Tolga Birdal

Simone Foti, Stefanos Zafeiriou, Tolga Birdal

Seams, distortions, wasted UV space, vertex-duplication, and varying resolution over the surface are the most prominent issues of the standard UV-based texturing of meshes. These issues are particularly acute when automatic UV-unwrapping techniques are used. For this reason, instead of generating textures in automatically generated UV-planes like most state-of-the-art methods, we propose to represent textures as coloured point-clouds whose colours are generated by a denoising diffusion probabilistic model constrained to operate on the surface of 3D objects. Our sampling and resolution agnostic generative model heavily relies on heat diffusion over the surface of the meshes for spatial communication between points. To enable processing of arbitrarily sampled point-cloud textures and ensure long-distance texture consistency we introduce a fast re-sampling of the mesh spectral properties used during the heat diffusion and introduce a novel heat-diffusion-based self-attention mechanism. Our code and pre-trained models are available at github.com/simofoti/UV3-TeD.

Mathilde Papillon, Mustafa Hajij, Helen Jenne et al.

This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competition asked participants to provide open-source implementations of topological neural networks from the literature by contributing to the python packages TopoNetX (data processing) and TopoModelX (deep learning). The challenge attracted twenty-eight qualifying submissions in its two-month duration. This paper describes the design of the challenge and summarizes its main findings.

Nathan Mankovich, Tolga Birdal

This paper presents a new, provably-convergent algorithm for computing the flag-mean and flag-median of a set of points on a flag manifold under the chordal metric. The flag manifold is a mathematical space consisting of flags, which are sequences of nested subspaces of a vector space that increase in dimension. The flag manifold is a superset of a wide range of known matrix spaces, including Stiefel and Grassmanians, making it a general object that is useful in a wide variety computer vision problems. To tackle the challenge of computing first order flag statistics, we first transform the problem into one that involves auxiliary variables constrained to the Stiefel manifold. The Stiefel manifold is a space of orthogonal frames, and leveraging the numerical stability and efficiency of Stiefel-manifold optimization enables us to compute the flag-mean effectively. Through a series of experiments, we show the competence of our method in Grassmann and rotation averaging, as well as principal component analysis. We release our source code under https://github.com/nmank/FlagAveraging.

Lucas Prieto, Edward Stevinson, Melih Barsbey et al.

A central idea in mechanistic interpretability is that neural networks represent more features than they have dimensions, arranging them in superposition to form an over-complete basis. This framing has been influential, motivating dictionary learning approaches such as sparse autoencoders. However, superposition has mostly been studied in idealized settings where features are sparse and uncorrelated. In these settings, superposition is typically understood as introducing interference that must be minimized geometrically and filtered out by non-linearities such as ReLUs, yielding local structures like regular polytopes. We show that this account is incomplete for realistic data by introducing Bag-of-Words Superposition (BOWS), a controlled setting to encode binary bag-of-words representations of internet text in superposition. Using BOWS, we find that when features are correlated, interference can be constructive rather than just noise to be filtered out. This is achieved by arranging features according to their co-activation patterns, making interference between active features constructive, while still using ReLUs to avoid false positives. We show that this kind of arrangement is more prevalent in models trained with weight decay and naturally gives rise to semantic clusters and cyclical structures which have been observed in real language models yet were not explained by the standard picture of superposition. Code for this paper can be found at https://github.com/LucasPrietoAl/correlations-feature-geometry.

Gabriel Nobis, Maximilian Springenberg, Marco Aversa et al.

We introduce the first continuous-time score-based generative model that leverages fractional diffusion processes for its underlying dynamics. Although diffusion models have excelled at capturing data distributions, they still suffer from various limitations such as slow convergence, mode-collapse on imbalanced data, and lack of diversity. These issues are partially linked to the use of light-tailed Brownian motion (BM) with independent increments. In this paper, we replace BM with an approximation of its non-Markovian counterpart, fractional Brownian motion (fBM), characterized by correlated increments and Hurst index $H \in (0,1)$, where $H=0.5$ recovers the classical BM. To ensure tractable inference and learning, we employ a recently popularized Markov approximation of fBM (MA-fBM) and derive its reverse-time model, resulting in generative fractional diffusion models (GFDM). We characterize the forward dynamics using a continuous reparameterization trick and propose augmented score matching to efficiently learn the score function, which is partly known in closed form, at minimal added cost. The ability to drive our diffusion model via MA-fBM offers flexibility and control. $H \leq 0.5$ enters the regime of rough paths whereas $H>0.5$ regularizes diffusion paths and invokes long-term memory. The Markov approximation allows added control by varying the number of Markov processes linearly combined to approximate fBM. Our evaluations on real image datasets demonstrate that GFDM achieves greater pixel-wise diversity and enhanced image quality, as indicated by a lower FID, offering a promising alternative to traditional diffusion models

Jan-Nico Zaech, Martin Danelljan, Tolga Birdal et al.

Adiabatic quantum computing (AQC) is a promising approach for discrete and often NP-hard optimization problems. Current AQCs allow to implement problems of research interest, which has sparked the development of quantum representations for many computer vision tasks. Despite requiring multiple measurements from the noisy AQC, current approaches only utilize the best measurement, discarding information contained in the remaining ones. In this work, we explore the potential of using this information for probabilistic balanced k-means clustering. Instead of discarding non-optimal solutions, we propose to use them to compute calibrated posterior probabilities with little additional compute cost. This allows us to identify ambiguous solutions and data points, which we demonstrate on a D-Wave AQC on synthetic tasks and real visual data.

Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou et al.

Topological deep learning is a rapidly growing field that pertains to the development of deep learning models for data supported on topological domains such as simplicial complexes, cell complexes, and hypergraphs, which generalize many domains encountered in scientific computations. In this paper, we present a unifying deep learning framework built upon a richer data structure that includes widely adopted topological domains. Specifically, we first introduce combinatorial complexes, a novel type of topological domain. Combinatorial complexes can be seen as generalizations of graphs that maintain certain desirable properties. Similar to hypergraphs, combinatorial complexes impose no constraints on the set of relations. In addition, combinatorial complexes permit the construction of hierarchical higher-order relations, analogous to those found in simplicial and cell complexes. Thus, combinatorial complexes generalize and combine useful traits of both hypergraphs and cell complexes, which have emerged as two promising abstractions that facilitate the generalization of graph neural networks to topological spaces. Second, building upon combinatorial complexes and their rich combinatorial and algebraic structure, we develop a general class of message-passing combinatorial complex neural networks (CCNNs), focusing primarily on attention-based CCNNs. We characterize permutation and orientation equivariances of CCNNs, and discuss pooling and unpooling operations within CCNNs in detail. Third, we evaluate the performance of CCNNs on tasks related to mesh shape analysis and graph learning. Our experiments demonstrate that CCNNs have competitive performance as compared to state-of-the-art deep learning models specifically tailored to the same tasks. Our findings demonstrate the advantages of incorporating higher-order relations into deep learning models in different applications.

