How capable are large language models (LLMs) in the domain of taxation? Although numerous studies have explored the legal domain in general, research dedicated to taxation remain scarce. Moreover, the datasets used in these studies are either simplified, failing to reflect the real-world complexities, or unavailable as open source. To address this gap, we introduce PLAT, a new benchmark designed to assess the ability of LLMs to predict the legitimacy of additional tax penalties. PLAT is constructed to evaluate LLMs' understanding of tax law, particularly in cases where resolving the issue requires more than just applying related statutes. Our experiments with six LLMs reveal that their baseline capabilities are limited, especially when dealing with conflicting issues that demand a comprehensive understanding. However, we found that enabling retrieval, self-reasoning, and discussion among multiple agents with specific role assignments, this limitation can be mitigated.

Physics-Informed Neural Networks (PINNs) solve partial differential equations (PDEs) by embedding governing equations and boundary/initial conditions into the loss function. However, enforcing Dirichlet boundary conditions accurately remains challenging, often leading to soft enforcement that compromises convergence and reliability in complex domains. We propose a hybrid approach, PINN-FEM, which combines PINNs with finite element methods (FEM) to impose strong Dirichlet boundary conditions via domain decomposition. This method incorporates FEM-based representations near the boundary, ensuring exact enforcement without compromising convergence. Through six experiments of increasing complexity, PINN-FEM outperforms standard PINN models, showcasing superior accuracy and robustness. While distance functions and similar techniques have been proposed for boundary condition enforcement, they lack generality for real-world applications. PINN-FEM bridges this gap by leveraging FEM near boundaries, making it well-suited for industrial and scientific problems.

Hamilton-Jacobi (HJ) reachability analysis is a verification tool that provides safety and performance guarantees for autonomous systems. It is widely adopted because of its ability to handle nonlinear dynamical systems with bounded adversarial disturbances and constraints on states and inputs. However, it involves solving a PDE to compute a safety value function, whose computational and memory complexity scales exponentially with the state dimension, making its direct usage in large-scale systems intractable. Recently, a learning-based approach called DeepReach, has been proposed to approximate high-dimensional reachable tubes using neural networks. While DeepReach has been shown to be effective, the accuracy of the learned solution decreases with the increase in system complexity. One of the reasons for this degradation is the inexact imposition of safety constraints during the learning process, which corresponds to the PDE's boundary conditions. Specifically, DeepReach imposes boundary conditions as soft constraints in the loss function, which leaves room for error during the value function learning. Moreover, one needs to carefully adjust the relative contributions from the imposition of boundary conditions and the imposition of the PDE in the loss function. This, in turn, induces errors in the overall learned solution. In this work, we propose a variant of DeepReach that exactly imposes safety constraints during the learning process by restructuring the overall value function as a weighted sum of the boundary condition and neural network output. This eliminates the need for a boundary loss during training, thus bypassing the need for loss adjustment. We demonstrate the efficacy of the proposed approach in significantly improving the accuracy of learned solutions for challenging high-dimensional reachability tasks, such as rocket-landing and multivehicle collision-avoidance problems.

In robotic deformable object manipulation (DOM) applications, constraints arise commonly from environments and task-specific requirements. Enabling DOM with constraints is therefore crucial for its deployment in practice. However, dealing with constraints turns out to be challenging due to many inherent factors such as inaccessible deformation models of deformable objects (DOs) and varying environmental setups. This article presents a systematic manipulation framework for DOM subject to constraints by proposing a novel path set planning and tracking scheme. First, constrained DOM tasks are formulated into a versatile optimization formalism which enables dynamic constraint imposition. Because of the lack of the local optimization objective and high state dimensionality, the formulated problem is not analytically solvable. To address this, planning of the path set, which collects paths of DO feedback points, is proposed subsequently to offer feasible path and motion references for DO in constrained setups. Both theoretical analyses and computationally efficient algorithmic implementation of path set planning are discussed. Lastly, a control architecture combining path set tracking and constraint handling is designed for task execution. The effectiveness of our methods is validated in a variety of DOM tasks with constrained experimental settings.

