NeurIPS 2025 Papers

Conference on Neural Information Processing Systems

Decision breakdown

5,812papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    931.6%
  • Spotlight
    73912.7%
  • Poster
    4,98085.7%

Browse all papers

VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment

Qing Li, Huifang Feng, Xun Gong, Yu-Shen Liu

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3D Gaussian Splatting has recently emerged as an efficient solution for high-quality and real-time novel view synthesis. However, its capability for accurate surface reconstruction remains underexplored. Due to the discrete and unstructured nature of Gaussians, supervision based solely on image rendering loss often leads to inaccurate geometry and inconsistent multi-view alignment. In this work, we propose a novel method that enhances the geometric representation of 3D Gaussians through view alignment (VA). Specifically, we incorporate edge-aware image cues into the rendering loss to improve surface boundary delineation. To enforce geometric consistency across views, we introduce a visibility-aware photometric alignment loss that models occlusions and encourages accurate spatial relationships among Gaussians. To further mitigate ambiguities caused by lighting variations, we incorporate normal-based constraints to refine the spatial orientation of Gaussians and improve local surface estimation. Additionally, we leverage deep image feature embeddings to enforce cross-view consistency, enhancing the robustness of the learned geometry under varying viewpoints and illumination. Extensive experiments on standard benchmarks demonstrate that our method achieves state-of-the-art performance in both surface reconstruction and novel view synthesis. The source code is available at https://github.com/LeoQLi/VA-GS.

Poster
OptiScene: LLM-driven Indoor Scene Layout Generation via Scaled Human-aligned Data Synthesis and Multi-Stage Preference Optimization

Yixuan Yang, Zhen Luo, Tongsheng Ding, Junru Lu, Mingqi Gao, JINYU YANG, Victor Sanchez, Feng Zheng

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Automatic indoor layout generation has attracted increasing attention due to its potential in interior design, virtual environment construction, and embodied AI. Existing methods fall into two categories: prompt-driven approaches that leverage proprietary LLM services (e.g., GPT APIs), and learning-based methods trained on layout data upon diffusion-based models. Prompt-driven methods often suffer from spatial inconsistency and high computational costs, while learning-based methods are typically constrained by coarse relational graphs and limited datasets, restricting their generalization to diverse room categories. In this paper, we revisit LLM-based indoor layout generation and present 3D-SynthPlace, a large-scale dataset that combines synthetic layouts generated via a `GPT synthesize, Human inspect' pipeline, upgraded from the 3D-Front dataset. 3D-SynthPlace contains nearly 17,000 scenes, covering four common room types—bedroom, living room, kitchen, and bathroom—enriched with diverse objects and high-level spatial annotations. We further introduce OptiScene, a strong open-source LLM optimized for indoor layout generation, fine-tuned based on our 3D-SynthPlace dataset through our two-stage training. For the warum-up stage I, we adopt supervised fine-tuning (SFT), which is taught to first generate high-level spatial descriptions then conditionally predict concrete object placements. For the reinforcing stage II, to better align the generated layouts with human design preferences, we apply multi-turn direct preference optimization (DPO), which significantly improving layout quality and generation success rates. Extensive experiments demonstrate that OptiScene outperforms traditional prompt-driven and learning-based baselines. Moreover, OptiScene shows promising potential in interactive tasks such as scene editing and robot navigation, highlighting its applicability beyond static layout generation.

Poster
Implicit Bias of Spectral Descent and Muon on Multiclass Separable Data

Chen Fan, Mark Schmidt, Christos Thrampoulidis

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Different gradient-based methods for optimizing overparameterized models can all achieve zero training error yet converge to distinctly different solutions inducing different generalization properties. We provide the first complete characterization of implicit optimization bias for p-norm normalized steepest descent (NSD) and momentum steepest descent (NMD) algorithms in multi-class linear classification with cross-entropy loss. Our key theoretical contribution is proving that these algorithms converge to solutions maximizing the margin with respect to the classifier matrix's p-norm, with established convergence rates. These results encompass important special cases including Spectral Descent and Muon, which we show converge to max-margin solutions with respect to the spectral norm. A key insight of our contribution is that the analysis of general entry-wise and Schatten p-norms can be reduced to the analysis of NSD/NMD with max-norm by exploiting a natural ordering property between all p-norms relative to the max-norm and its dual sum-norm. For the specific case of descent with respect to the max-norm, we further extend our analysis to include preconditioning, showing that Adam converges to the matrix's max-norm solution. Our results demonstrate that the multi-class linear setting, which is inherently richer than the binary counterpart, provides the most transparent framework for studying implicit biases of matrix-parameter optimization algorithms.

