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Text toxicity detection systems exhibit significant biases, producing disproportionate rates of false positives on samples mentioning demographic groups. But what about toxicity detection in speech? To investigate the extent to which text-based biases are mitigated by speech-based systems, we produce a set of high-quality group annotations for the multilingual MuTox dataset, and then leverage these annotations to systematically compare speech- and text-based toxicity classifiers. Our findings indicate that access to speech data during inference supports reduced bias against group mentions, particularly for ambiguous and disagreement-inducing samples. Our results also suggest that improving classifiers, rather than transcription pipelines, is more helpful for reducing group bias. We publicly release our annotations and provide recommendations for future toxicity dataset construction.

A monoid $S$ is said to be weakly right coherent if every finitely generated right ideal of $S$ is finitely presented as a right $S$-act. It is known that $S$ is weakly right coherent if and only if it satisfies the following conditions: $S$ is right ideal Howson, meaning that the intersection of any two finitely generated right ideals of $S$ is finitely generated; and the right annihilator congruences of $S$ are finitely generated as right congruences. We examine the behaviour of these two conditions (in the more general setting of semigroups) under certain algebraic constructions and deduce closure results for the class of weakly right coherent monoids. We also show that the property of being right ideal Howson is related to the axiomatisability of a class of left acts satisfying a condition related to flatness.

Natural-language assistants are designed to provide users with helpful responses while avoiding harmful outputs, largely achieved through alignment to human preferences. Yet there is limited understanding of whether alignment techniques may inadvertently perpetuate or even amplify harmful biases inherited from their pre-aligned base models. This issue is compounded by the choice of bias evaluation benchmarks in popular preference-finetuned models, which predominantly focus on dominant social categories, such as binary gender, thereby limiting insights into biases affecting underrepresented groups. Towards addressing this gap, we center transgender, nonbinary, and other gender-diverse identities to investigate how alignment procedures interact with pre-existing gender-diverse bias in LLMs. Our key contributions include: 1) a comprehensive survey of bias evaluation modalities across leading preference-finetuned LLMs, highlighting critical gaps in gender-diverse representation, 2) systematic evaluation of gender-diverse biases across 12 models spanning Direct Preference Optimization (DPO) stages, uncovering harms popular bias benchmarks fail to detect, and 3) a flexible framework for measuring harmful biases in implicit reward signals applicable to other social contexts. Our findings reveal that DPO-aligned models are particularly sensitive to supervised finetuning (SFT), and can amplify two forms of real-world gender-diverse harms from their base models: stigmatization and gender non-affirmative language. We conclude with recommendations tailored to DPO and broader alignment practices, advocating for the adoption of community-informed bias evaluation frameworks to more effectively identify and address underrepresented harms in LLMs., Comment: Accepted to 2024 Neurips Queer in AI Workshop

In real-world applications, as data availability increases, obtaining labeled data for machine learning (ML) projects remains challenging due to the high costs and intensive efforts required for data annotation. Many ML projects, particularly those focused on multi-label classification, also grapple with data imbalance issues, where certain classes may lack sufficient data to train effective classifiers. This study introduces and examines a novel oversampling method for multi-label text classification, designed to address performance challenges associated with data imbalance. The proposed method identifies potential new samples from unlabeled data by leveraging similarity measures between instances. By iteratively searching the unlabeled dataset, the method locates instances similar to those in underrepresented classes and evaluates their contribution to classifier performance enhancement. Instances that demonstrate performance improvement are then added to the labeled dataset. Experimental results indicate that the proposed approach effectively enhances classifier performance post-oversampling.

