Recent advances in geometric deep learning and generative modeling have enabled the design of novel proteins with a wide range of desired properties. However, current state-of-the-art approaches are typically restricted to generating proteins with only static target properties, such as motifs and symmetries. In this work, we take a step towards overcoming this limitation by proposing a framework to condition structure generation on flexibility, which is crucial for key functionalities such as catalysis or molecular recognition. We first introduce BackFlip, an equivariant neural network for predicting per-residue flexibility from an input backbone structure. Relying on BackFlip, we propose FliPS, an SE(3)-equivariant conditional flow matching model that solves the inverse problem, that is, generating backbones that display a target flexibility profile. In our experiments, we show that FliPS is able to generate novel and diverse protein backbones with the desired flexibility, verified by Molecular Dynamics (MD) simulations. FliPS and BackFlip are available at https://github.com/graeter-group/flips.

Dynamic graphs exhibit complex temporal dynamics due to the interplay between evolving node features and changing network structures. Recently, Graph Neural Controlled Differential Equations (Graph Neural CDEs) successfully adapted Neural CDEs from paths on Euclidean domains to paths on graph domains. Building on this foundation, we introduce \textit{Permutation Equivariant Graph Neural CDEs}, which project Graph Neural CDEs onto permutation equivariant function spaces. This significantly reduces the model's parameter count without compromising representational power, resulting in more efficient training and improved generalisation. We empirically demonstrate the advantages of our approach through experiments on simulated dynamical systems and real-world tasks, showing improved performance in both interpolation and extrapolation scenarios.

While large language models (LLMs) demonstrate impressive capabilities across numerous applications, their robustness remains a critical concern. This paper is motivated by a specific vulnerability: the order sensitivity of LLMs. This vulnerability manifests itself as the order bias observed when LLMs decide between possible options (for example, a preference for the first option) and the tendency of LLMs to provide different answers when options are reordered. The use cases for this scenario extend beyond the classical case of multiple-choice question answering to the use of LLMs for multidocument tasks and as automated evaluators in AI pipelines. We introduce Set-LLM, a novel architectural adaptation for pretrained LLMs that enables the processing of mixed set-text inputs with permutation invariance guarantees. The adaptations involve a new attention mask and new positional encodings specifically designed for sets. We provide a theoretical proof of invariance and demonstrate through experiments that Set-LLM can be trained effectively, achieving comparable or improved performance and maintaining the runtime of the original model, while altogether eliminating order sensitivity.

Deep generative models have recently been proposed for sampling protein conformations from the Boltzmann distribution, as an alternative to often prohibitively expensive Molecular Dynamics simulations. However, current state-of-the-art approaches rely on fine-tuning pre-trained folding models and evolutionary sequence information, limiting their applicability and efficiency, and introducing potential biases. In this work, we propose a flow matching model for sampling protein conformations based solely on backbone geometry - BBFlow. We introduce a geometric encoding of the backbone equilibrium structure as input and propose to condition not only the flow but also the prior distribution on the respective equilibrium structure, eliminating the need for evolutionary information. The resulting model is orders of magnitudes faster than current state-of-the-art approaches at comparable accuracy, is transferable to multi-chain proteins, and can be trained from scratch in a few GPU days. In our experiments, we demonstrate that the proposed model achieves competitive performance with reduced inference time, across not only an established benchmark of naturally occurring proteins but also de novo proteins, for which evolutionary information is scarce or absent. BBFlow is available at https://github.com/graeter-group/bbflow.

We introduce a generative model for protein backbone design utilizing geometric products and higher order message passing. In particular, we propose Clifford Frame Attention (CFA), an extension of the invariant point attention (IPA) architecture from AlphaFold2, in which the backbone residue frames and geometric features are represented in the projective geometric algebra. This enables to construct geometrically expressive messages between residues, including higher order terms, using the bilinear operations of the algebra. We evaluate our architecture by incorporating it into the framework of FrameFlow, a state-of-the-art flow matching model for protein backbone generation. The proposed model achieves high designability, diversity and novelty, while also sampling protein backbones that follow the statistical distribution of secondary structure elements found in naturally occurring proteins, a property so far only insufficiently achieved by many state-of-the-art generative models.

