Alexandru Paul Condurache

Steffen Hagedorn, Marcel Hallgarten, Martin Stoll et al.

Automated driving has the potential to revolutionize personal, public, and freight mobility. Beside accurately perceiving the environment, automated vehicles must plan a safe, comfortable, and efficient motion trajectory. To promote safety and progress, many works rely on modules that predict the future motion of surrounding traffic. Modular automated driving systems commonly handle prediction and planning as sequential, separate tasks. While this accounts for the influence of surrounding traffic on the ego vehicle, it fails to anticipate the reactions of traffic participants to the ego vehicle's behavior. Recent methods increasingly integrate prediction and planning in a joint or interdependent step to model bidirectional interactions. To date, a comprehensive overview of different integration principles is lacking. We systematically review state-of-the-art deep learning-based planning systems, and focus on how they integrate prediction. Different facets of the integration ranging from system architecture to high-level behavioral aspects are considered and related to each other. Moreover, we discuss the implications, strengths, and limitations of different integration principles. By pointing out research gaps, describing relevant future challenges, and highlighting trends in the research field, we identify promising directions for future research.

Christian Löwens, Thorben Funke, André Wagner et al.

Rigid point cloud registration is a fundamental problem and highly relevant in robotics and autonomous driving. Nowadays deep learning methods can be trained to match a pair of point clouds, given the transformation between them. However, this training is often not scalable due to the high cost of collecting ground truth poses. Therefore, we present a self-distillation approach to learn point cloud registration in an unsupervised fashion. Here, each sample is passed to a teacher network and an augmented view is passed to a student network. The teacher includes a trainable feature extractor and a learning-free robust solver such as RANSAC. The solver forces consistency among correspondences and optimizes for the unsupervised inlier ratio, eliminating the need for ground truth labels. Our approach simplifies the training procedure by removing the need for initial hand-crafted features or consecutive point cloud frames as seen in related methods. We show that our method not only surpasses them on the RGB-D benchmark 3DMatch but also generalizes well to automotive radar, where classical features adopted by others fail. The code is available at https://github.com/boschresearch/direg .

Paul Wimmer, Jens Mehnert, Alexandru Paul Condurache

State-of-the-art deep learning models have a parameter count that reaches into the billions. Training, storing and transferring such models is energy and time consuming, thus costly. A big part of these costs is caused by training the network. Model compression lowers storage and transfer costs, and can further make training more efficient by decreasing the number of computations in the forward and/or backward pass. Thus, compressing networks also at training time while maintaining a high performance is an important research topic. This work is a survey on methods which reduce the number of trained weights in deep learning models throughout the training. Most of the introduced methods set network parameters to zero which is called pruning. The presented pruning approaches are categorized into pruning at initialization, lottery tickets and dynamic sparse training. Moreover, we discuss methods that freeze parts of a network at its random initialization. By freezing weights, the number of trainable parameters is shrunken which reduces gradient computations and the dimensionality of the model's optimization space. In this survey we first propose dimensionality reduced training as an underlying mathematical model that covers pruning and freezing during training. Afterwards, we present and discuss different dimensionality reduced training methods.

Paul Wimmer, Jens Mehnert, Alexandru Paul Condurache

Unstructured pruning is well suited to reduce the memory footprint of convolutional neural networks (CNNs), both at training and inference time. CNNs contain parameters arranged in $K \times K$ filters. Standard unstructured pruning (SP) reduces the memory footprint of CNNs by setting filter elements to zero, thereby specifying a fixed subspace that constrains the filter. Especially if pruning is applied before or during training, this induces a strong bias. To overcome this, we introduce interspace pruning (IP), a general tool to improve existing pruning methods. It uses filters represented in a dynamic interspace by linear combinations of an underlying adaptive filter basis (FB). For IP, FB coefficients are set to zero while un-pruned coefficients and FBs are trained jointly. In this work, we provide mathematical evidence for IP's superior performance and demonstrate that IP outperforms SP on all tested state-of-the-art unstructured pruning methods. Especially in challenging situations, like pruning for ImageNet or pruning to high sparsity, IP greatly exceeds SP with equal runtime and parameter costs. Finally, we show that advances of IP are due to improved trainability and superior generalization ability.

