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Programs involving discontinuities introduced by control flow constructs such as conditional branches pose challenges to mathematical optimization methods that assume a degree of smoothness in the objective function's response surface. Smooth interpretation (SI) is a form of abstract interpretation that approximates the convolution of a program's output with a Gaussian kernel, thus smoothing its output in a principled manner. Here, we combine SI with automatic differentiation (AD) to efficiently compute gradients of smoothed programs. In contrast to AD across a regular program execution, these gradients also capture the effects of alternative control flow paths. The combination of SI with AD enables the direct gradient-based parameter synthesis for branching programs, allowing for instance the calibration of simulation models or their combination with neural network models in machine learning pipelines. We detail the effects of the approximations made for tractability in SI and propose a novel Monte Carlo estimator that avoids the underlying assumptions by estimating the smoothed programs' gradients through a combination of AD and sampling. Using DiscoGrad, our tool for automatically translating simple C++ programs to a smooth differentiable form, we perform an extensive evaluation. We compare the combination of SI with AD and our Monte Carlo estimator to existing gradient-free and stochastic methods on four non-trivial and originally discontinuous problems ranging from classical simulation-based optimization to neural network-driven control. While the optimization progress with the SI-based estimator depends on the complexity of the program's control flow, our Monte Carlo estimator is competitive in all problems, exhibiting the fastest convergence by a substantial margin in our highest-dimensional problem.

In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient search process would benefit from increased opportunities to explore promising regions where global optima or good local optima are situated. In this paper, we introduce a novel robust evolutionary algorithm named the dual-stage robust evolutionary algorithm (DREA) aimed at discovering robust solutions. DREA operates in two stages: the peak-detection stage and the robust solution-searching stage. The primary objective of the peak-detection stage is to identify peaks in the fitness landscape of the original optimization problem. Conversely, the robust solution-searching stage focuses on swiftly identifying the robust optimal solution using information obtained from the peaks discovered in the initial stage. These two stages collectively enable the proposed DREA to efficiently obtain the robust optimal solution for the optimization problem. This approach achieves a balance between solution optimality and robustness by separating the search processes for optimal and robust optimal solutions. Experimental results demonstrate that DREA significantly outperforms five state-of-the-art algorithms across 18 test problems characterized by diverse complexities. Moreover, when evaluated on higher-dimensional robust optimization problems (100-$D$ and 200-$D$), DREA also demonstrates superior performance compared to all five counterpart algorithms.

We study the following combinatorial problem. Given a set of $n$ y-monotone curves, which we call wires, a tangle determines the order of the wires on a number of horizontal layers such that any two consecutive layers differ only in swaps of neighboring wires. Given a multiset $L$ of swaps (that is, unordered pairs of wires) and an initial order of the wires, a tangle realizes $L$ if each pair of wires changes its order exactly as many times as specified by $L$. Deciding whether a given multiset of swaps admits a realizing tangle is known to be NP-hard [Yamanaka et al., CCCG 2018]. We prove that this problem remains NP-hard if every pair of wires swaps only a constant number of times. On the positive side, we improve the runtime of a previous exponential-time algorithm. We also show that the problem is in NP and fixed-parameter tractable with respect to the number of wires.

We introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper bound of the quantum entropy. Additionally, we present the Araki relative entropy for bimodule quantum channels, revealing its equivalence to the relative entropy for Fourier multipliers and demonstrating its left/right monotonicities and convexity. Notably, the quantum entropy attains its maximum if there is a downward Jones basic construction. By considering R\'{e}nyi entropy for Fourier multipliers, we find a continuous bridge between the logarithm of the Pimsner-Popa index and the Pimsner-Popa entropy. As a consequence, the R\'{e}nyi entropy at $1/2$ serves a criterion for the existence of a downward Jones basic construction.

Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von Neumann's bilinear minimax theorem. As in the bilinear case, the proof is based on relating the underlying optimizations to a primal-dual pair of linear programming problems, albeit more complicated LPs. The theorem together with its proof is of independent interest. Next, we use the theorem to associate to a multilinear form in NE a {\it multilinear minimax relaxation} (MMR), where the primal-dual pair of solutions induce an approximate equilibrium point that provides a nontrivial upper bound on a convex combination of {\it expected payoffs} in any NE solution. In fact we show any positive probability vector associated to the players induces a corresponding {\it diagonally-scaled} MMR approximate equilibrium with its associated upper bound. By virtue of the proof of the multilinear minimax theorem, MMR solution can be computed in polynomial-time. On the other hand, it is known that even in bimatrix games NE is {\it PPAD-complete}, a complexity class in NP not known to be in P. The quality of MMR solution and the efficiency of solving the underlying LPs are the subject of further investigation. However, as shown in a separate article, for a large set of test problems in bimatrix games, not only the MMR payoffs for both players are better than any NE payoffs, so is the computing time of MMR in contrast with that of Lemke-Howsen algorithm. In large size problems the latter algorithm even fails to produce a Nash equilibrium. In summary, solving MMR provides a worthy approximation even if Nash equilibrium is shown to be computable in polynomial-time.

Contrastive learning models have achieved great success in unsupervised visual representation learning, which maximize the similarities between feature representations of different views of the same image, while minimize the similarities between feature representations of views of different images. In text summarization, the output summary is a shorter form of the input document and they have similar meanings. In this paper, we propose a contrastive learning model for supervised abstractive text summarization, where we view a document, its gold summary and its model generated summaries as different views of the same mean representation and maximize the similarities between them during training. We improve over a strong sequence-to-sequence text generation model (i.e., BART) on three different summarization datasets. Human evaluation also shows that our model achieves better faithfulness ratings compared to its counterpart without contrastive objectives.

Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.

Behaviors of the synthetic characters in current military simulations are limited since they are generally generated by rule-based and reactive computational models with minimal intelligence. Such computational models cannot adapt to reflect the experience of the characters, resulting in brittle intelligence for even the most effective behavior models devised via costly and labor-intensive processes. Observation-based behavior model adaptation that leverages machine learning and the experience of synthetic entities in combination with appropriate prior knowledge can address the issues in the existing computational behavior models to create a better training experience in military training simulations. In this paper, we introduce a framework that aims to create autonomous synthetic characters that can perform coherent sequences of believable behavior while being aware of human trainees and their needs within a training simulation. This framework brings together three mutually complementary components. The first component is a Unity-based simulation environment - Rapid Integration and Development Environment (RIDE) - supporting One World Terrain (OWT) models and capable of running and supporting machine learning experiments. The second is Shiva, a novel multi-agent reinforcement and imitation learning framework that can interface with a variety of simulation environments, and that can additionally utilize a variety of learning algorithms. The final component is the Sigma Cognitive Architecture that will augment the behavior models with symbolic and probabilistic reasoning capabilities. We have successfully created proof-of-concept behavior models leveraging this framework on realistic terrain as an essential step towards bringing machine learning into military simulations.

Data augmentation has been widely used to improve generalizability of machine learning models. However, comparatively little work studies data augmentation for graphs. This is largely due to the complex, non-Euclidean structure of graphs, which limits possible manipulation operations. Augmentation operations commonly used in vision and language have no analogs for graphs. Our work studies graph data augmentation for graph neural networks (GNNs) in the context of improving semi-supervised node-classification. We discuss practical and theoretical motivations, considerations and strategies for graph data augmentation. Our work shows that neural edge predictors can effectively encode class-homophilic structure to promote intra-class edges and demote inter-class edges in given graph structure, and our main contribution introduces the GAug graph data augmentation framework, which leverages these insights to improve performance in GNN-based node classification via edge prediction. Extensive experiments on multiple benchmarks show that augmentation via GAug improves performance across GNN architectures and datasets.

In this paper, we propose a conceptually simple and geometrically interpretable objective function, i.e. additive margin Softmax (AM-Softmax), for deep face verification. In general, the face verification task can be viewed as a metric learning problem, so learning large-margin face features whose intra-class variation is small and inter-class difference is large is of great importance in order to achieve good performance. Recently, Large-margin Softmax and Angular Softmax have been proposed to incorporate the angular margin in a multiplicative manner. In this work, we introduce a novel additive angular margin for the Softmax loss, which is intuitively appealing and more interpretable than the existing works. We also emphasize and discuss the importance of feature normalization in the paper. Most importantly, our experiments on LFW BLUFR and MegaFace show that our additive margin softmax loss consistently performs better than the current state-of-the-art methods using the same network architecture and training dataset. Our code has also been made available at //github.com/happynear/AMSoftmax