arXiv subjects

Felix Petersen

Publications and source records attributed to Felix Petersen.

25 records · Page 2Linked to original sources

arXiv2021

Post-processing for Individual Fairness

Post-processing in algorithmic fairness is a versatile approach for correcting bias in ML systems that are already used in production. The main appeal of post-processing is that it avoids expensive retraining. In this work, we propose general post-processing algorithms for individual fairness (IF). We consider a setting where the learner only has access to the predictions of the original model and a similarity graph between individuals, guiding the desired fairness constraints. We cast the IF post-processing problem as a graph smoothing problem corresponding to graph Laplacian regularization that preserves the desired "treat similar individuals similarly" interpretation. Our theoretical results demonstrate the connection of the new objective function to a local relaxation of the original individual fairness. Empirically, our post-processing algorithms correct individual biases in large-scale NLP models such as BERT, while preserving accuracy.

stat.ML↗

arXiv2021

Learning with Algorithmic Supervision via Continuous Relaxations

The integration of algorithmic components into neural architectures has gained increased attention recently, as it allows training neural networks with new forms of supervision such as ordering constraints or silhouettes instead of using ground truth labels. Many approaches in the field focus on the continuous relaxation of a specific task and show promising results in this context. But the focus on single tasks also limits the applicability of the proposed concepts to a narrow range of applications. In this work, we build on those ideas to propose an approach that allows to integrate algorithms into end-to-end trainable neural network architectures based on a general approximation of discrete conditions. To this end, we relax these conditions in control structures such as conditional statements, loops, and indexing, so that resulting algorithms are smoothly differentiable. To obtain meaningful gradients, each relevant variable is perturbed via logistic distributions and the expectation value under this perturbation is approximated. We evaluate the proposed continuous relaxation model on four challenging tasks and show that it can keep up with relaxations specifically designed for each individual task.

cs.LG↗

arXiv2021

Style Agnostic 3D Reconstruction via Adversarial Style Transfer

Reconstructing the 3D geometry of an object from an image is a major challenge in computer vision. Recently introduced differentiable renderers can be leveraged to learn the 3D geometry of objects from 2D images, but those approaches require additional supervision to enable the renderer to produce an output that can be compared to the input image. This can be scene information or constraints such as object silhouettes, uniform backgrounds, material, texture, and lighting. In this paper, we propose an approach that enables a differentiable rendering-based learning of 3D objects from images with backgrounds without the need for silhouette supervision. Instead of trying to render an image close to the input, we propose an adversarial style-transfer and domain adaptation pipeline that allows to translate the input image domain to the rendered image domain. This allows us to directly compare between a translated image and the differentiable rendering of a 3D object reconstruction in order to train the 3D object reconstruction network. We show that the approach learns 3D geometry from images with backgrounds and provides a better performance than constrained methods for single-view 3D object reconstruction on this task.

cs.CV↗

arXiv2021

Differentiable Sorting Networks for Scalable Sorting and Ranking Supervision

Sorting and ranking supervision is a method for training neural networks end-to-end based on ordering constraints. That is, the ground truth order of sets of samples is known, while their absolute values remain unsupervised. For that, we propose differentiable sorting networks by relaxing their pairwise conditional swap operations. To address the problems of vanishing gradients and extensive blurring that arise with larger numbers of layers, we propose mapping activations to regions with moderate gradients. We consider odd-even as well as bitonic sorting networks, which outperform existing relaxations of the sorting operation. We show that bitonic sorting networks can achieve stable training on large input sets of up to 1024 elements.

cs.LG↗

arXiv2019

Pix2Vex: Image-to-Geometry Reconstruction using a Smooth Differentiable Renderer

The long-coveted task of reconstructing 3D geometry from images is still a standing problem. In this paper, we build on the power of neural networks and introduce Pix2Vex, a network trained to convert camera-captured images into 3D geometry. We present a novel differentiable renderer ($DR$) as a forward validation means during training. Our key insight is that $DR$s produce images of a particular appearance, different from typical input images. Hence, we propose adding an image-to-image translation component, converting between these rendering styles. This translation closes the training loop, while allowing to use minimal supervision only, without needing any 3D model as ground truth. Unlike state-of-the-art methods, our $DR$ is $C^\infty$ smooth and thus does not display any discontinuities at occlusions or dis-occlusions. Through our novel training scheme, our network can train on different types of images, where previous work can typically only train on images of a similar appearance to those rendered by a $DR$.

cs.CV↗

arXiv2019

AlgoNet: $C^\infty$ Smooth Algorithmic Neural Networks

Artificial neural networks revolutionized many areas of computer science in recent years since they provide solutions to a number of previously unsolved problems. On the other hand, for many problems, classic algorithms exist, which typically exceed the accuracy and stability of neural networks. To combine these two concepts, we present a new kind of neural networks$-$algorithmic neural networks (AlgoNets). These networks integrate smooth versions of classic algorithms into the topology of neural networks. A forward AlgoNet includes algorithmic layers into existing architectures while a backward AlgoNet can solve inverse problems without or with only weak supervision. In addition, we present the $\texttt{algonet}$ package, a PyTorch based library that includes, inter alia, a smoothly evaluated programming language, a smooth 3D mesh renderer, and smooth sorting algorithms.

cs.LG↗

arXiv2018

Towards Formula Translation using Recursive Neural Networks

While it has become common to perform automated translations on natural language, performing translations between different representations of mathematical formulae has thus far not been possible. We implemented the first translator for mathematical formulae based on recursive neural networks. We chose recursive neural networks because mathematical formulae inherently include a structural encoding. In our implementation, we developed new techniques and topologies for recursive tree-to-tree neural networks based on multi-variate multi-valued Long Short-Term Memory cells. We propose a novel approach for mini-batch training that utilizes clustering and tree traversal. We evaluate our translator and analyze the behavior of our proposed topologies and techniques based on a translation from generic LaTeX to the semantic LaTeX notation. We use the semantic LaTeX notation from the Digital Library for Mathematical Formulae and the Digital Repository for Mathematical Formulae at the National Institute for Standards and Technology. We find that a simple heuristics-based clustering algorithm outperforms the conventional clustering algorithms on the task of clustering binary trees of mathematical formulae with respect to their topology. Furthermore, we find a mask for the loss function, which can prevent the neural network from finding a local minimum of the loss function. Given our preliminary results, a complete translation from formula to formula is not yet possible. However, we achieved a prediction accuracy of 47.05% for predicting symbols at the correct position and an accuracy of 92.3% when ignoring the predicted position. Concluding, our work advances the field of recursive neural networks by improving the training speed and quality of training. In the future, we will work towards a complete translation allowing a machine-interpretation of LaTeX formulae.

cs.LG↗