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This paper studies solving the system of nonlinear equations $ {\bf F}(\bf x)={\bf 0}$, where ${\bf F}:{\mathbb R}^{d}\to{\mathbb R}^d$. 
We propose Gram-Reduced Levenberg--Marquardt (GRLM) method which updates the matrix ${\bf J}(\cdot)^\top{\bf J}(\cdot)$ in every $m$ iterations, where ${\bf J}(\cdot)$ is the Jacobian of ${\bf F}(\cdot)$.
Our method has  a global convergence guarantee without relying on any step of line-search or solving  sub-problems.  We prove our method takes at most $\mathcal{O}(m^2+m^{-0.5}\epsilon^{-2.5})$ iterations to find an $\epsilon$-stationary point of $\frac{1}{2}\|\|{\bf F}(\cdot)\|\|^2$, which leads to overall computation cost of $\mathcal{O}(d^3\epsilon^{-1}+d^2\epsilon^{-2})$ by taking $m=\Theta(\epsilon^{-1})$. Our results are strictly better than the cost of $\mathcal{O}(d^3\epsilon^{-2})$ for existing LM methods. We also show the proposed method enjoys local superlinear convergence rate under the non-degenerate assumption. We provide rigorous experiments on important applications of scientific computing and machine learning to validate the efficiency of the proposed methods.

AAAI 2025

An Enhanced Levenberg--Marquardt Method via Gram Reduction

poster

We are pleased to announce the Thirty-Ninth AAAI Conference on Artificial Intelligence (AAAI-25), which will be held in Philadelphia, Pennsylvania at the Pennsylvania Convention Center from February 25 to March 4, 2025.

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-25 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.

### [Invited Speakers](https://aaai.org/conference/aaai/aaai-25/aaai-25-invited-speakers/)

Register [here](https://aaai.org/conference/aaai/aaai-25/registration/)

The purpose of the AAAI conference series is to promote research in Artificial Intelligence (AI) and foster scientific exchange between researchers, practitioners, scientists, students, and engineers across the entirety of AI and its affiliated disciplines. AAAI-25 will feature technical paper presentations, special tracks, invited speakers, workshops, tutorials, poster sessions, senior member presentations, competitions, and exhibit programs, and a range of other activities to be announced.



For a data-generating process for random variables that can be described with a linear structural equation model, we consider a situation in which (i) a set of covariates satisfying the back-door criterion cannot be observed or (ii) such a set can be observed, but standard statistical estimation methods cannot be applied to estimate causal effects because of multicollinearity/high-dimensional data problems. We propose a novel two-stage penalized regression approach, the penalized covariate-mediator selection operator (PCM Selector), to estimate the causal effects in such scenarios. Unlike existing penalized regression analyses, when a set of intermediate variables is available, PCM Selector provides a consistent or less biased estimator of the causal effect. In addition, PCM Selector provides a variable selection procedure for intermediate variables to obtain better estimation accuracy of the causal effects than does the back-door criterion.

PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects

Universal domain adaptation (UniDA) transfers knowledge from a labelled source domain to an unlabelled target domain under domain-shift and category-shift for annotation. In reality, due to privacy protection or other limits, not only source data but also pre-trained models on it may be unavailable when training on target data. In this paper, we go a step further to explore the black-box universal domain adaptation (B$^{2}$-UniDA) problem. It requires tackling the labelling task under shifts by only accessing the interface of pre-trained source models. To this end, we introduce GSS which proposes a novel sample selection criterion based on gradient descent and Bayes' Theorem to identify samples of potential unknown classes. This criterion doesn't require manually-set thresholds depending on data used and is suitable for various datasets. GSS builds an open-set classifier and enables it to estimate probabilities of belonging to each class including the unknown category and adjust estimates adaptively. To overcome class-imbalance, especially imbalance between the unknown and known classes, we propose a balancing mechanism by measuring training status and estimating DA type. In addition to distilling knowledge from source model outputs, we focus on mining the categorical structure of target domain by self-training. Experiments on benchmarks show the state-of-the-art performance of GSS compared to typical methods, including source models or source data dependent methods.

