmark datasets with a flexible range of data generation processes and to train tabular synthesis models using these datasets for further evaluation. We propose multiple benchmark tasks, high-order metrics, and causal inference tasks as downstream tasks for evaluating the quality of synthetic data generated by the trained models. Our experiments demonstrate to leverage the benchmark framework for evaluating the model capability of capturing high-order structural causal information. Furthermore, our benchmarking results provide an initial assessment of state-of-the-art tabular synthesis models. They have clearly revealed significant gaps between ideal and actual performance and how baseline methods differ. Our benchmark framework is available at URL //github.com/TURuibo/CauTabBench.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.