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

FlowRefiner: A Robust Traffic Classification Framework against Label Noise

Mingwei Zhan, Ruijie Zhao, Xianwen Deng, Zhi Xue, Qi Li, Zhuotao Liu, Guang Cheng, Ke Xu

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Network traffic classification is essential for network management and security. In recent years, deep learning (DL) algorithms have emerged as essential tools for classifying complex traffic. However, they rely heavily on high-quality labeled training data. In practice, traffic data is often noisy due to human error or inaccurate automated labeling, which could render classification unreliable and lead to severe consequences. Although some studies have alleviated the label noise issue in specific scenarios, they are difficult to generalize to general traffic classification tasks due to the inherent semantic complexity of traffic data. In this paper, we propose FlowRefiner, a robust and general traffic classification framework against label noise. FlowRefiner consists of three core components: a traffic semantics-driven noise detector, a confidence-guided label correction mechanism, and a cross-granularity robust classifier. First, the noise detector utilizes traffic semantics extracted from a pre-trained encoder to identify mislabeled flows. Next, the confidence-guided label correction module fine-tunes a label predictor to correct noisy labels and construct refined flows. Finally, the cross-granularity robust classifier learns generalized patterns of both flow-level and packet-level, improving classification robustness against noisy labels. We evaluate our method on four traffic datasets with various classification scenarios across varying noise ratios. Experimental results demonstrate that FlowRefiner mitigates the impact of label noise and consistently outperforms state-of-the-art baselines by a large margin. The code is available at https://github.com/NSSL-SJTU/FlowRefiner.

Poster
Multiclass Loss Geometry Matters for Generalization of Gradient Descent in Separable Classification

Matan Schliserman, Tomer Koren

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We study the generalization performance of unregularized gradient methods for separable linear classification. While previous work mostly deal with the binary case, we focus on the multiclass setting with $k$ classes and establish novel population risk bounds for Gradient Descent for loss functions that decay to zero. In this setting, we show risk bounds that reveal that convergence rates are crucially influenced by the geometry of the loss template, as formalized by Wang and Scott (2024), rather than of the loss function itself. Particularly, we establish risk upper bounds that holds for any decay rate of the loss whose template is smooth with respect to the $p$-norm. In the case of exponentially decaying losses, our results indicates a contrast between the $p=\infty$ case, where the risk exhibits a logarithmic dependence on $k$, and $p=2$ where the risk scales linearly with $k$. To establish this separation formally, we also prove a lower bound in the latter scenario, demonstrating that the polynomial dependence on $k$ is unavoidable. Central to our analysis is a novel bound on the Rademacher complexity of low-noise vector-valued linear predictors with a loss template smooth w.r.t. general $p$-norms.

Poster
Unleashing the Potential of Multimodal LLMs for Zero-Shot Spatio-Temporal Video Grounding

Zaiquan Yang, Yuhao Liu, Gerhard Petrus Hancke, Rynson W. H. Lau

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Spatio-temporal video grounding (STVG) aims at localizing the spatio-temporal tube of a video, as specified by the input text query. In this paper, we utilize multimodal large language models (MLLMs) to explore a zero-shot solution in STVG. We reveal two key insights about MLLMs: (1) MLLMs tend to dynamically assign special tokens, referred to as \textit{grounding tokens}, for grounding the text query; and (2) MLLMs often suffer from suboptimal grounding due to the inability to fully integrate the cues in the text query (\textit{e.g.}, attributes, actions) for inference. Based on these insights, we propose a MLLM-based zero-shot framework for STVG, which includes novel decomposed spatio-temporal highlighting (DSTH) and temporal-augmented assembling (TAS) strategies to unleash the reasoning ability of MLLMs. The DSTH strategy first decouples the original query into attribute and action sub-queries for inquiring the existence of the target both spatially and temporally. It then uses a novel logit-guided re-attention (LRA) module to learn latent variables as spatial and temporal prompts, by regularizing token predictions for each sub-query. These prompts highlight attribute and action cues, respectively, directing the model's attention to reliable spatial and temporal related visual regions. In addition, as the spatial grounding by the attribute sub-query should be temporally consistent, we introduce the TAS strategy to assemble the predictions using the original video frames and the temporal-augmented frames as inputs to help improve temporal consistency. We evaluate our method on various MLLMs, and show that it outperforms SOTA methods on three common STVG benchmarks.