We present a novel framework for free-viewpoint facial performance relighting using diffusion-based image-to-image translation. Leveraging a subject-specific dataset containing diverse facial expressions captured under various lighting conditions, including flat-lit and one-light-at-a-time (OLAT) scenarios, we train a diffusion model for precise lighting control, enabling high-fidelity relit facial images from flat-lit inputs. Our framework includes spatially-aligned conditioning of flat-lit captures and random noise, along with integrated lighting information for global control, utilizing prior knowledge from the pre-trained Stable Diffusion model. This model is then applied to dynamic facial performances captured in a consistent flat-lit environment and reconstructed for novel-view synthesis using a scalable dynamic 3D Gaussian Splatting method to maintain quality and consistency in the relit results. In addition, we introduce unified lighting control by integrating a novel area lighting representation with directional lighting, allowing for joint adjustments in light size and direction. We also enable high dynamic range imaging (HDRI) composition using multiple directional lights to produce dynamic sequences under complex lighting conditions. Our evaluations demonstrate the models efficiency in achieving precise lighting control and generalizing across various facial expressions while preserving detailed features such as skintexture andhair. The model accurately reproduces complex lighting effects like eye reflections, subsurface scattering, self-shadowing, and translucency, advancing photorealism within our framework., Comment: 18 pages, SIGGRAPH Asia 2024 Conference Papers (SA Conference Papers '24), December 3--6, 2024, Tokyo, Japan. Project page: https://www.eyelinestudios.com/research/diffrelight.html

Machine-learned surrogate models to accelerate lengthy computer simulations are becoming increasingly important as engineers look to streamline the product design cycle. In many cases, these approaches offer the ability to predict relevant quantities throughout a geometry, but place constraints on the form of the input data. In a world of diverse data types, a preferred approach would not restrict the input to a particular structure. In this paper, we propose Topology-Agnostic Graph U-Net (TAG U-Net), a graph convolutional network that can be trained to input any mesh or graph structure and output a prediction of a target scalar field at each node. The model constructs coarsened versions of each input graph and performs a set of convolution and pooling operations to predict the node-wise outputs on the original graph. By training on a diverse set of shapes, the model can make strong predictions, even for shapes unlike those seen during training. A 3-D additive manufacturing dataset is presented, containing Laser Powder Bed Fusion simulation results for thousands of parts. The model is demonstrated on this dataset, and it performs well, predicting both 2-D and 3-D scalar fields with a median R-squared > 0.85 on test geometries. Code and datasets are available online., Comment: 18 pages, 10 figures

Machine learning models may capture and amplify biases present in data, leading to disparate test performance across social groups. To better understand, evaluate, and mitigate these possible biases, a deeper theoretical understanding of how model design choices and data distribution properties could contribute to bias is needed. In this work, we contribute a precise analytical theory in the context of ridge regression, both with and without random projections, where the former models neural networks in a simplified regime. Our theory offers a unified and rigorous explanation of machine learning bias, providing insights into phenomena such as bias amplification and minority-group bias in various feature and parameter regimes. For example, we demonstrate that there may be an optimal regularization penalty or training time to avoid bias amplification, and there can be fundamental differences in test error between groups that do not vanish with increased parameterization. Importantly, our theoretical predictions align with several empirical observations reported in the literature. We extensively empirically validate our theory on diverse synthetic and semi-synthetic datasets.

Scalar fields, such as stress or temperature fields, are often calculated in shape optimization and design problems in engineering. For complex problems where shapes have varying topology and cannot be parametrized, data-driven scalar field prediction can be faster than traditional finite element methods. However, current data-driven techniques to predict scalar fields are limited to a fixed grid domain, instead of arbitrary mesh structures. In this work, we propose a method to predict scalar fields on arbitrary meshes. It uses a convolutional neural network whose feature maps at multiple resolutions are interpolated to node positions before being fed into a multilayer perceptron to predict solutions to partial differential equations at mesh nodes. The model is trained on finite element von Mises stress fields, and once trained it can estimate stress values at each node on any input mesh. Two shape datasets are investigated, and the model has strong performance on both, with a median R-squared value of 0.91. We also demonstrate the model on a temperature field in a heat conduction problem, where its predictions have a median R-squared value of 0.99. Our method provides a potential flexible alternative to finite element analysis in engineering design contexts. Code and datasets are available online., Comment: 15 pages, 9 figures