Matthias Rath, Alexandru Paul Condurache

We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant convolutions are a popular approach to obtain equivariant representations. The desired corresponding invariance is then imposed using pooling operations. For rotations, it has been shown that using invariant integration instead of pooling further improves the sample complexity. In this contribution, we first expand invariant integration beyond rotations to flips and scale transformations. We then address the problem of incorporating multiple desired invariances into a single network. For this purpose, we propose a multi-stream architecture, where each stream is invariant to a different transformation such that the network can simultaneously benefit from multiple invariances. We demonstrate our approach with successful experiments on Scaled-MNIST, SVHN, CIFAR-10 and STL-10.

Lukas Meiner, Jens Mehnert, Alexandru Paul Condurache

To reduce the computational cost of convolutional neural networks (CNNs) on resource-constrained devices, structured pruning approaches have shown promise in lowering floating-point operations (FLOPs) without substantial drops in accuracy. However, most methods require fine-tuning or specific training procedures to achieve a reasonable trade-off between retained accuracy and reduction in FLOPs, adding computational overhead and requiring training data to be available. To this end, we propose HASTE (Hashing for Tractable Efficiency), a data-free, plug-and-play convolution module that instantly reduces a network's test-time inference cost without training or fine-tuning. Our approach utilizes locality-sensitive hashing (LSH) to detect redundancies in the channel dimension of latent feature maps, compressing similar channels to reduce input and filter depth simultaneously, resulting in cheaper convolutions. We demonstrate our approach on the popular vision benchmarks CIFAR-10 and ImageNet, where we achieve a 46.72% reduction in FLOPs with only a 1.25% loss in accuracy by swapping the convolution modules in a ResNet34 on CIFAR-10 for our HASTE module.

Julia Lust, Alexandru P. Condurache

Deep neural networks tend to make overconfident predictions and often require additional detectors for misclassifications, particularly for safety-critical applications. Existing detection methods usually only focus on adversarial attacks or out-of-distribution samples as reasons for false predictions. However, generalization errors occur due to diverse reasons often related to poorly learning relevant invariances. We therefore propose GIT, a holistic approach for the detection of generalization errors that combines the usage of gradient information and invariance transformations. The invariance transformations are designed to shift misclassified samples back into the generalization area of the neural network, while the gradient information measures the contradiction between the initial prediction and the corresponding inherent computations of the neural network using the transformed sample. Our experiments demonstrate the superior performance of GIT compared to the state-of-the-art on a variety of network architectures, problem setups and perturbation types.

Bin Yang, Mohamed Abdelsamad, Miao Zhang et al.

Recent advances in self-supervised learning (SSL) for point clouds have substantially improved 3D scene understanding without human annotations. Existing approaches emphasize semantic awareness by enforcing feature consistency across augmented views or by masked scene modeling. However, the resulting representations transfer poorly to instance localization, and often require full finetuning for strong performance. Instance awareness is a fundamental component of 3D perception, thus bridging this gap is crucial for progressing toward true 3D foundation models that support all downstream tasks on 3D data. In this work, we introduce PointINS, an instance-oriented self-supervised framework that enriches point cloud representations through geometry-aware learning. PointINS employs an orthogonal offset branch to jointly learn high-level semantic understanding and geometric reasoning, yielding instance awareness. We identify two consistent properties essential for robust instance localization and formulate them as complementary regularization strategies, Offset Distribution Regularization (ODR), which aligns predicted offsets with empirically observed geometric priors, and Spatial Clustering Regularization (SCR), which enforces local coherence by regularizing offsets with pseudo-instance masks. Through extensive experiments across five datasets, PointINS achieves on average +3.5% mAP improvement for indoor instance segmentation and +4.1% PQ gain for outdoor panoptic segmentation, paving the way for scalable 3D foundation models.

Bin Yang, Alexandru Paul Condurache

Annotating large-scale LiDAR point clouds for 3D semantic segmentation is costly and time-consuming, which motivates the use of semi-supervised learning (SemiSL). Standard LiDAR SemiSL methods typically adopt a two-step training paradigm, where pseudo-labels are separately generated from a single distillation source, either from the same or another LiDAR representation. Such supervision relies on a unique source of pseudo-labels, which can reinforce confirmation bias and propagate errors during training, ultimately limiting performance. To address this challenge, we introduce CoLLiS, a novel framework that leverages Collaborative Learning for LiDAR Semi-supervised segmentation. Unlike prior paradigms with decoupled pseudo-labeling and training phases, CoLLiS trains multiple representations collaboratively in a single step by treating them as coequal students. Each student is adaptively distilled from multiple representations, while inter-student disparities are monitored online to resolve contradictory supervision and effectively mitigate confirmation bias. Extensive experiments on three datasets demonstrate that CoLLiS consistently outperforms state-of-the-art LiDAR SemiSL methods, with particularly strong gains in low-label regimes.