Poster
SuperCLIP: CLIP with Simple Classification Supervision

Weiheng Zhao, Zilong Huang, Jiashi FENG, Xinggang Wang

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Contrastive Language-Image Pretraining (CLIP) achieves strong generalization in vision-language tasks by aligning images and texts in a shared embedding space. However, recent findings show that CLIP-like models still underutilize fine-grained semantic signals in text, and this issue becomes even more pronounced when dealing with long and detailed captions. This stems from CLIP’s training objective, which optimizes only global image-text similarity and overlooks token-level supervision—limiting its ability to achieve fine-grained visual-text alignment. To address this, we propose SuperCLIP, a simple yet effective framework that augments contrastive learning with classification-based supervision. By adding only a lightweight linear layer to the vision encoder, SuperCLIP leverages token-level cues to enhance visual-textual alignment — with just a 0.077\% increase in total FLOPs, and no need for additional annotated data. Experiments show that SuperCLIP consistently improves zero-shot classification, image-text retrieval, and purely visual tasks. These gains hold regardless of whether the model is trained on original web data or rich re-captioned data, demonstrating SuperCLIP’s ability to recover textual supervision in both cases. Furthermore, SuperCLIP alleviates CLIP’s small-batch performance drop through classification-based supervision that avoids reliance on large batch sizes. Code and models will be made open source.

Poster
ShapeX: Shapelet-Driven Post Hoc Explanations for Time Series Classification Models

Bosong Huang, Ming Jin, Yuxuan Liang, Johan Barthelemy, Debo Cheng, Qingsong Wen, Chenghao Liu, Shirui Pan

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Explaining time series classification models is crucial, particularly in high-stakes applications such as healthcare and finance, where transparency and trust play a critical role. Although numerous time series classification methods have identified key subsequences, known as shapelets, as core features for achieving state-of-the-art performance and validating their pivotal role in classification outcomes, existing post-hoc time series explanation (PHTSE) methods primarily focus on timestep-level feature attribution. These explanation methods overlook the fundamental prior that classification outcomes are predominantly driven by key shapelets. To bridge this gap, we present ShapeX, an innovative framework that segments time series into meaningful shapelet-driven segments and employs Shapley values to assess their saliency. At the core of ShapeX lies the Shapelet Describe-and-Detect (SDD) framework, which effectively learns a diverse set of shapelets essential for classification. We further demonstrate that ShapeX produces explanations which reveal causal relationships instead of just correlations, owing to the atomicity properties of shapelets. Experimental results on both synthetic and real-world datasets demonstrate that ShapeX outperforms existing methods in identifying the most relevant subsequences, enhancing both the precision and causal fidelity of time series explanations.

Poster
Zero-shot Denoising via Neural Compression: Theoretical and algorithmic framework

Ali Zafari, Xi Chen, Shirin Jalali

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Zero-shot denoising aims to denoise observations without access to training samples or clean reference images. This setting is particularly relevant in practical imaging scenarios involving specialized domains such as medical imaging or biology. In this work, we propose the *Zero-Shot Neural Compression Denoiser* (ZS-NCD), a novel denoising framework based on neural compression. ZS-NCD treats a neural compression network as an untrained model, optimized directly on patches extracted from a single noisy image. The final reconstruction is then obtained by aggregating the outputs of the trained model over overlapping patches. Thanks to the built-in entropy constraints of compression architectures, our method naturally avoids overfitting and does not require manual regularization or early stopping. Through extensive experiments, we show that ZS-NCD achieves state-of-the-art performance among zero-shot denoisers for both Gaussian and Poisson noise, and generalizes well to both natural and non-natural images. Additionally, we provide new finite-sample theoretical results that characterize upper bounds on the achievable reconstruction error of general maximum-likelihood compression-based denoisers. These results further establish the theoretical foundations of compression-based denoising. Our code is available at: https://github.com/Computational-Imaging-RU/ZS-NCDenoiser.

