Stefanos Pertigkiozoglou

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.

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.

Nikolaos Bousias, Stefanos Pertigkiozoglou, Kostas Daniilidis et al.

Multi-agent reinforcement learning has emerged as a powerful framework for enabling agents to learn complex, coordinated behaviors but faces persistent challenges regarding its generalization, scalability and sample efficiency. Recent advancements have sought to alleviate those issues by embedding intrinsic symmetries of the systems in the policy. Yet, most dynamical systems exhibit little to no symmetries to exploit. This paper presents a novel framework for embedding extrinsic symmetries in multi-agent system dynamics that enables the use of symmetry-enhanced methods to address systems with insufficient intrinsic symmetries, expanding the scope of equivariant learning to a wide variety of MARL problems. Central to our framework is the Group Equivariant Graphormer, a group-modular architecture specifically designed for distributed swarming tasks. Extensive experiments on a swarm of symmetry-breaking quadrotors validate the effectiveness of our approach, showcasing its potential for improved generalization and zero-shot scalability. Our method achieves significant reductions in collision rates and enhances task success rates across a diverse range of scenarios and varying swarm sizes.

Stefanos Pertigkiozoglou, Mircea Petrache, Shubhendu Trivedi et al.

Equivariant neural networks exploit underlying task symmetries to improve generalization, but strict equivariance constraints can induce more complex optimization dynamics that can hinder learning. Prior work addresses these limitations by relaxing strict equivariance during training, but typically relies on prespecified, explicit, or implicit target levels of relaxation for each network layer, which are task-dependent and costly to tune. We propose Recurrent Equivariant Constraint Modulation (RECM), a layer-wise constraint modulation mechanism that learns appropriate relaxation levels solely from the training signal and the symmetry properties of each layer's input-target distribution, without requiring any prior knowledge about the task-dependent target relaxation level. We demonstrate that under the proposed RECM update, the relaxation level of each layer provably converges to a value upper-bounded by its symmetry gap, namely the degree to which its input-target distribution deviates from exact symmetry. Consequently, layers processing symmetric distributions recover full equivariance, while those with approximate symmetries retain sufficient flexibility to learn non-symmetric solutions when warranted by the data. Empirically, RECM outperforms prior methods across diverse exact and approximate equivariant tasks, including the challenging molecular conformer generation on the GEOM-Drugs dataset.

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.

Stefanos Pertigkiozoglou, Petros Maragos

The great success of convolutional neural networks has caused a massive spread of the use of such models in a large variety of Computer Vision applications. However, these models are vulnerable to certain inputs, the adversarial examples, which although are not easily perceived by humans, they can lead a neural network to produce faulty results. This paper focuses on the detection of adversarial examples, which are created for convolutional neural networks that perform image classification. We propose three methods for detecting possible adversarial examples and after we analyze and compare their performance, we combine their best aspects to develop an even more robust approach. The first proposed method is based on the regularization of the feature vector that the neural network produces as output. The second method detects adversarial examples by using histograms, which are created from the outputs of the hidden layers of the neural network. These histograms create a feature vector which is used as the input of an SVM classifier, which classifies the original input either as an adversarial or as a real input. Finally, for the third method we introduce the concept of the residual image, which contains information about the parts of the input pattern that are ignored by the neural network. This method aims at the detection of possible adversarial examples, by using the residual image and reinforcing the parts of the input pattern that are ignored by the neural network. Each one of these methods has some novelties and by combining them we can further improve the detection results. For the proposed methods and their combination, we present the results of detecting adversarial examples on the MNIST dataset. The combination of the proposed methods offers some improvements over similar state of the art approaches.