Maximilian Pittner, Joel Janai, Mario Faigle et al.

3D lane detection has emerged as a critical challenge in autonomous driving, encompassing identification and localization of lane markings and the 3D road surface. Conventional 3D methods detect lanes from dense birds-eye-viewed (BEV) features, though erroneous transformations often result in a poor feature representation misaligned with the true 3D road surface. While recent sparse lane detectors have surpassed dense BEV approaches, they completely disregard valuable lane-specific priors. Furthermore, existing methods fail to utilize historic lane observations, which yield the potential to resolve ambiguities in situations of poor visibility. To address these challenges, we present SparseLaneSTP, a novel method that integrates both geometric properties of the lane structure and temporal information into a sparse lane transformer. It introduces a new lane-specific spatio-temporal attention mechanism, a continuous lane representation tailored for sparse architectures as well as temporal regularization. Identifying weaknesses of existing 3D lane datasets, we also introduce a precise and consistent 3D lane dataset using a simple yet effective auto-labeling strategy. Our experimental section proves the benefits of our contributions and demonstrates state-of-the-art performance across all detection and error metrics on existing 3D lane detection benchmarks as well as on our novel dataset.

Lukas Meiner, Jens Mehnert, Alexandru Paul Condurache

Deploying large convolutional neural networks (CNNs) on resource-constrained devices is challenging due to their high computational cost. While dynamic execution methods are promising, existing approaches for CNNs typically require specialized training or fine-tuning, limiting their effectiveness when applied to pre-trained models and requiring data access. To address this gap, we propose HASTE (Hashing for Tractable Efficiency), a plug-and-play convolution module that enables training-free, dynamic compression of large pre-trained CNNs. At inference time, HASTE uses locality-sensitive hashing to identify and merge redundant channels of latent feature maps on a patch-wise basis. This process simultaneously compresses the depth of both input features and their corresponding filters, resulting in computationally cheaper convolutions. We conduct extensive experiments on CIFAR-10 and ImageNet across a range of architectures, demonstrating a 46.2% FLOPs reduction in a ResNet34 on CIFAR-10 with only a 1.25% drop in accuracy, without any retraining. We support our claims by comprehensive ablation studies to validate our core design choices, an analysis of the method's properties and limitations, and a discussion that connects our channel merging scheme to the conceptually related task of token merging in Vision Transformers. Our results demonstrate that HASTE provides an effective solution for steerable compression of pre-trained CNNs at runtime, opening new possibilities for the deployment of efficient deep learning methods.

Steffen Hagedorn, Marcel Milich, Alexandru P. Condurache

Planning the trajectory of the controlled ego vehicle is a key challenge in automated driving. As for human drivers, predicting the motions of surrounding vehicles is important to plan the own actions. Recent motion prediction methods utilize equivariant neural networks to exploit geometric symmetries in the scene. However, no existing method combines motion prediction and trajectory planning in a joint step while guaranteeing equivariance under roto-translations of the input space. We address this gap by proposing a lightweight equivariant planning model that generates multi-modal joint predictions for all vehicles and selects one mode as the ego plan. The equivariant network design improves sample efficiency, guarantees output stability, and reduces model parameters. We further propose equivariant route attraction to guide the ego vehicle along a high-level route provided by an off-the-shelf GPS navigation system. This module creates a momentum from embedded vehicle positions toward the route in latent space while keeping the equivariance property. Route attraction enables goal-oriented behavior without forcing the vehicle to stick to the exact route. We conduct experiments on the challenging nuScenes dataset to investigate the capability of our planner. The results show that the planned trajectory is stable under roto-translations of the input scene which demonstrates the equivariance of our model. Despite using only a small split of the dataset for training, our method improves L2 distance at 3 s by 20.6 % and surpasses the state of the art.

