Daily Papers

Contrastive learning and Siamese embedding models have become the foundation of modern verification systems, where decisions are governed not by discrete classification boundaries, but by relational geometry in embedding space. However, existing adversarial attacks remain fundamentally classification-centric, overlooking the vulnerability of relational geometry. In this paper, we introduce a geometry-aware adversarial attack framework that reformulates attacks on contrastive systems as manifold-level relational corruption. Instead of targeting individual predictions, the proposed framework systematically distorts similarity organization within the embedding manifold by pushing positive pairs apart while simultaneously pulling negative pairs closer, ultimately collapsing and inverting pairwise similarity structure. To enable scalable deployment, we shift iterative online optimization into an offline adversarial geometry deformation prior learning stage and train a lightweight feed-forward generator that learns generalized geometry deformation patterns from the victim model. Once trained, the generator produces adversarial perturbations through a single forward pass without requiring online gradient computation, enabling real-time online attacks against similarity-based verification systems. Experimental results across multiple verification architectures demonstrate substantial degradation of verification performance together with severe manifold-level relational corruption. On the Markmatch verification system, the proposed attack reduces accuracy from 95.4% to 38.6% while completely reversing the positive-negative similarity structure.

We introduce a set of image transformations that can be used as corruptions to evaluate the robustness of models as well as data augmentation mechanisms for training neural networks. The primary distinction of the proposed transformations is that, unlike existing approaches such as Common Corruptions, the geometry of the scene is incorporated in the transformations -- thus leading to corruptions that are more likely to occur in the real world. We also introduce a set of semantic corruptions (e.g. natural object occlusions). We show these transformations are `efficient' (can be computed on-the-fly), `extendable' (can be applied on most image datasets), expose vulnerability of existing models, and can effectively make models more robust when employed as `3D data augmentation' mechanisms. The evaluations on several tasks and datasets suggest incorporating 3D information into benchmarking and training opens up a promising direction for robustness research.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

We introduce the MNIST-C dataset, a comprehensive suite of 15 corruptions applied to the MNIST test set, for benchmarking out-of-distribution robustness in computer vision. Through several experiments and visualizations we demonstrate that our corruptions significantly degrade performance of state-of-the-art computer vision models while preserving the semantic content of the test images. In contrast to the popular notion of adversarial robustness, our model-agnostic corruptions do not seek worst-case performance but are instead designed to be broad and diverse, capturing multiple failure modes of modern models. In fact, we find that several previously published adversarial defenses significantly degrade robustness as measured by MNIST-C. We hope that our benchmark serves as a useful tool for future work in designing systems that are able to learn robust feature representations that capture the underlying semantics of the input.

Graph-level anomaly detection aims to identify anomalous graphs from a collection of graphs in an unsupervised manner. A common assumption of anomaly detection is that a reasonable decision boundary has a hypersphere shape, but may appear some non-conforming phenomena in high dimensions. Towards this end, we firstly propose a novel deep graph-level anomaly detection model, which learns the graph representation with maximum mutual information between substructure and global structure features while exploring a hypersphere anomaly decision boundary. The idea is to ensure the training data distribution consistent with the decision hypersphere via an orthogonal projection layer. Moreover, we further perform the bi-hypersphere compression to emphasize the discrimination of anomalous graphs from normal graphs. Note that our method is not confined to graph data and is applicable to anomaly detection of other data such as images. The numerical and visualization results on benchmark datasets demonstrate the effectiveness and superiority of our methods in comparison to many baselines and state-of-the-arts.

Contrastive steering has been shown as a simple and effective method to adjust the generative behavior of LLMs at inference time. It uses examples of prompt responses with and without a trait to identify a direction in an intermediate activation layer, and then shifts activations in this 1-dimensional subspace. However, despite its growing use in AI safety applications, the robustness of contrastive steering to noisy or adversarial data corruption is poorly understood. We initiate a study of the robustness of this process with respect to corruption of the dataset of examples used to train the steering direction. Our first observation is that contrastive steering is quite robust to a moderate amount of corruption, but unwanted side effects can be clearly and maliciously manifested when a non-trivial fraction of the training data is altered. Second, we analyze the geometry of various types of corruption, and identify some safeguards. Notably, a key step in learning the steering direction involves high-dimensional mean computation, and we show that replacing this step with a recently developed robust mean estimator often mitigates most of the unwanted effects of malicious corruption.

Diagnosing and cleaning data is a crucial step for building robust machine learning systems. However, identifying problems within large-scale datasets with real-world distributions is challenging due to the presence of complex issues such as label errors, under-representation, and outliers. In this paper, we propose a unified approach for identifying the problematic data by utilizing a largely ignored source of information: a relational structure of data in the feature-embedded space. To this end, we present scalable and effective algorithms for detecting label errors and outlier data based on the relational graph structure of data. We further introduce a visualization tool that provides contextual information of a data point in the feature-embedded space, serving as an effective tool for interactively diagnosing data. We evaluate the label error and outlier/out-of-distribution (OOD) detection performances of our approach on the large-scale image, speech, and language domain tasks, including ImageNet, ESC-50, and SST2. Our approach achieves state-of-the-art detection performance on all tasks considered and demonstrates its effectiveness in debugging large-scale real-world datasets across various domains. We release codes at https://github.com/snu-mllab/Neural-Relation-Graph.

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

While decision-based black-box adversarial attacks present a severe security threat, current methodologies suffer from fundamental limitations. Pixel-wise attacks frequently introduce unnatural, high-frequency visual artifacts, while latent-space frameworks are confined by the limited search space of low-dimensional manifolds and inherent reconstruction flaws. To resolve these limitations, we propose Latent Geometric Chords (LGC) for Query-Efficient Decision-Based Adversarial Attacks alongside a variant, LGC-H. At its core, LGC navigates decision boundaries by executing a curvature-aware geometric search within a compressed semantic manifold. To guarantee high visual fidelity and circumvent dimensionality bottlenecks, we introduce a Residual-based Adversarial Generation (RAG) mechanism. RAG isolates semantic perturbations as geometric chords and superimposes them directly onto the original source image. RAG substantially resolves baseline reconstruction flaws and effectively doubles the permissible search space dimensions. Experimental results demonstrate that LGC achieves robust cross-dataset transferability and substantially outperforms state-of-the-art baselines. Notably, our method, LGC, minimizes perturbation magnitudes while achieving state-of-the-art visual fidelity--with a Structural Similarity Index Measure (SSIM) exceeding 0.99 and a Learned Perceptual Image Patch Similarity (LPIPS) below 0.01 at 5000 queries--and sustaining high attack success rates under stringent perceptual constraints, successfully compromising adversarially trained robust models. The source code is available at: https://github.com/eihmuekhine/Latent-Geometric-Chords.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

3D perception, especially point cloud classification, has achieved substantial progress. However, in real-world deployment, point cloud corruptions are inevitable due to the scene complexity, sensor inaccuracy, and processing imprecision. In this work, we aim to rigorously benchmark and analyze point cloud classification under corruptions. To conduct a systematic investigation, we first provide a taxonomy of common 3D corruptions and identify the atomic corruptions. Then, we perform a comprehensive evaluation on a wide range of representative point cloud models to understand their robustness and generalizability. Our benchmark results show that although point cloud classification performance improves over time, the state-of-the-art methods are on the verge of being less robust. Based on the obtained observations, we propose several effective techniques to enhance point cloud classifier robustness. We hope our comprehensive benchmark, in-depth analysis, and proposed techniques could spark future research in robust 3D perception.

Effective image restoration with large-size corruptions, such as blind image inpainting, entails precise detection of corruption region masks which remains extremely challenging due to diverse shapes and patterns of corruptions. In this work, we present a novel method for automatic corruption detection, which allows for blind corruption restoration without known corruption masks. Specifically, we develop a hierarchical contrastive learning framework to detect corrupted regions by capturing the intrinsic semantic distinctions between corrupted and uncorrupted regions. In particular, our model detects the corrupted mask in a coarse-to-fine manner by first predicting a coarse mask by contrastive learning in low-resolution feature space and then refines the uncertain area of the mask by high-resolution contrastive learning. A specialized hierarchical interaction mechanism is designed to facilitate the knowledge propagation of contrastive learning in different scales, boosting the modeling performance substantially. The detected multi-scale corruption masks are then leveraged to guide the corruption restoration. Detecting corrupted regions by learning the contrastive distinctions rather than the semantic patterns of corruptions, our model has well generalization ability across different corruption patterns. Extensive experiments demonstrate following merits of our model: 1) the superior performance over other methods on both corruption detection and various image restoration tasks including blind inpainting and watermark removal, and 2) strong generalization across different corruption patterns such as graffiti, random noise or other image content. Codes and trained weights are available at https://github.com/xyfJASON/HCL .

A significant gap exists between theory and practice in deep learning. Generalization and approximation error bounds are often derived for simplified models or are too loose to be informative. Many rely on the manifold hypothesis and on geometric regularity such as intrinsic dimension, curvature, and reach. Progress requires insight into data-manifold geometry and suitable benchmarks, yet existing options are polarized: analytic manifolds with known geometry but limited applicability, or real-world datasets where geometry is only coarsely estimable. We introduce a benchmarking framework for studying data geometry. We repurpose and extend dSprites and COIL-20 with additional transformation dimensions and dense, axis-aligned sampling, and pair them with finite-difference estimators that recover curvature, reach, and volume at near-ground-truth accuracy in a regime where general-purpose estimators are unreliable or difficult to deploy. The framework is intended as a controlled testbed, useful as a calibration environment for geometric estimators and a sandbox for probing theoretical assumptions. To illustrate its use, we present two application studies, namely assessing the scaling behavior of the bounds of Genovese et al. and Fefferman et al., and tracking the layer-wise geometry of a β-VAE, highlighting the behavior of current bounds and the value of controlled benchmarks for guiding and validating future theory. A reference implementation is available at https://github.com/koulakis/manifold-microscope.

Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are neural networks by introducing a distance between the hidden layer representations of the neural networks. These distances are then fed to the non-linear dimensionality reduction algorithm PHATE to create a manifold of neural networks. We characterize this manifold using features of the representation, including class separation, hierarchical cluster structure, spectral entropy, and topological structure. Our analysis reveals that high-performing networks cluster together in the manifold, displaying consistent embedding patterns across all these features. Finally, we demonstrate the utility of this approach for guiding hyperparameter optimization and neural architecture search by sampling from the manifold.

The detection of small infrared targets against blurred and cluttered backgrounds has remained an enduring challenge. In recent years, learning-based schemes have become the mainstream methodology to establish the mapping directly. However, these methods are susceptible to the inherent complexities of changing backgrounds and real-world disturbances, leading to unreliable and compromised target estimations. In this work, we propose a bi-level adversarial framework to promote the robustness of detection in the presence of distinct corruptions. We first propose a bi-level optimization formulation to introduce dynamic adversarial learning. Specifically, it is composited by the learnable generation of corruptions to maximize the losses as the lower-level objective and the robustness promotion of detectors as the upper-level one. We also provide a hierarchical reinforced learning strategy to discover the most detrimental corruptions and balance the performance between robustness and accuracy. To better disentangle the corruptions from salient features, we also propose a spatial-frequency interaction network for target detection. Extensive experiments demonstrate our scheme remarkably improves 21.96% IOU across a wide array of corruptions and notably promotes 4.97% IOU on the general benchmark. The source codes are available at https://github.com/LiuZhu-CV/BALISTD.

Robust 3D perception under corruption has become an essential task for the realm of 3D vision. While current data augmentation techniques usually perform random transformations on all point cloud objects in an offline way and ignore the structure of the samples, resulting in over-or-under enhancement. In this work, we propose an alternative to make sample-adaptive transformations based on the structure of the sample to cope with potential corruption via an auto-augmentation framework, named as AdaptPoint. Specially, we leverage a imitator, consisting of a Deformation Controller and a Mask Controller, respectively in charge of predicting deformation parameters and producing a per-point mask, based on the intrinsic structural information of the input point cloud, and then conduct corruption simulations on top. Then a discriminator is utilized to prevent the generation of excessive corruption that deviates from the original data distribution. In addition, a perception-guidance feedback mechanism is incorporated to guide the generation of samples with appropriate difficulty level. Furthermore, to address the paucity of real-world corrupted point cloud, we also introduce a new dataset ScanObjectNN-C, that exhibits greater similarity to actual data in real-world environments, especially when contrasted with preceding CAD datasets. Experiments show that our method achieves state-of-the-art results on multiple corruption benchmarks, including ModelNet-C, our ScanObjectNN-C, and ShapeNet-C.