Yang Zheng, Tolga Birdal, Fei Xia et al.

We propose a novel method to reliably estimate the pose of a camera given a sequence of images acquired in extreme environments such as deep seas or extraterrestrial terrains. Data acquired under these challenging conditions are corrupted by textureless surfaces, image degradation, and presence of repetitive and highly ambiguous structures. When naively deployed, the state-of-the-art methods can fail in those scenarios as confirmed by our empirical analysis. In this paper, we attempt to make camera relocalization work in these extreme situations. To this end, we propose: (i) a hierarchical localization system, where we leverage temporal information and (ii) a novel environment-aware image enhancement method to boost the robustness and accuracy. Our extensive experimental results demonstrate superior performance in favor of our method under two extreme settings: localizing an autonomous underwater vehicle and localizing a planetary rover in a Mars-like desert. In addition, our method achieves comparable performance with state-of-the-art methods on the indoor benchmark (7-Scenes dataset) using only 20% training data.

Hippolyte Verninas, Caner Korkmaz, Stefanos Zafeiriou et al.

Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the non-differentiability of their discrete counterparts, and poor parallelisation capabilities have been the main obstacles to the development of the field on meshes. A principled framework to compute the exponential map on Riemannian surfaces discretised as meshes is straightest geodesics, which also allows to trace geodesics and parallel-transport vectors as a by-product. We provide a parallel GPU implementation and derive two different methods for differentiating through the straightest geodesics, one leveraging an extrinsic proxy function and one based upon a geodesic finite differences scheme. After proving our parallelisation performance and accuracy, we demonstrate how our differentiable exponential map can improve learning and optimisation pipelines on general geometries. In particular, to showcase the versatility of our method, we propose a new geodesic convolutional layer, a new flow matching method for learning on meshes, and a second-order optimiser that we apply to centroidal Voronoi tessellation. Our code, models, and pip-installable library (digeo) are available at: circle-group.github.io/research/DSG.

Alp Yurtsever, Tolga Birdal, Vladislav Golyanik

We present a hybrid classical-quantum framework based on the Frank-Wolfe algorithm, Q-FW, for solving quadratic, linearly-constrained, binary optimization problems on quantum annealers (QA). The computational premise of quantum computers has cultivated the re-design of various existing vision problems into quantum-friendly forms. Experimental QA realizations can solve a particular non-convex problem known as the quadratic unconstrained binary optimization (QUBO). Yet a naive-QUBO cannot take into account the restrictions on the parameters. To introduce additional structure in the parameter space, researchers have crafted ad-hoc solutions incorporating (linear) constraints in the form of regularizers. However, this comes at the expense of a hyper-parameter, balancing the impact of regularization. To date, a true constrained solver of quadratic binary optimization (QBO) problems has lacked. Q-FW first reformulates constrained-QBO as a copositive program (CP), then employs Frank-Wolfe iterations to solve CP while satisfying linear (in)equality constraints. This procedure unrolls the original constrained-QBO into a set of unconstrained QUBOs all of which are solved, in a sequel, on a QA. We use D-Wave Advantage QA to conduct synthetic and real experiments on two important computer vision problems, graph matching and permutation synchronization, which demonstrate that our approach is effective in alleviating the need for an explicit regularization coefficient.

Maximilian Krahn, Michele Sasdelli, Fengyi Yang et al.

We present, QP-SBGD, a novel layer-wise stochastic optimiser tailored towards training neural networks with binary weights, known as binary neural networks (BNNs), on quantum hardware. BNNs reduce the computational requirements and energy consumption of deep learning models with minimal loss in accuracy. However, training them in practice remains to be an open challenge. Most known BNN-optimisers either rely on projected updates or binarise weights post-training. Instead, QP-SBGD approximately maps the gradient onto binary variables, by solving a quadratic constrained binary optimisation. Under practically reasonable assumptions, we show that this update rule converges with a rate of $\mathcal{O}(1 / \sqrt{T})$. Moreover, we show how the $\mathcal{NP}$-hard projection can be effectively executed on an adiabatic quantum annealer, harnessing recent advancements in quantum computation. We also introduce a projected version of this update rule and prove that if a fixed point exists in the binary variable space, the modified updates will converge to it. Last but not least, our algorithm is implemented layer-wise, making it suitable to train larger networks on resource-limited quantum hardware. Through extensive evaluations, we show that QP-SBGD outperforms or is on par with competitive and well-established baselines such as BinaryConnect, signSGD and ProxQuant when optimising the Rosenbrock function, training BNNs as well as binary graph neural networks.

Moayed Haji Ali, Andrew Bond, Tolga Birdal et al.

We propose $\textbf{VidStyleODE}$, a spatiotemporally continuous disentangled $\textbf{Vid}$eo representation based upon $\textbf{Style}$GAN and Neural-$\textbf{ODE}$s. Effective traversal of the latent space learned by Generative Adversarial Networks (GANs) has been the basis for recent breakthroughs in image editing. However, the applicability of such advancements to the video domain has been hindered by the difficulty of representing and controlling videos in the latent space of GANs. In particular, videos are composed of content (i.e., appearance) and complex motion components that require a special mechanism to disentangle and control. To achieve this, VidStyleODE encodes the video content in a pre-trained StyleGAN $\mathcal{W}_+$ space and benefits from a latent ODE component to summarize the spatiotemporal dynamics of the input video. Our novel continuous video generation process then combines the two to generate high-quality and temporally consistent videos with varying frame rates. We show that our proposed method enables a variety of applications on real videos: text-guided appearance manipulation, motion manipulation, image animation, and video interpolation and extrapolation. Project website: https://cyberiada.github.io/VidStyleODE

Shishir Reddy Vutukur, Rasmus Laurvig Haugaard, Junwen Huang et al.

Object pose distribution estimation is crucial in robotics for better path planning and handling of symmetric objects. Recent distribution estimation approaches employ contrastive learning-based approaches by maximizing the likelihood of a single pose estimate in the absence of a CAD model. We propose a pose distribution estimation method leveraging symmetry respecting correspondence distributions and shape information obtained using a CAD model. Contrastive learning-based approaches require an exhaustive amount of training images from different viewpoints to learn the distribution properly, which is not possible in realistic scenarios. Instead, we propose a pipeline that can leverage correspondence distributions and shape information from the CAD model, which are later used to learn pose distributions. Besides, having access to pose distribution based on correspondences before learning pose distributions conditioned on images, can help formulate the loss between distributions. The prior knowledge of distribution also helps the network to focus on getting sharper modes instead. With the CAD prior, our approach converges much faster and learns distribution better by focusing on learning sharper distribution near all the valid modes, unlike contrastive approaches, which focus on a single mode at a time. We achieve benchmark results on SYMSOL-I and T-Less datasets.

