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Solving systems of ordinary differential equations (ODEs) is essential when it comes to understanding the behavior of dynamical systems. Yet, automated solving remains challenging, in particular for nonlinear systems.  Computer algebra systems (CASs) provide support for solving ODEs by first simplifying them, in particular through the use of Lie point symmetries. Finding these symmetries is, however, itself a difficult problem for CASs. Recent works in symbolic regression have shown promising results for recovering symbolic expressions from data. Here, we adapt search-based symbolic regression to the task of finding generators of Lie point symmetries. 
With this approach, we can find symmetries of ODEs that existing CASs cannot find.

AAAI 2025

Discovering Symmetries of ODEs by Symbolic Regression

classification and regression

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.



poster

Solutions of symbolic regression problems are expressions that are composed of input variables and operators from a finite set of function symbols. One measure for evaluating symbolic regression algorithms is their ability to recover formulae, up to symbolic equivalence, from finite samples. Not unexpectedly, the recovery problem becomes harder when the formula gets more complex, that is, when the number of variables and operators gets larger. Variables in naturally occurring symbolic formulas often appear only in fixed combinations. This can be exploited in symbolic regression by substituting one new variable for the combination, effectively reducing the number of variables. However, finding valid substitutions is challenging. Here, we address this challenge by searching over the expression space of small substitutions and testing for validity. The validity test is reduced to a test of functional dependence. The resulting iterative dimension reduction procedure can be used with any symbolic regression approach. We show that it reliably identifies valid substitutions and significantly boosts the performance of different types of state-of-the-art symbolic regression algorithms.

Dimension Reduction for Symbolic Regression

The independence assumption is a useful tool to increase the tractability of one's modelling framework.  However, this assumption does not match reality; failing to take dependencies into account can cause models to fail dramatically.  The field of multi-axis graphical modelling (also called multi-way modelling, Kronecker-separable modelling) has seen growth over the past decade, but these models require that the data have zero mean.  In the multi-axis case, inference is typically done in the single sample scenario, making mean inference impossible.

In this paper, we demonstrate how the zero-mean assumption can cause egregious modelling errors, as well as propose a relaxation to the zero-mean assumption that allows the avoidance of such errors.  Specifically, we propose the "Kronecker-sum-structured mean" assumption, which leads to models with nonconvex-but-unimodal log-likelihoods that can be solved efficiently with coordinate descent.

Gaussian Graphical Modelling Without Independence Assumptions for Uncentered Data

In recent years, there has been a growing demand to stylize a given 3D scene to align with the artistic style of reference images for creative purposes. While 3D Gaussian Splatting (GS) has emerged as a promising and efficient method for realistic 3D scene modeling, there remains a challenge in adapting it to stylize 3D GS to match with multiple styles through automatic local style transfer or manual designation, while maintaining memory efficiency for stylization training. In this paper, we introduce a novel 3D GS stylization solution termed Multi-StyleGS to tackle these challenges. In particular, we employ a bipartite matching mechanism to automatically identify correspondences between the style images and the local regions of the rendered images. To facilitate local style transfer, we introduce a novel semantic style loss function that employs a segmentation network to apply distinct styles to various objects of the scene and propose a local-global feature matching to enhance the multi-view consistency. Furthermore, this technique can achieve memory-efficient training, more texture details and better color match. To better assign a robust semantic label to each Gaussian, we propose several techniques to regularize the segmentation network. As demonstrated by our comprehensive experiments, our approach outperforms existing ones in producing plausible stylization results and offering flexible editing.

Multi-StyleGS: Stylized Gaussian Splatting with Multiple Styles

Event cameras encode visual information by generating asynchronous and sparse event streams, which hold great potential for low latency and low power consumption. Despite many successful implementations of event camera-based applications, most of them accumulate the events into frames and then utilize conventional frame-based computer vision algorithms. These frame-based methods, though typically effective, diminish the inherent advantages of the event camera's low latency and low power consumption. To solve the above problems, we propose ASGCN, which efficiently processes data on an event-by-event basis and dynamically evolves into a corresponding dynamic representation, enabling low latency and high sparsity of data representation. The sparsity computation is further improved by introducing brain-inspired spiking neural networks, resulting in low power consumption for ASGCN. Extensive and diverse experiments demonstrate the energy efficiency and low latency advantages of our processing pipeline. Especially on real-world event camera datasets, our pipeline consumes more than 10,000 times less energy and achieves similar performance compared to current frame-based methods.

Leveraging Asynchronous Spiking Neural Networks for Ultra Efficient Event-Based Visual Processing

Video scene detection involves assessing whether each shot and its surroundings belong to the same scene.
Achieving this requires meticulously correlating multi-modal cues, $\textit{e.g.}$, visual entity and place modalities, among shots and comparing semantic changes around each shot.
However, most methods treat multi-modal semantics equally and do not examine contextual differences between the two sides of a shot, leading to sub-optimal detection performance.
In this paper, we propose the $\textbf{M}$odality-$\textbf{A}$ware $\textbf{S}$hot $\textbf{R}$elating and $\textbf{C}$omparing approach (MASRC), which enables relating shots per their own characteristics of visual entity and place modalities, as well as comparing multi-shots similarities to have scene changes explicitly encoded. Specifically, 
to fully harness the potential of visual entity and place modalities in modeling shot relations, we mine long-term shot correlations from entity semantics while simultaneously revealing short-term shot correlations from place semantics.
In this way, we can learn distinctive shot features that consolidate coherence within scenes and amplify distinguishability across scenes.
Once equipped with distinctive shot features, we further encode the relations between preceding and succeeding shots of each target shot by similarity convolution, aiding in the identification of scene ending shots.
We validate the broad applicability of the proposed components in MASRC. Extensive experimental results on public benchmark datasets demonstrate that the proposed MASRC significantly advances video scene detection. The code will be released.