Self driving vehicles should be able to perform parallel parking or a similar maneuver successfully. With this motivation, the S shaped maneuverability test of the Ohio driver license examination is chosen here for automatic execution by a self driving vehicle with drive by wire capability and longitudinal and lateral controls. The Ohio maneuverability test requires the driver to start within an area enclosed by four pylons and the driver is asked to go to the left of the fifth pylon directly in front of the vehicle in a smooth and continuous manner while ending in a parallel direction to the initial one. The driver is then asked to go backwards to the starting location of the vehicle without stopping the vehicle or hitting the pylons. As a self driving vehicle should do a much better job repeatably than a driver, a high order polynomial path model is built along with speed profiling to start and stop smoothly at the ends of the path without large longitudinal and lateral accelerations. In contrast to the long horizon, higher speed path planning and path tracking control applications in the literature, this paper treats low speed and very short horizon path planning and path tracking control with stopping and direction reversal. The path is constructed using a segmented polynomial fit optimization routine that guarantees path curvature smoothness. A linear path tracking model is utilized as the basis of the designed control system consisting of a disturbance observer based curvature rejection filter and a speed scheduled, parameter space robust PID controller. Simulation studies indicate that it has better performance compared to other common control systems such as standalone PID controller and combined PID and feedforward control. indicate that it has better performance compared to other common control systems such as standalone PID controller and combined PID and feedforward control., Comment: 12 pages, 19 figures

The current approach for new Advanced Driver Assistance System (ADAS) and Connected and Automated Driving (CAD) function development involves a significant amount of public road testing which is inefficient due to the number miles that need to be driven for rare and extreme events to take place, thereby being very costly also, and unsafe as the rest of the road users become involuntary test subjects. A new development, evaluation and demonstration method for safe, efficient, and repeatable development, demonstration and evaluation of ADAS and CAD functions called VehicleInVirtualEnvironment (VVE) was recently introduced as a solution to this problem. The vehicle is operated in a large, empty, and flat area during VVE while its localization and perception sensor data is fed from the virtual environment with other traffic and rare and extreme events being generated as needed. The virtual environment can be easily configured and modified to construct different testing scenarios on demand. This paper focuses on the VVE approach and introduces the coordinate transformations needed to sync pose (location and orientation) in the virtual and physical worlds and handling of localization and perception sensor data using the highly realistic 3D simulation model of a recent autonomous shuttle deployment site in Columbus, Ohio as the virtual world. As a further example that uses multiple actors, the use of VVE for VehicleToVRU communication based Vulnerable Road User (VRU) safety is presented in the paper using VVE experiments and real pedestrian(s) in a safe and repeatable manner. VVE experiments are used to demonstrate the efficacy of the method., Comment: 8 pages, 16 figures

The semiconductor industry's paradigm shift towards fabless integrated circuit (IC) manufacturing has introduced security threats, including piracy, counterfeiting, hardware Trojans, and overproduction. In response to these challenges, various countermeasures, including Logic locking (LL), have been proposed to protect designs and mitigate security risks. LL is likely the most researched form of intellectual property (IP) protection for ICs. A significant advance has been made with the introduction of compound logic locking (CLL), where two LL techniques are concurrently utilized for improved resiliency against attacks. However, the vulnerabilities of LL techniques, particularly CLL, need to be explored further. This paper presents a novel framework, RESAA, designed to classify CLL-locked designs, identify critical gates, and execute various attacks to uncover secret keys. RESAA is agnostic to specific LL techniques, offering comprehensive insights into CLL's security scenarios. Experimental results demonstrate RESAA's efficacy in identifying critical gates, distinguishing segments corresponding to different LL techniques, and determining associated keys based on different threat models. In particular, for the oracle-less threat model, RESAA can achieve up to 92.6% accuracy on a relatively complex ITC'99 benchmark circuit. The results reported in this paper emphasize the significance of evaluation and thoughtful selection of LL techniques, as all studied CLL variants demonstrated vulnerability to our framework. RESAA is also open-sourced for the community at large., Comment: 12 pages, IEEE Transaction format