Levent Karacan, Tolga Kerimoğlu, İsmail İnan et al.

Giving machines the ability to imagine possible new objects or scenes from linguistic descriptions and produce their realistic renderings is arguably one of the most challenging problems in computer vision. Recent advances in deep generative models have led to new approaches that give promising results towards this goal. In this paper, we introduce a new method called DiCoMoGAN for manipulating videos with natural language, aiming to perform local and semantic edits on a video clip to alter the appearances of an object of interest. Our GAN architecture allows for better utilization of multiple observations by disentangling content and motion to enable controllable semantic edits. To this end, we introduce two tightly coupled networks: (i) a representation network for constructing a concise understanding of motion dynamics and temporally invariant content, and (ii) a translation network that exploits the extracted latent content representation to actuate the manipulation according to the target description. Our qualitative and quantitative evaluations demonstrate that DiCoMoGAN significantly outperforms existing frame-based methods, producing temporally coherent and semantically more meaningful results.

Yannan He, Garvita Tiwari, Xiaohan Zhang et al.

We introduce MoLingo, a text-to-motion (T2M) model that generates realistic, lifelike human motion by denoising in a continuous latent space. Recent works perform latent space diffusion, either on the whole latent at once or auto-regressively over multiple latents. In this paper, we study how to make diffusion on continuous motion latents work best. We focus on two questions: (1) how to build a semantically aligned latent space so diffusion becomes more effective, and (2) how to best inject text conditioning so the motion follows the description closely. We propose a semantic-aligned motion encoder trained with frame-level text labels so that latents with similar text meaning stay close, which makes the latent space more diffusion-friendly. We also compare single-token conditioning with a multi-token cross-attention scheme and find that cross-attention gives better motion realism and text-motion alignment. With semantically aligned latents, auto-regressive generation, and cross-attention text conditioning, our model sets a new state of the art in human motion generation on standard metrics and in a user study. We will release our code and models for further research and downstream usage.

Tony Danjun Wang, Ka Young Kim, Tolga Birdal et al.

Surgical Scene Graphs abstract the complexity of surgical operating rooms (OR) into a structure of entities and their relations, but existing paradigms suffer from strictly dyadic structural limitations. Frameworks that predominantly rely on pairwise message passing or tokenized sequences flatten the manifold geometry inherent to relational structures and lose structure in the process. We introduce TopoOR, a new paradigm that models multimodal operating rooms as a higher-order structure, innately preserving pairwise and group relationships. By lifting interactions between entities into higher-order topological cells, TopoOR natively models complex dynamics and multimodality present in the OR. This topological representation subsumes traditional scene graphs, thereby offering strictly greater expressivity. We also propose a higher-order attention mechanism that explicitly preserves manifold structure and modality-specific features throughout hierarchical relational attention. In this way, we circumvent combining 3D geometry, audio, and robot kinematics into a single joint latent representation, preserving the precise multimodal structure required for safety-critical reasoning, unlike existing methods. Extensive experiments demonstrate that our approach outperforms traditional graph and LLM-based baselines across sterility breach detection, robot phase prediction, and next-action anticipation

Zhengdi Yu, Shaoli Huang, Yongkang Cheng et al.

We present SignAvatars, the first large-scale, multi-prompt 3D sign language (SL) motion dataset designed to bridge the communication gap for Deaf and hard-of-hearing individuals. While there has been an exponentially growing number of research regarding digital communication, the majority of existing communication technologies primarily cater to spoken or written languages, instead of SL, the essential communication method for Deaf and hard-of-hearing communities. Existing SL datasets, dictionaries, and sign language production (SLP) methods are typically limited to 2D as annotating 3D models and avatars for SL is usually an entirely manual and labor-intensive process conducted by SL experts, often resulting in unnatural avatars. In response to these challenges, we compile and curate the SignAvatars dataset, which comprises 70,000 videos from 153 signers, totaling 8.34 million frames, covering both isolated signs and continuous, co-articulated signs, with multiple prompts including HamNoSys, spoken language, and words. To yield 3D holistic annotations, including meshes and biomechanically-valid poses of body, hands, and face, as well as 2D and 3D keypoints, we introduce an automated annotation pipeline operating on our large corpus of SL videos. SignAvatars facilitates various tasks such as 3D sign language recognition (SLR) and the novel 3D SL production (SLP) from diverse inputs like text scripts, individual words, and HamNoSys notation. Hence, to evaluate the potential of SignAvatars, we further propose a unified benchmark of 3D SL holistic motion production. We believe that this work is a significant step forward towards bringing the digital world to the Deaf and hard-of-hearing communities as well as people interacting with them.

Rayna Andreeva, Benjamin Dupuis, Rik Sarkar et al.

We present a novel set of rigorous and computationally efficient topology-based complexity notions that exhibit a strong correlation with the generalization gap in modern deep neural networks (DNNs). DNNs show remarkable generalization properties, yet the source of these capabilities remains elusive, defying the established statistical learning theory. Recent studies have revealed that properties of training trajectories can be indicative of generalization. Building on this insight, state-of-the-art methods have leveraged the topology of these trajectories, particularly their fractal dimension, to quantify generalization. Most existing works compute this quantity by assuming continuous- or infinite-time training dynamics, complicating the development of practical estimators capable of accurately predicting generalization without access to test data. In this paper, we respect the discrete-time nature of training trajectories and investigate the underlying topological quantities that can be amenable to topological data analysis tools. This leads to a new family of reliable topological complexity measures that provably bound the generalization error, eliminating the need for restrictive geometric assumptions. These measures are computationally friendly, enabling us to propose simple yet effective algorithms for computing generalization indices. Moreover, our flexible framework can be extended to different domains, tasks, and architectures. Our experimental results demonstrate that our new complexity measures correlate highly with generalization error in industry-standards architectures such as transformers and deep graph networks. Our approach consistently outperforms existing topological bounds across a wide range of datasets, models, and optimizers, highlighting the practical relevance and effectiveness of our complexity measures.

Lucas Prieto, Melih Barsbey, Pedro A. M. Mediano et al.

