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We study the Solid Isotropic Material Penalisation (SIMP) method with a density field generated by a fully-connected neural network, taking the coordinates as inputs. In the large width limit, we show that the use of DNNs leads to a filtering effect similar to traditional filtering techniques for SIMP, with a filter described by the Neural Tangent Kernel (NTK). This filter is however not invariant under translation, leading to visual artifacts and non-optimal shapes. We propose two embeddings of the input coordinates, which lead to (approximate) spatial invariance of the NTK and of the filter. We empirically confirm our theoretical observations and study how the filter size is affected by the architecture of the network. Our solution can easily be applied to any other coordinates-based generation method.

Traffic flows in a distributed computing network require both transmission and processing, and can be interdicted by removing either communication or computation resources. We study the robustness of a distributed computing network under the failures of communication links and computation nodes. We define cut metrics that measure the connectivity, and show a non-zero gap between the maximum flow and the minimum cut. Moreover, we study a network flow interdiction problem that minimizes the maximum flow by removing communication and computation resources within a given budget. We develop mathematical programs to compute the optimal interdiction, and polynomial-time approximation algorithms that achieve near-optimal interdiction in simulation.

Solving the Schr\"odinger equation is key to many quantum mechanical properties. However, an analytical solution is only tractable for single-electron systems. Recently, neural networks succeeded at modeling wave functions of many-electron systems. Together with the variational Monte-Carlo (VMC) framework, this led to solutions on par with the best known classical methods. Still, these neural methods require tremendous amounts of computational resources as one has to train a separate model for each molecular geometry. In this work, we combine a Graph Neural Network (GNN) with a neural wave function to simultaneously solve the Schr\"odinger equation for multiple geometries via VMC. This enables us to model continuous subsets of the potential energy surface with a single training pass. Compared to existing state-of-the-art networks, our Potential Energy Surface Network PESNet speeds up training for multiple geometries by up to 40 times while matching or surpassing their accuracy. This may open the path to accurate and orders of magnitude cheaper quantum mechanical calculations.

Implicit functions represented as deep learning approximations are powerful for reconstructing 3D surfaces. However, they can only produce static surfaces that are not controllable, which provides limited ability to modify the resulting model by editing its pose or shape parameters. Nevertheless, such features are essential in building flexible models for both computer graphics and computer vision. In this work, we present methodology that combines detail-rich implicit functions and parametric representations in order to reconstruct 3D models of people that remain controllable and accurate even in the presence of clothing. Given sparse 3D point clouds sampled on the surface of a dressed person, we use an Implicit Part Network (IP-Net)to jointly predict the outer 3D surface of the dressed person, the and inner body surface, and the semantic correspondences to a parametric body model. We subsequently use correspondences to fit the body model to our inner surface and then non-rigidly deform it (under a parametric body + displacement model) to the outer surface in order to capture garment, face and hair detail. In quantitative and qualitative experiments with both full body data and hand scans we show that the proposed methodology generalizes, and is effective even given incomplete point clouds collected from single-view depth images. Our models and code can be downloaded from //virtualhumans.mpi-inf.mpg.de/ipnet.

We address the problem of fitting 3D human models to 3D scans of dressed humans. Classical methods optimize both the data-to-model correspondences and the human model parameters (pose and shape), but are reliable only when initialized close to the solution. Some methods initialize the optimization based on fully supervised correspondence predictors, which is not differentiable end-to-end, and can only process a single scan at a time. Our main contribution is LoopReg, an end-to-end learning framework to register a corpus of scans to a common 3D human model. The key idea is to create a self-supervised loop. A backward map, parameterized by a Neural Network, predicts the correspondence from every scan point to the surface of the human model. A forward map, parameterized by a human model, transforms the corresponding points back to the scan based on the model parameters (pose and shape), thus closing the loop. Formulating this closed loop is not straightforward because it is not trivial to force the output of the NN to be on the surface of the human model - outside this surface the human model is not even defined. To this end, we propose two key innovations. First, we define the canonical surface implicitly as the zero level set of a distance field in R3, which in contrast to morecommon UV parameterizations, does not require cutting the surface, does not have discontinuities, and does not induce distortion. Second, we diffuse the human model to the 3D domain R3. This allows to map the NN predictions forward,even when they slightly deviate from the zero level set. Results demonstrate that we can train LoopRegmainly self-supervised - following a supervised warm-start, the model becomes increasingly more accurate as additional unlabelled raw scans are processed. Our code and pre-trained models can be downloaded for research.

Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.

The generation of tailored light with multi-core fiber (MCF) lensless microendoscopes is widely used in biomedicine. However, the computer-generated holograms (CGHs) used for such applications are typically generated by iterative algorithms, which demand high computation effort, limiting advanced applications like in vivo optogenetic stimulation and fiber-optic cell manipulation. The random and discrete distribution of the fiber cores induces strong spatial aliasing to the CGHs, hence, an approach that can rapidly generate tailored CGHs for MCFs is highly demanded. We demonstrate a novel phase encoder deep neural network (CoreNet), which can generate accurate tailored CGHs for MCFs at a near video-rate. Simulations show that CoreNet can speed up the computation time by two magnitudes and increase the fidelity of the generated light field compared to the conventional CGH techniques. For the first time, real-time generated tailored CGHs are on-the-fly loaded to the phase-only SLM for dynamic light fields generation through the MCF microendoscope in experiments. This paves the avenue for real-time cell rotation and several further applications that require real-time high-fidelity light delivery in biomedicine.

Current deep learning research is dominated by benchmark evaluation. A method is regarded as favorable if it empirically performs well on the dedicated test set. This mentality is seamlessly reflected in the resurfacing area of continual learning, where consecutively arriving sets of benchmark data are investigated. The core challenge is framed as protecting previously acquired representations from being catastrophically forgotten due to the iterative parameter updates. However, comparison of individual methods is nevertheless treated in isolation from real world application and typically judged by monitoring accumulated test set performance. The closed world assumption remains predominant. It is assumed that during deployment a model is guaranteed to encounter data that stems from the same distribution as used for training. This poses a massive challenge as neural networks are well known to provide overconfident false predictions on unknown instances and break down in the face of corrupted data. In this work we argue that notable lessons from open set recognition, the identification of statistically deviating data outside of the observed dataset, and the adjacent field of active learning, where data is incrementally queried such that the expected performance gain is maximized, are frequently overlooked in the deep learning era. Based on these forgotten lessons, we propose a consolidated view to bridge continual learning, active learning and open set recognition in deep neural networks. Our results show that this not only benefits each individual paradigm, but highlights the natural synergies in a common framework. We empirically demonstrate improvements when alleviating catastrophic forgetting, querying data in active learning, selecting task orders, while exhibiting robust open world application where previously proposed methods fail.

In this paper, we focus on the question: how might mobile robots take advantage of affordable RGB-D sensors for object detection? Although current CNN-based object detectors have achieved impressive results, there are three main drawbacks for practical usage on mobile robots: 1) It is hard and time-consuming to collect and annotate large-scale training sets. 2) It usually needs a long training time. 3) CNN-based object detection shows significant weakness in predicting location. We propose a novel approach for the detection of planar objects, which rectifies images with geometric information to compensate for the perspective distortion before feeding it to the CNN detector module, typically a CNN-based detector like YOLO or MASK RCNN. By dealing with the perspective distortion in advance, we eliminate the need for the CNN detector to learn that. Experiments show that this approach significantly boosts the detection performance. Besides, it effectively reduces the number of training images required. In addition to the novel detection framework proposed, we also release an RGB-D dataset for hazmat sign detection. To the best of our knowledge, this is the first public-available hazmat sign detection dataset with RGB-D sensors.

Current top-performing object detectors depend on deep CNN backbones, such as ResNet-101 and Inception, benefiting from their powerful feature representations but suffering from high computational costs. Conversely, some lightweight model based detectors fulfil real time processing, while their accuracies are often criticized. In this paper, we explore an alternative to build a fast and accurate detector by strengthening lightweight features using a hand-crafted mechanism. Inspired by the structure of Receptive Fields (RFs) in human visual systems, we propose a novel RF Block (RFB) module, which takes the relationship between the size and eccentricity of RFs into account, to enhance the feature discriminability and robustness. We further assemble RFB to the top of SSD, constructing the RFB Net detector. To evaluate its effectiveness, experiments are conducted on two major benchmarks and the results show that RFB Net is able to reach the performance of advanced very deep detectors while keeping the real-time speed. Code is available at //github.com/ruinmessi/RFBNet.