Spotlight
Bridging Critical Gaps in Convergent Learning: How Representational Alignment Evolves Across Layers, Training, and Distribution Shifts

Chaitanya Kapoor, Sudhanshu Srivastava, Meenakshi Khosla

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Understanding convergent learning---the degree to which independently trained neural systems---whether multiple artificial networks or brains and models---arrive at similar internal representations---is crucial for both neuroscience and AI. Yet, the literature remains narrow in scope---typically examining just a handful of models with one dataset, relying on one alignment metric, and evaluating networks at a single post-training checkpoint. We present a large-scale audit of convergent learning, spanning dozens of vision models and thousands of layer-pair comparisons, to close these long-standing gaps. First, we pit three alignment families against one another---linear regression (affine-invariant), orthogonal Procrustes (rotation-/reflection-invariant), and permutation/soft-matching (unit-order-invariant). We find that orthogonal transformations align representations nearly as effectively as more flexible linear ones, and although permutation scores are lower, they significantly exceed chance, indicating a privileged representational basis. Tracking convergence throughout training further shows that nearly all eventual alignment crystallizes within the first epoch---well before accuracy plateaus---indicating it is largely driven by shared input statistics and architectural biases, not by the final task solution. Finally, when models are challenged with a battery of out-of-distribution images, early layers remain tightly aligned, whereas deeper layers diverge in proportion to the distribution shift. These findings fill critical gaps in our understanding of representational convergence, with implications for neuroscience and AI.

Poster
Generalization or Hallucination? Understanding Out-of-Context Reasoning in Transformers

Yixiao Huang, Hanlin Zhu, Tianyu Guo, Jiantao Jiao, Somayeh Sojoudi, Michael I. Jordan, Stuart Russell, Song Mei

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Large language models (LLMs) can acquire new knowledge through fine-tuning, but this process exhibits a puzzling duality: models can generalize remarkably from new facts, yet are also prone to hallucinating incorrect information. However, the reasons for this phenomenon remain poorly understood. In this work, we argue that both behaviors stem from a single mechanism known as out-of-context reasoning (OCR): the ability to deduce implications by associating concepts, even those without a causal link. Our experiments across five prominent LLMs confirm that OCR indeed drives both generalization and hallucination, depending on whether the associated concepts are causally related. To build a rigorous theoretical understanding of this phenomenon, we then formalize OCR as a synthetic factual recall task. We empirically show that a one-layer single-head attention-only transformer with factorized output and value matrices can learn to solve this task, while a model with combined weights cannot, highlighting the crucial role of matrix factorization. Our theoretical analysis shows that the OCR capability can be attributed to the implicit bias of gradient descent, which favors solutions that minimize the nuclear norm of the combined output-value matrix. This structure explains why the model learns to associate facts and implications with high sample efficiency, regardless of whether the correlation is causal or merely spurious. Ultimately, our work provides a theoretical foundation for understanding the OCR phenomenon, offering a new lens for analyzing and mitigating undesirable behaviors from knowledge injection.

Poster
GeoRanker: Distance-Aware Ranking for Worldwide Image Geolocalization

Pengyue Jia, Seongheon Park, Song Gao, Xiangyu Zhao, Sharon Li

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Worldwide image geolocalization—the task of predicting GPS coordinates from images taken anywhere on Earth—poses a fundamental challenge due to the vast diversity in visual content across regions. While recent approaches adopt a two-stage pipeline of retrieving candidates and selecting the best match, they typically rely on simplistic similarity heuristics and point-wise supervision, failing to model spatial relationships among candidates. In this paper, we propose **GeoRanker**, a distance-aware ranking framework that leverages large vision-language models to jointly encode query–candidate interactions and predict geographic proximity. In addition, we introduce a *multi-order distance loss* that ranks both absolute and relative distances, enabling the model to reason over structured spatial relationships. To support this, we curate GeoRanking, the first dataset explicitly designed for geographic ranking tasks with multimodal candidate information. GeoRanker achieves state-of-the-art results on two well-established benchmarks (IM2GPS3K and YFCC4K), significantly outperforming current best methods. We also release our code, checkpoint, and dataset online for ease of reproduction.