Grokking, the sudden generalization that occurs after prolonged overfitting, is a surprising phenomenon challenging our understanding of deep learning. Although significant progress has been made in understanding grokking, the reasons behind the delayed generalization and its dependence on regularization remain unclear. In this work, we argue that without regularization, grokking tasks push models to the edge of numerical stability, introducing floating point errors in the Softmax function, which we refer to as Softmax Collapse (SC). We demonstrate that SC prevents grokking and that mitigating SC enables grokking without regularization. Investigating the root cause of SC, we find that beyond the point of overfitting, the gradients strongly align with what we call the naïve loss minimization (NLM) direction. This component of the gradient does not alter the model's predictions but decreases the loss by scaling the logits, typically by scaling the weights along their current direction. We show that this scaling of the logits explains the delay in generalization characteristic of grokking and eventually leads to SC, halting further learning. To validate our hypotheses, we introduce two key contributions that address the challenges in grokking tasks: StableMax, a new activation function that prevents SC and enables grokking without regularization, and $\perp$Grad, a training algorithm that promotes quick generalization in grokking tasks by preventing NLM altogether. These contributions provide new insights into grokking, elucidating its delayed generalization, reliance on regularization, and the effectiveness of existing grokking-inducing methods. Code for this paper is available at https://github.com/LucasPrietoAl/grokking-at-the-edge-of-numerical-stability.

Rembert Daems, Manfred Opper, Guillaume Crevecoeur et al.

We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world continuous-time dynamic systems with inherent noise and randomness. Combining SDEs with the powerful inference capabilities of variational methods, enables the learning of representative function distributions through stochastic gradient descent. However, conventional SDEs typically assume the underlying noise to follow a Brownian motion (BM), which hinders their ability to capture long-term dependencies. In contrast, fractional Brownian motion (fBM) extends BM to encompass non-Markovian dynamics, but existing methods for inferring fBM parameters are either computationally demanding or statistically inefficient. In this paper, building upon the Markov approximation of fBM, we derive the evidence lower bound essential for efficient variational inference of posterior path measures, drawing from the well-established field of stochastic analysis. Additionally, we provide a closed-form expression to determine optimal approximation coefficients. Furthermore, we propose the use of neural networks to learn the drift, diffusion and control terms within our variational posterior, leading to the variational training of neural-SDEs. In this framework, we also optimize the Hurst index, governing the nature of our fractional noise. Beyond validation on synthetic data, we contribute a novel architecture for variational latent video prediction,-an approach that, to the best of our knowledge, enables the first variational neural-SDE application to video perception.

Yiming Huang, Tolga Birdal

Graph generation is a critical yet challenging task as empirical analyses require a deep understanding of complex, non-Euclidean structures. Diffusion models have recently made significant achievements in graph generation, but these models are typically adapted from image generation frameworks and overlook inherent higher-order topology, leaving them ill-suited for capturing the topological properties of graphs. In this work, we propose Higher-order Guided Diffusion (HOG-Diff), a principled framework that progressively generates plausible graphs with inherent topological structures. HOG-Diff follows a coarse-to-fine generation curriculum guided by higher-order topology and implemented via diffusion bridges. We further prove that our model exhibits a stronger theoretical guarantee than classical diffusion frameworks. Extensive experiments on both molecular and generic graph generation tasks demonstrate that our method consistently outperforms or remains competitive with state-of-the-art baselines. Our code is available at https://github.com/Yiminghh/HOG-Diff.

Lennart Bastian, Mohammad Rashed, Nassir Navab et al.

Modeling the rotation of moving objects is a fundamental task in computer vision, yet $SO(3)$ extrapolation still presents numerous challenges: (1) unknown quantities such as the moment of inertia complicate dynamics, (2) the presence of external forces and torques can lead to non-conservative kinematics, and (3) estimating evolving state trajectories under sparse, noisy observations requires robustness. We propose modeling trajectories of noisy pose estimates on the manifold of 3D rotations in a physically and geometrically meaningful way by leveraging Neural Controlled Differential Equations guided with $SO(3)$ Savitzky-Golay paths. Existing extrapolation methods often rely on energy conservation or constant velocity assumptions, limiting their applicability in real-world scenarios involving non-conservative forces. In contrast, our approach is agnostic to energy and momentum conservation while being robust to input noise, making it applicable to complex, non-inertial systems. Our approach is easily integrated as a module in existing pipelines and generalizes well to trajectories with unknown physical parameters. By learning to approximate object dynamics from noisy states during training, our model attains robust extrapolation capabilities in simulation and various real-world settings. Code is available at https://github.com/bastianlb/forecasting-rotational-dynamics

Tony Danjun Wang, Tolga Birdal, Nassir Navab et al.

3D pose estimation from sparse multi-views is a critical task for numerous applications, including action recognition, sports analysis, and human-robot interaction. Optimization-based methods typically follow a two-stage pipeline, first detecting 2D keypoints in each view and then associating these detections across views to triangulate the 3D pose. Existing methods rely on mere pairwise associations to model this correspondence problem, treating global consistency between views (i.e., cycle consistency) as a soft constraint. Yet, reconciling these constraints for multiple views becomes brittle when spurious associations propagate errors. We thus propose COMPOSE, a novel framework that formulates multi-view pose correspondence matching as a hypergraph partitioning problem rather than through pairwise association. While the complexity of the resulting integer linear program grows exponentially in theory, we introduce an efficient geometric pruning strategy to substantially reduce the search space. COMPOSE achieves improvements of up to 23% in average precision over previous optimization-based methods and up to 11% over self-supervised end-to-end learned methods, offering a promising solution to a widely studied problem.

Gabriel Nobis, Maximilian Springenberg, Arina Belova et al.

We present Fractional Diffusion Bridge Models (FDBM), a novel generative diffusion bridge framework driven by an approximation of the rich and non-Markovian fractional Brownian motion (fBM). Real stochastic processes exhibit a degree of memory effects (correlations in time), long-range dependencies, roughness and anomalous diffusion phenomena that are not captured in standard diffusion or bridge modeling due to the use of Brownian motion (BM). As a remedy, leveraging a recent Markovian approximation of fBM (MA-fBM), we construct FDBM that enable tractable inference while preserving the non-Markovian nature of fBM. We prove the existence of a coupling-preserving generative diffusion bridge and leverage it for future state prediction from paired training data. We then extend our formulation to the Schrödinger bridge problem and derive a principled loss function to learn the unpaired data translation. We evaluate FDBM on both tasks: predicting future protein conformations from aligned data, and unpaired image translation. In both settings, FDBM achieves superior performance compared to the Brownian baselines, yielding lower root mean squared deviation (RMSD) of C$_α$ atomic positions in protein structure prediction and lower Fréchet Inception Distance (FID) in unpaired image translation.

Yaman Kindap, Manfred Opper, Benjamin Dupuis et al.