Spotlight
IA-GGAD: Zero-shot Generalist Graph Anomaly Detection via Invariant and Affinity Learning

Xiong Zhang, Zhenli He, Changlong Fu, Cheng Xie

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Generalist Graph Anomaly Detection (GGAD) extends traditional Graph Anomaly Detection (GAD) from one-for-one to one-for-all scenarios, posing significant challenges due to Feature Space Shift (FSS) and Graph Structure Shift (GSS). This paper first formalizes these challenges and proposes quantitative metrics to measure their severity. To tackle FSS, we develop an anomaly-driven graph invariant learning module that learns domain-invariant node representations. To address GSS, a novel structure-insensitive affinity learning module is introduced, capturing cross-domain structural correspondences via affinity-based features. Our unified framework, IA-GGAD, integrates these modules, enabling anomaly prediction on unseen graphs without target-domain retraining or fine-tuning. Extensive experiments on benchmark datasets from varied domains demonstrate IA-GGAD’s superior performance, significantly outperforming state-of-the-art methods (e.g., achieving up to +12.28\% AUROC over ARC on ACM). Ablation studies further confirm the effectiveness of each proposed module. The code is available at \url{https://github.com/kg-cc/IA-GGAD/}.

Spotlight
ORIGEN: Zero-Shot 3D Orientation Grounding in Text-to-Image Generation

Yunhong Min, Daehyeon Choi, Kyeongmin Yeo, Jihyun Lee, Minhyuk Sung

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We introduce ORIGEN, the first zero-shot method for 3D orientation grounding in text-to-image generation across multiple objects and diverse categories. While previous work on spatial grounding in image generation has mainly focused on 2D positioning, it lacks control over 3D orientation. To address this, we propose a reward-guided sampling approach using a pretrained discriminative model for 3D orientation estimation and a one-step text-to-image generative flow model. While gradient-ascent-based optimization is a natural choice for reward-based guidance, it struggles to maintain image realism. Instead, we adopt a sampling-based approach using Langevin dynamics, which extends gradient ascent by simply injecting random noise—requiring just a single additional line of code. Additionally, we introduce adaptive time rescaling based on the reward function to accelerate convergence. Our experiments show that \textsc{Origen} outperforms both training-based and test-time guidance methods across quantitative metrics and user studies.

Poster
ZEBRA: Towards Zero-Shot Cross-Subject Generalization for Universal Brain Visual Decoding

Haonan Wang, Jingyu Lu, Hongrui Li, Xiaomeng Li

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Recent advances in neural decoding have enabled the reconstruction of visual experiences from brain activity, positioning fMRI-to-image reconstruction as a promising bridge between neuroscience and computer vision. However, current methods predominantly rely on subject-specific models or require subject-specific fine-tuning, limiting their scalability and real-world applicability. In this work, we introduce ZEBRA, the first zero-shot brain visual decoding framework that eliminates the need for subject-specific adaptation. Z EBRA is built on the key insight that fMRI representations can be decomposed into subject-related and semantic-related components. By leveraging adversarial training, our method explicitly disentangles these components to isolate subject-invariant, semantic-specific representations. This disentanglement allows ZEBRA to generalize to unseen subjects without any additional fMRI data or retraining. Extensive experiments show that ZEBRA significantly outperforms zero-shot baselines and achieves performance comparable to fully finetuned models on several metrics. Our work represents a scalable and practical step toward universal neural decoding. Code and model weights are available at: https://github.com/xmed-lab/ZEBRA.

Poster
Cancer Survival Analysis via Zero-shot Tumor Microenvironment Segmentation on Low-resolution Whole Slide Pathology Images

Jiao Tang, Wei Shao, Daoqiang Zhang

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The whole-slide pathology images (WSIs) are widely recognized as the golden standard for cancer survival analysis. However, due to the high-resolution of WSIs, the existing studies require dividing WSIs into patches and identify key components before building the survival prediction system, which is time-consuming and cannot reflect the overall spatial organization of WSIs. Inspired by the fact that the spatial interactions among different tumor microenvironment (TME) components in WSIs are associated with the cancer prognosis, some studies attempt to capture the complex interactions among different TME components to improve survival predictions. However, they require extra efforts for building the TME segmentation model, which involves substantial annotation workloads on different TME components and is independent to the construction of the survival prediction model. To address the above issues, we propose ZTSurv, a novel end-to-end cancer survival analysis framework via efficient zero-shot TME segmentation on low-resolution WSIs. Specifically, by leveraging tumor infiltrating lymphocyte (TIL) maps on the 50x down-sampled WSIs, ZTSurv enables zero-shot segmentation on other two important TME components (i.e., tumor and stroma) that can reduce the annotation efforts from the pathologists. Then, based on the visual and semantic information extracted from different TME components, we construct a heterogeneous graph to capture their spatial intersections for clinical outcome prediction. We validate ZTSurv across four cancer cohorts derived from The Cancer Genome Atlas (TCGA), and the experimental results indicate that our method can not only achieve superior prediction results but also significantly reduce the computational costs in comparison with the state-of-the-art methods.