Poster
LBMKGC: Large Model-Driven Balanced Multimodal Knowledge Graph Completion

Yuan Guo, Qian Ma, Hui Li, Qiao Ning, Furui Zhan, Yu Gu, Ge Yu, Shikai Guo

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Multi-modal Knowledge Graph Completion (MMKGC) aims to predict missing entities, relations, or attributes in knowledge graphs by collaboratively modeling the triple structure and multimodal information (e.g., text, images, videos) associated with entities. This approach facilitates the automatic discovery of previously unobserved factual knowledge. However, existing MMKGC methods encounter several critical challenges: (i) the imbalance of inter-entity information across different modalities; (ii) the heterogeneity of intra-entity multimodal information; and (iii) for a given entity, the informational contributions of different modalities are inconsistent across contexts. In this paper, we propose a novel **L**arge model-driven **B**alanced **M**ultimodal **K**nowledge **G**raph **C**ompletion framework, termed LBMKGC. Subsequently, to bridge the semantic gap between heterogeneous modalities, LBMKGC aligns the multimodal embeddings of entities semantically by using the CLIP (Contrastive Language-Image Pre-Training) model. Furthermore, LBMKGC adaptively fuses multimodal embeddings with relational guidance by distinguishing between the perceptual and conceptual attributes of triples. Finally, extensive experiments conducted against 21 state-of-the-art baselines demonstrate that LBMKGC achieves superior performance across diverse datasets and scenarios while maintaining efficiency and generalizability. Our code and data are publicly available at: https://github.com/guoynow/LBMKGC.

Poster
Sequential Monte Carlo for Policy Optimization in Continuous POMDPs

Hany Abdulsamad, Sahel Iqbal, Simo Särkkä

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Optimal decision-making under partial observability requires agents to balance reducing uncertainty (exploration) against pursuing immediate objectives (exploitation). In this paper, we introduce a novel policy optimization framework for continuous partially observable Markov decision processes (POMDPs) that explicitly addresses this challenge. Our method casts policy learning as probabilistic inference in a non-Markovian Feynman--Kac model that inherently captures the value of information gathering by anticipating future observations, without requiring suboptimal approximations or handcrafted heuristics. To optimize policies under this model, we develop a nested sequential Monte Carlo (SMC) algorithm that efficiently estimates a history-dependent policy gradient under samples from the optimal trajectory distribution induced by the POMDP. We demonstrate the effectiveness of our algorithm across standard continuous POMDP benchmarks, where existing methods struggle to act under uncertainty.

Poster
GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insights

Shengbo Gong, Juntong Ni, Noveen Sachdeva, Carl Yang, Wei Jin

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Graph condensation (GC) is an emerging technique designed to learn a significantly smaller graph that retains the essential information of the original graph. This condensed graph has shown promise in accelerating graph neural networks while preserving performance comparable to those achieved with the original, larger graphs. Additionally, this technique facilitates downstream applications like neural architecture search and deepens our understanding of redundancies in large graphs. Despite the rapid development of GC methods, particularly for node classification, a unified evaluation framework is still lacking to systematically compare different GC methods or clarify key design choices for improving their effectiveness. To bridge these gaps, we introduce GC4NC, a comprehensive framework for evaluating diverse GC methods on node classification across multiple dimensions including performance, efficiency, privacy preservation, denoising ability, NAS effectiveness, and transferability. Our systematic evaluation offers novel insights into how condensed graphs behave and the critical design choices that drive their success. These findings pave the way for future advancements in GC methods, enhancing both performance and expanding their real-world applications. The code is available at https://github.com/Emory-Melody/GraphSlim/tree/main/benchmark.