Modelling extreme events and heavy-tailed phenomena is central to building reliable predictive systems in domains such as finance, climate science, and safety-critical AI. While Lévy processes provide a natural mathematical framework for capturing jumps and heavy tails, Bayesian inference for Lévy-driven stochastic differential equations (SDEs) remains intractable with existing methods: Monte Carlo approaches are rigorous but lack scalability, whereas neural variational inference methods are efficient but rely on Gaussian assumptions that fail to capture discontinuities. We address this tension by introducing a neural exponential tilting framework for variational inference in Lévy-driven SDEs. Our approach constructs a flexible variational family by exponentially reweighting the Lévy measure using neural networks. This parametrization preserves the jump structure of the underlying process while remaining computationally tractable. To enable efficient inference, we develop a quadratic neural parametrization that yields closed-form normalization of the tilted measure, a conditional Gaussian representation for stable processes that facilitates simulation, and symmetry-aware Monte Carlo estimators for scalable optimization. Empirically, we demonstrate that the method accurately captures jump dynamics and yields reliable posterior inference in regimes where Gaussian-based variational approaches fail, on both synthetic and real-world datasets.

Zan Gojcic, Or Litany, Andreas Wieser et al.

We propose a data-driven scene flow estimation algorithm exploiting the observation that many 3D scenes can be explained by a collection of agents moving as rigid bodies. At the core of our method lies a deep architecture able to reason at the \textbf{object-level} by considering 3D scene flow in conjunction with other 3D tasks. This object level abstraction, enables us to relax the requirement for dense scene flow supervision with simpler binary background segmentation mask and ego-motion annotations. Our mild supervision requirements make our method well suited for recently released massive data collections for autonomous driving, which do not contain dense scene flow annotations. As output, our model provides low-level cues like pointwise flow and higher-level cues such as holistic scene understanding at the level of rigid objects. We further propose a test-time optimization refining the predicted rigid scene flow. We showcase the effectiveness and generalization capacity of our method on four different autonomous driving datasets. We release our source code and pre-trained models under \url{github.com/zgojcic/Rigid3DSceneFlow}.

Zan Gojcic, Caifa Zhou, Jan D. Wegner et al.

We present a novel, end-to-end learnable, multiview 3D point cloud registration algorithm. Registration of multiple scans typically follows a two-stage pipeline: the initial pairwise alignment and the globally consistent refinement. The former is often ambiguous due to the low overlap of neighboring point clouds, symmetries and repetitive scene parts. Therefore, the latter global refinement aims at establishing the cyclic consistency across multiple scans and helps in resolving the ambiguous cases. In this paper we propose, to the best of our knowledge, the first end-to-end algorithm for joint learning of both parts of this two-stage problem. Experimental evaluation on well accepted benchmark datasets shows that our approach outperforms the state-of-the-art by a significant margin, while being end-to-end trainable and computationally less costly. Moreover, we present detailed analysis and an ablation study that validate the novel components of our approach. The source code and pretrained models are publicly available under https://github.com/zgojcic/3D_multiview_reg.

Theodore Papamarkou, Tolga Birdal, Michael Bronstein et al.

Topological deep learning (TDL) is a rapidly evolving field that uses topological features to understand and design deep learning models. This paper posits that TDL is the new frontier for relational learning. TDL may complement graph representation learning and geometric deep learning by incorporating topological concepts, and can thus provide a natural choice for various machine learning settings. To this end, this paper discusses open problems in TDL, ranging from practical benefits to theoretical foundations. For each problem, it outlines potential solutions and future research opportunities. At the same time, this paper serves as an invitation to the scientific community to actively participate in TDL research to unlock the potential of this emerging field.

Mustafa Hajij, Mathilde Papillon, Florian Frantzen et al.

We introduce TopoX, a Python software suite that provides reliable and user-friendly building blocks for computing and machine learning on topological domains that extend graphs: hypergraphs, simplicial, cellular, path and combinatorial complexes. TopoX consists of three packages: TopoNetX facilitates constructing and computing on these domains, including working with nodes, edges and higher-order cells; TopoEmbedX provides methods to embed topological domains into vector spaces, akin to popular graph-based embedding algorithms such as node2vec; TopoModelX is built on top of PyTorch and offers a comprehensive toolbox of higher-order message passing functions for neural networks on topological domains. The extensively documented and unit-tested source code of TopoX is available under MIT license at https://pyt-team.github.io/}{https://pyt-team.github.io/.

Yannan He, Garvita Tiwari, Tolga Birdal et al.

Faithfully modeling the space of articulations is a crucial task that allows recovery and generation of realistic poses, and remains a notorious challenge. To this end, we introduce Neural Riemannian Distance Fields (NRDFs), data-driven priors modeling the space of plausible articulations, represented as the zero-level-set of a neural field in a high-dimensional product-quaternion space. To train NRDFs only on positive examples, we introduce a new sampling algorithm, ensuring that the geodesic distances follow a desired distribution, yielding a principled distance field learning paradigm. We then devise a projection algorithm to map any random pose onto the level-set by an adaptive-step Riemannian optimizer, adhering to the product manifold of joint rotations at all times. NRDFs can compute the Riemannian gradient via backpropagation and by mathematical analogy, are related to Riemannian flow matching, a recent generative model. We conduct a comprehensive evaluation of NRDF against other pose priors in various downstream tasks, i.e., pose generation, image-based pose estimation, and solving inverse kinematics, highlighting NRDF's superior performance. Besides humans, NRDF's versatility extends to hand and animal poses, as it can effectively represent any articulation.

Mustafa Hajij, Ghada Zamzmi, Theodore Papamarkou et al.

Graph-based signal processing techniques have become essential for handling data in non-Euclidean spaces. However, there is a growing awareness that these graph models might need to be expanded into `higher-order' domains to effectively represent the complex relations found in high-dimensional data. Such higher-order domains are typically modeled either as hypergraphs, or as simplicial, cubical or other cell complexes. In this context, cell complexes are often seen as a subclass of hypergraphs with additional algebraic structure that can be exploited, e.g., to develop a spectral theory. In this article, we promote an alternative perspective. We argue that hypergraphs and cell complexes emphasize \emph{different} types of relations, which may have different utility depending on the application context. Whereas hypergraphs are effective in modeling set-type, multi-body relations between entities, cell complexes provide an effective means to model hierarchical, interior-to-boundary type relations. We discuss the relative advantages of these two choices and elaborate on the previously introduced concept of a combinatorial complex that enables co-existing set-type and hierarchical relations. Finally, we provide a brief numerical experiment to demonstrate that this modelling flexibility can be advantageous in learning tasks.