A neural network with the widely-used ReLU activation has been shown to partition the sample space into many convex polytopes for prediction. However, the parameterized way a neural network and other machine learning models use to partition the space has imperfections, e.g., the compromised interpretability for complex models, the inflexibility in decision boundary construction due to the generic character of the model, and the risk of being trapped into shortcut solutions. In contrast, although the non-parameterized models can adorably avoid or downplay these issues, they are usually insufficiently powerful either due to over-simplification or the failure to accommodate the manifold structures of data. In this context, we first propose a new type of machine learning models referred to as Manifoldron that directly derives decision boundaries from data and partitions the space via manifold structure discovery. Then, we systematically analyze the key characteristics of the Manifoldron such as manifold characterization capability and its link to neural networks. The experimental results on 4 synthetic examples, 20 public benchmark datasets, and 1 real-world application demonstrate that the proposed Manifoldron performs competitively compared to the mainstream machine learning models. We have shared our code in https://github.com/wdayang/Manifoldron for free download and evaluation.

Boundary representation (B-Rep) generation is a fundamental task in computer-aided design, yet the direct synthesis of high-fidelity and structurally valid B-Reps remains a major challenge. Existing deep generative methods suffer from two forms of brittleness: representation brittleness, caused by padding noise and feature contamination in the latent space, and generation brittleness, stemming from sequential error propagation and a train-inference mismatch due to non-differentiable validity enforcement. We propose HiFi-BRep, a novel framework that addresses these limitations through two synergistic contributions. First, a topology-aware encoder constructs a high-fidelity latent representation by eliminating padding via learnable queries and preventing feature contamination with topology-guided attention. Second, a single-stage decoder jointly predicts geometry and topology in parallel, embedding core manifold constraints as a differentiable learning objective. This design ensures mutual guidance between geometry and topology while avoiding cascaded errors. Extensive experiments show that HiFi-BRep significantly outperforms state-of-the-art methods in both structural validity and geometric fidelity, providing a robust solution for high-quality B-Rep synthesis. Code and models are publicly available at https://github.com/1nnoh/HiFi-BRep.

Relational databases (RDBs) are widely regarded as the gold standard for storing structured information. Consequently, predictive tasks leveraging this data format hold significant application promise. Recently, Relational Deep Learning (RDL) has emerged as a novel paradigm wherein RDBs are conceptualized as graph structures, enabling the application of various graph neural architectures to effectively address these tasks. However, given its novelty, there is a lack of analysis into the relationships between the performance of various RDL models and the characteristics of the underlying RDBs. In this study, we present REDELEX-a comprehensive exploration framework for evaluating RDL models of varying complexity on the most diverse collection of over 70 RDBs, which we make available to the community. Benchmarked alongside key representatives of classic methods, we confirm the generally superior performance of RDL while providing insights into the main factors shaping performance, including model complexity, database sizes and their structural properties.

Large Language model (LLM)-based Multi-Agent Systems (MAS) are prone to cascading risks, where early-stage interactions remain semantically fluent and policy-compliant, yet the underlying interaction dynamics begin to distort in ways that amplify latent instability or misalignment. Traditional auditing methods that focus on per-message semantic content are inherently reactive and lagging, failing to capture these early structural precursors. In this paper, we propose a principled framework for cascading-risk detection grounded in semantic--geometric co-evolution. We model MAS interactions as dynamic graphs and introduce Ollivier--Ricci Curvature (ORC) -- a discrete geometric measure -- to characterize information redundancy and bottleneck formation in communication topologies. By coupling semantic flow signals with graph geometry, the framework learns the normal co-evolutionary dynamics of trusted collaboration and treats deviations from this coupled manifold as early-warning signals. Experiments on a suite of cascading-risk scenarios aligned with the risk category demonstrate that curvature anomalies systematically precede explicit semantic violations by several interaction turns, enabling proactive intervention. Furthermore, the local nature of Ricci curvature provides principled interpretability for root-cause attribution, identifying specific agents or links that precipitate the collapse of trustworthy collaboration.

Existing benchmarks evaluate Tool-Integrated Reasoning (TIR) in LLMs on idealized ''happy paths'', largely overlooking real-world tool failures. We introduce ToolMaze, a benchmark for dynamic path discovery and error recovery in TIR agents. To separate systematic replanning from blind trial-and-error, ToolMaze adopts a two-dimensional design: DAG-based topological complexity and a 2 times 2 taxonomy of tool perturbations (explicit/implicit, transient/permanent). Evaluations show that perturbations degrade performance across nearly all models, with the sharpest drops under implicit semantic failures. Driven by systemic over-trust in corrupted outputs, Perturbation Recovery Rate (PRR) plummets by around 37\% in these scenarios, while complex topologies trap agents in futile trial-and-error loops. Crucially, agentic fault-tolerance improves with model scale 3.66times slower than basic task execution, highlighting dynamic replanning as a distinct bottleneck unaddressed by model scaling or prompting. Data and code are available at https://github.com/Zhudongsheng75/ToolMaze.

Normalizing Flows explicitly maximize a full-dimensional likelihood on the training data. However, real data is typically only supported on a lower-dimensional manifold leading the model to expend significant compute on modeling noise. Injective Flows fix this by jointly learning a manifold and the distribution on it. So far, they have been limited by restrictive architectures and/or high computational cost. We lift both constraints by a new efficient estimator for the maximum likelihood loss, compatible with free-form bottleneck architectures. We further show that naively learning both the data manifold and the distribution on it can lead to divergent solutions, and use this insight to motivate a stable maximum likelihood training objective. We perform extensive experiments on toy, tabular and image data, demonstrating the competitive performance of the resulting model.

PGD adversarial training, the standard robustness method, can reduce Jacobian Frobenius norm yet worsen clean-input geometry (e.g., TDI 1.336 vs. ERM 1.093). We show this is not an implementation artifact but a theorem-level consequence of supervised learning. We prove that any encoder minimizing supervised loss must retain non-zero sensitivity along directions correlated with training labels, including directions that are nuisance at test time. This holds across proper scoring rules, architectures, and dataset sizes. We call this the geometric blind spot of supervised learning. This theorem unifies four empirical phenomena often treated separately: non-robust features, texture bias, corruption fragility, and the robustness-accuracy tradeoff. It also explains why suppressing sensitivity in one adversarial direction can redistribute sensitivity elsewhere. We introduce Trajectory Deviation Index (TDI), a diagnostic of geometric isotropy. Unlike CKA, intrinsic dimension, or Jacobian Frobenius norm alone, TDI captures the failure mode above. In our experiments, PGD attains low Frobenius norm but high TDI, while PMH attains the lowest TDI with one additional training term and no architectural changes. Across seven tasks, BERT/SST-2, and ImageNet ViT-B/16 (backbone family underlying CLIP/DINO/SAM), the blind spot is measurable and repairable. It appears at foundation-model scale, worsens with model scale and task-specific fine-tuning, and is substantially reduced by PMH. PMH also leads on non-Gaussian corruption types (blur/brightness/contrast) without corruption-specific training.

Graph neural networks (GNNs) have brought superb performance to various applications utilizing graph structural data, such as social analysis and fraud detection. The graph links, e.g., social relationships and transaction history, are sensitive and valuable information, which raises privacy concerns when using GNNs. To exploit these vulnerabilities, we propose VertexSerum, a novel graph poisoning attack that increases the effectiveness of graph link stealing by amplifying the link connectivity leakage. To infer node adjacency more accurately, we propose an attention mechanism that can be embedded into the link detection network. Our experiments demonstrate that VertexSerum significantly outperforms the SOTA link inference attack, improving the AUC scores by an average of 9.8% across four real-world datasets and three different GNN structures. Furthermore, our experiments reveal the effectiveness of VertexSerum in both black-box and online learning settings, further validating its applicability in real-world scenarios.

k-nearest neighbor (k-NN) search is a fundamental primitive in geometry processing and computer graphics. While spatial partitioning structures such as kd-trees are standard, they are often manifold-blind, failing to exploit the intrinsic low-dimensional structure of points sampled from 2-manifolds. Recent advances in dynamic programming-based nearest neighbor search (DP-NNS) leverage incrementally constructed Voronoi diagrams to accelerate queries, where each site p maintains a list of successors that progressively refine its Voronoi cell. However, DP-NNS is restricted to single nearest neighbor (k=1) searches, precluding their adoption in applications that require local neighborhood statistics. In this paper, we generalize the DP-NNS framework to support arbitrary k-NN queries for manifold-aligned data. Our approach is founded on the geometric observation that if p_i is the nearest neighbor of a query q in P, then the second nearest neighbor of q must reside either within the prefix set P_{1:i-1} = {p_1, \dots, p_{i-1}} or within p_i's successor list. By recursively extending this principle, we introduce Manifold k-NN, a recursive algorithmic scheme that significantly outperforms conventional kd-trees for manifold-aligned data. Our method achieves a 1\times--10\times speedup in volume-to-surface query scenarios and inherently supports dynamic prefix queries -- enabling k-NN searches within any subset P_{1:m} (m \leq n) with zero overhead. Furthermore, we extend the framework to support point deletion via local Delaunay updates, providing a complete suite of dynamic operations for point set modification. Comprehensive experiments on diverse geometric datasets demonstrate the efficiency and broad applicability of our approach for modern graphics pipelines. Source code is available at https://github.com/sssomeone/manifold-knn.

Most real-world networks are noisy and incomplete samples from an unknown target distribution. Refining them by correcting corruptions or inferring unobserved regions typically improves downstream performance. Inspired by the impressive generative capabilities that have been used to correct corruptions in images, and the similarities between "in-painting" and filling in missing nodes and edges conditioned on the observed graph, we propose a novel graph generative framework, SGDM, which is based on subgraph diffusion. Our framework not only improves the scalability and fidelity of graph diffusion models, but also leverages the reverse process to perform novel, conditional generation tasks. In particular, through extensive empirical analysis and a set of novel metrics, we demonstrate that our proposed model effectively supports the following refinement tasks for partially observable networks: T1: denoising extraneous subgraphs, T2: expanding existing subgraphs and T3: performing "style" transfer by regenerating a particular subgraph to match the characteristics of a different node or subgraph.

Deep Neural Networks are highly susceptible to shortcut learning, frequently memorizing low-dimensional spurious correlations instead of underlying causal mechanisms. This phenomenon not only degrades out-of-distribution robustness but also induces severe demographic biases in sensitive applications. In this paper, we propose a geometric a priori methodology to mitigate shortcut learning. By deploying a zero-hidden-layer (N=1) Topological Auditor, we mathematically isolate features that monopolize the gradient without human intervention. We empirically demonstrate a Capacity Phase Transition: once linear shortcuts are pruned, networks are forced to utilize higher geometric capacity (N geq 16) to curve the decision boundary and learn ethical representations. Our approach outperforms L1 Regularization -- which collapses into demographic bias -- and operates at a fraction of the computational cost of post-hoc methods like Just Train Twice (JTT), successfully reducing counterfactual gender vulnerability from 21.18\% to 7.66\%.

3D object detection is an important task in autonomous driving to perceive the surroundings. Despite the excellent performance, the existing 3D detectors lack the robustness to real-world corruptions caused by adverse weathers, sensor noises, etc., provoking concerns about the safety and reliability of autonomous driving systems. To comprehensively and rigorously benchmark the corruption robustness of 3D detectors, in this paper we design 27 types of common corruptions for both LiDAR and camera inputs considering real-world driving scenarios. By synthesizing these corruptions on public datasets, we establish three corruption robustness benchmarks -- KITTI-C, nuScenes-C, and Waymo-C. Then, we conduct large-scale experiments on 24 diverse 3D object detection models to evaluate their corruption robustness. Based on the evaluation results, we draw several important findings, including: 1) motion-level corruptions are the most threatening ones that lead to significant performance drop of all models; 2) LiDAR-camera fusion models demonstrate better robustness; 3) camera-only models are extremely vulnerable to image corruptions, showing the indispensability of LiDAR point clouds. We release the benchmarks and codes at https://github.com/kkkcx/3D_Corruptions_AD. We hope that our benchmarks and findings can provide insights for future research on developing robust 3D object detection models.

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.

Object detectors achieve strong performance under nominal imaging conditions but can fail silently when exposed to blur, noise, compression, adverse weather, or resolution changes. In safety-critical settings, it is therefore insufficient to produce predictions without assessing whether the input remains within the detector's nominal operating regime. We refer to this capability as self-aware object detection. We introduce a degradation-aware self-awareness framework based on degradation manifolds, which explicitly structure a detector's feature space according to image degradation rather than semantic content. Our method augments a standard detection backbone with a lightweight embedding head trained via multi-layer contrastive learning. Images sharing the same degradation composition are pulled together, while differing degradation configurations are pushed apart, yielding a geometrically organized representation that captures degradation type and severity without requiring degradation labels or explicit density modeling. To anchor the learned geometry, we estimate a pristine prototype from clean training embeddings, defining a nominal operating point in representation space. Self-awareness emerges as geometric deviation from this reference, providing an intrinsic, image-level signal of degradation-induced shift that is independent of detection confidence. Extensive experiments on synthetic corruption benchmarks, cross-dataset zero-shot transfer, and natural weather-induced distribution shifts demonstrate strong pristine-degraded separability, consistent behavior across multiple detector architectures, and robust generalization under semantic shift. These results suggest that degradation-aware representation geometry provides a practical and detector-agnostic foundation.

