Evangelos Chatzipantazis

Stefanos Pertigkiozoglou, Evangelos Chatzipantazis, Shubhendu Trivedi et al.

Equivariant neural networks have been widely used in a variety of applications due to their ability to generalize well in tasks where the underlying data symmetries are known. Despite their successes, such networks can be difficult to optimize and require careful hyperparameter tuning to train successfully. In this work, we propose a novel framework for improving the optimization of such models by relaxing the hard equivariance constraint during training: We relax the equivariance constraint of the network's intermediate layers by introducing an additional non-equivariant term that we progressively constrain until we arrive at an equivariant solution. By controlling the magnitude of the activation of the additional relaxation term, we allow the model to optimize over a larger hypothesis space containing approximate equivariant networks and converge back to an equivariant solution at the end of training. We provide experimental results on different state-of-the-art network architectures, demonstrating how this training framework can result in equivariant models with improved generalization performance. Our code is available at https://github.com/StefanosPert/Equivariant_Optimization_CR

Evangelos Chatzipantazis, Stefanos Pertigkiozoglou, Edgar Dobriban et al.

We propose a method for 3D shape reconstruction from unoriented point clouds. Our method consists of a novel SE(3)-equivariant coordinate-based network (TF-ONet), that parametrizes the occupancy field of the shape and respects the inherent symmetries of the problem. In contrast to previous shape reconstruction methods that align the input to a regular grid, we operate directly on the irregular point cloud. Our architecture leverages equivariant attention layers that operate on local tokens. This mechanism enables local shape modelling, a crucial property for scalability to large scenes. Given an unoriented, sparse, noisy point cloud as input, we produce equivariant features for each point. These serve as keys and values for the subsequent equivariant cross-attention blocks that parametrize the occupancy field. By querying an arbitrary point in space, we predict its occupancy score. We show that our method outperforms previous SO(3)-equivariant methods, as well as non-equivariant methods trained on SO(3)-augmented datasets. More importantly, local modelling together with SE(3)-equivariance create an ideal setting for SE(3) scene reconstruction. We show that by training only on single, aligned objects and without any pre-segmentation, we can reconstruct novel scenes containing arbitrarily many objects in random poses without any performance loss.

Mariliza Tzes, Nikolaos Bousias, Evangelos Chatzipantazis et al.

This paper addresses the Multi-Robot Active Information Acquisition (AIA) problem, where a team of mobile robots, communicating through an underlying graph, estimates a hidden state expressing a phenomenon of interest. Applications like target tracking, coverage and SLAM can be expressed in this framework. Existing approaches, though, are either not scalable, unable to handle dynamic phenomena or not robust to changes in the communication graph. To counter these shortcomings, we propose an Information-aware Graph Block Network (I-GBNet), an AIA adaptation of Graph Neural Networks, that aggregates information over the graph representation and provides sequential-decision making in a distributed manner. The I-GBNet, trained via imitation learning with a centralized sampling-based expert solver, exhibits permutation equivariance and time invariance, while harnessing the superior scalability, robustness and generalizability to previously unseen environments and robot configurations. Experiments on significantly larger graphs and dimensionality of the hidden state and more complex environments than those seen in training validate the properties of the proposed architecture and its efficacy in the application of localization and tracking of dynamic targets.

Royina Karegoudra Jayanth, Yinshuang Xu, Ziyun Wang et al.

Neural networks are seeing rapid adoption in purely inertial odometry, where accelerometer and gyroscope measurements from commodity inertial measurement units (IMU) are used to regress displacements and associated uncertainties. They can learn informative displacement priors, which can be directly fused with the raw data with off-the-shelf non-linear filters. Nevertheless, these networks do not consider the physical roto-reflective symmetries inherent in IMU data, leading to the need to memorize the same priors for every possible motion direction, which hinders generalization. In this work, we characterize these symmetries and show that the IMU data and the resulting displacement and covariance transform equivariantly, when rotated around the gravity vector and reflected with respect to arbitrary planes parallel to gravity. We design a neural network that respects these symmetries by design through equivariant processing in three steps: First, it estimates an equivariant gravity-aligned frame from equivariant vectors and invariant scalars derived from IMU data, leveraging expressive linear and non-linear layers tailored to commute with the underlying symmetry transformation. We then map the IMU data into this frame, thereby achieving an invariant canonicalization that can be directly used with off-the-shelf inertial odometry networks. Finally, we map these network outputs back into the original frame, thereby obtaining equivariant covariances and displacements. We demonstrate the generality of our framework by applying it to the filter-based approach based on TLIO, and the end-to-end RONIN architecture, and show better performance on the TLIO, Aria, RIDI and OxIOD datasets than existing methods.