Zhengdi Yu, Stefanos Zafeiriou, Tolga Birdal

We propose Dyn-HaMR, to the best of our knowledge, the first approach to reconstruct 4D global hand motion from monocular videos recorded by dynamic cameras in the wild. Reconstructing accurate 3D hand meshes from monocular videos is a crucial task for understanding human behaviour, with significant applications in augmented and virtual reality (AR/VR). However, existing methods for monocular hand reconstruction typically rely on a weak perspective camera model, which simulates hand motion within a limited camera frustum. As a result, these approaches struggle to recover the full 3D global trajectory and often produce noisy or incorrect depth estimations, particularly when the video is captured by dynamic or moving cameras, which is common in egocentric scenarios. Our Dyn-HaMR consists of a multi-stage, multi-objective optimization pipeline, that factors in (i) simultaneous localization and mapping (SLAM) to robustly estimate relative camera motion, (ii) an interacting-hand prior for generative infilling and to refine the interaction dynamics, ensuring plausible recovery under (self-)occlusions, and (iii) hierarchical initialization through a combination of state-of-the-art hand tracking methods. Through extensive evaluations on both in-the-wild and indoor datasets, we show that our approach significantly outperforms state-of-the-art methods in terms of 4D global mesh recovery. This establishes a new benchmark for hand motion reconstruction from monocular video with moving cameras. Our project page is at https://dyn-hamr.github.io/.

Nathan Mankovich, Gustau Camps-Valls, Tolga Birdal

Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its variants, and introduce a framework based on the flags of linear subspaces, ie a hierarchy of nested linear subspaces of increasing dimension, which not only allows for a common implementation but also yields novel variants, not explored previously. We begin by generalizing traditional PCA methods that either maximize variance or minimize reconstruction error. We expand these interpretations to develop a wide array of new dimensionality reduction algorithms by accounting for outliers and the data manifold. To devise a common computational approach, we recast robust and dual forms of PCA as optimization problems on flag manifolds. We then integrate tangent space approximations of principal geodesic analysis (tangent-PCA) into this flag-based framework, creating novel robust and dual geodesic PCA variations. The remarkable flexibility offered by the 'flagification' introduced here enables even more algorithmic variants identified by specific flag types. Last but not least, we propose an effective convergent solver for these flag-formulations employing the Stiefel manifold. Our empirical results on both real-world and synthetic scenarios, demonstrate the superiority of our novel algorithms, especially in terms of robustness to outliers on manifolds.

Mario Tuci, Caner Korkmaz, Umut Şimşekli et al.

Training modern neural networks often relies on large learning rates, operating at the edge of stability, where the optimization dynamics exhibit oscillatory and chaotic behavior. Empirically, this regime often yields improved generalization performance, yet the underlying mechanism remains poorly understood. In this work, we represent stochastic optimizers as random dynamical systems, which often converge to a fractal attractor set (rather than a point) with a smaller intrinsic dimension. Building on this connection and inspired by Lyapunov dimension theory, we introduce a novel notion of dimension, coined the `sharpness dimension', and prove a generalization bound based on this dimension. Our results show that generalization in the chaotic regime depends on the complete Hessian spectrum and the structure of its partial determinants, highlighting a complexity that cannot be captured by the trace or spectral norm considered in prior work. Experiments across various MLPs and transformers validate our theory while also providing new insights into the recently observed phenomenon of grokking.

Zhiying Leng, Tolga Birdal, Xiaohui Liang et al.

3D shape generation from text is a fundamental task in 3D representation learning. The text-shape pairs exhibit a hierarchical structure, where a general text like ``chair" covers all 3D shapes of the chair, while more detailed prompts refer to more specific shapes. Furthermore, both text and 3D shapes are inherently hierarchical structures. However, existing Text2Shape methods, such as SDFusion, do not exploit that. In this work, we propose HyperSDFusion, a dual-branch diffusion model that generates 3D shapes from a given text. Since hyperbolic space is suitable for handling hierarchical data, we propose to learn the hierarchical representations of text and 3D shapes in hyperbolic space. First, we introduce a hyperbolic text-image encoder to learn the sequential and multi-modal hierarchical features of text in hyperbolic space. In addition, we design a hyperbolic text-graph convolution module to learn the hierarchical features of text in hyperbolic space. In order to fully utilize these text features, we introduce a dual-branch structure to embed text features in 3D feature space. At last, to endow the generated 3D shapes with a hierarchical structure, we devise a hyperbolic hierarchical loss. Our method is the first to explore the hyperbolic hierarchical representation for text-to-shape generation. Experimental results on the existing text-to-shape paired dataset, Text2Shape, achieved state-of-the-art results. We release our implementation under HyperSDFusion.github.io.

Rubén Ballester, Pablo Hernández-García, Mathilde Papillon et al.

Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that can be seen as generalizations of graphs. In this work, we introduce the Cellular Transformer (CT), a novel architecture that generalizes graph-based transformers to cell complexes. First, we propose a new formulation of the usual self- and cross-attention mechanisms, tailored to leverage incidence relations in cell complexes, e.g., edge-face and node-edge relations. Additionally, we propose a set of topological positional encodings specifically designed for cell complexes. By transforming three graph datasets into cell complex datasets, our experiments reveal that CT not only achieves state-of-the-art performance, but it does so without the need for more complex enhancements such as virtual nodes, in-domain structural encodings, or graph rewiring.

Melih Barsbey, Antônio H. Ribeiro, Umut Şimşekli et al.

Modern neural networks are expected to simultaneously satisfy a host of desirable properties: accurate fitting to training data, generalization to unseen inputs, parameter and computational efficiency, and robustness to adversarial perturbations. While compressibility and robustness have each been studied extensively, a unified understanding of their interaction still remains elusive. In this work, we develop a principled framework to analyze how different forms of compressibility - such as neuron-level sparsity and spectral compressibility - affect adversarial robustness. We show that these forms of compression can induce a small number of highly sensitive directions in the representation space, which adversaries can exploit to construct effective perturbations. Our analysis yields a simple yet instructive robustness bound, revealing how neuron and spectral compressibility impact $L_\infty$ and $L_2$ robustness via their effects on the learned representations. Crucially, the vulnerabilities we identify arise irrespective of how compression is achieved - whether via regularization, architectural bias, or implicit learning dynamics. Through empirical evaluations across synthetic and realistic tasks, we confirm our theoretical predictions, and further demonstrate that these vulnerabilities persist under adversarial training and transfer learning, and contribute to the emergence of universal adversarial perturbations. Our findings show a fundamental tension between structured compressibility and robustness, and suggest new pathways for designing models that are both efficient and secure.

Rembert Daems, Manfred Opper, Guillaume Crevecoeur et al.