Poster
Evolving and Regularizing Meta-Environment Learner for Fine-Grained Few-Shot Class-Incremental Learning

Li-Jun Zhao, Zhen-Duo Chen, Yongxin Wang, Xin Luo, Xin-Shun Xu

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Recently proposed Fine-Grained Few-Shot Class-Incremental Learning (FG-FSCIL) offers a practical and efficient solution for enabling models to incrementally learn new fine-grained categories under limited data conditions. However, existing methods still settle for the fine-grained feature extraction capabilities learned from the base classes. Unlike conventional datasets, fine-grained categories exhibit subtle inter-class variations, naturally fostering latent synergy among sub-categories. Meanwhile, the incremental learning framework offers an opportunity to progressively strengthen this synergy by incorporating new sub-category data over time. Motivated by this, we theoretically formulate the FSCIL problem and derive a generalization error bound within a shared fine-grained meta-category environment. Guided by our theoretical insights, we design a novel Meta-Environment Learner (MEL) for FG-FSCIL, which evolves fine-grained feature extraction to enhance meta-environment understanding and simultaneously regularizes hypothesis space complexity. Extensive experiments demonstrate that our method consistently and significantly outperforms existing approaches.

Poster
Multitask Learning with Stochastic Interpolants

Hugo Negrel, Florentin Coeurdoux, Michael Samuel Albergo, Eric Vanden-Eijnden

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We propose a framework for learning maps between probability distributions that broadly generalizes the time dynamics of flow and diffusion models. To enable this, we generalize stochastic interpolants by replacing the scalar time variable with vectors, matrices, or linear operators, allowing us to bridge probability distributions across multiple dimensional spaces. This approach enables the construction of versatile generative models capable of fulfilling multiple tasks without task-specific training. Our operator-based interpolants not only provide a unifying theoretical perspective for existing generative models but also extend their capabilities. Through numerical experiments, we demonstrate the zero-shot efficacy of our method on conditional generation and inpainting, fine-tuning and posterior sampling, and multiscale modeling, suggesting its potential as a generic task-agnostic alternative to specialized models.

Spotlight
Fuse2Match: Training-Free Fusion of Flow, Diffusion, and Contrastive Models for Zero-Shot Semantic Matching

Jing Zuo, Jiaqi Wang, Yonggang Qi, Yi-Zhe Song

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Recent work shows that features from Stable Diffusion (SD) and contrastively pretrained models like DINO can be directly used for zero-shot semantic correspondence via naive feature concatenation. In this paper, we explore the stronger potential of Stable Diffusion 3 (SD3), a rectified flow-based model with a multimodal transformer backbone (MM-DiT). We show that semantic signals in SD3 are scattered across multiple timesteps and transformer layers, and propose a multi-level fusion scheme to extract discriminative features. Moreover, we identify that naive fusion across models suffers from inconsistent distributions, thus leading to suboptimal performance. To address this, we propose a simple yet effective confidence-aware feature fusion strategy that re-weights each model’s contribution based on prediction confidence scores derived from their matching uncertainties. Notably, this fusion approach is not only training-free but also enables per-pixel adaptive integration of heterogeneous features. The resulting representation, Fuse2Match, significantly outperforms strong baselines on SPair-71k, PF-Pascal, and PSC6K, validating the benefit of combining SD3, SD, and DINO through our proposed confidence-aware feature fusion. Code is available at https://github.com/panda7777777/fuse2match

Poster
Hierarchical Demonstration Order Optimization for Many-shot In-Context Learning

Yinhan He, Wendy Zheng, Song Wang, Zaiyi Zheng, Yushun Dong, Yaochen Zhu, Jundong Li