Generalization, the ability to perform well beyond the training context, is a hallmark of biological and artificial intelligence, yet anticipating unseen failures remains a central challenge. Conventional approaches often take a ``bottom-up'' mechanistic route by reverse-engineering interpretable features or circuits to build explanatory models. While insightful, these methods often struggle to provide the high-level, predictive signals for anticipating failure in real-world deployment. Here, we propose using a ``top-down'' approach to studying generalization failures inspired by medical biomarkers: identifying system-level measurements that serve as robust indicators of a model's future performance. Rather than mapping out detailed internal mechanisms, we systematically design and test network markers to probe structure, function links, identify prognostic indicators, and validate predictions in real-world settings. In image classification, we find that task-relevant geometric properties of in-distribution (ID) object manifolds consistently forecast poor out-of-distribution (OOD) generalization. In particular, reductions in two geometric measures, effective manifold dimensionality and utility, predict weaker OOD performance across diverse architectures, optimizers, and datasets. We apply this finding to transfer learning with ImageNet-pretrained models. We consistently find that the same geometric patterns predict OOD transfer performance more reliably than ID accuracy. This work demonstrates that representational geometry can expose hidden vulnerabilities, offering more robust guidance for model selection and AI interpretability.

Aligned large language models (LLMs) remain vulnerable to adversarial manipulation, and their reliance on web-scale pretraining creates a subtle but consequential attack surface. We study Stealth Pretraining Seeding (SPS), a threat model in which adversaries distribute small amounts of poisoned content across stealth websites, increasing the likelihood that such material is absorbed into future training corpora derived from sources such as Common Crawl. Because each individual payload is tiny, diffuse, and superficially benign, the attack is difficult to detect during dataset construction or filtering. The result is a latent form of poisoning that remains largely invisible under standard evaluation, yet can later be activated by a precise trigger such as <00TRIGGER00>. We call this attack PermaFrost, reflecting its latent and reactivatable nature. We study it through PermaFrost-Attack, a controlled framework for latent conceptual poisoning, together with three geometric diagnostics: Thermodynamic Length, Spectral Curvature, and the Infection Traceback Graph. Across multiple model families and scales, we show that this controlled SPS proxy can induce persistent unsafe behavior that often remains hidden under standard evaluation. Our results identify SPS as a practical and underappreciated threat to future foundation models. This paper introduces a novel geometric diagnostic lens for systematically examining latent model behavior, providing a principled foundation for detecting, characterizing, and understanding vulnerabilities that may remain invisible under standard evaluation.

Graph-based Retrieval-Augmented Generation (GraphRAG) enhances the reasoning capabilities of Large Language Models (LLMs) by grounding their responses in structured knowledge graphs. Leveraging community detection and relation filtering techniques, GraphRAG systems demonstrate inherent resistance to traditional RAG attacks, such as text poisoning and prompt injection. However, in this paper, we find that the security of GraphRAG systems fundamentally relies on the topological integrity of the underlying graph, which can be undermined by implicitly corrupting the logical connections, without altering surface-level text semantics. To exploit this vulnerability, we propose LogicPoison, a novel attack framework that targets logical reasoning rather than injecting false contents. Specifically, LogicPoison employs a type-preserving entity swapping mechanism to perturb both global logic hubs for disrupting overall graph connectivity and query-specific reasoning bridges for severing essential multi-hop inference paths. This approach effectively reroutes valid reasoning into dead ends while maintaining surface-level textual plausibility. Comprehensive experiments across multiple benchmarks demonstrate that LogicPoison successfully bypasses GraphRAG's defenses, significantly degrading performance and outperforming state-of-the-art baselines in both effectiveness and stealth. Our code is available at bluehttps://github.com/Jord8061/logicPoison.

Generative multimodal models can exhibit safety failures that are inherently relational: two benign concepts can become unsafe when linked by a specific action or relation (e.g., child-drinking-wine). Existing unlearning and concept-erasure approaches often target isolated concepts or image-text pairs, which can cause collateral damage to benign uses of the same objects and relations. We propose relationship-aware safety unlearning: a framework that explicitly represents unsafe object-relation-object (O-R-O) tuples and applies targeted parameter-efficient edits (LoRA) to suppress unsafe tuples while preserving object marginals and safe neighboring relations. We include CLIP-based experiments and robustness evaluation under paraphrase, contextual, and out-of-distribution image attacks.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Graph-structured knowledge systems -- from knowledge graphs to GraphRAG pipelines -- organize information into hierarchical communities, yet lack a principled mechanism for continuous resolution control: where do the qualitative boundaries between abstraction levels lie, and how should an agent navigate them? Current approaches rely on discrete community detection with manually tuned resolution parameters (e.g., Leiden γ), offering no continuous zoom and no formal guarantees. We introduce Semantic Level of Detail (SLoD), a framework that addresses both problems by defining a continuous zoom operator via heat kernel diffusion on a graph Laplacian whose kNN structure is induced by a Poincare-ball embedding. We prove hierarchical coherence in the tree limit (exact tree with Sarkar embedding), with bounded approximation error, and demonstrate consistent boundary-detection behaviour on noisy hierarchies; spectral gaps in the graph Laplacian then induce emergent scale boundaries -- scales where the representation undergoes qualitative transitions -- detectable without manual resolution tuning. On synthetic hierarchies (HSBM, 1024 nodes), spectral clustering at the BoundaryScan-detected scale recovers planted levels, with macro ARI saturating at 1.00 in the high-SNR regime (50-seed median) and meso ARI reaching 0.89 [0.86, 0.92] at r=200. On the full WordNet noun hierarchy (82K synsets), using 100 stratified leaf queries, detected boundaries align with true taxonomic depth (τ= 0.79), demonstrating meaningful abstraction-level discovery in real-world knowledge graphs without resolution-parameter tuning. The composite weights, MAD threshold, and kNN-parameter rule (k = max(10, min(lfloorNrfloor, 50))) use defaults that transferred unchanged between HSBM and WordNet; their behaviour on graphs with implicit or qualitatively different hierarchical structure is open.

The rapid evolution of generative models has enabled the creation of hyper-realistic facial deepfakes, exposing a critical vulnerability in modern digital forensics: the inability of detectors to generalize to unseen manipulation techniques. Traditional networks suffer from representation collapse, overfitting to localized artifact fingerprints of specific training generators. This work investigates whether modern Vision Foundation Models can serve as generalizable, out-of-the-box feature extractors capable of tracking forensic anomalies across entirely unseen generative manifolds. We conduct a systematic cross-domain evaluation comparing three foundational learning paradigms: fully supervised macro-semantic features (RoPE-ViT), pure self-supervised geometric features (DINOv3), and multi-teacher agglomerative representations (NVIDIA C-RADIOv4-H). By deploying frozen backbones subjected to downstream linear probing, we map the performance limitations of these architectures on the challenging DF40 benchmark. Our empirical findings expose the intrinsic trade-offs between pre-training paradigms and parameter scale, proving that while foundation models retain high discriminative capabilities for entire face synthesis, localized face editing techniques expose fundamental boundaries in linear probe evaluation structures. Source code and model weights are available in http://github.com/mribrahim/deepfake

Standard benchmarks for optical flow, scene flow, and stereo vision algorithms generally focus on model accuracy rather than robustness to image corruptions like noise or rain. Hence, the resilience of models to such real-world perturbations is largely unquantified. To address this, we present RobustSpring, a comprehensive dataset and benchmark for evaluating robustness to image corruptions for optical flow, scene flow, and stereo models. RobustSpring applies 20 different image corruptions, including noise, blur, color changes, quality degradations, and weather distortions, in a time-, stereo-, and depth-consistent manner to the high-resolution Spring dataset, creating a suite of 20,000 corrupted images that reflect challenging conditions. RobustSpring enables comparisons of model robustness via a new corruption robustness metric. Integration with the Spring benchmark enables public two-axis evaluations of both accuracy and robustness. We benchmark a curated selection of initial models, observing that accurate models are not necessarily robust and that robustness varies widely by corruption type. RobustSpring is a new computer vision benchmark that treats robustness as a first-class citizen to foster models that combine accuracy with resilience. It will be available at https://spring-benchmark.org.

The field of image generation has made significant progress thanks to the introduction of Diffusion Models, which learn to progressively reverse a given image corruption. Recently, a few studies introduced alternative ways of corrupting images in Diffusion Models, with an emphasis on blurring. However, these studies are purely empirical and it remains unclear what is the optimal procedure for corrupting an image. In this work, we hypothesize that the optimal procedure minimizes the length of the path taken when corrupting an image towards a given final state. We propose the Fisher metric for the path length, measured in the space of probability distributions. We compute the shortest path according to this metric, and we show that it corresponds to a combination of image sharpening, rather than blurring, and noise deblurring. While the corruption was chosen arbitrarily in previous work, our Shortest Path Diffusion (SPD) determines uniquely the entire spatiotemporal structure of the corruption. We show that SPD improves on strong baselines without any hyperparameter tuning, and outperforms all previous Diffusion Models based on image blurring. Furthermore, any small deviation from the shortest path leads to worse performance, suggesting that SPD provides the optimal procedure to corrupt images. Our work sheds new light on observations made in recent works and provides a new approach to improve diffusion models on images and other types of data.

Latent visual reasoning (LVR) inserts supervised latent tokens between perception and answer generation in vision-language models (VLMs). The field uses alignment between these latents and their visual targets, i.e., cosine similarity or mean squared error (MSE), as both the training loss and the quality metric, assuming that better alignment yields a better answer. We test this with a designed matrix of five LVR variants and find the assumption inverted: cosine alignment is negatively correlated with accuracy across all five (r=-0.94). To explain this, we introduce PRISM, a pair of inference-time diagnostics: a linear probe that asks where the answer is decodable, and a corruption test that asks whether the latent is load-bearing. The supervised latents are largely bypassed. Corrupting them shifts accuracy by at most four points. The answer is decodable downstream of the latent but not at it, and the size of this decodability gap predicts how much each variant relies on its latent under perturbation. Consistent with an Information Bottleneck reading of the loss, the auxiliary objective reshapes the language model via shared parameters rather than via the latent variable it nominally optimizes.

The outstanding performance of Large Multimodal Models (LMMs) has made them widely applied in vision-related tasks. However, various corruptions in the real world mean that images will not be as ideal as in simulations, presenting significant challenges for the practical application of LMMs. To address this issue, we introduce R-Bench, a benchmark focused on the **Real-world Robustness of LMMs**. Specifically, we: (a) model the complete link from user capture to LMMs reception, comprising 33 corruption dimensions, including 7 steps according to the corruption sequence, and 7 groups based on low-level attributes; (b) collect reference/distorted image dataset before/after corruption, including 2,970 question-answer pairs with human labeling; (c) propose comprehensive evaluation for absolute/relative robustness and benchmark 20 mainstream LMMs. Results show that while LMMs can correctly handle the original reference images, their performance is not stable when faced with distorted images, and there is a significant gap in robustness compared to the human visual system. We hope that R-Bench will inspire improving the robustness of LMMs, **extending them from experimental simulations to the real-world application**. Check https://q-future.github.io/R-Bench for details.

Nonlinear manifolds are widespread in deep visual features, where Euclidean distances often fail to capture true similarity. This limitation becomes particularly severe in prototype-based interpretable fine-grained recognition, where subtle semantic distinctions are essential. To address this challenge, we propose a novel paradigm for prototype-based recognition that anchors similarity within the intrinsic geometry of deep features. Specifically, we distill the latent manifold structure of each class into a diffusion space and introduce a differentiable Nystr\"om interpolation, making the geometry accessible to both unseen samples and learnable prototypes. To ensure efficiency, we employ compact per-class landmark sets with periodic updates. This design keeps the embedding aligned with the evolving backbone, enabling fast and scalable inference. Extensive experiments on the CUB-200-2011 and Stanford Cars datasets show that our GeoProto framework produces prototypes focusing on semantically aligned parts, significantly outperforming Euclidean prototype networks.

In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles. Local approximations obtained by local PCAs are collected into a rank k tangent subbundle on R^d, k<d, which we call a principal subbundle. This determines a sub-Riemannian metric on R^d. We show that sub-Riemannian geodesics with respect to this metric can successfully be applied to a number of important problems, such as: explicit construction of an approximating submanifold M, construction of a representation of the point-cloud in R^k, and computation of distances between observations, taking the learned geometry into account. The reconstruction is guaranteed to equal the true submanifold in the limit case where tangent spaces are estimated exactly. Via simulations, we show that the framework is robust when applied to noisy data. Furthermore, the framework generalizes to observations on an a priori known Riemannian manifold.

