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Ordinary differential equations (ODEs) are foundational in modeling intricate dynamics across a gamut of scientific disciplines. Yet, a possibility to represent a single phenomenon through multiple ODE models, driven by different understandings of nuances in internal mechanisms or abstraction levels, presents a model selection challenge. This study introduces a testing-based approach for ODE model selection amidst statistical noise. Rooted in the model misspecification framework, we adapt foundational insights from classical statistical paradigms (Vuong and Hotelling) to the ODE context, allowing for the comparison and ranking of diverse causal explanations without the constraints of nested models. Our simulation studies validate the theoretical robustness of our proposed test, revealing its consistent size and power. Real-world data examples further underscore the algorithm's applicability in practice. To foster accessibility and encourage real-world applications, we provide a user-friendly Python implementation of our model selection algorithm, bridging theoretical advancements with hands-on tools for the scientific community.

Tackling unfairness in graph learning models is a challenging task, as the unfairness issues on graphs involve both attributes and topological structures. Existing work on fair graph learning simply assumes that attributes of all nodes are available for model training and then makes fair predictions. In practice, however, the attributes of some nodes might not be accessible due to missing data or privacy concerns, which makes fair graph learning even more challenging. In this paper, we propose FairAC, a fair attribute completion method, to complement missing information and learn fair node embeddings for graphs with missing attributes. FairAC adopts an attention mechanism to deal with the attribute missing problem and meanwhile, it mitigates two types of unfairness, i.e., feature unfairness from attributes and topological unfairness due to attribute completion. FairAC can work on various types of homogeneous graphs and generate fair embeddings for them and thus can be applied to most downstream tasks to improve their fairness performance. To our best knowledge, FairAC is the first method that jointly addresses the graph attribution completion and graph unfairness problems. Experimental results on benchmark datasets show that our method achieves better fairness performance with less sacrifice in accuracy, compared with the state-of-the-art methods of fair graph learning. Code is available at: //github.com/donglgcn/FairAC.

We develop a new class of spatial voting models for binary preference data that can accommodate both monotonic and non-monotonic response functions, and are more flexible than alternative "unfolding" models previously introduced in the literature. We then use these models to estimate revealed preferences for legislators in the U.S. House of Representatives and justices on the U.S. Supreme Court. The results from these applications indicate that the new models provide superior complexity-adjusted performance to various alternatives and also that the additional flexibility leads to preferences' estimates that are closer matches to the perceived ideological positions of legislators and justices.

Unlike conventional grid and mesh based methods for solving partial differential equations (PDEs), neural networks have the potential to break the curse of dimensionality, providing approximate solutions to problems where using classical solvers is difficult or impossible. While global minimization of the PDE residual over the network parameters works well for boundary value problems, catastrophic forgetting impairs the applicability of this approach to initial value problems (IVPs). In an alternative local-in-time approach, the optimization problem can be converted into an ordinary differential equation (ODE) on the network parameters and the solution propagated forward in time; however, we demonstrate that current methods based on this approach suffer from two key issues. First, following the ODE produces an uncontrolled growth in the conditioning of the problem, ultimately leading to unacceptably large numerical errors. Second, as the ODE methods scale cubically with the number of model parameters, they are restricted to small neural networks, significantly limiting their ability to represent intricate PDE initial conditions and solutions. Building on these insights, we develop Neural IVP, an ODE based IVP solver which prevents the network from getting ill-conditioned and runs in time linear in the number of parameters, enabling us to evolve the dynamics of challenging PDEs with neural networks.

In answer set programming (ASP), answer sets capture solutions to search problems of interest and thus the efficient computation of answer sets is of utmost importance. One viable implementation strategy is provided by translation-based ASP where logic programs are translated into other KR formalisms such as Boolean satisfiability (SAT), SAT modulo theories (SMT), and mixed-integer programming (MIP). Consequently, existing solvers can be harnessed for the computation of answer sets. Many of the existing translations rely on program completion and level rankings to capture the minimality of answer sets and default negation properly. In this work, we take level ranking constraints into reconsideration, aiming at their generalizations to cover aggregate-based extensions of ASP in more systematic way. By applying a number of program transformations, ranking constraints can be rewritten in a general form that preserves the structure of monotone and convex aggregates and thus offers a uniform basis for their incorporation into translation-based ASP. The results open up new possibilities for the implementation of translators and solver pipelines in practice.

When applying deep learning to remote sensing data in archaeological research, a notable obstacle is the limited availability of suitable datasets for training models. The application of transfer learning is frequently employed to mitigate this drawback. However, there is still a need to explore its effectiveness when applied across different archaeological datasets. This paper compares the performance of various transfer learning configurations using two semantic segmentation deep neural networks on two LiDAR datasets. The experimental results indicate that transfer learning-based approaches in archaeology can lead to performance improvements, although a systematic enhancement has not yet been observed. We provide specific insights about the validity of such techniques that can serve as a baseline for future works.

The quantum alternating operator ansatz (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to combinatorial optimization problems, such as Maximum Satisfiability. While QAOA is well-studied, theoretical results as to its runtime or approximation ratio guarantees are still relatively sparse. We provide some of the first lower bounds for the number of rounds (the dominant component of QAOA runtimes) required for QAOA. For our main result, (i) we leverage a connection between quantum annealing times and the angles of QAOA to derive a lower bound on the number of rounds of QAOA with respect to the guaranteed approximation ratio. We apply and calculate this bound with Grover-style mixing unitaries and (ii) show that this type of QAOA requires at least a polynomial number of rounds to guarantee any constant approximation ratios for most problems. We also (iii) show that the bound depends only on the statistical values of the objective functions, and when the problem can be modeled as a $k$-local Hamiltonian, can be easily estimated from the coefficients of the Hamiltonians. For the conventional transverse field mixer, (iv) our framework gives a trivial lower bound to all bounded occurrence local cost problems and all strictly $k$-local cost Hamiltonians matching known results that constant approximation ratio is obtainable with constant round QAOA for a few optimization problems from these classes. Using our novel proof framework, (v) we recover the Grover lower bound for unstructured search and -- with small modification -- show that our bound applies to any QAOA-style search protocol that starts in the ground state of the mixing unitaries.

Dynamically scheduled high-level synthesis (HLS) achieves higher throughput than static HLS for codes with unpredictable memory accesses and control flow. However, excessive dataflow scheduling results in circuits that use more resources and have a slower critical path, even when only a part of the circuit exhibits dynamic behavior. Recent work has shown that marking parts of a dataflow circuit for static scheduling can save resources and improve performance (hybrid scheduling), but the dynamic part of the circuit still bottlenecks the critical path. We propose instead to selectively introduce dynamic scheduling into static HLS. This paper presents an algorithm for identifying code regions amenable to dynamic scheduling and shows a methodology for introducing dynamically scheduled basic blocks, loops, and memory operations into static HLS. Our algorithm is informed by modulo-scheduling and can be integrated into any modulo-scheduled HLS tool. On a set of ten benchmarks, we show that our approach achieves on average an up to 3.7$\times$ and 3$\times$ speedup against dynamic and hybrid scheduling, respectively, with an area overhead of 1.3$\times$ and frequency degradation of 0.74$\times$ when compared to static HLS.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.