Uranik Berisha, Jens Mehnert, Alexandru Paul Condurache

Vision Transformers have emerged as the state-of-the-art models in various Computer Vision tasks, but their high computational and resource demands pose significant challenges. While Mixture-of-Experts (MoE) can make these models more efficient, they often require costly retraining or even training from scratch. Recent developments aim to reduce these computational costs by leveraging pretrained networks. These have been shown to produce sparse activation patterns in the Multi-Layer Perceptrons (MLPs) of the encoder blocks, allowing for conditional activation of only relevant subnetworks for each sample. Building on this idea, we propose a new method to construct MoE variants from pretrained models. Our approach extracts expert subnetworks from the model's MLP layers post-training in two phases. First, we cluster output activations to identify distinct activation patterns. In the second phase, we use these clusters to extract the corresponding subnetworks responsible for producing them. On ImageNet-1k recognition tasks, we demonstrate that these extracted experts can perform surprisingly well out of the box and require only minimal fine-tuning to regain 98% of the original performance, all while reducing MACs and model size, by up to 36% and 32% respectively.

Lukas Meiner, Jens Mehnert, Alexandru Paul Condurache

Convolutional neural networks (CNNs) are crucial for computer vision tasks on resource-constrained devices. Quantization effectively compresses these models, reducing storage size and energy cost. However, in modern depthwise-separable architectures, the computational cost is distributed unevenly across its components, with pointwise operations being the most expensive. By applying a general quantization scheme to this imbalanced cost distribution, existing quantization approaches fail to fully exploit potential efficiency gains. To this end, we introduce PROM, a straightforward approach for quantizing modern depthwise-separable convolutional networks by selectively using two distinct bit-widths. Specifically, pointwise convolutions are quantized to ternary weights, while the remaining modules use 8-bit weights, which is achieved through a simple quantization-aware training procedure. Additionally, by quantizing activations to 8-bit, our method transforms pointwise convolutions with ternary weights into int8 additions, which enjoy broad support across hardware platforms and effectively eliminates the need for expensive multiplications. Applying PROM to MobileNetV2 reduces the model's energy cost by more than an order of magnitude (23.9x) and its storage size by 2.7x compared to the float16 baseline while retaining similar classification performance on ImageNet. Our method advances the Pareto frontier for energy consumption vs. top-1 accuracy for quantized convolutional models on ImageNet. PROM addresses the challenges of quantizing depthwise-separable convolutional networks to both ternary and 8-bit weights, offering a simple way to reduce energy cost and storage size.

Uranik Berisha, Jens Mehnert, Alexandru Paul Condurache

Increasingly expensive training of ever larger models such as Vision Transfomers motivate reusing the vast library of already trained state-of-the-art networks. However, their latency, high computational costs and memory demands pose significant challenges for deployment, especially on resource-constrained hardware. While structured pruning methods can reduce these factors, they often require costly retraining, sometimes for up to hundreds of epochs, or even training from scratch to recover the lost accuracy resulting from the structural modifications. Maintaining the provided performance of trained models after structured pruning and thereby avoiding extensive retraining remains a challenge. To solve this, we introduce Variance-Based Pruning, a simple and structured one-shot pruning technique for efficiently compressing networks, with minimal finetuning. Our approach first gathers activation statistics, which are used to select neurons for pruning. Simultaneously the mean activations are integrated back into the model to preserve a high degree of performance. On ImageNet-1k recognition tasks, we demonstrate that directly after pruning DeiT-Base retains over 70% of its original performance and requires only 10 epochs of fine-tuning to regain 99% of the original accuracy while simultaneously reducing MACs by 35% and model size by 36%, thus speeding up the model by 1.44x.

Ali Alawieh, Alexandru P. Condurache

We present Frame-Averaging Kernel-Point Convolution (FA-KPConv), a neural network architecture built on top of the well-known KPConv, a widely adopted backbone for 3D point cloud analysis. Even though invariance and/or equivariance to Euclidean transformations are required for many common tasks, KPConv-based networks can only approximately achieve such properties when training on large datasets or with significant data augmentations. Using Frame Averaging, we allow to flexibly customize point cloud neural networks built with KPConv layers, by making them exactly invariant and/or equivariant to translations, rotations and/or reflections of the input point clouds. By simply wrapping around an existing KPConv-based network, FA-KPConv embeds geometrical prior knowledge into it while preserving the number of learnable parameters and not compromising any input information. We showcase the benefit of such an introduced bias for point cloud classification and point cloud registration, especially in challenging cases such as scarce training data or randomly rotated test data.