We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it is computationally challenging due to the iterative nature of maximizing the ELBO. In this work, we propose to decompose the control term into linear and residual non-linear components and derive an optimal control term for linear SDEs, using stochastic optimal control. Modeling the non-linear component by a neural network, we show how to efficiently train neural SDEs without sacrificing their expressive power. Since the linear part of the control term is optimal and does not need to be learned, the training is initialized at a lower cost and we observe faster convergence.

Nathan Mankovich, Ignacio Santamaria, Gustau Camps-Valls et al.

Flag manifolds encode nested sequences of subspaces and serve as powerful structures for various computer vision and machine learning applications. Despite their utility in tasks such as dimensionality reduction, motion averaging, and subspace clustering, current applications are often restricted to extracting flags using common matrix decomposition methods like the singular value decomposition. Here, we address the need for a general algorithm to factorize and work with hierarchical datasets. In particular, we propose a novel, flag-based method that decomposes arbitrary hierarchical real-valued data into a hierarchy-preserving flag representation in Stiefel coordinates. Our work harnesses the potential of flag manifolds in applications including denoising, clustering, and few-shot learning.

Karthik Prakhya, Tolga Birdal, Alp Yurtsever

Solving non-convex, NP-hard optimization problems is crucial for training machine learning models, including neural networks. However, non-convexity often leads to black-box machine learning models with unclear inner workings. While convex formulations have been used for verifying neural network robustness, their application to training neural networks remains less explored. In response to this challenge, we reformulate the problem of training infinite-width two-layer ReLU networks as a convex completely positive program in a finite-dimensional (lifted) space. Despite the convexity, solving this problem remains NP-hard due to the complete positivity constraint. To overcome this challenge, we introduce a semidefinite relaxation that can be solved in polynomial time. We then experimentally evaluate the tightness of this relaxation, demonstrating its competitive performance in test accuracy across a range of classification tasks.

Caner Korkmaz, Brighton Nuwagira, Barış Coşkunuzer et al.

We present CuMPerLay, a novel differentiable vectorization layer that enables the integration of Cubical Multiparameter Persistence (CMP) into deep learning pipelines. While CMP presents a natural and powerful way to topologically work with images, its use is hindered by the complexity of multifiltration structures as well as the vectorization of CMP. In face of these challenges, we introduce a new algorithm for vectorizing MP homologies of cubical complexes. Our CuMPerLay decomposes the CMP into a combination of individual, learnable single-parameter persistence, where the bifiltration functions are jointly learned. Thanks to the differentiability, its robust topological feature vectors can be seamlessly used within state-of-the-art architectures such as Swin Transformers. We establish theoretical guarantees for the stability of our vectorization under generalized Wasserstein metrics. Our experiments on benchmark medical imaging and computer vision datasets show the benefit CuMPerLay on classification and segmentation performance, particularly in limited-data scenarios. Overall, CuMPerLay offers a promising direction for integrating global structural information into deep networks for structured image analysis.

Mustafa Hajij, Lennart Bastian, Sarah Osentoski et al.

We introduce copresheaf topological neural networks (CTNNs), a powerful unifying framework that encapsulates a wide spectrum of deep learning architectures, designed to operate on structured data, including images, point clouds, graphs, meshes, and topological manifolds. While deep learning has profoundly impacted domains ranging from digital assistants to autonomous systems, the principled design of neural architectures tailored to specific tasks and data types remains one of the field's most persistent open challenges. CTNNs address this gap by formulating model design in the language of copresheaves, a concept from algebraic topology that generalizes most practical deep learning models in use today. This abstract yet constructive formulation yields a rich design space from which theoretically sound and practically effective solutions can be derived to tackle core challenges in representation learning, such as long-range dependencies, oversmoothing, heterophily, and non-Euclidean domains. Our empirical results on structured data benchmarks demonstrate that CTNNs consistently outperform conventional baselines, particularly in tasks requiring hierarchical or localized sensitivity. These results establish CTNNs as a principled multi-scale foundation for the next generation of deep learning architectures.

Edward Stevinson, Lucas Prieto, Melih Barsbey et al.

Fundamental questions remain about when and why adversarial examples arise in neural networks, with competing views characterising them either as artifacts of the irregularities in the decision landscape or as products of sensitivity to non-robust input features. In this paper, we instead argue that adversarial vulnerability can stem from efficient information encoding in neural networks. Specifically, we show how superposition - where networks represent more features than they have dimensions - creates arrangements of latent representations that adversaries can exploit. We demonstrate that adversarial perturbations leverage interference between superposed features, making attack patterns predictable from feature arrangements. Our framework provides a mechanistic explanation for two known phenomena: adversarial attack transferability between models with similar training regimes and class-specific vulnerability patterns. In synthetic settings with precisely controlled superposition, we establish that superposition suffices to create adversarial vulnerability. We then demonstrate that these findings persist in a ViT trained on CIFAR-10. These findings reveal adversarial vulnerability can be a byproduct of networks' representational compression, rather than flaws in the learning process or non-robust inputs.

Natacha Kuete Meli, Shuteng Wang, Marcel Seelbach Benkner et al.

Quantum-enhanced Computer Vision (QeCV) is a new research field at the intersection of computer vision, optimisation theory, machine learning and quantum computing. It has high potential to transform how visual signals are processed and interpreted with the help of quantum computing that leverages quantum-mechanical effects in computations inaccessible to classical (i.e. non-quantum) computers. In scenarios where existing non-quantum methods cannot find a solution in a reasonable time or compute only approximate solutions, quantum computers can provide, among others, advantages in terms of better time scalability for multiple problem classes. Parametrised quantum circuits can also become, in the long term, a considerable alternative to classical neural networks in computer vision. However, specialised and fundamentally new algorithms must be developed to enable compatibility with quantum hardware and unveil the potential of quantum computational paradigms in computer vision. This survey contributes to the existing literature on QeCV with a holistic review of this research field. It is designed as a quantum computing reference for the computer vision community, targeting computer vision students, scientists and readers with related backgrounds who want to familiarise themselves with QeCV. We provide a comprehensive introduction to QeCV, its specifics, and methodologies for formulations compatible with quantum hardware and QeCV methods, leveraging two main quantum computational paradigms, i.e. gate-based quantum computing and quantum annealing. We elaborate on the operational principles of quantum computers and the available tools to access, program and simulate them in the context of QeCV. Finally, we review existing quantum computing tools and learning materials and discuss aspects related to publishing and reviewing QeCV papers, open challenges and potential social implications.

Zhengdi Yu, Simone Foti, Linguang Zhang et al.