In this work, we introduce a new perspective on comparative image assessment by representing an image pair as a structured composition of its regions. In contrast, existing methods focus on whole image analysis, while implicitly relying on region-level understanding. We extend the intra-image notion of a scene graph to inter-image, and propose a novel task of Distortion Graph (DG). DG treats paired images as a structured topology grounded in regions, and represents dense degradation information such as distortion type, severity, comparison and quality score in a compact interpretable graph structure. To realize the task of learning a distortion graph, we contribute (i) a region-level dataset, PandaSet, (ii) a benchmark suite, PandaBench, with varying region-level difficulty, and (iii) an efficient architecture, Panda, to generate distortion graphs. We demonstrate that PandaBench poses a significant challenge for state-of-the-art multimodal large language models (MLLMs) as they fail to understand region-level degradations even when fed with explicit region cues. We show that training on PandaSet or prompting with DG elicits region-wise distortion understanding, opening a new direction for fine-grained, structured pairwise image assessment.

Diffusion models (DMs) have shown remarkable capabilities in generating realistic high-quality images, audios, and videos. They benefit significantly from extensive pre-training on large-scale datasets, including web-crawled data with paired data and conditions, such as image-text and image-class pairs. Despite rigorous filtering, these pre-training datasets often inevitably contain corrupted pairs where conditions do not accurately describe the data. This paper presents the first comprehensive study on the impact of such corruption in pre-training data of DMs. We synthetically corrupt ImageNet-1K and CC3M to pre-train and evaluate over 50 conditional DMs. Our empirical findings reveal that various types of slight corruption in pre-training can significantly enhance the quality, diversity, and fidelity of the generated images across different DMs, both during pre-training and downstream adaptation stages. Theoretically, we consider a Gaussian mixture model and prove that slight corruption in the condition leads to higher entropy and a reduced 2-Wasserstein distance to the ground truth of the data distribution generated by the corruptly trained DMs. Inspired by our analysis, we propose a simple method to improve the training of DMs on practical datasets by adding condition embedding perturbations (CEP). CEP significantly improves the performance of various DMs in both pre-training and downstream tasks. We hope that our study provides new insights into understanding the data and pre-training processes of DMs.

Deep neural networks can approximate functions on different types of data, from images to graphs, with varied underlying structure. This underlying structure can be viewed as the geometry of the data manifold. By extending recent advances in the theoretical understanding of neural networks, we study how a randomly initialized neural network with piece-wise linear activation splits the data manifold into regions where the neural network behaves as a linear function. We derive bounds on the density of boundary of linear regions and the distance to these boundaries on the data manifold. This leads to insights into the expressivity of randomly initialized deep neural networks on non-Euclidean data sets. We empirically corroborate our theoretical results using a toy supervised learning problem. Our experiments demonstrate that number of linear regions varies across manifolds and the results hold with changing neural network architectures. We further demonstrate how the complexity of linear regions is different on the low dimensional manifold of images as compared to the Euclidean space, using the MetFaces dataset.

The integration of neural-network-based systems into clinical practice is limited by challenges related to domain generalization and robustness. The computer vision community established benchmarks such as ImageNet-C as a fundamental prerequisite to measure progress towards those challenges. Similar datasets are largely absent in the medical imaging community which lacks a comprehensive benchmark that spans across imaging modalities and applications. To address this gap, we create and open-source MedMNIST-C, a benchmark dataset based on the MedMNIST+ collection covering 12 datasets and 9 imaging modalities. We simulate task and modality-specific image corruptions of varying severity to comprehensively evaluate the robustness of established algorithms against real-world artifacts and distribution shifts. We further provide quantitative evidence that our simple-to-use artificial corruptions allow for highly performant, lightweight data augmentation to enhance model robustness. Unlike traditional, generic augmentation strategies, our approach leverages domain knowledge, exhibiting significantly higher robustness when compared to widely adopted methods. By introducing MedMNIST-C and open-sourcing the corresponding library allowing for targeted data augmentations, we contribute to the development of increasingly robust methods tailored to the challenges of medical imaging. The code is available at https://github.com/francescodisalvo05/medmnistc-api .

Real-world databases are predominantly relational, comprising multiple interlinked tables that contain complex structural and statistical dependencies. Learning generative models on relational data has shown great promise in generating synthetic data and imputing missing values. However, existing methods often struggle to capture this complexity, typically reducing relational data to conditionally generated flat tables and imposing limiting structural assumptions. To address these limitations, we introduce RelDiff, a novel diffusion generative model that synthesizes complete relational databases by explicitly modeling their foreign key graph structure. RelDiff combines a joint graph-conditioned diffusion process across all tables for attribute synthesis, and a 2K+SBM graph generator based on the Stochastic Block Model for structure generation. The decomposition of graph structure and relational attributes ensures both high fidelity and referential integrity, both of which are crucial aspects of synthetic relational database generation. Experiments on 11 benchmark datasets demonstrate that RelDiff consistently outperforms prior methods in producing realistic and coherent synthetic relational databases. Code is available at https://github.com/ValterH/RelDiff.

Graph Domain Adaptation (GDA) typically uses adversarial learning to align graph embeddings in Euclidean space. However, this paradigm suffers from two critical challenges: Structural Degeneration, where hierarchical and semantic representations are entangled, and Optimization Instability, which arises from oscillatory dynamics of minimax adversarial training. To tackle these issues, we propose DisRFM, a geometry-aware GDA framework that unifies Riemannian embedding and flow-based transport. First, to overcome structural degeneration, we embed graphs into a Riemannian manifold. By adopting polar coordinates, we explicitly disentangle structure (radius) from semantics (angle). Then, we enforce topology preservation through radial Wasserstein alignment and semantic discrimination via angular clustering, thereby preventing feature entanglement and collapse. Second, we address the instability of adversarial alignment by using Riemannian flow matching. This method learns a smooth vector field to guide source features toward the target along geodesic paths, guaranteeing stable convergence. The geometric constraints further guide the flow to maintain the disentangled structure during transport. Theoretically, we prove the asymptotic stability of the flow matching and derive a tighter bound for the target risk. Extensive experiments demonstrate that DisRFM consistently outperforms state-of-the-art methods.

Recently, the proliferation of highly realistic synthetic images, facilitated through a variety of GANs and Diffusions, has significantly heightened the susceptibility to misuse. While the primary focus of deepfake detection has traditionally centered on the design of detection algorithms, an investigative inquiry into the generator architectures has remained conspicuously absent in recent years. This paper contributes to this lacuna by rethinking the architectures of CNN-based generators, thereby establishing a generalized representation of synthetic artifacts. Our findings illuminate that the up-sampling operator can, beyond frequency-based artifacts, produce generalized forgery artifacts. In particular, the local interdependence among image pixels caused by upsampling operators is significantly demonstrated in synthetic images generated by GAN or diffusion. Building upon this observation, we introduce the concept of Neighboring Pixel Relationships(NPR) as a means to capture and characterize the generalized structural artifacts stemming from up-sampling operations. A comprehensive analysis is conducted on an open-world dataset, comprising samples generated by 28 distinct generative models. This analysis culminates in the establishment of a novel state-of-the-art performance, showcasing a remarkable 11.6\% improvement over existing methods. The code is available at https://github.com/chuangchuangtan/NPR-DeepfakeDetection.

Data synthesis is gaining momentum as a privacy-enhancing technology. While single-table tabular data generation has seen considerable progress, current methods for multi-table data often lack the flexibility and expressiveness needed to capture complex relational structures. In particular, they struggle with long-range dependencies and complex foreign-key relationships, such as tables with multiple parent tables or multiple types of links between the same pair of tables. We propose a generative model for relational data that generates the content of a relational dataset given the graph formed by the foreign-key relationships. We do this by learning a deep generative model of the content of the whole relational database by flow matching, where the neural network trained to denoise records leverages a graph neural network to obtain information from connected records. Our method is flexible, as it can support relational datasets with complex structures, and expressive, as the generation of each record can be influenced by any other record within the same connected component. We evaluate our method on several benchmark datasets and show that it achieves state-of-the-art performance in terms of synthetic data fidelity.

Recent text-to-video (T2V) diffusion models rely heavily on auxiliary reward signals (e.g., via reward models or DPO) to align generated content with human aesthetics and improve realism. These signals, however, incur substantial computational overhead, require costly human annotations, and often yield limited improvement in fine-grained local details. In this paper, we argue that your data manifold is secretly a reward model. By explicitly modeling the manifold structure of high-quality Supervised Fine-Tuning (SFT) data and encouraging video latents to lie on this manifold, we derive dense, differentiable, and nearly cost-free reward signals that significantly improve video quality, particularly in mitigating low-level distortions. Our modeling builds upon Local Coordinate Coding (LCC), which captures the `skeleton' of the manifold. However, directly applying LCC suffers from mean regression, pulling latents toward the geometric mean and losing high-frequency details. We therefore extend it to Shell Local Coordinate Coding (Shell-LCC), which models the manifold `surface' as an isotropic shell to align with the true high-density region. Experiments demonstrate that our approach improves realism, enhances high-frequency details, reduces over-smoothing artifacts, and alleviates motion blur.

The quality of generative models depends on the quality of the data they are trained on. Creating large-scale, high-quality datasets is often expensive and sometimes impossible, e.g. in certain scientific applications where there is no access to clean data due to physical or instrumentation constraints. Ambient Diffusion and related frameworks train diffusion models with solely corrupted data (which are usually cheaper to acquire) but ambient models significantly underperform models trained on clean data. We study this phenomenon at scale by training more than 80 models on data with different corruption levels across three datasets ranging from 30,000 to approx 1.3M samples. We show that it is impossible, at these sample sizes, to match the performance of models trained on clean data when only training on noisy data. Yet, a combination of a small set of clean data (e.g.~10% of the total dataset) and a large set of highly noisy data suffices to reach the performance of models trained solely on similar-size datasets of clean data, and in particular to achieve near state-of-the-art performance. We provide theoretical evidence for our findings by developing novel sample complexity bounds for learning from Gaussian Mixtures with heterogeneous variances. Our theoretical model suggests that, for large enough datasets, the effective marginal utility of a noisy sample is exponentially worse than that of a clean sample. Providing a small set of clean samples can significantly reduce the sample size requirements for noisy data, as we also observe in our experiments.

Understanding how Large Language Models (LLMs) perform complex reasoning and their failure mechanisms is a challenge in interpretability research. To provide a measurable geometric analysis perspective, we define the concept of the Reasoning Manifold, a latent low-dimensional geometric structure formed by the internal representations corresponding to all correctly reasoned generations. This structure can be conceptualized as the embodiment of the effective thinking paths that the model has learned to successfully solve a given task. Based on this concept, we build REMA, a framework that explains the origins of failures by quantitatively comparing the spatial relationships of internal model representations corresponding to both erroneous and correct reasoning samples. Specifically, REMA first quantifies the geometric deviation of each erroneous representation by calculating its k-nearest neighbors distance to the approximated manifold formed by correct representations, thereby providing a unified failure signal. It then localizes the divergence points where these deviations first become significant by tracking this deviation metric across the model's layers and comparing it against a baseline of internal fluctuations from correct representations, thus identifying where the reasoning chain begins to go off-track. Our extensive experiments on diverse language and multimodal models and tasks demonstrate the low-dimensional nature of the reasoning manifold and the high separability between erroneous and correct reasoning representations. The results also validate the effectiveness of the REMA framework in analyzing the origins of reasoning failures. This research connects abstract reasoning failures to measurable geometric deviations in representations, providing new avenues for in-depth understanding and diagnosis of the internal computational processes of black-box models.

Large Multimodal Models (LMMs) such as LLaVA are typically trained with an autoregressive language modeling objective, providing only indirect supervision to visual tokens. This often yields weak internal visual representations and brittle behavior under distribution shift. Inspired by recent progress on latent denoising for learning high-quality visual tokenizers, we show that the same principle provides an effective form of visual supervision for improving internal visual feature alignment and multimodal understanding in LMMs. We propose a latent denoising framework that corrupts projected visual tokens using a saliency-aware mixture of masking and Gaussian noising. The LMM is trained to denoise these corrupted tokens by recovering clean teacher patch features from hidden states at a selected intermediate LLM layer using a decoder. To prevent representation collapse, our framework also preserves the teacher's intra-image similarity structure and applies intra-image contrastive patch distillation. During inference, corruption and auxiliary heads are disabled, introducing no additional inference-time overhead. Across a broad suite of standard multimodal benchmarks, our method consistently improves visual understanding and reasoning over strong baselines, and yields clear gains on compositional robustness benchmarks (e.g., NaturalBench). Moreover, under ImageNet-C-style non-adversarial common corruptions applied to benchmark images, our method maintains higher accuracy and exhibits reduced degradation at both moderate and severe corruption levels. Our code is available at https://github.com/dhruvashp/latent-denoising-for-lmms.