Stefanos Pertigkiozoglou, Evangelos Chatzipantazis, Kostas Daniilidis

The goal of this paper is to address the problem of global point cloud registration (PCR) i.e., finding the optimal alignment between point clouds irrespective of the initial poses of the scans. This problem is notoriously challenging for classical optimization methods due to computational constraints. First, we show that state-of-the-art deep learning methods suffer from huge performance degradation when the point clouds are arbitrarily placed in space. We propose that equivariant deep learning should be utilized for solving this task and we characterize the specific type of bi-equivariance of PCR. Then, we design BiEquiformer a novel and scalable bi-equivariant pipeline i.e. equivariant to the independent transformations of the input point clouds. While a naive approach would process the point clouds independently we design expressive bi-equivariant layers that fuse the information from both point clouds. This allows us to extract high-quality superpoint correspondences and in turn, robust point-cloud registration. Extensive comparisons against state-of-the-art methods show that our method achieves comparable performance in the canonical setting and superior performance in the robust setting in both the 3DMatch and the challenging low-overlap 3DLoMatch dataset.

Georgios Mentzelopoulos, Evangelos Chatzipantazis, Ashwin G. Ramayya et al.

Deep learning based neural decoding from stereotactic electroencephalography (sEEG) would likely benefit from scaling up both dataset and model size. To achieve this, combining data across multiple subjects is crucial. However, in sEEG cohorts, each subject has a variable number of electrodes placed at distinct locations in their brain, solely based on clinical needs. Such heterogeneity in electrode number/placement poses a significant challenge for data integration, since there is no clear correspondence of the neural activity recorded at distinct sites between individuals. Here we introduce seegnificant: a training framework and architecture that can be used to decode behavior across subjects using sEEG data. We tokenize the neural activity within electrodes using convolutions and extract long-term temporal dependencies between tokens using self-attention in the time dimension. The 3D location of each electrode is then mixed with the tokens, followed by another self-attention in the electrode dimension to extract effective spatiotemporal neural representations. Subject-specific heads are then used for downstream decoding tasks. Using this approach, we construct a multi-subject model trained on the combined data from 21 subjects performing a behavioral task. We demonstrate that our model is able to decode the trial-wise response time of the subjects during the behavioral task solely from neural data. We also show that the neural representations learned by pretraining our model across individuals can be transferred in a few-shot manner to new subjects. This work introduces a scalable approach towards sEEG data integration for multi-subject model training, paving the way for cross-subject generalization for sEEG decoding.

Evangelos Chatzipantazis, Stefanos Pertigkiozoglou, Kostas Daniilidis et al.

We propose a new \emph{Transformed Risk Minimization} (TRM) framework as an extension of classical risk minimization. In TRM, we optimize not only over predictive models, but also over data transformations; specifically over distributions thereof. As a key application, we focus on learning augmentations; for instance appropriate rotations of images, to improve classification performance with a given class of predictors. Our TRM method (1) jointly learns transformations and models in a \emph{single training loop}, (2) works with any training algorithm applicable to standard risk minimization, and (3) handles any transforms, such as discrete and continuous classes of augmentations. To avoid overfitting when implementing empirical transformed risk minimization, we propose a novel regularizer based on PAC-Bayes theory. For learning augmentations of images, we propose a new parametrization of the space of augmentations via a stochastic composition of blocks of geometric transforms. This leads to the new \emph{Stochastic Compositional Augmentation Learning} (SCALE) algorithm. The performance of TRM with SCALE compares favorably to prior methods on CIFAR10/100. Additionally, we show empirically that SCALE can correctly learn certain symmetries in the data distribution (recovering rotations on rotated MNIST) and can also improve calibration of the learned model.