Bin Yang, Alexandru Paul Condurache

3D scene understanding is a critical yet challenging task in autonomous driving, primarily due to the irregularity and sparsity of LiDAR data, as well as the computational demands of processing large-scale point clouds. Recent methods leverage the range-view representation to improve processing efficiency. To mitigate the performance drop caused by information loss inherent to the "many-to-one" problem, where multiple nearby 3D points are mapped to the same 2D grids and only the closest is retained, prior works tend to choose a higher azimuth resolution for range-view projection. However, this can bring the drawback of reducing the proportion of pixels that carry information and heavier computation within the network. We argue that it is not the optimal solution and show that, in contrast, decreasing the resolution is more advantageous in both efficiency and accuracy. In this work, we present a comprehensive re-design of the workflow for range-view-based LiDAR semantic segmentation. Our approach addresses data representation, augmentation, and post-processing methods for improvements. Through extensive experiments on two public datasets, we demonstrate that our pipeline significantly enhances the performance of various network architectures over their baselines, paving the way for more effective LiDAR-based perception in autonomous systems.

Maximilian Pittner, Joel Janai, Alexandru P. Condurache

Monocular 3D lane detection has become a fundamental problem in the context of autonomous driving, which comprises the tasks of finding the road surface and locating lane markings. One major challenge lies in a flexible but robust line representation capable of modeling complex lane structures, while still avoiding unpredictable behavior. While previous methods rely on fully data-driven approaches, we instead introduce a novel approach LaneCPP that uses a continuous 3D lane detection model leveraging physical prior knowledge about the lane structure and road geometry. While our sophisticated lane model is capable of modeling complex road structures, it also shows robust behavior since physical constraints are incorporated by means of a regularization scheme that can be analytically applied to our parametric representation. Moreover, we incorporate prior knowledge about the road geometry into the 3D feature space by modeling geometry-aware spatial features, guiding the network to learn an internal road surface representation. In our experiments, we show the benefits of our contributions and prove the meaningfulness of using priors to make 3D lane detection more robust. The results show that LaneCPP achieves state-of-the-art performance in terms of F-Score and geometric errors.

Matthias Rath, Alexandru Paul Condurache

Leveraging prior knowledge on intraclass variance due to transformations is a powerful method to improve the sample complexity of deep neural networks. This makes them applicable to practically important use-cases where training data is scarce. Rather than being learned, this knowledge can be embedded by enforcing invariance to those transformations. Invariance can be imposed using group-equivariant convolutions followed by a pooling operation. For rotation-invariance, previous work investigated replacing the spatial pooling operation with invariant integration which explicitly constructs invariant representations. Invariant integration uses monomials which are selected using an iterative approach requiring expensive pre-training. We propose a novel monomial selection algorithm based on pruning methods to allow an application to more complex problems. Additionally, we replace monomials with different functions such as weighted sums, multi-layer perceptrons and self-attention, thereby streamlining the training of invariant-integration-based architectures. We demonstrate the improved sample complexity on the Rotated-MNIST, SVHN and CIFAR-10 datasets where rotation-invariant-integration-based Wide-ResNet architectures using monomials and weighted sums outperform the respective baselines in the limited sample regime. We achieve state-of-the-art results using full data on Rotated-MNIST and SVHN where rotation is a main source of intraclass variation. On STL-10 we outperform a standard and a rotation-equivariant convolutional neural network using pooling.

Paul Wimmer, Jens Mehnert, Alexandru Condurache

State-of-the-art deep neural network (DNN) pruning techniques, applied one-shot before training starts, evaluate sparse architectures with the help of a single criterion -- called pruning score. Pruning weights based on a solitary score works well for some architectures and pruning rates but may also fail for other ones. As a common baseline for pruning scores, we introduce the notion of a generalized synaptic score (GSS). In this work we do not concentrate on a single pruning criterion, but provide a framework for combining arbitrary GSSs to create more powerful pruning strategies. These COmbined Pruning Scores (COPS) are obtained by solving a constrained optimization problem. Optimizing for more than one score prevents the sparse network to overly specialize on an individual task, thus COntrols Pruning before training Starts. The combinatorial optimization problem given by COPS is relaxed on a linear program (LP). This LP is solved analytically and determines a solution for COPS. Furthermore, an algorithm to compute it for two scores numerically is proposed and evaluated. Solving COPS in such a way has lower complexity than the best general LP solver. In our experiments we compared pruning with COPS against state-of-the-art methods for different network architectures and image classification tasks and obtained improved results.