Wireless communication is critical for the non-invasive in-situ monitoring of vital signs in deep tissues. Wireless ultrasonic links demonstrated so far solved the shortcomings of electromagnetic wave-based communication methods. However, they either require highly customized and complex designs for the implant electronics or rely on physical changes in implanted metamaterials. Here, we report a wireless, passive, frequency-based, and electronics-free ultrasonic communication method for deep tissue sensor implants. The device consists of a piezoelectric crystal used as the ultrasonic antenna, considerably simplifying the implant design, and can be integrated with any capacitive implantable sensor. We demonstrate the applicability of the passive communication method using a commercial pressure sensor at a depth of 5 cm with decent precision and accuracy.

Neural networks can fail when the data contains spurious correlations. To understand this phenomenon, researchers have proposed numerous spurious correlations benchmarks upon which to evaluate mitigation methods. However, we observe that these benchmarks exhibit substantial disagreement, with the best methods on one benchmark performing poorly on another. We explore this disagreement, and examine benchmark validity by defining three desiderata that a benchmark should satisfy in order to meaningfully evaluate methods. Our results have implications for both benchmarks and mitigations: we find that certain benchmarks are not meaningful measures of method performance, and that several methods are not sufficiently robust for widespread use. We present a simple recipe for practitioners to choose methods using the most similar benchmark to their given problem.

Advances in CAD and CAM have enabled engineers and design teams to digitally design parts with unprecedented ease. Software solutions now come with a range of modules for optimizing designs for performance requirements, generating instructions for manufacturing, and digitally tracking the entire process from design to procurement in the form of product life-cycle management tools. However, existing solutions force design teams and corporations to take a primarily serial approach where manufacturing and procurement decisions are largely contingent on design, rather than being an integral part of the design process. In this work, we propose a new approach to part making where design, manufacturing, and supply chain requirements and resources can be jointly considered and optimized. We present the Generative Manufacturing compiler that accepts as input the following: 1) An engineering part requirements specification that includes quantities such as loads, domain envelope, mass, and compliance, 2) A business part requirements specification that includes production volume, cost, and lead time, 3) Contextual knowledge about the current manufacturing state such as availability of relevant manufacturing equipment, materials, and workforce, both locally and through the supply chain. Based on these factors, the compiler generates and evaluates manufacturing process alternatives and the optimal derivative designs that are implied by each process, and enables a user guided iterative exploration of the design space. As part of our initial implementation of this compiler, we demonstrate the effectiveness of our approach on examples of a cantilever beam problem and a rocket engine mount problem and showcase its utility in creating and selecting optimal solutions according to the requirements and resources.

We specify a Turing machine $T_{\text{Mordell}}$ with the following properties. 1. On input $(K,C/K)$, with $K/\mathbb{Q}$ a number field and $C/K$ a smooth projective hyperbolic curve, if $T_{\text{Mordell}}$ terminates, then it outputs $C(K)$. 2. The Hodge, Tate, and Fontaine-Mazur conjectures imply that $T_{\text{Mordell}}$ always terminates. Similarly we specify a Turing machine $T_{\text{Shafarevich}}$ with the following properties. 1. On input $(g, K,S, d)$, with $g, d \in \mathbb{Z}^+$, $K/\mathbb{Q}$ a number field, and $S$ a finite set of places of $K$, if $T_{\text{Shafarevich}}$ terminates, then it outputs the finitely many polarized $g$-dimensional abelian varieties $A/K$, with polarization of degree $d$, having good reduction outside $S$. 2. The Hodge, Tate, and Fontaine-Mazur conjectures imply that $T_{\text{Shafarevich}}$ always terminates.