Gradient-Based Sample Selection for Black-Box Universal Domain Adaptation

Detecting anomalies in business processes is crucial for ensuring operational success. While many existing methods rely on statistical frequency to detect anomalies, it's important to note that infrequent behavior doesn't necessarily imply undesirability. To address this challenge, detecting anomalies from a semantic viewpoint proves to be a more effective approach. However, current semantic anomaly detection methods  treat a trace (i.e., process instance) as multiple event pairs, disrupting long-distance dependencies. In this paper, we introduce DABL, a novel approach for detecting semantic anomalies in business processes using large language models (LLMs). We collect 143,137 real-world process models from various domains. By generating normal traces through the playout of these process models and simulating both ordering and exclusion anomalies, we fine-tune Llama 2 using the resulting log. Through extensive experiments, we demonstrate that DABL surpasses existing state-of-the-art semantic anomaly detection methods in terms of both generalization ability and learning of given processes. Users can directly apply DABL to detect semantic anomalies in their own datasets without the need for additional training. Furthermore, DABL offers the ability to interpret anomalies' causes in natural language, providing valuable insights into the detected anomalies.

DABL: Detecting Semantic Anomalies in Business Processes Using Large Language Models

We propose GGS, a Generalizable Gaussian Splatting method for Autonomous Driving which can achieve realistic rendering under large viewpoint changes. Previous generalizable 3D gaussian splatting methods are limited to rendering novel views that are very close to the original pair of images, which cannot handle large differences in viewpoint. Especially in autonomous driving scenarios, images are typically collected from a single lane. The limited training perspective makes rendering images of a different lane very challenging. To further improve the rendering capability of GGS under large viewpoint changes,  we introduces a novel virtual lane generation module into GSS method
to enables high-quality lane switching even without a multi-lane dataset. Besides, we design a diffusion loss to supervise the generation of virtual lane image to further address the problem of lack of data in the virtual lanes. 
Finally, we also propose a depth refinement module to optimize depth estimation in the GSS model. Extensive validation of our method, compared to existing approaches, demonstrates state-of-the-art performance.

GGS: Generalizable Gaussian Splatting for Lane Switching in Autonomous Driving

Multi-object tracking faces a major challenge in handling the variations of tracked targets within complex scenes. In existing transformer-based tracking methods, typically each tracked target is only associated with one track query. However, trajectories in crowded scenes often experience varying levels of occlusion, making the association brittle for using a single track query to identify the tracked target. Therefore, we argue that relying on a single track query to track a target in complex scenes is inadequate. In this paper, we introduce TGFormer, with the core idea of designing a Track Query Group for each tracked target. Each group encompasses track queries that handle the same tracked target across different levels of occlusion scenes. To achieve long-term robust association, we propose a novel updater that integrates temporal memories and occlusion-aware features to update the Track Query Group, ensuring the tracked target can be consistently captured in complex scenes. Additionally, we introduce a Position Predictor that allows TGFormer to forecast motion trends, helping the model accurately locate moving tracklets. Experiments show that our method enhances the metrics of the baseline method on the MOT Challenge and DanceTrack datasets, showing highly competitive performance.

TGFormer: Transformer with Track Query Group for Multi-Object Tracking

Contrastive learning underpins most current self-supervised time series representation methods. The strategy for constructing positive and negative sample pairs significantly affects the final representation quality. However, due to the continuous nature of time series semantics, the modeling approach of contrastive learning struggles to accommodate the characteristics of time series data. This results in issues such as difficulties in constructing hard negative samples and the potential introduction of inappropriate biases during positive sample construction. Although some recent works have developed several scientific strategies for constructing positive and negative sample pairs with improved effectiveness, they remain constrained by the contrastive learning framework. To fundamentally overcome the limitations of contrastive learning, this paper introduces Frequency-masked Embedding Inference (FEI), a novel non-contrastive method that completely eliminates the need for positive and negative samples. The proposed FEI constructs 2 inference branches based on a prompting strategy: 1) Using frequency masking as prompts to infer the embedding representation of the target series with missing frequency bands in the embedding space, and 2) Using the target series as prompts to infer its frequency masking embedding. This enables continuous semantic relationship modeling for time series. Experiments on 8 widely used time series datasets for classification and regression tasks, using linear evaluation and end-to-end fine-tuning, show that FEI significantly outperforms existing contrastive-based methods in terms of generalization. This study provides new insights into self-supervised representation learning for time series.