Poster
Gate to the Vessel: Residual Experts Restore What SAM Overlooks

Weili Jiang, Jinrong Lv, Xun Gong, Xiaomeng Li, Chubin Ou

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Foundation segmentation models like Segment Anything (SAM) exhibit strong generalization on natural images but struggle with localized failures in medical imaging, especially on fine-grained structures such as vessels with complex morphology and indistinct boundaries. To address this, we propose FineSAM++, a structure-aware sparse expert framework designed to refine SAM outputs by introducing a confidence-driven soft Routing Module. This module dynamically identifies structurally uncertain regions and activates a lightweight Residual Expert to model and correct residual structural errors only within these areas, thereby achieving efficient "refinement over retraining." Extensive experiments on five public vascular segmentation datasets demonstrate that FineSAM++ consistently outperforms both SAM-adapted baselines and task-specific models in terms of accuracy, topological consistency. Our results highlight the effectiveness of sparse, structure-driven Mixture-of-Experts (MoE) strategies for enhancing the reliability of foundation vision models in clinical image understanding tasks.

Poster
Online Mixture of Experts: No-Regret Learning for Optimal Collective Decision-Making

Larkin Liu, Jalal Etesami

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We explore the use of expert-guided bandit learning, which we refer to as online mixture-of-experts (OMoE). In this setting, given a context, a candidate committee of experts must determine how to aggregate their outputs to achieve optimal results in terms of aggregate accuracy. We propose two algorithms to address this problem. The first algorithm combines aggregate voting with UCB-driven successive elimination, efficiently pruning suboptimal exploration actions. The second algorithm employs an online weighted-majority-voting mechanism, leveraging the respective voting power of each expert proportional to their predictive power. We derive theoretical guarantees for the regret properties in the bandit setting under ideal circumstances, and empirical results are provided accordingly. As a modern study on applications, these methods are applied to the online fine-tuning of a set of expert large language models (LLMs), where after each response, the generative LLM dynamically reweighs its set of experts and/or selects the optimal committee of experts to generate the most accurate response. Our results introduce new methodologies and no-regret guarantees for combining multiple experts to improve on the performance of the an aggregate model overall.

Poster
DeblurDiff: Real-Word Image Deblurring with Generative Diffusion Models

Lingshun Kong, Jiawei Zhang, Dongqing Zou, Fu Lee Wang, Jimmy Ren, Xiaohe Wu, Jiangxin Dong, Jinshan Pan

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Diffusion models have achieved significant progress in image generation and the pre-trained Stable Diffusion (SD) models are helpful for image deblurring by providing clear image priors. However, directly using a blurry image or a pre-deblurred one as a conditional control for SD will either hinder accurate structure extraction or make the results overly dependent on the deblurring network. In this work, we propose a Latent Kernel Prediction Network (LKPN) to achieve robust real-world image deblurring. Specifically, we co-train the LKPN in the latent space with conditional diffusion. The LKPN learns a spatially variant kernel to guide the restoration of sharp images in the latent space. By applying element-wise adaptive convolution (EAC), the learned kernel is utilized to adaptively process the blurry feature, effectively preserving the information of the blurry input. This process thereby more effectively guides the generative process of SD, enhancing both the deblurring efficacy and the quality of detail reconstruction. Moreover, the results at each diffusion step are utilized to iteratively estimate the kernels in LKPN to better restore the sharp latent by EAC in the subsequent step. This iterative refinement enhances the accuracy and robustness of the deblurring process. Extensive experimental results demonstrate that the proposed method outperforms state-of-the-art image deblurring methods on both benchmark and real-world images.

Poster
Causal Differentiating Concepts: Interpreting LM Behavior via Causal Representation Learning

Navita Goyal, Hal Daumé III, Alexandre Drouin, Dhanya Sridhar

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Language model activations entangle concepts that mediate their behavior, making it difficult to interpret these factors, which has implications for generalizability and robustness. We introduce an approach for disentangling these concepts without supervision. Existing methods for concept discovery often rely on external labels, contrastive prompts, or known causal structures, which limits their scalability and biases them toward predefined, easily annotatable features. In contrast, we propose a new unsupervised algorithm that identifies causal differentiating concepts—interpretable latent directions in LM activations that must be changed to elicit a different model behavior. These concepts are discovered using a constrained contrastive learning objective, guided by the insight that eliciting a target behavior requires only sparse changes to the underlying concepts. We formalize this notion and show that, under a particular assumption about the sparsity of these causal differentiating concepts, our method learns disentangled representations that align with human-interpretable factors influencing LM decisions. We empirically show the ability of our method to recover ground-truth causal factors in synthetic and semi-synthetic settings. Additionally, we illustrate the utility of our method through a case study on refusal behavior in language models. Our approach offers a scalable and interpretable lens into the internal workings of LMs, providing a principled foundation for interpreting language model behavior.