Modality-Aware Shot Relating and Comparing for Video Scene Detection

Partially relevant video retrieval (PRVR) is a task that performs video retrieval where only a specific segment of the video is relevant to a text query. Previously, typical approaches were to enhance the video clip modeling to prepare for queries describing diverse moments. In this paper, we tackle the underexplored problem of ambiguous relationships between text-video pairs. Typical training processes of PRVR assume a one-to-one relationship where each text query is relevant to only one video. However, we point out the inherent ambiguity between text and video content based on their conceptual scope and propose a framework that incorporates this ambiguity into the model learning process. To achieve this, we utilize online uncertainty and similarity measures during training to detect and exclude ambiguity in text-video representation learning. Specifically, we grant the model freedom to handle ambiguous relationships instead of forcing them to be negative. Additionally, we delve into fine-grained relationships within the video instance. Whereas only the relationships with a video as the base unit were considered previously to provide training guidance, we explore the various contexts within the same untrimmed video with our framework. Lastly, we employ the co-teaching framework to mitigate the impact of ambiguous labels and confirmation bias during ambiguity predictions within a single network. With all components combined, our proposed method demonstrates its effectiveness in PRVR.

Ambiguity-Restrained Text-Video Representation Learning for Partially Relevant Video Retrieval

While visual question-answering (VQA) benchmarks have catalyzed the development of reasoning techniques, they have focused on vertical thinking. Effective problem-solving also necessitates lateral thinking, which remains understudied in AI and has not been used to test visual perception systems. To bridge this gap, we formulate visual lateral thinking as a multiple-choice question-answering task and describe a three-step taxonomy-driven methodology for instantiating task examples. Then, we develop COLUMBUS, a synthetic benchmark that applies the task pipeline to create QA sets with text and icon rebus puzzles based on publicly available collections of compounds and common phrases. COLUMBUS comprises over 1,000 puzzles, each with four answer candidates. While the SotA vision language models (VLMs) achieve decent performance, our evaluation demonstrates a substantial gap between humans and models. VLMs benefit from human-curated descriptions but struggle to self-generate such representations at the right level of abstraction.

COLUMBUS: Evaluating COgnitive Lateral Understanding Through Multiple-Choice reBUSes

3D part assembly is a promising task in 3D computer vision and robotics, focusing on assembling 3D parts together by predicting their 6-DoF poses. 
Like most 3D shape understanding tasks, existing methods primarily address this task by memorizing the poses of parts during the training process, leading to inaccuracies in complex assemblies and poor generalization to novel categories. 
In order to essentially improve the performance, structure knowledge of the target assembly is indispensable before assembling, which abstracts the potential part composition and their structural relationships. 
An image of the target assembly can serve as a common source for constructing this structure knowledge. 
Nevertheless, the image is far from enough, as its knowledge can be incomplete and ambiguous due to part occlusion and varying views.
To tackle these issues, we propose **Imagine**, a novel **Imag**e-gu**i**ded 3D part assembly framework with structure k**n**owl**e**dge graph. 
As a novel assembly prior, the structure knowledge graph originates from the image and is refined as understanding the 3D parts. It encodes robust part-aware structural and semantic information of the assembly, guides the 3D parts from a coarse super-structure to a fine assembly, and co-evolves progressively throughout the assembly process.
Extensive experiments demonstrate the state-of-the-art performance of our framework, along with strong generalization to novel images and categories.

Imagine: Image-Guided 3D Part Assembly with Structure Knowledge Graph

Balancing predictive power and interpretability has long been a challenging research area, particularly in powerful yet complex models like neural networks, where nonlinearity obstructs direct interpretation. This paper introduces a novel approach to constructing an explainable neural network that harmonizes predictiveness and explainability. Our model is designed as a linear combination of a sparse set of jointly learned features, each derived from a different trainable function applied to a single 1-dimensional input feature. Leveraging the ability to learn arbitrarily complex relationships, our neural network architecture enables automatic selection of a sparse set of important features, with the final prediction being a sum of rescaled versions of these features. We demonstrate the ability to select significant features while maintaining comparable predictive performance and direct interpretability through extensive experiments on synthetic and real-world datasets. We also provide theoretical analysis on the generalization bounds of our framework, which is favorably linear in the number of selected features and only logarithmic in the number of input features. We further lift any dependence of sample complexity on the number of parameters or the architectural details under very mild conditions. Our research paves the way for further research on sparse and explainable neural networks with guarantee.

Explainable Neural Networks with Guarantee: A Sparse Estimation Approach

Evaluation metric of visual captioning is important yet not thoroughly explored. Traditional metrics like BLEU, METEOR, CIDEr, and ROUGE often miss semantic depth, while trained metrics such as CLIP-Score, PAC-S, and Polos are limited in zero-shot scenarios. Advanced Language Model-based metrics also struggle with aligning to nuanced human preferences. To address these issues, we introduce G-VEval, a novel metric inspired by G-Eval and powered by the new GPT-4o. G-VEval uses chain-of-thought reasoning in large multimodal models and supports three modes: reference-free, reference-only, and combined, accommodating both video and image inputs. We also propose MSVD-Eval, a new dataset for video captioning evaluation, to establish a more transparent and consistent framework for both human experts and evaluation metrics. It is designed to address the lack of clear criteria in existing datasets by introducing distinct dimensions of Accuracy, Completeness, Conciseness, and Relevance (ACCR). Extensive results show that G-VEval outperforms existing methods in correlation with human annotations, as measured by Kendall tau-b and Kendall tau-c. This provides a flexible solution for diverse captioning tasks and suggests a straightforward yet effective approach for large language models to understand video content, paving the way for advancements in automated captioning.

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