The robustness of 3D perception systems under natural corruptions from environments and sensors is pivotal for safety-critical applications. Existing large-scale 3D perception datasets often contain data that are meticulously cleaned. Such configurations, however, cannot reflect the reliability of perception models during the deployment stage. In this work, we present Robo3D, the first comprehensive benchmark heading toward probing the robustness of 3D detectors and segmentors under out-of-distribution scenarios against natural corruptions that occur in real-world environments. Specifically, we consider eight corruption types stemming from adversarial weather conditions, external disturbances, and internal sensor failure. We uncover that, although promising results have been progressively achieved on standard benchmarks, state-of-the-art 3D perception models are at risk of being vulnerable to corruptions. We draw key observations on the use of data representations, augmentation schemes, and training strategies, that could severely affect the model's performance. To pursue better robustness, we propose a density-insensitive training framework along with a simple flexible voxelization strategy to enhance the model resiliency. We hope our benchmark and approach could inspire future research in designing more robust and reliable 3D perception models. Our robustness benchmark suite is publicly available.

Despite their tremendous success in modelling high-dimensional data manifolds, deep neural networks suffer from the threat of adversarial attacks - Existence of perceptually valid input-like samples obtained through careful perturbation that lead to degradation in the performance of the underlying model. Major concerns with existing defense mechanisms include non-generalizability across different attacks, models and large inference time. In this paper, we propose a generalized defense mechanism capitalizing on the expressive power of regularized latent space based generative models. We design an adversarial filter, devoid of access to classifier and adversaries, which makes it usable in tandem with any classifier. The basic idea is to learn a Lipschitz constrained mapping from the data manifold, incorporating adversarial perturbations, to a quantized latent space and re-map it to the true data manifold. Specifically, we simultaneously auto-encode the data manifold and its perturbations implicitly through the perturbations of the regularized and quantized generative latent space, realized using variational inference. We demonstrate the efficacy of the proposed formulation in providing resilience against multiple attack types (black and white box) and methods, while being almost real-time. Our experiments show that the proposed method surpasses the state-of-the-art techniques in several cases.

This paper introduces the Manifold Probe, a supervised method for discovering representation manifolds in superposition. The method generalizes linear regression probes by learning the space of features of a concept that can be linearly predicted from the representations, and then learning the directions used to encode them. We demonstrate the probe on representations of time and space in Llama 2-7b, finding manifolds which linearly represent an interpretable set of features in each case. In the case of time, we show that by steering along the manifold, we can influence the model's completions about the years in which famous songs, movies and books were released, providing evidence that the Manifold Probe can discover manifolds which are causally involved in model behaviour.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Latent Diffusion Models (LDMs) achieve high-fidelity synthesis but suffer from latent space brittleness, causing discontinuous semantic jumps during editing. We introduce a Riemannian framework to diagnose this instability by analyzing the generative Jacobian, decomposing geometry into Local Scaling (capacity) and Local Complexity (curvature). Our study uncovers a ``Geometric Decoupling": while curvature in normal generation functionally encodes image detail, OOD generation exhibits a functional decoupling where extreme curvature is wasted on unstable semantic boundaries rather than perceptible details. This geometric misallocation identifies ``Geometric Hotspots" as the structural root of instability, providing a robust intrinsic metric for diagnosing generative reliability.

Annotation errors are widespread in computer vision datasets and can significantly degrade the performance of systems trained on them, particularly in complex tasks such as object detection. Several approaches exist to identify annotation errors, including training-free feature-space methods which provide a fast and interpretable way to analyze annotations. However, the behavior on object detection annotations, which include semantic and spatial information, remains largely unexplored. In this work we analyze the applicability of feature-space-based approaches for detecting annotation errors in object detection datasets. By adapting an existing feature-space method, we show that such approaches reliably expose semantic mislabel, while positional errors remain difficult to detect. We evaluate this behavior across multiple pretrained embedding models, synthetic noise types (symmetric, asymmetric, and positional), and real-world annotation errors using VOC2012 and KITTI. All code and real-world corruptions are publicly available at the following repository: https://github.com/ ChristianSieberichs/BoundingBox\_corruption\_detection

Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step followed by a projection-based measurement consistency step, often produce suboptimal results. By studying the generative sampling path, here we show that current solvers throw the sample path off the data manifold, and hence the error accumulates. To address this, we propose an additional correction term inspired by the manifold constraint, which can be used synergistically with the previous solvers to make the iterations close to the manifold. The proposed manifold constraint is straightforward to implement within a few lines of code, yet boosts the performance by a surprisingly large margin. With extensive experiments, we show that our method is superior to the previous methods both theoretically and empirically, producing promising results in many applications such as image inpainting, colorization, and sparse-view computed tomography. Code available https://github.com/HJ-harry/MCG_diffusion

Multi-domain graph pre-training integrates knowledge from diverse domains to enhance performance in the target domains, which is crucial for building graph foundation models. Despite initial success, existing solutions often fall short of answering a fundamental question: how is knowledge integrated or transferred across domains? This theoretical limitation motivates us to rethink the consistency and transferability between model pre-training and domain adaptation. In this paper, we propose a fresh Riemannian geometry perspective, whose core idea is to merge any graph dataset into a unified, smooth Riemannian manifold, enabling a systematic understanding of knowledge integration and transfer. To achieve this, our key contribution is the theoretical establishment of neural manifold gluing, which first characterizes local geometry using an adaptive orthogonal frame and then "glues" the local pieces together into a coherent whole. Building on this theory, we present the GraphGlue framework, which supports batched pre-training with EMA prototyping and provides a transferability measure based on geometric consistence. Extensive experiments demonstrate its superior performance across diverse graph domains. Moreover, we empirically validated GraphGlue's geometric scaling law, showing that larger quantities of datasets improve model transferability by producing a smoother manifold. Codes are available at https://github.com/RiemannGraph/GraphGlue.

The presence of composite degradations poses a significant challenge, since the underlying corruption factors exhibit complex and interdependent interactions. Even when the degradation types are known, accurately restoring the image remains difficult due to the intertwined nature of their effects and the need for selective control during the recovery process. To address this, we introduce CURE, a unified framework that enables controllable restoration in complex degradation settings by learning disentangled and adjustable representations. CURE is driven by four complementary objectives. First, an identity embedding is incorporated, along with a reconstruction constraint, to ensure that the model can reproduce the input image when restoration is unnecessary. Second, the ratio control mechanism blends the identity embedding with degradation-specific embeddings using user-regulated mixing ratios, allowing continuous control over restoration intensity. Third, an intermediate loss is applied to supervise stepwise outputs, each encouraged to tackle the removal of only a single degradation factor within a composite mixture. Finally, a permutation-invariant loss ensures that the model achieves consistent restoration quality regardless of the order in which multiple degradations are addressed. Since CURE modifies only the training strategy and not the underlying network architecture, it can be seamlessly integrated into existing controllable restoration models. Experiments demonstrate that CURE delivers state-of-the-art performance on composite degradation benchmarks, while enabling both selective and jointly fused restoration through flexible modulation of embedding ratios. The code and dataset are available at https://github.com/bo-oseng/CURE.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Topological deep learning has emerged for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. Although combinatorial complexes offer a unified topological framework, most existing topological deep learning methods rely on local message passing via attention mechanisms, which incur quadratic complexity and remain low-dimensional, limiting scalability and rank-aware information aggregation in higher-order complexes.We propose Combinatorial Complex Mamba (CCMamba), the first unified mamba-based neural framework for learning on combinatorial complexes. CCMamba reformulates message passing as a selective state-space modeling problem by organizing multi-rank incidence relations into structured sequences processed by rank-aware state-space models. This enables adaptive, directional, and long range information propagation in linear time without self attention. We further establish the theoretical analysis that the expressive power upper-bound of CCMamba message passing is the 1-Weisfeiler-Lehman test. Experiments on graph, hypergraph, and simplicial benchmarks demonstrate that CCMamba consistently outperforms existing methods while exhibiting improved scalability and robustness to depth.

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data, and on estimating local Hessian matrices of neural network loss landscapes.

Deep neural networks excel at learning the training data, but often provide incorrect and confident predictions when evaluated on slightly different test examples. This includes distribution shifts, outliers, and adversarial examples. To address these issues, we propose Manifold Mixup, a simple regularizer that encourages neural networks to predict less confidently on interpolations of hidden representations. Manifold Mixup leverages semantic interpolations as additional training signal, obtaining neural networks with smoother decision boundaries at multiple levels of representation. As a result, neural networks trained with Manifold Mixup learn class-representations with fewer directions of variance. We prove theory on why this flattening happens under ideal conditions, validate it on practical situations, and connect it to previous works on information theory and generalization. In spite of incurring no significant computation and being implemented in a few lines of code, Manifold Mixup improves strong baselines in supervised learning, robustness to single-step adversarial attacks, and test log-likelihood.

We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.

In a graph convolutional network, we assume that the graph G is generated wrt some observation noise. During learning, we make small random perturbations ΔG of the graph and try to improve generalization. Based on quantum information geometry, ΔG can be characterized by the eigendecomposition of the graph Laplacian matrix. We try to minimize the loss wrt the perturbed G+Δ{G} while making Δ{G} to be effective in terms of the Fisher information of the neural network. Our proposed model can consistently improve graph convolutional networks on semi-supervised node classification tasks with reasonable computational overhead. We present three different geometries on the manifold of graphs: the intrinsic geometry measures the information theoretic dynamics of a graph; the extrinsic geometry characterizes how such dynamics can affect externally a graph neural network; the embedding geometry is for measuring node embeddings. These new analytical tools are useful in developing a good understanding of graph neural networks and fostering new techniques.

Practitioners prune neural networks for efficiency gains and generalization improvements, but few scrutinize the factors determining the prunability of a neural network the maximum fraction of weights that pruning can remove without compromising the model's test accuracy. In this work, we study the properties of input data that may contribute to the prunability of a neural network. For high dimensional input data such as images, text, and audio, the manifold hypothesis suggests that these high dimensional inputs approximately lie on or near a significantly lower dimensional manifold. Prior work demonstrates that the underlying low dimensional structure of the input data may affect the sample efficiency of learning. In this paper, we investigate whether the low dimensional structure of the input data affects the prunability of a neural network.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

We introduce the first comprehensive 3D dataset for the task of unsupervised anomaly detection and localization. It is inspired by real-world visual inspection scenarios in which a model has to detect various types of defects on manufactured products, even if it is trained only on anomaly-free data. There are defects that manifest themselves as anomalies in the geometric structure of an object. These cause significant deviations in a 3D representation of the data. We employed a high-resolution industrial 3D sensor to acquire depth scans of 10 different object categories. For all object categories, we present a training and validation set, each of which solely consists of scans of anomaly-free samples. The corresponding test sets contain samples showing various defects such as scratches, dents, holes, contaminations, or deformations. Precise ground-truth annotations are provided for every anomalous test sample. An initial benchmark of 3D anomaly detection methods on our dataset indicates a considerable room for improvement.

There is an increasingly apparent need for validating the classifications made by deep learning systems in safety-critical applications like autonomous vehicle systems. A number of recent papers have proposed methods for detecting anomalous image data that appear different from known inlier data samples, including reconstruction-based autoencoders. Autoencoders optimize the compression of input data to a latent space of a dimensionality smaller than the original input and attempt to accurately reconstruct the input using that compressed representation. Since the latent vector is optimized to capture the salient features from the inlier class only, it is commonly assumed that images of objects from outside of the training class cannot effectively be compressed and reconstructed. Some thus consider reconstruction error as a kind of novelty measure. Here we suggest that reconstruction-based approaches fail to capture particular anomalies that lie far from known inlier samples in latent space but near the latent dimension manifold defined by the parameters of the model. We propose incorporating the Mahalanobis distance in latent space to better capture these out-of-distribution samples and our results show that this method often improves performance over the baseline approach.

Medical Vision-Language Models (MVLMs) have achieved par excellence generalization in medical image analysis, yet their performance under noisy, corrupted conditions remains largely untested. Clinical imaging is inherently susceptible to acquisition artifacts and noise; however, existing evaluations predominantly assess generally clean datasets, overlooking robustness -- i.e., the model's ability to perform under real-world distortions. To address this gap, we first introduce MediMeta-C, a corruption benchmark that systematically applies several perturbations across multiple medical imaging datasets. Combined with MedMNIST-C, this establishes a comprehensive robustness evaluation framework for MVLMs. We further propose RobustMedCLIP, a visual encoder adaptation of a pretrained MVLM that incorporates few-shot tuning to enhance resilience against corruptions. Through extensive experiments, we benchmark 5 major MVLMs across 5 medical imaging modalities, revealing that existing models exhibit severe degradation under corruption and struggle with domain-modality tradeoffs. Our findings highlight the necessity of diverse training and robust adaptation strategies, demonstrating that efficient low-rank adaptation when paired with few-shot tuning, improves robustness while preserving generalization across modalities.