Spotlight
REVE: A Foundation Model for EEG - Adapting to Any Setup with Large-Scale Pretraining on 25,000 Subjects

Yassine El Ouahidi, Jonathan Lys, Philipp Thölke, Nicolas Farrugia, Bastien Pasdeloup, Vincent Gripon, Karim Jerbi, Giulia Lioi

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Foundation models have transformed AI by reducing reliance on task-specific data through large-scale pretraining. While successful in language and vision, their adoption in EEG has lagged due to the heterogeneity of public datasets, which are collected under varying protocols, devices, and electrode configurations. Existing EEG foundation models struggle to generalize across these variations, often restricting pretraining to a single setup, resulting in suboptimal performance, in particular under linear probing. We present REVE (Representation for EEG with Versatile Embeddings), a pretrained model explicitly designed to generalize across diverse EEG signals. REVE introduces a novel 4D positional encoding scheme that enables it to process signals of arbitrary length and electrode arrangement. Using a masked autoencoding objective, we pretrain REVE on over 60,000 hours of EEG data from 92 datasets spanning 25,000 subjects, representing the largest EEG pretraining effort to date. REVE achieves state-of-the-art results on 10 downstream EEG tasks, including motor imagery classification, seizure detection, sleep staging, cognitive load estimation, and emotion recognition. With little to no fine-tuning, it demonstrates strong generalization, and nuanced spatio-temporal modeling. We release code, pretrained weights, and tutorials to support standardized EEG research and accelerate progress in clinical neuroscience.

Poster
Breaking the Frozen Subspace: Importance Sampling for Low-Rank Optimization in LLM Pretraining

Haochen Zhang, Junze Yin, Guanchu Wang, Zirui Liu, Lin Yang, Tianyi Zhang, Anshumali Shrivastava, Vladimir Braverman

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Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is selecting suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling for low-rank optimization in LLM pretraining with a provable convergence guarantee, which the dominant subspace approach does not have. Empirically, we demonstrate that our method significantly outperforms previous methods in LLM pretraining tasks.

Poster
Make Information Diffusion Explainable: LLM-based Causal Framework for Diffusion Prediction

Wenbo Shang, Zihan Feng, Yajun Yang, Xin Huang

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Information diffusion prediction, which aims to forecast future infected users during the information spreading process on social platforms, is a challenging and critical task for public opinion analysis. With the development of social platforms, mass communication has become increasingly widespread. However, most existing methods based on GNNs and sequence models mainly focus on structural and temporal patterns in social networks, suffering from spurious diffusion connections and insufficient information for the diffusion analysis. We leverage strong reasoning capability of LLMs and develop a LL**M**-based causal framework for d**i**ffusion inf**l**uence **d**erivation (MILD). Comprehensively integrating four key factors of social diffusion, i.e., connections, active timelines, user profiles, and comments, MILD causally infers authentic diffusion links to construct a diffusion influence graph $G_I$. To validate the quality and reliability of our constructed graph $G_I$, we proposed a newly designed set of evaluation metrics w.r.t. diffusion prediction. We show MILD provides a reliable information diffusion structure that 12% absolutely better than the social network structure and achieves the state-of-the-art performance on diffusion prediction. MILD is expected to contribute to high-quality, more explainable, and more trustworthy public opinion analysis.

Poster
ElasticMM: Efficient Multimodal LLMs Serving with Elastic Multimodal Parallelism

Zedong Liu, Shenggan Cheng, Guangming Tan, Yang You, Dingwen Tao

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Multimodal large language models (MLLMs) extend LLMs to handle images, videos, and audio by incorporating feature extractors and projection modules. However, these additional components—combined with complex inference pipelines and heterogeneous workloads—introduce significant inference overhead. Therefore, efficiently serving MLLMs remains a major challenge. Current tightly coupled serving architectures struggle to distinguish between mixed request types or adapt parallelism strategies to different inference stages, leading to increased time-to-first-token (TTFT) and poor resource utilization. To address this, we introduce Elastic Multimodal Parallelism (EMP), a new serving paradigm that elastically adapts to resource heterogeneity across request types and inference stages. Building upon EMP, we develop ElasticMM, an MLLM serving system that (1) separates requests into independent modality groups with dynamic resource allocation via a modality-aware load balancer; (2) decouples inference stages and enables parallelism adjustment and adaptive scaling via elastic partition scheduling; and (3) improves inference efficiency through unified multimodal prefix caching and non-blocking encoding. Experiments on diverse real-world datasets show that ElasticMM outperforms state-of-the-art (SOTA) serving systems, reducing TTFT by up to 4.2$\times$ and achieving 3.2–4.5$\times$ higher throughput while meeting service-level objectives (SLOs).