Few-shot learning (FSL) is an important and topical problem in computer vision that has motivated extensive research into numerous methods spanning from sophisticated metalearning methods to simple transfer learning baselines. We seek to push the limits of a simple-but-effective pipeline for real-worldfew-shot image classification in practice. To this end, we explore few-shot learning from the perspective of neural architecture, as well as a three stage pipeline of pre-training on external data, meta-training with labelled few-shot tasks, and task-specific fine-tuning on unseen tasks. We investigate questions such as: ① How pre-training on external data benefits FSL? ② How state of the art transformer architectures can be exploited? and ③ How to best exploit finetuning? Ultimately, we show that a simple transformer-based pipeline yields surprisingly good performance on standard benchmarks such as Mini-ImageNet, CIFAR-FS, CDFSL and Meta-Dataset. Our code is available at https://hushell.github.io/pmf.

We present a comprehensive framework for egocentric interaction recognition using markerless 3D annotations of two hands manipulating objects. To this end, we propose a method to create a unified dataset for egocentric 3D interaction recognition. Our method produces annotations of the 3D pose of two hands and the 6D pose of the manipulated objects, along with their interaction labels for each frame. Our dataset, called H2O (2 Hands and Objects), provides synchronized multi-view RGB-D images, interaction labels, object classes, ground-truth 3D poses for left & right hands, 6D object poses, ground-truth camera poses, object meshes and scene point clouds. To the best of our knowledge, this is the first benchmark that enables the study of first-person actions with the use of the pose of both left and right hands manipulating objects and presents an unprecedented level of detail for egocentric 3D interaction recognition. We further propose the method to predict interaction classes by estimating the 3D pose of two hands and the 6D pose of the manipulated objects, jointly from RGB images. Our method models both inter- and intra-dependencies between both hands and objects by learning the topology of a graph convolutional network that predicts interactions. We show that our method facilitated by this dataset establishes a strong baseline for joint hand-object pose estimation and achieves state-of-the-art accuracy for first person interaction recognition.

Recently there has been an increased interest in unsupervised learning of disentangled representations using the Variational Autoencoder (VAE) framework. Most of the existing work has focused largely on modifying the variational cost function to achieve this goal. We first show that these modifications, e.g. beta-VAE, simplify the tendency of variational inference to underfit, causing pathological over-pruning and over-orthogonalization of learned components. Second, we propose a complementary approach: to modify the probabilistic model with a structured latent prior. This prior discovers latent variable representations that are structured into a hierarchy of independent vector spaces. The proposed prior has three major advantages: First, in contrast to the standard VAE normal prior, the proposed prior is not rotationally invariant. This feature of our approach resolves the problem of unidentifiability of the standard VAE normal prior. Second, we demonstrate that the proposed prior encourages a disentangled latent representation which facilitates learning of disentangled representations. Third, extensive quantitative experiments demonstrate that the prior significantly mitigates the trade-off between reconstruction loss and disentanglement over the state of the art.

Consumer depth cameras have dramatically improved our ability to track rigid, articulated, and deformable 3D objects in real-time. However, depth cameras have a limited temporal resolution (frame-rate) that restricts the accuracy and robustness of tracking, especially for fast or unpredictable motion. In this paper, we show how to perform model-based object tracking which allows to reconstruct the object's depth at an order of magnitude higher frame-rate through simple modifications to an off-the-shelf depth camera. We focus on phase-based time-of-flight (ToF) sensing, which reconstructs each low frame-rate depth image from a set of short exposure 'raw' infrared captures. These raw captures are taken in quick succession near the beginning of each depth frame, and differ in the modulation of their active illumination. We make two contributions. First, we detail how to perform model-based tracking against these raw captures. Second, we show that by reprogramming the camera to space the raw captures uniformly in time, we obtain a 10x higher frame-rate, and thereby improve the ability to track fast-moving objects.

In this work we propose a novel method to include a connectivity prior into image segmentation that is based on a binary labeling of a directed graph, in this case a geodesic shortest path tree. Specifically we make two contributions: First, we construct a geodesic shortest path tree with a distance measure that is related to the image data and the bending energy of each path in the tree. Second, we include a connectivity prior in our segmentation model, that allows to segment not only a single elongated structure, but instead a whole connected branching tree. Because both our segmentation model and the connectivity constraint are convex a global optimal solution can be found. To this end, we generalize a recent primal-dual algorithm for continuous convex optimization to an arbitrary graph structure. To validate our method we present results on data from medical imaging in angiography and retinal blood vessel segmentation.