Frequency-Masked Embedding Inference: A Non-Contrastive Approach for Time Series Representation Learning

Semi-supervised medical image segmentation (SSMIS) uses consistency learning to regularize model training, which alleviates the burden of pixel-wise manual annotations. However, it often suffers from error supervision from low-quality pseudo labels. Vision-Language Model (VLM) has great potential to enhance pseudo labels by introducing text prompt guided multimodal supervision information. It nevertheless faces the cross-modal problem: the obtained messages tend to correspond to multiple targets. To address aforementioned problems, we propose a Dual Semantic Similarity-Supervised VLM (DuSSS) for SSMIS. Specifically, 1) a Dual Contrastive Learning (DCL) is designed to improve cross-modal semantic consistency by capturing intrinsic representations within each modality and semantic correlations across modalities. 2) To encourage the learning of multiple semantic correspondences, a Semantic Similarity-Supervision strategy (SSS) is proposed and injected into each contrastive learning process in DCL, supervising semantic similarity via the distribution-based uncertainty levels. Furthermore, a novel VLM-based SSMIS network is designed to compensate for the quality deficiencies of pseudo-labels. It utilizes the pretrained VLM to generate text prompt guided supervision information, refining the pseudo label for better consistency regularization. Experimental results demonstrate that our DuSSS achieves outstanding performance with Dice of 82.52%, 74.61% and 78.03% on three public datasets (QaTa-COV19, BM-Seg and MoNuSeg). Our code will be available.

DuSSS: Dual Semantic Similarity-Supervised Vision-Language Model for Semi-Supervised Medical Image Segmentation

Referring Multi-Object Tracking (RMOT) is an important topic in the current tracking field. Its task form is to guide the tracker to track objects that match the language description. Current research mainly focuses on referring multi-object tracking under single-view, which refers to a view sequence or multiple unrelated view sequences. However, in the single-view, some appearances of objects are easily invisible, resulting in incorrect matching of objects with the language description. In this work, we propose a new task, called Cross-view Referring Multi-Object Tracking (CRMOT). It introduces the cross-view to obtain the appearances of objects from multiple views, avoiding the problem of the invisible appearances of objects in RMOT task. CRMOT is a more challenging task of accurately tracking the objects that match the language description and maintaining the identity consistency of objects in each cross-view. To advance CRMOT task, we construct a cross-view referring multi-object tracking benchmark based on CAMPUS and DIVOTrack datasets, named CRTrack. Specifically, it provides 13 different scenes and 221 language descriptions. Furthermore, we propose an end-to-end cross-view referring multi-object tracking method, named CRTracker. Extensive experiments on the CRTrack benchmark verify the effectiveness of our method.

Cross-View Referring Multi-Object Tracking

As digital media manipulation becomes increasingly sophisticated, accurately detecting and localizing image forgeries with minimal supervision has become a critical challenge. 
Existing weakly supervised image forgery detection (W-IFD) methods often rely on convolutional neural networks (CNNs) and limited exploration of internal relationships, leading to poor detection and localization performance with only image-level labels. 
To address these limitations, we introduce a novel Multi-View and Multi-Level Relation Learning Network (M$^2$RL-Net) for W-IFD. 
M$^2$RL-Net effectively identifies forged images using only image-level annotations by exploring relationships between different views and hierarchical levels within images. 
Specifically, M$^2$RL-Net achieves patch-level self-consistency learning (PSL) and feature-level contrastive learning (FCL) across different views, facilitating more generalized self-supervised learning of forgery features.
In detail, PSL employs self-supervised learning to distinguish consistent and inconsistent regions within images, enhancing its ability to accurately locate tampered areas. 
FCL utilizes feature-level self-view and multi-view contrastive learning to differentiate between genuine and tampered image features, thereby improving the recognition of authentic and manipulated content across different views.
Extensive experiments on various datasets demonstrate that M$^2$RL-Net outperforms existing weakly-supervised methods in both detection and localization accuracy. This research sets a new benchmark for weakly-supervised image forgery detection and lays a robust foundation for future studies in this field.

M²RL-Net: Multi-View and Multi-Level Relation Learning Network for Weakly-Supervised Image Forgery Detection

Prompt instruction tuning is a popular approach to better adjust monolithic, pretrained LLMs for downstream tasks. Yet, how to extend this approach to handle multiple tasks and data distributions is an open question.  To address this gap, we propose using \emph{Mixture of Prompts} (MoPs) with smart gating functionality. The latter identifies relevant skills embedded in different groups of prompts and dynamically weighs experts (i.e., collection of prompts) based on the target task. Experiments show that MoPs are resilient to model compression, data source, and task composition, making them highly versatile and applicable in various contexts. 
In practice, MoPs can simultaneously mitigate prompt training ``interference'' in multi-task, multi-source scenarios (e.g., task and data heterogeneity across sources) and possible implications from model approximations. Empirically, MoPs can reduce final perplexity from 9\% up to 70\% in federated cases and from 3\% up to 30\% in centralized cases, compared to baselines.

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PCM Selector: Penalized Covariate-Mediator Selection Operator for Evaluating Linear Causal Effects

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