In a neural network with ReLU activations, the number of piecewise linear regions in the output can grow exponentially with depth. However, this is highly unlikely to happen when the initial parameters are sampled randomly, which therefore often leads to the use of networks that are unnecessarily large. To address this problem, we introduce a novel parameterization of the network that restricts its weights so that a depth $d$ network produces exactly $2^d$ linear regions at initialization and maintains those regions throughout training under the parameterization. This approach allows us to learn approximations of convex, one-dimensional functions that are several orders of magnitude more accurate than their randomly initialized counterparts. We further demonstrate a preliminary extension of our construction to multidimensional and non-convex functions, allowing the technique to replace traditional dense layers in various architectures.

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these classical domains and numerically examine their suitability for and performance on this problem. Our methods are evaluated on single-qubit systems as well as on larger systems. While the first part of our proposed method outputs a single unitary matrix representing the composite effects of a quantum circuit or algorithm, we use existing tools—and assess the performance of these—to factor such a matrix into a product of elementary quantum gates. This enables our pipeline to be truly end-to-end: starting from desired input/output examples, our code ultimately results in a quantum circuit diagram. The code implementation is publicly available at https://github.com/DABH/qule .

We present a novel, physically-based morphing technique for elastic shapes, leveraging the differentiable material point method (MPM) with space-time control through per-particle deformation gradients to accommodate complex topology changes. This approach, grounded in MPM's natural handling of dynamic topologies, is enhanced by a chained iterative optimization technique, allowing for the creation of both succinct and extended morphing sequences that maintain coherence over time. Demonstrated across various challenging scenarios, our method is able to produce detailed elastic deformation and topology transitions, all grounded within our physics-based simulation framework.

Forecasting companies’ financial metrics, such as profit or revenue, from textual data is typically heuristic and subjective due to the qualitative nature of business models and data. However, this paper shows that these metrics can be predicted with surprising accuracy using only a textual description of a company’s business and public data from peer companies using our novel framework CUBAN (Contextual Understanding of Business performance through Analysis of Neighboring companies). We introduce a multimodal transformer model with an annotation-gating mechanism that effectively integrates textual context with financial statements. Trained on 10-K reports from public companies since 2000, our model predicts the future log revenue and operating profit from descriptions of a company’s business and those of its peers (along with peer financial data), achieving a correlation coefficient (Pearson’s R) of 0.78 for log revenue prediction and a 79% F1-score for operating profit classification, demonstrating its efficacy in forecasting financial performance from primarily qualitative data.

Abstract The creation of a volumetric mesh representing the interior of an input polygonal mesh is a common requirement in graphics and computational mechanics applications. Most mesh creation techniques assume that the input surface is not self‐intersecting. However, due to numerical and/or user error, input surfaces are commonly self‐intersecting to some degree. The removal of self‐intersection is a burdensome task that complicates workflow and generally slows down the process of creating simulation‐ready digital assets. We present a method for the creation of a volumetric embedding hexahedron mesh from a self‐intersecting input triangle mesh. Our method is designed for efficiency by minimizing use of computationally expensive exact/adaptive precision arithmetic. Although our approach allows for nearly no limit on the degree of self‐intersection in the input surface, our focus is on efficiency in the most common case: many minimal self‐intersections. The embedding hexahedron mesh is created from a uniform background grid and consists of hexahedron elements that are geometrical copies of grid cells. Multiple copies of a single grid cell are used to resolve regions of self‐intersection/overlap. Lastly, we develop a novel topology‐aware embedding mesh coarsening technique to allow for user‐specified mesh resolution as well as a topology‐aware tetrahedralization of the hexahedron mesh.

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. Motivated by the conjugate gradients algorithm that iteratively selects search directions for minimizing the matrix norm of the approximation error, we design an approach that utilizes a deep neural network to accelerate convergence via data-driven improvement of the search direction at each iteration. Our method leverages a carefully chosen convolutional network to approximate the action of the inverse of the linear operator up to an arbitrary constant. We demonstrate the efficacy of our approach on spatially discretized Poisson equations, which arise in computational fluid dynamics applications, with millions of degrees of freedom. Unlike state-of-the-art learning approaches, our algorithm is capable of reducing the linear system residual to a given tolerance in a small number of iterations, independent of the problem size. Moreover, our method generalizes effectively to various systems beyond those encountered during training.

We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based on the surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with a novel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with Affine-Particle-In-Cell (APIC) [Jiang et al. 2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects, such as water, wine and wax.

Koopman operator theory, applied via numerical techniques such as dynamic mode decomposition (DMD) and autoencoders, has recently emerged as an interesting mathematical framework for understanding how complex, high-dimensional dynamical systems evolve. In this paper, we apply several DMD and autoencoder algorithms to a dataset of gang involvement and activity to assess the effectiveness City of Los Angeles Mayor's Office of Gang Reduction and Youth Development's (GRYD) Intervention Family Case Management Program. We compare various subsets of the data to explore differences in sub-populations. We then control for different covariates in our analysis of dynamical changes in population characteristics over time. Statistically significant results suggest the efficacy of the GRYD FCM Program.