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In-Context Learning (ICL) is a technique where large language models (LLMs) leverage multiple demonstrations (i.e., examples) to perform tasks. With the recent expansion of LLM context windows, many-shot ICL (generally with more than 50 demonstrations) can lead to significant performance improvements on a variety of language tasks such as text classification and question answering. Nevertheless, ICL faces the issue of demonstration order instability (ICL-DOI), which means that performance varies significantly depending on the order of demonstrations. Moreover, ICL-DOI persists in many-shot ICL, validated by our thorough experimental investigation. Current strategies for handling ICL-DOI are not applicable to many-shot ICL due to two critical challenges: (1) Most existing methods assess demonstration order quality by first prompting the LLM, then using heuristic metrics based on the LLM's predictions. In the many-shot scenarios, these metrics without theoretical grounding become unreliable, where the LLMs struggle to effectively utilize information from long input contexts, making order distinctions less clear. The requirement to examine all orders for the large number of demonstrations is computationally infeasible due to the super-exponential complexity of the order space in many-shot ICL. To tackle the first challenge, we design a demonstration order evaluation metric based on information theory for measuring order quality, which effectively quantifies the usable information gain of a given demonstration order. To address the second challenge, we propose a hierarchical demonstration order optimization method named \texttt{HIDO} that enables a more refined exploration of the order space, achieving high ICL performance without the need to evaluate all possible orders. Extensive experiments on multiple LLMs and real-world datasets demonstrate that our \texttt{HIDO} method consistently and efficiently outperforms other baselines. Our code project can be found at https://github.com/YinhanHe123/HIDO/.

Poster
BeliefMapNav: 3D Voxel-Based Belief Map for Zero-Shot Object Navigation

Zibo Zhou, Yue Hu, Lingkai Zhang, Zonglin Li, Siheng Chen

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Zero-shot object navigation (ZSON) allows robots to find target objects in unfamiliar environments using natural language instructions, without relying on pre-built maps or task-specific training. Recent general-purpose models, such as large language models (LLMs) and vision-language models (VLMs), equip agents with semantic reasoning abilities to estimate target object locations in a zero-shot manner. However, these models often greedily select the next goal without maintaining a global understanding of the environment and are fundamentally limited in the spatial reasoning necessary for effective navigation. To overcome these limitations, we propose a novel 3D voxel-based belief map that estimates the target’s prior presence distribution within a voxelized 3D space. This approach enables agents to integrate semantic priors from LLMs and visual embeddings with hierarchical spatial structure, alongside real-time observations, to build a comprehensive 3D global posterior belief of the target’s location. Building on this 3D voxel map, we introduce BeliefMapNav, an efficient navigation system with two key advantages: i) grounding LLM semantic reasoning within the 3D hierarchical semantics voxel space for precise target position estimation, and ii) integrating sequential path planning to enable efficient global navigation decisions. Experiments on HM3D and HSSD benchmarks show that BeliefMapNav achieves state-of-the-art (SOTA) Success Rate (SR) and Success weighted by Path Length (SPL), with a notable 9.7 SPL improvement over the previous best SR method, validating its effectiveness and efficiency.

Poster
InvFusion: Bridging Supervised and Zero-shot Diffusion for Inverse Problems

Noam Elata, Hyungjin Chung, Jong Chul Ye, Tomer Michaeli, Michael Elad

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Diffusion Models have demonstrated remarkable capabilities in handling inverse problems, offering high-quality posterior-sampling-based solutions. Despite significant advances, a fundamental trade-off persists regarding the way the conditioned synthesis is employed: Zero-shot approaches can accommodate any linear degradation but rely on approximations that reduce accuracy. In contrast, training-based methods model the posterior correctly, but cannot adapt to the degradation at test-time. Here we introduce InvFusion, the first training-based degradation-aware posterior sampler. InvFusion combines the best of both worlds - the strong performance of supervised approaches and the flexibility of zero-shot methods. This is achieved through a novel architectural design that seamlessly integrates the degradation operator directly into the diffusion denoiser. We compare InvFusion against existing general-purpose posterior samplers, both degradation-aware zero-shot techniques and blind training-based methods. Experiments on the FFHQ and ImageNet datasets demonstrate state-of-the-art performance. Beyond posterior sampling, we further demonstrate the applicability of our architecture, operating as a general Minimum Mean Square Error predictor, and as a Neural Posterior Principal Component estimator.