Large language models (LLMs) generalize smoothly across continuous semantic spaces, yet strict logical reasoning demands the formation of discrete decision boundaries. Prevailing theories relying on linear isometric projections fail to resolve this fundamental tension. In this work, we argue that task context operates as a non-isometric dynamical operator that enforces a necessary "topological distortion." By applying Gram-Schmidt decomposition to residual-stream activations , we reveal a dual-modulation mechanism driving this process: a class-agnostic topological preservation that anchors global structure to prevent semantic collapse, and a specific algebraic divergence that directionally tears apart cross-class concepts to forge logical boundaries. We validate this geometric evolution across a gradient of tasks, from simple mapping to complex primality testing. Crucially, targeted specific vector ablation establishes a strict causal binding between this topology and model function: algebraically erasing the divergence component collapses parity classification accuracy from 100% to chance levels (38.57%). Furthermore, we uncover a three-phase layer-wise geometric dynamic and demonstrate that under social pressure prompts, models fail to generate sufficient divergence. This results in a "manifold entanglement" that geometrically explains sycophancy and hallucination. Ultimately, our findings revise the linear-isometric presumption, demonstrating that the emergence of discrete logic in LLMs is purchased at an irreducible cost of topological deformation.

Indiscriminate data poisoning attacks aim to decrease a model's test accuracy by injecting a small amount of corrupted training data. Despite significant interest, existing attacks remain relatively ineffective against modern machine learning (ML) architectures. In this work, we introduce the notion of model poisoning reachability as a technical tool to explore the intrinsic limits of data poisoning attacks towards target parameters (i.e., model-targeted attacks). We derive an easily computable threshold to establish and quantify a surprising phase transition phenomenon among popular ML models: data poisoning attacks can achieve certain target parameters only when the poisoning ratio exceeds our threshold. Building on existing parameter corruption attacks and refining the Gradient Canceling attack, we perform extensive experiments to confirm our theoretical findings, test the predictability of our transition threshold, and significantly improve existing indiscriminate data poisoning baselines over a range of datasets and models. Our work highlights the critical role played by the poisoning ratio, and sheds new insights on existing empirical results, attacks and mitigation strategies in data poisoning.

The era of foundation models has revolutionized AI research, yet Graph Foundation Models (GFMs) remain constrained by the scarcity of large-scale graph corpora. Traditional graph data synthesis techniques primarily focus on simplistic structural operations, lacking the capacity to generate semantically rich nodes with meaningful textual attributes: a critical limitation for real-world applications. While large language models (LLMs) demonstrate exceptional text generation capabilities, their direct application to graph synthesis is impeded by context window limitations, hallucination phenomena, and structural consistency challenges. To address these issues, we introduce GraphMaster, the first multi-agent framework specifically designed for graph data synthesis in data-limited environments. GraphMaster orchestrates four specialized LLM agents (Manager, Perception, Enhancement, and Evaluation) that collaboratively optimize the synthesis process through iterative refinement, ensuring both semantic coherence and structural integrity. To rigorously evaluate our approach, we create new data-limited "Sub" variants of six standard graph benchmarks, specifically designed to test synthesis capabilities under realistic constraints. Additionally, we develop a novel interpretability assessment framework that combines human evaluation with a principled Grassmannian manifold-based analysis, providing both qualitative and quantitative measures of semantic coherence. Experimental results demonstrate that GraphMaster significantly outperforms traditional synthesis methods across multiple datasets, establishing a strong foundation for advancing GFMs in data-scarce environments.

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering.

Despite their empirical success, pushing Transformer architectures to extreme depth often leads to a paradoxical failure: representations become increasingly redundant, lose rank, and ultimately collapse. Existing explanations largely attribute this phenomenon to optimization instability or vanishing gradients, yet such accounts fail to explain why collapse persists even under modern normalization and initialization schemes. In this paper, we argue that the collapse of deep Transformers is fundamentally a geometric problem. Standard residual updates implicitly assume that feature accumulation is always beneficial, but offer no mechanism to constrain update directions or to erase outdated information. As depth increases, this leads to systematic drift off the semantic manifold and monotonic feature accumulation, causing representational degeneracy. We propose a unified geometric framework that addresses these failures through two orthogonal principles. First, manifold-constrained hyper-connections restrict residual updates to valid local tangent directions, preventing uncontrolled manifold drift. Second, deep delta learning introduces data-dependent, non-monotonic updates that enable reflection and erasure of redundant features rather than their unconditional accumulation. Together, these mechanisms decouple the direction and sign of feature updates, yielding a stable geometric evolution across depth. We term the resulting architecture the Manifold-Geometric Transformer (MGT). Our analysis predicts that enforcing geometric validity while allowing dynamic erasure is essential for avoiding rank collapse in ultra-deep networks. We outline an evaluation protocol for Transformers exceeding 100 layers to test the hypothesis that geometry, rather than depth itself, is the key limiting factor in deep representation learning.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.

Action Quality Assessment (AQA) evaluates diverse skills but models struggle with non-stationary data. We propose Continual AQA (CAQA) to refine models using sparse new data. Feature replay preserves memory without storing raw inputs. However, the misalignment between static old features and the dynamically changing feature manifold causes severe catastrophic forgetting. To address this novel problem, we propose Manifold-Aligned Graph Regularization (MAGR), which first aligns deviated old features to the current feature manifold, ensuring representation consistency. It then constructs a graph jointly arranging old and new features aligned with quality scores. Experiments show MAGR outperforms recent strong baselines with up to 6.56%, 5.66%, 15.64%, and 9.05% correlation gains on the MTL-AQA, FineDiving, UNLV-Dive, and JDM-MSA split datasets, respectively. This validates MAGR for continual assessment challenges arising from non-stationary skill variations.

Differential privacy is a widely adopted framework designed to safeguard the sensitive information of data providers within a data set. It is based on the application of controlled noise at the interface between the server that stores and processes the data, and the data consumers. Local differential privacy is a variant that allows data providers to apply the privatization mechanism themselves on their data individually. Therefore it provides protection also in contexts in which the server, or even the data collector, cannot be trusted. The introduction of noise, however, inevitably affects the utility of the data, particularly by distorting the correlations between individual data components. This distortion can prove detrimental to tasks such as causal discovery. In this paper, we consider various well-known locally differentially private mechanisms and compare the trade-off between the privacy they provide, and the accuracy of the causal structure produced by algorithms for causal learning when applied to data obfuscated by these mechanisms. Our analysis yields valuable insights for selecting appropriate local differentially private protocols for causal discovery tasks. We foresee that our findings will aid researchers and practitioners in conducting locally private causal discovery.

Adversarial training is effective on balanced datasets, but its robustness degrades under longtailed class distributions, where tail classes suffer high robust error and unstable decision boundaries. We propose Manifold-Constrained Adversarial Training (MCAT), a unified framework that enforces the semantic validity of adversarial examples by penalizing deviations from class-conditional manifolds in feature space, while promoting balanced geometric separation across classes via an ETF-inspired regularization. We provide theoretical results that link geometric separation to lower bounds on adversarially robust margins, and show that manifold-constrained adversarial risk upperbounds robust risk on high-density semantic regions. Extensive experiments on standard longtailed benchmarks demonstrate consistent improvements in overall, balanced, and tail-class adversarial robustness.

Adversarial threats against LLMs are escalating faster than current defenses can adapt. We expose a critical geometric blind spot in alignment: adversarial prompts exploit latent camouflage, embedding perilously close to the safe representation manifold while encoding unsafe intent thereby evading surface level defenses like Direct Preference Optimization (DPO), which remain blind to the latent geometry. We introduce ALKALI, the first rigorously curated adversarial benchmark and the most comprehensive to date spanning 9,000 prompts across three macro categories, six subtypes, and fifteen attack families. Evaluation of 21 leading LLMs reveals alarmingly high Attack Success Rates (ASRs) across both open and closed source models, exposing an underlying vulnerability we term latent camouflage, a structural blind spot where adversarial completions mimic the latent geometry of safe ones. To mitigate this vulnerability, we introduce GRACE - Geometric Representation Aware Contrastive Enhancement, an alignment framework coupling preference learning with latent space regularization. GRACE enforces two constraints: latent separation between safe and adversarial completions, and adversarial cohesion among unsafe and jailbreak behaviors. These operate over layerwise pooled embeddings guided by a learned attention profile, reshaping internal geometry without modifying the base model, and achieve up to 39% ASR reduction. Moreover, we introduce AVQI, a geometry aware metric that quantifies latent alignment failure via cluster separation and compactness. AVQI reveals when unsafe completions mimic the geometry of safe ones, offering a principled lens into how models internally encode safety. We make the code publicly available at https://anonymous.4open.science/r/alkali-B416/README.md.

Although RDBs store vast amounts of rich, informative data spread across interconnected tables, the progress of predictive machine learning models as applied to such tasks arguably falls well behind advances in other domains such as computer vision or natural language processing. This deficit stems, at least in part, from the lack of established/public RDB benchmarks as needed for training and evaluation purposes. As a result, related model development thus far often defaults to tabular approaches trained on ubiquitous single-table benchmarks, or on the relational side, graph-based alternatives such as GNNs applied to a completely different set of graph datasets devoid of tabular characteristics. To more precisely target RDBs lying at the nexus of these two complementary regimes, we explore a broad class of baseline models predicated on: (i) converting multi-table datasets into graphs using various strategies equipped with efficient subsampling, while preserving tabular characteristics; and (ii) trainable models with well-matched inductive biases that output predictions based on these input subgraphs. Then, to address the dearth of suitable public benchmarks and reduce siloed comparisons, we assemble a diverse collection of (i) large-scale RDB datasets and (ii) coincident predictive tasks. From a delivery standpoint, we operationalize the above four dimensions (4D) of exploration within a unified, scalable open-source toolbox called 4DBInfer. We conclude by presenting evaluations using 4DBInfer, the results of which highlight the importance of considering each such dimension in the design of RDB predictive models, as well as the limitations of more naive approaches such as simply joining adjacent tables. Our source code is released at https://github.com/awslabs/multi-table-benchmark .

Foundation models for biology and physics optimize predictive accuracy, but their internal representations systematically fail to preserve the continuous geometry of the systems they model. We identify the root cause: the Geometric Alignment Tax, an intrinsic cost of forcing continuous manifolds through discrete categorical bottlenecks. Controlled ablations on synthetic dynamical systems demonstrate that replacing cross-entropy with a continuous head on an identical encoder reduces geometric distortion by up to 8.5x, while learned codebooks exhibit a non-monotonic double bind where finer quantization worsens geometry despite improving reconstruction. Under continuous objectives, three architectures differ by 1.3x; under discrete tokenization, they diverge by 3,000x. Evaluating 14 biological foundation models with rate-distortion theory and MINE, we identify three failure regimes: Local-Global Decoupling, Representational Compression, and Geometric Vacuity. A controlled experiment confirms that Evo 2's reverse-complement robustness on real DNA reflects conserved sequence composition, not learned symmetry. No model achieves simultaneously low distortion, high mutual information, and global coherence.

Real-world datasets collected from sensors or human inputs are prone to noise and errors, posing significant challenges for applying offline reinforcement learning (RL). While existing methods have made progress in addressing corrupted actions and rewards, they remain insufficient for handling corruption in high-dimensional state spaces and for cases where multiple elements in the dataset are corrupted simultaneously. Diffusion models, known for their strong denoising capabilities, offer a promising direction for this problem-but their tendency to overfit noisy samples limits their direct applicability. To overcome this, we propose Ambient Diffusion-Guided Dataset Recovery (ADG), a novel approach that pioneers the use of diffusion models to tackle data corruption in offline RL. First, we introduce Ambient Denoising Diffusion Probabilistic Models (DDPM) from approximated distributions, which enable learning on partially corrupted datasets with theoretical guarantees. Second, we use the noise-prediction property of Ambient DDPM to distinguish between clean and corrupted data, and then use the clean subset to train a standard DDPM. Third, we employ the trained standard DDPM to refine the previously identified corrupted data, enhancing data quality for subsequent offline RL training. A notable strength of ADG is its versatility-it can be seamlessly integrated with any offline RL algorithm. Experiments on a range of benchmarks, including MuJoCo, Kitchen, and Adroit, demonstrate that ADG effectively mitigates the impact of corrupted data and improves the robustness of offline RL under various noise settings, achieving state-of-the-art results.

Pickle deserialization vulnerabilities have persisted throughout Python's history, remaining widely recognized yet unresolved. Due to its ability to transparently save and restore complex objects into byte streams, many AI/ML frameworks continue to adopt pickle as the model serialization protocol despite its inherent risks. As the open-source model ecosystem grows, model-sharing platforms such as Hugging Face have attracted massive participation, significantly amplifying the real-world risks of pickle exploitation and opening new avenues for model supply chain poisoning. Although several state-of-the-art scanners have been developed to detect poisoned models, their incomplete understanding of the poisoning surface leaves the detection logic fragile and allows attackers to bypass them. In this work, we present the first systematic disclosure of the pickle-based model poisoning surface from both model loading and risky function perspectives. Our research demonstrates how pickle-based model poisoning can remain stealthy and highlights critical gaps in current scanning solutions. On the model loading surface, we identify 22 distinct pickle-based model loading paths across five foundational AI/ML frameworks, 19 of which are entirely missed by existing scanners. We further develop a bypass technique named Exception-Oriented Programming (EOP) and discover 9 EOP instances, 7 of which can bypass all scanners. On the risky function surface, we discover 133 exploitable gadgets, achieving almost a 100% bypass rate. Even against the best-performing scanner, these gadgets maintain an 89% bypass rate. By systematically revealing the pickle-based model poisoning surface, we achieve practical and robust bypasses against real-world scanners. We responsibly disclose our findings to corresponding vendors, receiving acknowledgments and a $6000 bug bounty.