We provide a primal-dual framework for randomized approximation algorithms utilizing semidefinite programming (SDP) relaxations. Our framework pairs a continuum of APX-complete problems including MaxCut, Max2Sat, MaxDicut, and more generally, Max-Boolean Constraint Satisfaction and MaxQ (maximization of a positive semidefinite quadratic form over the hypercube) with new APX-complete problems which are stated as convex optimization problems with exponentially many variables. These new dual counterparts, based on what we call Grothendieck covers, range from fractional cut covering problems (for MaxCut) to tensor sign covering problems (for MaxQ). For each of these problem pairs, our framework transforms the randomized approximation algorithms with the best known approximation factors for the primal problems to randomized approximation algorithms for their dual counterparts with reciprocal approximation factors which are tight with respect to the Unique Games Conjecture. For each APX-complete pair, our algorithms solve a single SDP relaxation and generate feasible solutions for both problems which also provide approximate optimality certificates for each other. Our work utilizes techniques from areas of randomized approximation algorithms, convex optimization, spectral sparsification, as well as Chernoff-type concentration results for random matrices.

Designing for manufacturing poses significant challenges in part due to the computation bottleneck of Computer-Aided Manufacturing (CAM) simulations. Although deep learning as an alternative offers fast inference, its performance is dependently bounded by the need for abundant training data. Representation learning, particularly through pre-training, offers promise for few-shot learning, aiding in manufacturability tasks where data can be limited. This work introduces VIRL, a Volume-Informed Representation Learning approach to pre-train a 3D geometric encoder. The pretrained model is evaluated across four manufacturability indicators obtained from CAM simulations: subtractive machining (SM) time, additive manufacturing (AM) time, residual von Mises stress, and blade collisions during Laser Power Bed Fusion process. Across all case studies, the model pre-trained by VIRL shows substantial enhancements on demonstrating improved generalizability with limited data and superior performance with larger datasets. Regarding deployment strategy, case-specific phenomenon exists where finetuning VIRL-pretrained models adversely affects AM tasks with limited data but benefits SM time prediction. Moreover, the efficacy of Low-rank adaptation (LoRA), which balances between probing and finetuning, is explored. LoRA shows stable performance akin to probing with limited data, while achieving a higher upper bound than probing as data size increases, without the computational costs of finetuning. Furthermore, static normalization of manufacturing indicators consistently performs well across tasks, while dynamic normalization enhances performance when a reliable task dependent input is available.

Pseudocode in a scholarly paper provides a concise way to express the algorithms implemented therein. Pseudocode can also be thought of as an intermediary representation that helps bridge the gap between programming languages and natural languages. Having access to a large collection of pseudocode can provide various benefits ranging from enhancing algorithmic understanding, facilitating further algorithmic design, to empowering NLP or computer vision based models for tasks such as automated code generation and optical character recognition (OCR). We have created a large pseudocode collection by extracting nearly 320,000 pseudocode examples from arXiv papers. This process involved scanning over $2.2$ million scholarly papers, with 1,000 of them being manually inspected and labeled. Our approach encompasses an extraction mechanism tailored to optimize the coverage and a validation mechanism based on random sampling to check its accuracy and reliability, given the inherent heterogeneity of the collection. In addition, we offer insights into common pseudocode structures, supported by clustering and statistical analyses. Notably, these analyses indicate an exponential-like growth in the usage of pseudocodes, highlighting their increasing significance.

Recent research interest in the learning-based processing of garments, from virtual fitting to generation and reconstruction, stumbles on a scarcity of high-quality public data in the domain. We contribute to resolving this need by presenting the first large-scale synthetic dataset of 3D made-to-measure garments with sewing patterns, as well as its generation pipeline. GarmentCodeData contains 115,000 data points that cover a variety of designs in many common garment categories: tops, shirts, dresses, jumpsuits, skirts, pants, etc., fitted to a variety of body shapes sampled from a custom statistical body model based on CAESAR, as well as a standard reference body shape, applying three different textile materials. To enable the creation of datasets of such complexity, we introduce a set of algorithms for automatically taking tailor's measures on sampled body shapes, sampling strategies for sewing pattern design, and propose an automatic, open-source 3D garment draping pipeline based on a fast XPBD simulator, while contributing several solutions for collision resolution and drape correctness to enable scalability. Project Page: https://igl.ethz.ch/projects/GarmentCodeData/, Comment: Accepted to ECCV 2024. Sept 4th, 2024: release of GarmentCodeData(v2)