Oral
Conservative classifiers do consistently well with improving agents: characterizing statistical and online learning

Dravyansh Sharma, Alec Sun

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Machine learning is now ubiquitous in societal decision-making, for example in evaluating job candidates or loan applications, and it is increasingly important to take into account how classified agents will react to the learning algorithms. The majority of recent literature on strategic classification has focused on reducing and countering deceptive behaviors by the classified agents, but recent work of Attias et al. identifies surprising properties of learnability when the agents genuinely improve in order to attain the desirable classification, such as smaller generalization error than standard PAC-learning. In this paper we characterize so-called learnability with improvements across multiple new axes. We introduce an asymmetric variant of minimally consistent concept classes and use it to provide an exact characterization of proper learning with improvements in the realizable setting. While prior work studies learnability only under general, arbitrary agent improvement regions, we give positive results for more natural Euclidean ball improvement sets. In particular, we characterize improper learning under a generative assumption on the data distribution. We further show how to learn in more challenging settings, achieving lower generalization error under well-studied bounded noise models and obtaining mistake bounds in realizable and agnostic online learning. We resolve open questions posed by Attias et al. for both proper and improper learning.

Spotlight
RDB2G-Bench: A Comprehensive Benchmark for Automatic Graph Modeling of Relational Databases

Dongwon Choi, Sunwoo Kim, Juyeon Kim, Kyungho Kim, Geon Lee, Shinhwan Kang, Myunghwan Kim, Kijung Shin

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Recent advances have demonstrated the effectiveness of graph-based machine learning on relational databases (RDBs) for predictive tasks. Such approaches require transforming RDBs into graphs, a process we refer to as RDB-to-graph modeling, where rows of tables are represented as nodes and foreign-key relationships as edges. Yet, effective modeling of RDBs into graphs remains challenging. Specifically, there exist numerous ways to model RDBs into graphs, and performance on predictive tasks varies significantly depending on the chosen graph model of RDBs. In our analysis, we find that the best-performing graph model can yield up to a 10\% higher performance compared to the common heuristic rule for graph modeling, which remains non-trivial to identify. To foster research on intelligent RDB-to-graph modeling, we introduce RDB2G-Bench, the first benchmark framework for evaluating such methods. We construct extensive datasets covering 5 real-world RDBs and 12 predictive tasks, resulting in around 50k graph model–performance pairs for efficient and reproducible evaluations. Thanks to our precomputed datasets, we were able to benchmark 10 automatic RDB-to-graph modeling methods on the $12$ tasks about 380$\times$ faster than on-the-fly evaluation, which requires repeated GNN training. Our analysis of the datasets and benchmark results reveals key structural patterns affecting graph model effectiveness, along with practical implications for effective graph modeling. Our datasets and code are available at https://github.com/chlehdwon/RDB2G-Bench.

Poster
Dense Associative Memory with Epanechnikov Energy

Benjamin Hoover, Zhaoyang Shi, Krishna Balasubramanian, Dmitry Krotov, Parikshit Ram

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We propose a novel energy function for Dense Associative Memory (DenseAM) networks, the log-sum-ReLU (LSR), inspired by optimal kernel density estimation. Unlike the common log-sum-exponential (LSE) function, LSR is based on the Epanechnikov kernel and enables exact memory retrieval with exponential capacity without requiring exponential separation functions. Uniquely, it introduces abundant additional emergent local minima while preserving perfect pattern recovery --- a characteristic previously unseen in DenseAM literature. Empirical results show that LSR energy has significantly more local minima (memories) that have comparable log-likelihood to LSE-based models. Analysis of LSR's emergent memories on image datasets reveals a degree of creativity and novelty, hinting at this method's potential for both large-scale memory storage and generative tasks.

Spotlight