We relate the problem of computing pointwise robustness of these networks to that of computing the maximum norm ball with a fixed center that can be contained in a non-convex polytope. This isachallenging problem ingeneral, howeverweshowthat there exists an efficient algorithm to compute this for polyhedral complices. Further we show that piecewise linear neural networks partition the input space into a polyhedralcomplex.

Thehandwritten digits are written by 500 writers (250 writers for training and test set, respectively), introducing a largevariation interms ofstyleofthesecharacters.

Cutting-planes are one of the most important building blocks for solving large-scale integer programming (IP) problems to (near) optimality. The majority of cutting plane approaches rely on explicit rules to derive valid inequalities that can separate the target point from the feasible set. Local cuts, on the other hand, seek to directly derive the facets of the underlying polyhedron and use them as cutting planes. However, current approaches rely on solving Linear Programming (LP) problems in order to derive such a hyperplane. In this paper, we present a novel generic approach for learning the facets of the underlying polyhedron by accessing it implicitly via an enumeration oracle in a reduced dimension. This is achieved by embedding the oracle in a variant of the Frank-Wolfe algorithm which is capable of generating strong cutting planes, effectively turning the enumeration oracle into a separation oracle. We demonstrate the effectiveness of our approach with a case study targeting the multidimensional knapsack problem (MKP).

Working memory (WM), a fundamental cognitive process facilitating the temporary storage, integration, manipulation, and retrieval of information, plays a vital role in reasoning and decision-making tasks. Robust benchmark datasets that capture the multifaceted nature of WM are crucial for the effective development and evaluation of AI WM models. Here, we introduce a comprehensive Working Memory (WorM) benchmark dataset for this purpose. WorM comprises 10 tasks and a total of 1 million trials, assessing 4 functionalities, 3 domains, and 11 behavioral and neural characteristics of WM. We jointly trained and tested state-of-the-art recurrent neural networks and transformers on all these tasks. We also include human behavioral benchmarks as an upper bound for comparison. Our results suggest that AI models replicate some characteristics of WM in the brain, most notably primacy and recency effects, and neural clusters and correlates specialized for different domains and functionalities of WM. In the experiments, we also reveal some limitations in existing models to approximate human behavior. This dataset serves as a valuable resource for communities in cognitive psychology, neuroscience, and AI, offering a standardized framework to compare and enhance WM models, investigate WM's neural underpinnings, and develop WM models with human-like capabilities.

In AI research and practice, rigor remains largely understood in terms of methodological rigor -- such as whether mathematical, statistical, or computational methods are correctly applied. We argue that this narrow conception of rigor has contributed to the concerns raised by the responsible AI community, including overblown claims about the capabilities of AI systems. Our position is that a broader conception of what rigorous AI research and practice should entail is needed. We believe such a conception -- in addition to a more expansive understanding of (1) methodological rigor -- should include aspects related to (2) what background knowledge informs what to work on (epistemic rigor); (3) how disciplinary, community, or personal norms, standards, or beliefs influence the work (normative rigor); (4) how clearly articulated the theoretical constructs under use are (conceptual rigor); (5) what is reported and how (reporting rigor); and (6) how well-supported the inferences from existing evidence are (interpretative rigor). In doing so, we also provide useful language and a framework for much-needed dialogue about the AI community's work by researchers, policymakers, journalists, and other stakeholders.

Current state-of-the-art solutions for motion capture from a single camera are optimization driven: they optimize the parameters of a 3D human model so that its re-projection matches measurements in the video (e.g.

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