Paul Wimmer, Jens Mehnert, Alexandru Condurache

Pruning generates sparse networks by setting parameters to zero. In this work we improve one-shot pruning methods, applied before training, without adding any additional storage costs while preserving the sparse gradient computations. The main difference to pruning is that we do not sparsify the network's weights but learn just a few key parameters and keep the other ones fixed at their random initialized value. This mechanism is called freezing the parameters. Those frozen weights can be stored efficiently with a single 32bit random seed number. The parameters to be frozen are determined one-shot by a single for- and backward pass applied before training starts. We call the introduced method FreezeNet. In our experiments we show that FreezeNets achieve good results, especially for extreme freezing rates. Freezing weights preserves the gradient flow throughout the network and consequently, FreezeNets train better and have an increased capacity compared to their pruned counterparts. On the classification tasks MNIST and CIFAR-10/100 we outperform SNIP, in this setting the best reported one-shot pruning method, applied before training. On MNIST, FreezeNet achieves 99.2% performance of the baseline LeNet-5-Caffe architecture, while compressing the number of trained and stored parameters by a factor of x 157.

Julia Lust, Alexandru Paul Condurache

Deep Neural Networks (DNNs) achieve state-of-the-art performance on numerous applications. However, it is difficult to tell beforehand if a DNN receiving an input will deliver the correct output since their decision criteria are usually nontransparent. A DNN delivers the correct output if the input is within the area enclosed by its generalization envelope. In this case, the information contained in the input sample is processed reasonably by the network. It is of large practical importance to assess at inference time if a DNN generalizes correctly. Currently, the approaches to achieve this goal are investigated in different problem set-ups rather independently from one another, leading to three main research and literature fields: predictive uncertainty, out-of-distribution detection and adversarial example detection. This survey connects the three fields within the larger framework of investigating the generalization performance of machine learning methods and in particular DNNs. We underline the common ground, point at the most promising approaches and give a structured overview of the methods that provide at inference time means to establish if the current input is within the generalization envelope of a DNN.

Matthias Rath, Alexandru Paul Condurache

Deep Neural Networks achieve state-of-the-art results in many different problem settings by exploiting vast amounts of training data. However, collecting, storing and - in the case of supervised learning - labelling the data is expensive and time-consuming. Additionally, assessing the networks' generalization abilities or predicting how the inferred output changes under input transformations is complicated since the networks are usually treated as a black box. Both of these problems can be mitigated by incorporating prior knowledge into the neural network. One promising approach, inspired by the success of convolutional neural networks in computer vision tasks, is to incorporate knowledge about symmetric geometrical transformations of the problem to solve that affect the output in a predictable way. This promises an increased data efficiency and more interpretable network outputs. In this survey, we try to give a concise overview about different approaches that incorporate geometrical prior knowledge into neural networks. Additionally, we connect those methods to 3D object detection for autonomous driving, where we expect promising results when applying those methods.

Julia Lust, Alexandru Paul Condurache

Deep neural networks (DNNs) are vulnerable to adversarial examples and other data perturbations. Especially in safety critical applications of DNNs, it is therefore crucial to detect misclassified samples. The current state-of-the-art detection methods require either significantly more runtime or more parameters than the original network itself. This paper therefore proposes GraN, a time- and parameter-efficient method that is easily adaptable to any DNN. GraN is based on the layer-wise norm of the DNN's gradient regarding the loss of the current input-output combination, which can be computed via backpropagation. GraN achieves state-of-the-art performance on numerous problem set-ups.

Matthias Rath, Alexandru Paul Condurache

In this contribution, we show how to incorporate prior knowledge to a deep neural network architecture in a principled manner. We enforce feature space invariances using a novel layer based on invariant integration. This allows us to construct a complete feature space invariant to finite transformation groups. We apply our proposed layer to explicitly insert invariance properties for vision-related classification tasks, demonstrate our approach for the case of rotation invariance and report state-of-the-art performance on the Rotated-MNIST dataset. Our method is especially beneficial when training with limited data.