Relational databases (RDBs) are composed of interconnected tables, where relationships between them are defined through foreign keys. Recent research on applying machine learning to RDBs has explored graph-based representations of RDBs, where rows of tables are modeled as nodes, and foreign key relationships are modeled as edges. RDB-to-graph modeling helps capture cross-table dependencies, ultimately leading to enhanced performance across diverse tasks. However, there are numerous ways to model RDBs as graphs, and performance varies significantly depending on the chosen graph model. In our analysis, applying a common heuristic rule for graph modeling leads to up to a 10% drop in performance compared to the best-performing graph model, 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-performance pairs for efficient and reproducible evaluations. Thanks to our precomputed datasets, we were able to benchmark 9 automatic RDB-to-graph modeling methods on the 12 tasks over 600x faster than on-the-fly evaluation, which requires repeated model 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.

Tabular machine learning presents a paradox: modern models achieve state-of-the-art performance using high-dimensional (high-D), collinear, error-prone data, defying the "Garbage In, Garbage Out" mantra. To help resolve this, we synthesize principles from Information Theory, Latent Factor Models, and Psychometrics, clarifying that predictive robustness arises not solely from data cleanliness, but from the synergy between data architecture and model capacity. Partitioning predictor-space "noise" into "Predictor Error" and "Structural Uncertainty" (informational deficits from stochastic generative mappings), we prove that leveraging high-D sets of error-prone predictors asymptotically overcomes both types of noise, whereas cleaning a low-D set is fundamentally bounded by Structural Uncertainty. We demonstrate why "Informative Collinearity" (dependencies from shared latent causes) enhances reliability and convergence efficiency, and explain why increased dimensionality reduces the latent inference burden, enabling feasibility with finite samples. To address practical constraints, we propose "Proactive Data-Centric AI" to identify predictors that enable robustness efficiently. We also derive boundaries for Systematic Error Regimes and show why models that absorb "rogue" dependencies can mitigate assumption violations. Linking latent architecture to Benign Overfitting, we offer a first step towards a unified view of robustness to Outcome Error and predictor-space noise, while also delineating when traditional DCAI's focus on label cleaning remains powerful. By redefining data quality from item-level perfection to portfolio-level architecture, we provide a theoretical rationale for "Local Factories" -- learning from live, uncurated enterprise "data swamps" -- supporting a deployment paradigm shift from "Model Transfer" to "Methodology Transfer'' to overcome static generalizability limitations.

Multi-modal 3D object detection models for automated driving have demonstrated exceptional performance on computer vision benchmarks like nuScenes. However, their reliance on densely sampled LiDAR point clouds and meticulously calibrated sensor arrays poses challenges for real-world applications. Issues such as sensor misalignment, miscalibration, and disparate sampling frequencies lead to spatial and temporal misalignment in data from LiDAR and cameras. Additionally, the integrity of LiDAR and camera data is often compromised by adverse environmental conditions such as inclement weather, leading to occlusions and noise interference. To address this challenge, we introduce MultiCorrupt, a comprehensive benchmark designed to evaluate the robustness of multi-modal 3D object detectors against ten distinct types of corruptions. We evaluate five state-of-the-art multi-modal detectors on MultiCorrupt and analyze their performance in terms of their resistance ability. Our results show that existing methods exhibit varying degrees of robustness depending on the type of corruption and their fusion strategy. We provide insights into which multi-modal design choices make such models robust against certain perturbations. The dataset generation code and benchmark are open-sourced at https://github.com/ika-rwth-aachen/MultiCorrupt.

We develop tools for explicitly constructing categories enriched over generating data and that compose via ordinary scalar and matrix arithmetic arithmetic operations. We characterize meaningful size maps, weightings, and magnitude that reveal features analogous to outliers that these same notions have previously been shown to reveal in the context of metric spaces. Throughout, we provide examples of such "outlier detection" relevant to the analysis of computer programs, neural networks, cyber-physical systems, and networks of communications channels.

Graph-based retrieval-augmented generation (Graph RAG) is increasingly deployed to support LLM applications by augmenting user queries with structured knowledge retrieved from a knowledge graph. While Graph RAG improves relational reasoning, it introduces a largely understudied threat: adversaries can reconstruct subgraphs from a target RAG system's knowledge graph, enabling privacy inference and replication of curated knowledge assets. We show that existing attacks are largely ineffective against Graph RAG even with simple prompt-based safeguards, because these attacks expose explicit exfiltration intent and are therefore easily suppressed by lightweight safe prompts. We identify three technical challenges for practical Graph RAG extraction under realistic safeguards and introduce GRASP, a closed-box, multi-turn subgraph reconstruction attack. GRASP (i) reframes extraction as a context-processing task, (ii) enforces format-compliant, instance-grounded outputs via per-record identifiers to reduce hallucinations and preserve relational details, and (iii) diversifies goal-driven attack queries using a momentum-aware scheduler to operate within strict query budgets. Across two real-world knowledge graphs, four safety-aligned LLMs, and multiple Graph RAG frameworks, GRASP attains the strongest type-faithful reconstruction where prior methods fail, reaching up to 82.9 F1. We further evaluate defenses and propose two lightweight mitigations that substantially reduce reconstruction fidelity without utility loss.

We propose a new approach for generative modeling based on training a neural network to be idempotent. An idempotent operator is one that can be applied sequentially without changing the result beyond the initial application, namely f(f(z))=f(z). The proposed model f is trained to map a source distribution (e.g, Gaussian noise) to a target distribution (e.g. realistic images) using the following objectives: (1) Instances from the target distribution should map to themselves, namely f(x)=x. We define the target manifold as the set of all instances that f maps to themselves. (2) Instances that form the source distribution should map onto the defined target manifold. This is achieved by optimizing the idempotence term, f(f(z))=f(z) which encourages the range of f(z) to be on the target manifold. Under ideal assumptions such a process provably converges to the target distribution. This strategy results in a model capable of generating an output in one step, maintaining a consistent latent space, while also allowing sequential applications for refinement. Additionally, we find that by processing inputs from both target and source distributions, the model adeptly projects corrupted or modified data back to the target manifold. This work is a first step towards a ``global projector'' that enables projecting any input into a target data distribution.

Backdoor and data poisoning attacks can achieve high attack success while evading existing spectral and optimisation based defences. We show that this behaviour is not incidental, but arises from a fundamental geometric mechanism in input space. Using kernel ridge regression as an exact model of wide neural networks, we prove that clustered dirty label poisons induce a rank one spike in the input Hessian whose magnitude scales quadratically with attack efficacy. Crucially, for nonlinear kernels we identify a near clone regime in which poison efficacy remains order one while the induced input curvature vanishes, making the attack provably spectrally undetectable. We further show that input gradient regularisation contracts poison aligned Fisher and Hessian eigenmodes under gradient flow, yielding an explicit and unavoidable safety efficacy trade off by reducing data fitting capacity. For exponential kernels, this defence admits a precise interpretation as an anisotropic high pass filter that increases the effective length scale and suppresses near clone poisons. Extensive experiments on linear models and deep convolutional networks across MNIST and CIFAR 10 and CIFAR 100 validate the theory, demonstrating consistent lags between attack success and spectral visibility, and showing that regularisation and data augmentation jointly suppress poisoning. Our results establish when backdoors are inherently invisible, and provide the first end to end characterisation of poisoning, detectability, and defence through input space curvature.

The proliferation of Large Language Models (LLMs) accessed via black-box APIs introduces a significant trust challenge: users pay for services based on advertised model capabilities (e.g., size, performance), but providers may covertly substitute the specified model with a cheaper, lower-quality alternative to reduce operational costs. This lack of transparency undermines fairness, erodes trust, and complicates reliable benchmarking. Detecting such substitutions is difficult due to the black-box nature, typically limiting interaction to input-output queries. This paper formalizes the problem of model substitution detection in LLM APIs. We systematically evaluate existing verification techniques, including output-based statistical tests, benchmark evaluations, and log probability analysis, under various realistic attack scenarios like model quantization, randomized substitution, and benchmark evasion. Our findings reveal the limitations of methods relying solely on text outputs, especially against subtle or adaptive attacks. While log probability analysis offers stronger guarantees when available, its accessibility is often limited. We conclude by discussing the potential of hardware-based solutions like Trusted Execution Environments (TEEs) as a pathway towards provable model integrity, highlighting the trade-offs between security, performance, and provider adoption. Code is available at https://github.com/sunblaze-ucb/llm-api-audit

State-of-the-art embedding models are increasingly derived from decoder-only Large Language Model (LLM) backbones adapted via contrastive learning. Given the emergence of reasoning models trained via Reinforcement Learning with Verifiable Rewards (RLVR), a natural question arises: do enhanced reasoning translate to superior semantic representations when these models serve as embedding initializations? Contrary to expectation, our evaluation on MTEB and BRIGHT reveals a **null effect**: embedding models initialized from RLVR-tuned backbones yield no consistent performance advantage over their base counterparts when subjected to identical training recipes. To unpack this paradox, we introduce **H**ierarchical **R**epresentation **S**imilarity **A**nalysis (HRSA), a framework that decomposes similarity across representation, geometry, and function levels. HRSA reveals that while RLVR induces irreversible latent manifold's local geometry reorganization and reversible coordinate basis drift, it preserves the global manifold geometry and linear readout. Consequently, subsequent contrastive learning drives strong alignment between base- and reasoning-initialized models, a phenomenon we term **Manifold Realignment**. Empirically, our findings suggest that unlike Supervised Fine-Tuning (SFT), RLVR optimizes trajectories within an existing semantic landscape rather than fundamentally restructuring the landscape itself.

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models often focus on structured inputs such as tables, graphs, or synthetic tasks, and do not isolate the difficulty introduced by higher-arity relational binding. We study this problem through the lens of Relational Complexity (RC), which we define as the minimum number of independent entities or operands that must be simultaneously bound to apply a relation. RC provides a principled way to vary reasoning difficulty while controlling for confounders such as input size, vocabulary, and representational choices. Building on RC, we introduce REL, a generative benchmark framework spanning algebra, chemistry, and biology that varies RC within each domain. Across frontier LLMs, performance degrades consistently and monotonically as RC increases, even when the total number of entities is held fixed. This failure mode persists with increased test-time compute and in-context learning, suggesting a limitation tied to the arity of the required relational binding rather than to insufficient inference steps or lack of exposure to examples. Our results identify a regime of higher-arity reasoning in which current models struggle, and motivate re-examining benchmarks through the lens of relational complexity.

An important challenge when using computer vision models in the real world is to evaluate their performance in potential out-of-distribution (OOD) scenarios. While simple synthetic corruptions are commonly applied to test OOD robustness, they often fail to capture nuisance shifts that occur in the real world. Recently, diffusion models have been applied to generate realistic images for benchmarking, but they are restricted to binary nuisance shifts. In this work, we introduce CNS-Bench, a Continuous Nuisance Shift Benchmark to quantify OOD robustness of image classifiers for continuous and realistic generative nuisance shifts. CNS-Bench allows generating a wide range of individual nuisance shifts in continuous severities by applying LoRA adapters to diffusion models. To address failure cases, we propose a filtering mechanism that outperforms previous methods, thereby enabling reliable benchmarking with generative models. With the proposed benchmark, we perform a large-scale study to evaluate the robustness of more than 40 classifiers under various nuisance shifts. Through carefully designed comparisons and analyses, we find that model rankings can change for varying shifts and shift scales, which cannot be captured when applying common binary shifts. Additionally, we show that evaluating the model performance on a continuous scale allows the identification of model failure points, providing a more nuanced understanding of model robustness. Project page including code and data: https://genintel.github.io/CNS.

Today's denoising diffusion models do not "denoise" in the classical sense, i.e., they do not directly predict clean images. Rather, the neural networks predict noise or a noised quantity. In this paper, we suggest that predicting clean data and predicting noised quantities are fundamentally different. According to the manifold assumption, natural data should lie on a low-dimensional manifold, whereas noised quantities do not. With this assumption, we advocate for models that directly predict clean data, which allows apparently under-capacity networks to operate effectively in very high-dimensional spaces. We show that simple, large-patch Transformers on pixels can be strong generative models: using no tokenizer, no pre-training, and no extra loss. Our approach is conceptually nothing more than "Just image Transformers", or JiT, as we call it. We report competitive results using JiT with large patch sizes of 16 and 32 on ImageNet at resolutions of 256 and 512, where predicting high-dimensional noised quantities can fail catastrophically. With our networks mapping back to the basics of the manifold, our research goes back to basics and pursues a self-contained paradigm for Transformer-based diffusion on raw natural data.