We introduce Neural Riemannian Motion Fields (NRMF), a novel 3D generative human motion prior that enables robust, temporally consistent, and physically plausible 3D motion recovery. Unlike existing VAE or diffusion-based methods, our higher-order motion prior explicitly models the human motion in the zero level set of a collection of neural distance fields (NDFs) corresponding to pose, transition (velocity), and acceleration dynamics. Our framework is rigorous in the sense that our NDFs are constructed on the product space of joint rotations, their angular velocities, and angular accelerations, respecting the geometry of the underlying articulations. We further introduce: (i) a novel adaptive-step hybrid algorithm for projecting onto the set of plausible motions, and (ii) a novel geometric integrator to "roll out" realistic motion trajectories during test-time-optimization and generation. Our experiments show significant and consistent gains: trained on the AMASS dataset, NRMF remarkably generalizes across multiple input modalities and to diverse tasks ranging from denoising to motion in-betweening and fitting to partial 2D / 3D observations.

Melih Barsbey, Lucas Prieto, Stefanos Zafeiriou et al.

Robustness and resource-efficiency are two highly desirable properties for modern machine learning models. However, achieving them jointly remains a challenge. In this paper, we identify high learning rates as a facilitator for simultaneously achieving robustness to spurious correlations and network compressibility. We demonstrate that large learning rates also produce desirable representation properties such as invariant feature utilization, class separation, and activation sparsity. Our findings indicate that large learning rates compare favorably to other hyperparameters and regularization methods, in consistently satisfying these properties in tandem. In addition to demonstrating the positive effect of large learning rates across diverse spurious correlation datasets, models, and optimizers, we also present strong evidence that the previously documented success of large learning rates in standard classification tasks is related to addressing hidden/rare spurious correlations in the training dataset. Our investigation of the mechanisms underlying this phenomenon reveals the importance of confident mispredictions of bias-conflicting samples under large learning rates.

Mario Tuci, Lennart Bastian, Benjamin Dupuis et al.

Providing generalization guarantees for stochastic optimization algorithms is a major challenge in modern learning theory. Recently, several studies highlighted the impact of the geometry of training trajectories on the generalization error, both theoretically and empirically. Among these works, a series of topological generalization bounds have been proposed, relating the generalization error to notions of topological complexity that stem from topological data analysis (TDA). Despite their empirical success, these bounds rely on intricate information-theoretic (IT) terms that can be bounded in specific cases but remain intractable for practical algorithms (such as ADAM), potentially reducing the relevance of the derived bounds. In this paper, we seek to formulate comprehensive and interpretable topological generalization bounds free of intractable mutual information terms. To this end, we introduce a novel learning theoretic framework that departs from the existing strategies via proof techniques rooted in algorithmic stability. By extending an existing notion of \textit{hypothesis set stability}, to \textit{trajectory stability}, we prove that the generalization error of trajectory-stable algorithms can be upper bounded in terms of (i) TDA quantities describing the complexity of the trajectory of the optimizer in the parameter space, and (ii) the trajectory stability parameter of the algorithm. Through a series of experimental evaluations, we demonstrate that the TDA terms in the bound are of great importance, especially as the number of training samples grows. This ultimately forms an explanation of the empirical success of the topological generalization bounds.

Ming Hu, Zhengdi Yu, Feilong Tang et al.

Accurate 3D reconstruction of hands and instruments is critical for vision-based analysis of ophthalmic microsurgery, yet progress has been hampered by the lack of realistic, large-scale datasets and reliable annotation tools. In this work, we introduce OphNet-3D, the first extensive RGB-D dynamic 3D reconstruction dataset for ophthalmic surgery, comprising 41 sequences from 40 surgeons and totaling 7.1 million frames, with fine-grained annotations of 12 surgical phases, 10 instrument categories, dense MANO hand meshes, and full 6-DoF instrument poses. To scalably produce high-fidelity labels, we design a multi-stage automatic annotation pipeline that integrates multi-view data observation, data-driven motion prior with cross-view geometric consistency and biomechanical constraints, along with a combination of collision-aware interaction constraints for instrument interactions. Building upon OphNet-3D, we establish two challenging benchmarks-bimanual hand pose estimation and hand-instrument interaction reconstruction-and propose two dedicated architectures: H-Net for dual-hand mesh recovery and OH-Net for joint reconstruction of two-hand-two-instrument interactions. These models leverage a novel spatial reasoning module with weak-perspective camera modeling and collision-aware center-based representation. Both architectures outperform existing methods by substantial margins, achieving improvements of over 2mm in Mean Per Joint Position Error (MPJPE) and up to 23% in ADD-S metrics for hand and instrument reconstruction, respectively.

Shishir Reddy Vutukur, Heike Brock, Benjamin Busam et al.

Object Pose Estimation is a crucial component in robotic grasping and augmented reality. Learning based approaches typically require training data from a highly accurate CAD model or labeled training data acquired using a complex setup. We address this by learning to estimate pose from weakly labeled data without a known CAD model. We propose to use a NeRF to learn object shape implicitly which is later used to learn view-invariant features in conjunction with CNN using a contrastive loss. While NeRF helps in learning features that are view-consistent, CNN ensures that the learned features respect symmetry. During inference, CNN is used to predict view-invariant features which can be used to establish correspondences with the implicit 3d model in NeRF. The correspondences are then used to estimate the pose in the reference frame of NeRF. Our approach can also handle symmetric objects unlike other approaches using a similar training setup. Specifically, we learn viewpoint invariant, discriminative features using NeRF which are later used for pose estimation. We evaluated our approach on LM, LM-Occlusion, and T-Less dataset and achieved benchmark accuracy despite using weakly labeled data.

Mikaela Angelina Uy, Yen-yu Chang, Minhyuk Sung et al.

We propose Point2Cyl, a supervised network transforming a raw 3D point cloud to a set of extrusion cylinders. Reverse engineering from a raw geometry to a CAD model is an essential task to enable manipulation of the 3D data in shape editing software and thus expand their usages in many downstream applications. Particularly, the form of CAD models having a sequence of extrusion cylinders -- a 2D sketch plus an extrusion axis and range -- and their boolean combinations is not only widely used in the CAD community/software but also has great expressivity of shapes, compared to having limited types of primitives (e.g., planes, spheres, and cylinders). In this work, we introduce a neural network that solves the extrusion cylinder decomposition problem in a geometry-grounded way by first learning underlying geometric proxies. Precisely, our approach first predicts per-point segmentation, base/barrel labels and normals, then estimates for the underlying extrusion parameters in differentiable and closed-form formulations. Our experiments show that our approach demonstrates the best performance on two recent CAD datasets, Fusion Gallery and DeepCAD, and we further showcase our approach on reverse engineering and editing.