Poster
DualCnst: Enhancing Zero-Shot Out-of-Distribution Detection via Text-Image Consistency in Vision-Language Models

Fayi Le, Wenwu He, Chentao Cao, Dong Liang, Zhuo-Xu Cui

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Pretrained vision-language models (VLMs), such as CLIP, have shown promising zero-shot out-of-distribution (OOD) detection capabilities by leveraging semantic similarities between input images and textual labels. However, most existing approaches focus solely on expanding the label space in the text domain, ignoring complementary visual cues that can further enhance discriminative power. In this paper, we introduce DualCnst, a novel framework that integrates text-image dual consistency for improved zero-shot OOD detection. Specifically, we generate synthetic images from both ID and mined OOD textual labels using a text-to-image generative model, and jointly evaluate each test image based on (i) its semantic similarity to class labels and (ii) its visual similarity to the synthesized images. The resulting unified score function effectively combines multimodal information without requiring access to in-distribution images or additional training. We further provide theoretical analysis showing that incorporating multimodal negative labels reduces score variance and improves OOD separability. Extensive experiments across diverse OOD benchmarks demonstrate that DualCnst achieves state-of-the-art performance while remaining scalable, data-agnostic, and fully compatible with prior text-only VLM-based methods.

Poster
Preference-driven Knowledge Distillation for Few-shot Node Classification

Xing Wei, Chunchun Chen, Rui Fan, Xiaofeng Cao, Sourav Medya, Wei Ye

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Graph neural networks (GNNs) can efficiently process text-attributed graphs (TAGs) due to their message-passing mechanisms, but their training heavily relies on the human-annotated labels. Moreover, the complex and diverse local topologies of nodes of real-world TAGs make it challenging for a single mechanism to handle. Large language models (LLMs) perform well in zero-/few-shot learning on TAGs but suffer from a scalability challenge. Therefore, we propose a preference-driven knowledge distillation (PKD) framework to synergize the complementary strengths of LLMs and various GNNs for few-shot node classification. Specifically, we develop a GNN-preference-driven node selector that effectively promotes prediction distillation from LLMs to teacher GNNs. To further tackle nodes' intricate local topologies, we develop a node-preference-driven GNN selector that identifies the most suitable teacher GNN for each node, thereby facilitating tailored knowledge distillation from teacher GNNs to the student GNN. Extensive experiments validate the efficacy of our proposed framework in few-shot node classification on real-world TAGs. Our code can be available at <https://github.com/GEEX-Weixing/PKD>.

Poster
Zero-shot protein stability prediction by inverse folding models: a free energy interpretation

Jes Frellsen, Maher M. Kassem, Tone Bengtsen, Lars Olsen, Kresten Lindorff-Larsen, Jesper Ferkinghoff-Borg, Wouter Boomsma

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Inverse folding models have proven to be highly effective zero-shot predictors of protein stability. Despite this success, the link between the amino acid preferences of an inverse folding model and the free-energy considerations underlying thermodynamic stability remains incompletely understood. A better understanding would be of interest not only from a theoretical perspective, but also potentially provide the basis for stronger zero-shot stability prediction. In this paper, we take steps to clarify the free-energy foundations of inverse folding models. Our derivation reveals the standard practice of likelihood ratios as a simplistic approximation and suggests several paths towards better estimates of the relative stability. We empirically assess these approaches and demonstrate that considerable gains in zero-shot performance can be achieved with fairly simple means.

Poster
Embedding Principle of Homogeneous Neural Network for Classification Problem

Jiahan Zhang, Yaoyu Zhang, Tao Luo

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In this paper, we study the Karush-Kuhn-Tucker (KKT) points of the associated maximum-margin problem in homogeneous neural networks, including fully-connected and convolutional neural networks. In particular, We investigates the relationship between such KKT points across networks of different widths generated. We introduce and formalize the \textbf{KKT point embedding principle}, establishing that KKT points of a homogeneous network's max-margin problem ($P_{\Phi}$) can be embedded into the KKT points of a larger network's problem ($P_{\tilde{\Phi}}$) via specific linear isometric transformations. We rigorously prove this principle holds for neuron splitting in fully-connected networks and channel splitting in convolutional neural networks. Furthermore, we connect this static embedding to the dynamics of gradient flow training with smooth losses. We demonstrate that trajectories initiated from appropriately mapped points remain mapped throughout training and that the resulting $\omega$-limit sets of directions are correspondingly mapped , thereby preserving the alignment with KKT directions dynamically when directional convergence occurs. We conduct several experiments to justify that trajectories are preserved. Our findings offer insights into the effects of network width, parameter redundancy, and the structural connections between solutions found via optimization in homogeneous networks of varying sizes.

Poster