We present a geometric framework for filtered approximate nearest neighbor (ANN) search. Filtering a proximity graph by a metadata predicate produces a subgraph, a fiber, whose connectivity and geometry can differ sharply from the full graph. Using local signals, we propose a two-phase search algorithm that combines full-graph exploration with filtered-neighbor descent when the local geometry is favorable. These signals also classify search failures into three regimes: topological cuts, geometric folds, and genuine basins. A key observation is that all three share a common resolution: restarting the search in a fiber-present cluster near the query. To support this, we introduce a lightweight anchor structure that identifies such regions and restarts the search accordingly. We show empirically that the method outperforms FAISS HNSW on filtered search and the three failure regimes separate cleanly and shift predictably with filter selectivity.

The topic of stitching images with globally natural structures holds paramount significance. Current methodologies exhibit the ability to preserve local geometric structures, yet fall short in maintaining relationships between these geometric structures. In this paper, we endeavor to safeguard the overall, OBJect-level structures within images based on Global Similarity Prior, while concurrently mitigating distortion and ghosting artifacts with OBJ-GSP. Our approach leverages the Segment Anything Model to extract geometric structures with semantic information, enhancing the algorithm's ability to preserve objects in a manner that aligns more intuitively with human perception. We seek to identify spatial constraints that govern the relationships between various geometric boundaries. Recognizing that multiple geometric boundaries collectively define complete objects, we employ triangular meshes to safeguard not only individual geometric structures but also the overall shapes of objects within the images. Empirical evaluations across multiple image stitching datasets demonstrate that our method establishes a new state-of-the-art benchmark in image stitching. Our implementation and dataset is publicly available at https://github.com/RussRobin/OBJ-GSP .

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

The manifold hypothesis posits that high-dimensional data often lies on a lower-dimensional manifold and that utilizing this manifold as the target space yields more efficient representations. While numerous traditional manifold-based techniques exist for dimensionality reduction, their application in self-supervised learning has witnessed slow progress. The recent MSimCLR method combines manifold encoding with SimCLR but requires extremely low target encoding dimensions to outperform SimCLR, limiting its applicability. This paper introduces a novel learning paradigm using an unbalanced atlas (UA), capable of surpassing state-of-the-art self-supervised learning approaches. We investigated and engineered the DeepInfomax with an unbalanced atlas (DIM-UA) method by adapting the Spatiotemporal DeepInfomax (ST-DIM) framework to align with our proposed UA paradigm. The efficacy of DIM-UA is demonstrated through training and evaluation on the Atari Annotated RAM Interface (AtariARI) benchmark, a modified version of the Atari 2600 framework that produces annotated image samples for representation learning. The UA paradigm improves existing algorithms significantly as the number of target encoding dimensions grows. For instance, the mean F1 score averaged over categories of DIM-UA is ~75% compared to ~70% of ST-DIM when using 16384 hidden units.

Multimodal misinformation, encompassing textual, visual, and cross-modal distortions, poses an increasing societal threat that is amplified by generative AI. Existing methods typically focus on a single type of distortion and struggle to generalize to unseen scenarios. In this work, we observe that different distortion types share common reasoning capabilities while also requiring task-specific skills. We hypothesize that joint training across distortion types facilitates knowledge sharing and enhances the model's ability to generalize. To this end, we introduce TRUST-VL, a unified and explainable vision-language model for general multimodal misinformation detection. TRUST-VL incorporates a novel Question-Aware Visual Amplifier module, designed to extract task-specific visual features. To support training, we also construct TRUST-Instruct, a large-scale instruction dataset containing 198K samples featuring structured reasoning chains aligned with human fact-checking workflows. Extensive experiments on both in-domain and zero-shot benchmarks demonstrate that TRUST-VL achieves state-of-the-art performance, while also offering strong generalization and interpretability.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

Recent work has shown how denoising and contractive autoencoders implicitly capture the structure of the data-generating density, in the case where the corruption noise is Gaussian, the reconstruction error is the squared error, and the data is continuous-valued. This has led to various proposals for sampling from this implicitly learned density function, using Langevin and Metropolis-Hastings MCMC. However, it remained unclear how to connect the training procedure of regularized auto-encoders to the implicit estimation of the underlying data-generating distribution when the data are discrete, or using other forms of corruption process and reconstruction errors. Another issue is the mathematical justification which is only valid in the limit of small corruption noise. We propose here a different attack on the problem, which deals with all these issues: arbitrary (but noisy enough) corruption, arbitrary reconstruction loss (seen as a log-likelihood), handling both discrete and continuous-valued variables, and removing the bias due to non-infinitesimal corruption noise (or non-infinitesimal contractive penalty).

Knowledge graph (KG) embeddings learn low-dimensional representations of entities and relations to predict missing facts. KGs often exhibit hierarchical and logical patterns which must be preserved in the embedding space. For hierarchical data, hyperbolic embedding methods have shown promise for high-fidelity and parsimonious representations. However, existing hyperbolic embedding methods do not account for the rich logical patterns in KGs. In this work, we introduce a class of hyperbolic KG embedding models that simultaneously capture hierarchical and logical patterns. Our approach combines hyperbolic reflections and rotations with attention to model complex relational patterns. Experimental results on standard KG benchmarks show that our method improves over previous Euclidean- and hyperbolic-based efforts by up to 6.1% in mean reciprocal rank (MRR) in low dimensions. Furthermore, we observe that different geometric transformations capture different types of relations while attention-based transformations generalize to multiple relations. In high dimensions, our approach yields new state-of-the-art MRRs of 49.6% on WN18RR and 57.7% on YAGO3-10.

Reinforcement learning (RL) post-training has shown to improve reasoning in large language models (LLMs). However, there has been little exploration on the problem of data contamination in RL post-training, potentially undermining generalization and evaluation reliability of the training process itself. Existing detection methods primarily rely on output-level signals such as likelihood or entropy, which become unreliable for RL-trained models since RL shapes behavior through trajectory-level rewards rather than token likelihoods. We propose LaRA, a layer-wise representation analysis framework for detecting contamination in RL post-trained LLMs. LaRA introduces three complementary metrics, measuring perturbation sensitivity, directional collapse, and local representation rigidity under controlled perturbations. We find that contamination produces progressive geometric deviations across layers, including amplified perturbation sensitivity, stronger directional collapse, and enhanced local rigidity. Based on our findings, we also develop a contamination detection protocol that aggregates representation-level deviations across layers and metrics. Experiments on RL-trained reasoning models show that our protocol outperforms existing output-level baselines for contamination detection.

In real-world scenarios, image impairments often manifest as composite degradations, presenting a complex interplay of elements such as low light, haze, rain, and snow. Despite this reality, existing restoration methods typically target isolated degradation types, thereby falling short in environments where multiple degrading factors coexist. To bridge this gap, our study proposes a versatile imaging model that consolidates four physical corruption paradigms to accurately represent complex, composite degradation scenarios. In this context, we propose OneRestore, a novel transformer-based framework designed for adaptive, controllable scene restoration. The proposed framework leverages a unique cross-attention mechanism, merging degraded scene descriptors with image features, allowing for nuanced restoration. Our model allows versatile input scene descriptors, ranging from manual text embeddings to automatic extractions based on visual attributes. Our methodology is further enhanced through a composite degradation restoration loss, using extra degraded images as negative samples to fortify model constraints. Comparative results on synthetic and real-world datasets demonstrate OneRestore as a superior solution, significantly advancing the state-of-the-art in addressing complex, composite degradations.

In anomaly segmentation for complex driving scenes, state-of-the-art approaches utilize anomaly scoring functions to calculate anomaly scores. For these functions, accurately predicting the logits of inlier classes for each pixel is crucial for precisely inferring the anomaly score. However, in real-world driving scenarios, the diversity of scenes often results in distorted manifolds of pixel embeddings in the space. This effect is not conducive to directly using the pixel embeddings for the logit prediction during inference, a concern overlooked by existing methods. To address this problem, we propose a novel method called Random Walk on Pixel Manifolds (RWPM). RWPM utilizes random walks to reveal the intrinsic relationships among pixels to refine the pixel embeddings. The refined pixel embeddings alleviate the distortion of manifolds, improving the accuracy of anomaly scores. Our extensive experiments show that RWPM consistently improve the performance of the existing anomaly segmentation methods and achieve the best results. Code is available at: https://github.com/ZelongZeng/RWPM.

Deep learning approaches have provided state-of-the-art performance in many applications by relying on large and overparameterized neural networks. However, such networks have been shown to be very brittle and are difficult to deploy on resource-limited platforms. Model pruning, i.e., reducing the size of the network, is a widely adopted strategy that can lead to a more robust and compact model. Many heuristics exist for model pruning, but empirical studies show that some heuristics improve performance whereas others can make models more brittle or have other side effects. This work aims to shed light on how different pruning methods alter the network's internal feature representation and the corresponding impact on model performance. To facilitate a comprehensive comparison and characterization of the high-dimensional model feature space, we introduce a visual geometric analysis of feature representations. We decomposed and evaluated a set of critical geometric concepts from the common adopted classification loss, and used them to design a visualization system to compare and highlight the impact of pruning on model performance and feature representation. The proposed tool provides an environment for in-depth comparison of pruning methods and a comprehensive understanding of how model response to common data corruption. By leveraging the proposed visualization, machine learning researchers can reveal the similarities between pruning methods and redundant in robustness evaluation benchmarks, obtain geometric insights about the differences between pruned models that achieve superior robustness performance, and identify samples that are robust or fragile to model pruning and common data corruption to model pruning and data corruption but also obtain insights and explanations on how some pruned models achieve superior robustness performance.

We introduce behavioral fidelity -- a third evaluation dimension for synthetic tabular data that measures whether generated data preserves the temporal, sequential, and structural behavioral patterns that distinguish real-world entity activity. Existing frameworks evaluate statistical fidelity (marginal distributions and correlations) and downstream utility (classifier AUROC on synthetic-trained models), but neither tests for the behavioral signals that operational detection and analysis systems actually rely on. We formalize a taxonomy of four behavioral fraud patterns (P1-P4) covering inter-event timing, burst structure, multi-account graph motifs, and velocity-rule trigger rates; define a degradation ratio metric calibrated to a real-data noise floor (1.0 = matches real variability, k = k-times worse); and prove that row-independent generators -- the dominant paradigm -- are structurally incapable of reproducing P3 graph motifs (Proposition 1) and produce non-positive within-entity IET autocorrelation (Proposition 2), making the positive burst fingerprint of fraud sequences unachievable regardless of architecture or training data size. We benchmark CTGAN, TVAE, GaussianCopula, and TabularARGN on IEEE-CIS Fraud Detection and the Amazon Fraud Dataset. All four fail severely: on IEEE-CIS composite degradation ratios range from 24.4x (TVAE) to 39.0x (GaussianCopula); on Amazon FDB, row-independent generators score 81.6-99.7x, while TabularARGN achieves 17.2x. We document generator-specific failure modes and their resolutions. The P1-P4 framework extends to any domain with entity-level sequential tabular data, including healthcare and network security. We release our evaluation framework as open source.

We introduce HoloClean, a framework for holistic data repairing driven by probabilistic inference. HoloClean unifies existing qualitative data repairing approaches, which rely on integrity constraints or external data sources, with quantitative data repairing methods, which leverage statistical properties of the input data. Given an inconsistent dataset as input, HoloClean automatically generates a probabilistic program that performs data repairing. Inspired by recent theoretical advances in probabilistic inference, we introduce a series of optimizations which ensure that inference over HoloClean's probabilistic model scales to instances with millions of tuples. We show that HoloClean scales to instances with millions of tuples and find data repairs with an average precision of ~90% and an average recall of above ~76% across a diverse array of datasets exhibiting different types of errors. This yields an average F1 improvement of more than 2x against state-of-the-art methods.

The R-Learner is a powerful, theoretically-grounded framework for estimating heterogeneous treatment effects, prized for its robustness to nuisance model errors. However, its application to network data, where causal heterogeneity is often graph-dependent, presents a critical challenge to its core assumption of a well-specified final-stage model. In this paper, we conduct a large-scale empirical study to systematically dissect the R-Learner framework on graphs. We provide the first rigorous evidence that the primary driver of performance is the inductive bias of the final-stage CATE estimator, an effect that dominates the choice of nuisance models. Our central finding is the quantification of a catastrophic "representation bottleneck": we prove with overwhelming statistical significance (p < 0.001) that R-Learners with a graph-blind final stage fail completely (MSE > 4.0), even when paired with powerful GNN nuisance models. Conversely, our proposed end-to-end Graph R-Learner succeeds and significantly outperforms a strong, non-DML GNN T-Learner baseline. Furthermore, we identify and provide a mechanistic explanation for a subtle, topology-dependent "nuisance bottleneck," linking it to GNN over-squashing via a targeted "Hub-Periphery Trade-off" analysis. Our findings are validated across diverse synthetic and semi-synthetic benchmarks. We release our code as a reproducible benchmark to facilitate future research on this critical "final-stage bottleneck."

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, global utility, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present TabStruct, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.