We study a recent dataset documenting the nature of gang involvement among 14-25 year-olds participating in the Los Angeles Mayor's Office of Gang Reduction and Youth Development (GRYD) Intervention Family Case Management Program. We use natural language processing techniques, including emotion classification and textual clustering, to perform quantitative analyses of free-form responses in the data. These analyses yield insights into the effectiveness of the program and provide a better understanding of its participants. We also compare several computational techniques and remark on their relative effectiveness in application to this dataset.

Autonomous vehicle system performance is limited by uncertainties inherent in the driving environment and challenges in processing sensor data. Engineers thus face the design decision of biasing systems toward lower sensitivity to potential threats (more misses) or higher sensitivity (more false alarms). We explored this problem for Automatic Emergency Braking systems in Level 3 autonomous vehicles, where the driver is required to monitor the system for failures. Participants (N=48) drove through a simulated suburban environment and experienced detection misses, perfect performance, or false alarms. We found that driver vigilance was greater for less-sensitive braking systems, resulting in improved performance during a potentially fatal failure. In addition, regardless of system bias, greater levels of autonomy resulted in significantly worse driver performance. Our results demonstrate that accounting for the effects of system bias on driver vigilance and performance will be critical design considerations as vehicle autonomy levels increase.

Autonomous vehicle systems and their users need to collaborate to navigate the driving environment, particularly during an unstructured transition of control from automation, when the system releases control and expects the human to immediately assume driving responsibility. We investigated how such transitions affect the user's trust in the system and subsequent performance. In a full-vehicle driving simulator, participants encountered two system failures: the first varied in severity (mild or severe failure), and the second required a transition of control that was either detected and alerted (loud failure) or not (silent failure). We observed (i) significant changes in user trust in the system over time and between events, and (ii) that the first failure's severity level did not affect user performance in the subsequent failure; rather, the system's detection and alert both times was sufficient to successfully complete the transition of control.

Abstract We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle‐based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid‐based advection in other regions of the flow. A novel Backward Semi‐Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C1 continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B‐spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut‐cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.

We present an updated Lagrangian discretization of surface tension forces for the simulation of liquids with moderate to extreme surface tension effects. The potential energy associated with surface tension is proportional to the surface area of the liquid. We design discrete forces as gradients of this energy with respect to the motion of the fluid over a time step. We show that this naturally allows for inversion of the Hessian of the potential energy required with the use of Newton's method to solve the systems of nonlinear equations associated with implicit time stepping. The rotational invariance of the surface tension energy makes it non-convex and we define a definiteness fix procedure as in [Teran et al. 2005]. We design a novel level-set-based boundary quadrature technique to discretize the surface area calculation in our energy based formulation. Our approach works most naturally with Particle-In-Cell [Harlow 1964] techniques and we demonstrate our approach with a weakly incompressible model for liquid discretized with the Material Point Method [Sulsky et al. 1994]. We show that our approach is essential for allowing efficient implicit numerical integration in the limit of high surface tension materials like liquid metals.

We propose a novel framework for hair animation as well as hair-water interaction that supports millions of hairs. First, we develop a hair animation framework that embeds hair into a tetrahedralized volume mesh that we kinematically skin to deform and follow the exterior of an animated character. Allowing the hairs to follow their precomputed embedded locations in the kinematically deforming skinned mesh already provides visually plausible behavior. Creating a copy of the tetrahedral mesh, endowing it with springs, and attaching it to the kinematically skinned mesh creates more dynamic behavior. Notably, the springs can be quite weak and thus efficient to simulate because they are structurally supported by the kinematic mesh. If independent simulation of individual hairs or guide hairs is desired, they too benefit from being anchored to the kinematic mesh dramatically increasing efficiency as weak springs can be used while still supporting interesting and dramatic hairstyles. Furthermore, we explain how to embed these dynamic simulations into the kinematically deforming skinned mesh so that they can be used as part of a blendshape system where an artist can make many subsequent iterations without requiring any additional simulation. Although there are many applications for our newly proposed approach to hair animation, we mostly focus on the particularly challenging problem of hair-water interaction. While doing this, we discuss how porosities are stored in the kinematic mesh, how the kinematically deforming mesh can be used to apply drag and adhesion forces to the water, etc.

We present FRC, a high-performance concurrent parallel reference counter for unmanaged languages. It is well known that high-performance garbage collectors help developers write memory-safe, highly concurrent systems and data structures. While C++, C, and other unmanaged languages are used in high-performance applications, adding concurrent memory management to these languages has proven to be difficult. Unmanaged languages like C++ use pointers instead of references, and have uncooperative mutators which do not pause easily at a safe point. Thus, scanning mutator stack root references is challenging.

Abstract This paper describes a general algorithm and a system for load balancing sparse fluid simulations. Automatically distributing sparse fluid simulations efficiently is challenging because the computational load varies across the simulation domain and time. A key challenge with load balancing is that optimal decision making requires knowing the fluid distribution across partitions for future time steps, but computing this state for an arbitrary simulation requires running the simulation itself. The key insight of this paper is that it is possible to predict future load by running a speculative low resolution simulation in parallel. We mathematically formulate the problem of load balancing over multiple time steps and present a polynomial time algorithm to compute an approximate solution to it. Our experimental results show that distributing and speculatively load balancing sparse FLIP simulations over 8 nodes speeds them up by 5.3× to 7.9×, and that speculative load balancing generates assignments that perform within 20% of optimal.