When a group acts on a set, it naturally partitions it into orbits, giving rise to orbit problems. These are natural algorithmic problems, as symmetries are central in numerous questions and structures in physics, mathematics, computer science, optimization, and more. Accordingly, it is of high interest to understand their computational complexity. Recently, B\"urgisser et al. gave the first polynomial-time algorithms for orbit problems of torus actions, that is, actions of commutative continuous groups on Euclidean space. In this work, motivated by theoretical and practical applications, we study the computational complexity of robust generalizations of these orbit problems, which amount to approximating the distance of orbits in $\mathbb{C}^n$ up to a factor $\gamma>1$. In particular, this allows deciding whether two inputs are approximately in the same orbit or far from being so. On the one hand, we prove the NP-hardness of this problem for $\gamma = n^{\Omega(1/\log\log n)}$ by reducing the closest vector problem for lattices to it. On the other hand, we describe algorithms for solving this problem for an approximation factor $\gamma = \exp(\mathrm{poly}(n))$. Our algorithms combine tools from invariant theory and algorithmic lattice theory, and they also provide group elements witnessing the proximity of the given orbits (in contrast to the algebraic algorithms of prior work). We prove that they run in polynomial time if and only if a version of the famous number-theoretic $abc$-conjecture holds -- establishing a new and surprising connection between computational complexity and number theory.

Reduced order modeling lowers the computational cost of solving PDEs by learning a low-order spatial representation from data and dynamically evolving these representations using manifold projections of the governing equations. While commonly used, linear subspace reduced-order models (ROMs) are often suboptimal for problems with a slow decay of Kolmogorov $n$-width, such as advection-dominated fluid flows at high Reynolds numbers. There has been a growing interest in nonlinear ROMs that use state-of-the-art representation learning techniques to accurately capture such phenomena with fewer degrees of freedom. We propose smooth neural field ROM (SNF-ROM), a nonlinear reduced modeling framework that combines grid-free reduced representations with Galerkin projection. The SNF-ROM architecture constrains the learned ROM trajectories to a smoothly varying path, which proves beneficial in the dynamics evaluation when the reduced manifold is traversed in accordance with the governing PDEs. Furthermore, we devise robust regularization schemes to ensure the learned neural fields are smooth and differentiable. This allows us to compute physics-based dynamics of the reduced system nonintrusively with automatic differentiation and evolve the reduced system with classical time-integrators. SNF-ROM leads to fast offline training as well as enhanced accuracy and stability during the online dynamics evaluation. Numerical experiments reveal that SNF-ROM is able to accelerate the full-order computation by up to $199\times$. We demonstrate the efficacy of SNF-ROM on a range of advection-dominated linear and nonlinear PDE problems where we consistently outperform state-of-the-art ROMs.

Data driven and learning based solutions for modeling dynamic garments have significantly advanced, especially in the context of digital humans. However, existing approaches often focus on modeling garments with respect to a fixed parametric human body model and are limited to garment geometries that were seen during training. In this work, we take a different approach and model the dynamics of a garment by exploiting its local interactions with the underlying human body. Specifically, as the body moves, we detect local garment-body collisions, which drive the deformation of the garment. At the core of our approach is a mesh-agnostic garment representation and a manifold-aware transformer network design, which together enable our method to generalize to unseen garment and body geometries. We evaluate our approach on a wide variety of garment types and motion sequences and provide competitive qualitative and quantitative results with respect to the state of the art., Comment: EUROGRAPHICS 2024. Project page: https://peizhuoli.github.io/manifold-aware-transformers/ Video: https://www.youtube.com/watch?v=v6FCTHmjyqI