As future musical AIs adhere closely to human music, they may form their own attachments to particular human artists in their databases, and these biases may in the worst case lead to potential existential threats to all musical history. AI super fans may act to corrupt the historical record and extant recordings in favour of their own preferences, and preservation of the diversity of world music culture may become even more of a pressing issue than the imposition of 12 tone equal temperament or other Western homogenisations. We discuss the technical capability of AI cover software and produce Taylor's Versions of famous tracks from Western pop history as provocative examples; the quality of these productions does not affect the overall argument (which might even see a future AI try to impose the sound of paperclips onto all existing audio files, let alone Taylor Swift). We discuss some potential defenses against the danger of future musical monopolies, whilst analysing the feasibility of a maximal 'Taylor Swiftication' of the complete musical record.

We present a simple argument using Promise Theory and dimensional analysis for the Dunbar scaling hierarchy, supported by recent data from group formation in Wikipedia editing. We show how the assumption of a common priority seeds group alignment until the costs associated with attending to the group outweigh the benefits in a detailed balance scenario. Subject to partial efficiency of implementing promised intentions, we can reproduce a series of compatible rates that balance growth with entropy.

Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function. While PINNs are successfully used for solving forward and inverse problems, their accuracy decreases significantly for parameterized systems. PINNs also have a soft implementation of boundary conditions resulting in boundary conditions not being exactly imposed everywhere on the boundary. With these challenges at hand, we present first-order physics-informed neural networks (FO-PINNs). These are PINNs that are trained using a first-order formulation of the PDE loss function. We show that, compared to standard PINNs, FO-PINNs offer significantly higher accuracy in solving parameterized systems, and reduce time-per-iteration by removing the extra backpropagations needed to compute the second or higher-order derivatives. Additionally, FO-PINNs can enable exact imposition of boundary conditions using approximate distance functions, which pose challenges when applied on high-order PDEs. Through three examples, we demonstrate the advantages of FO-PINNs over standard PINNs in terms of accuracy and training speedup.

Top South African data scientists are solving critical challenges in society and making their mark on the global industry. From deliveries to cyber security, advanced analytics is driving change; but it's the leading thinkers behind these solutions that are really impressive. If you've ordered a delivery from South Africa's largest on-demand grocery delivery service, the driver's route was optimised by a "travelling salesman" algorithm that Kimberly Taylor originally developed as a Wits engineering student. She has since built a company and an award-winning app around this innovation which helps logistics companies scale their delivery volume. Multi-stop route optimisation is critical for perishable deliveries and through Taylor's solution, data science is helping on-demand delivery companies in the Quick Service Restaurant and grocery space keep their promise of 30 60 minutes.

The year is 2029, and you wake up one morning living in a community called Hope, a dystopian dictatorship. "Everyone here wears the same outfit, lives the same repetitive routine, and is happy … For many, Hope is their entire universe. They are uninterested in the outside world. However, you are different--you have the ability to choose." This is how you are introduced to the game Name of the Will on Kickstarter.

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in $\mathbb{R}^{n_1 \times n_2 \times \cdots \times n_d}$. This work focuses on the task of estimating the regression tensor from $m$ realizations of the response variable and the predictors where $m\ll n = \prod \nolimits_{i} n_i$. Despite the ill-posedness of this estimation problem, it can still be solved if the parameter tensor belongs to the space of sparse, low Tucker-rank tensors. Accordingly, the estimation procedure is posed as a non-convex optimization program over the space of sparse, low Tucker-rank tensors, and a tensor variant of projected gradient descent is proposed to solve the resulting non-convex problem. In addition, mathematical guarantees are provided that establish the proposed method converges to the correct solution under the right set of conditions. Further, an upper bound on sample complexity of tensor parameter estimation for the model under consideration is characterized for the special case when the individual (scalar) predictors independently draw values from a sub-Gaussian distribution. The sample complexity bound is shown to have a polylogarithmic dependence on $\bar{n} = \max \big\{n_i: i\in \{1,2,\ldots,d \} \big\}$ and, orderwise, it matches the bound one can obtain from a heuristic parameter counting argument. Finally, numerical experiments demonstrate the efficacy of the proposed tensor model and estimation method on a synthetic dataset and a neuroimaging dataset pertaining to attention deficit hyperactivity disorder. Specifically, the proposed method exhibits better sample complexities on both synthetic and real datasets, demonstrating the usefulness of the model and the method in settings where $n \gg m$.