Conventional trajectory planning approaches for autonomous racing are based on the sequential execution of prediction of the opposing vehicles and subsequent trajectory planning for the ego vehicle. If the opposing vehicles do not react to the ego vehicle, they can be predicted accurately. However, if there is interaction between the vehicles, the prediction loses its validity. For high interaction, instead of a planning approach that reacts exclusively to the fixed prediction, a trajectory planning approach is required that incorporates the interaction with the opposing vehicles. This paper demonstrates the limitations of a widely used conventional sampling-based approach within a highly interactive blocking scenario. We show that high success rates are achieved for less aggressive blocking behavior but that the collision rate increases with more significant interaction. We further propose a novel Reinforcement Learning (RL)-based trajectory planning approach for racing that explicitly exploits the interaction with the opposing vehicle without requiring a prediction. In contrast to the conventional approach, the RL-based approach achieves high success rates even for aggressive blocking behavior. Furthermore, we propose a novel safety layer (SL) that intervenes when the trajectory generated by the RL-based approach is infeasible. In that event, the SL generates a sub-optimal but feasible trajectory, avoiding termination of the scenario due to a not found valid solution., Comment: 8 pages, accepted to be published at the 27th IEEE International Conference on Intelligent Transportation Systems, September 24 - 27, 2024, Edmonton, Canada

A long-standing challenge is designing multi-scale structures with good connectivity between cells while optimizing each cell to reach close to the theoretical performance limit. We propose a new method for direct multi-scale topology optimization using neural networks. Our approach focuses on inverse homogenization that seamlessly maintains compatibility across neighboring microstructure cells. Our approach consists of a topology neural network that optimizes the microstructure shape and distribution across the design domain as a continuous field. Each microstructure cell is optimized based on a specified elasticity tensor that also accommodates in-plane rotations. The neural network takes as input the local coordinates within a cell to represent the density distribution within a cell, as well as the global coordinates of each cell to design spatially varying microstructure cells. As such, our approach models an n-dimensional multi-scale optimization problem as a 2n-dimensional inverse homogenization problem using neural networks. During the inverse homogenization of each unit cell, we extend the boundary of each cell by scaling the input coordinates such that the boundaries of neighboring cells are combined. Inverse homogenization on the combined cell improves connectivity. We demonstrate our method through the design and optimization of graded multi-scale structures.

Existing approaches to trajectory planning for autonomous racing employ sampling-based methods, generating numerous jerk-optimal trajectories and selecting the most favorable feasible trajectory based on a cost function penalizing deviations from an offline-calculated racing line. While successful on oval tracks, these methods face limitations on complex circuits due to the simplistic geometry of jerk-optimal edges failing to capture the complexity of the racing line. Additionally, they only consider two-dimensional tracks, potentially neglecting or surpassing the actual dynamic potential. In this paper, we present a sampling-based local trajectory planning approach for autonomous racing that can maintain the lap time of the racing line even on complex race tracks and consider the race track's three-dimensional effects. In simulative experiments, we demonstrate that our approach achieves lower lap times and improved utilization of dynamic limits compared to existing approaches. We also investigate the impact of online racing line generation, in which the time-optimal solution is planned from the current vehicle state for a limited spatial horizon, in contrast to a closed racing line calculated offline. We show that combining the sampling-based planner with the online racing line generation can significantly reduce lap times in multi-vehicle scenarios., Comment: 8 pages, accepted to be published at the 35th IEEE Intelligent Vehicles Symposium, June 2 - 5, 2024, Jeju Shinhwa World, Jeju Island, Korea

This study deals with certain harmonic zeta functions, one of them occurs in the study of the multiplication property of the harmonic Hurwitz zeta function. The values at the negative even integers are found and Laurent expansions at poles are described. Closed-form expressions are derived for the Stieltjes constants that occur in Laurent expansions in a neighborhood of s=1. Moreover, as a bonus, it is obtained that the values at the positive odd integers of three harmonic zeta functions can be expressed in closed-form evaluations in terms of zeta values and log-sine integrals.