Understanding logical entailments derived by a description logic reasoner is not always straight-forward for ontology users. For this reason, various methods for explaining entailments using justifications and proofs have been developed and implemented as plug-ins for the ontology editor Prot\'eg\'e. However, when the user expects a missing consequence to hold, it is equally important to explain why it does not follow from the ontology. In this paper, we describe a new version of $\rm E{\scriptsize VEE}$, a Prot\'eg\'e plugin that now also provides explanations for missing consequences, via existing and new techniques based on abduction and counterexamples.

Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min, +)$-convolution hypothesis ([K{\"u}nnemann, Paturi and Stefan Schneider, ICALP 2017] and [Cygan, Mucha, Wegrzycki and Wlodarczyk, 2017]), the best algorithm is randomized and runs in $\tilde O(n + (1 / \epsilon) ^ {11/5})$ time [Deng, Jin and Mao, SODA 2023], and it remains an important open problem whether an algorithm with a running time that matches the lower bound (up to a sub-polynomial factor) exists. We answer the problem positively by showing a deterministic $(1 - \epsilon)$-approximation scheme for knapsack that runs in $\tilde O(n + (1 / \epsilon) ^ {2})$ time. We first extend a known lemma in a recursive way to reduce the problem to $n \epsilon$-additve approximation for $n$ items. Then we give a simple efficient geometry-based algorithm for the reduced problem.

Aerial-to-ground image synthesis is an emerging and challenging problem that aims to synthesize a ground image from an aerial image. Due to the highly different layout and object representation between the aerial and ground images, existing approaches usually fail to transfer the components of the aerial scene into the ground scene. In this paper, we propose a novel framework to explore the challenges by imposing enhanced structural alignment and semantic awareness. We introduce a novel semantic-attentive feature transformation module that allows to reconstruct the complex geographic structures by aligning the aerial feature to the ground layout. Furthermore, we propose semantic-aware loss functions by leveraging a pre-trained segmentation network. The network is enforced to synthesize realistic objects across various classes by separately calculating losses for different classes and balancing them. Extensive experiments including comparisons with previous methods and ablation studies show the effectiveness of the proposed framework both qualitatively and quantitatively.

In this study, we propose using an over-the-air computation (OAC) scheme for the federated k-means clustering algorithm to reduce the per-round communication latency when it is implemented over a wireless network. The OAC scheme relies on an encoder exploiting the representation of a number in a balanced number system and computes the sum of the updates for the federated k-means via signal superposition property of wireless multiple-access channels non-coherently to eliminate the need for precise phase and time synchronization. Also, a reinitialization method for ineffectively used centroids is proposed to improve the performance of the proposed method for heterogeneous data distribution. For a customer-location clustering scenario, we demonstrate the performance of the proposed algorithm and compare it with the standard k-means clustering. Our results show that the proposed approach performs similarly to the standard k-means while reducing communication latency.

There has been extensive evidence demonstrating that deep neural networks are vulnerable to adversarial examples, which motivates the development of defenses against adversarial attacks. Existing adversarial defenses typically improve model robustness against individual specific perturbation types (\eg, $\ell_{\infty}$-norm bounded adversarial examples). However, adversaries are likely to generate multiple types of perturbations in practice (\eg, $\ell_1$, $\ell_2$, and $\ell_{\infty}$ perturbations). Some recent methods improve model robustness against adversarial attacks in multiple $\ell_p$ balls, but their performance against each perturbation type is still far from satisfactory. In this paper, we observe that different $\ell_p$ bounded adversarial perturbations induce different statistical properties that can be separated and characterized by the statistics of Batch Normalization (BN). We thus propose Gated Batch Normalization (GBN) to adversarially train a perturbation-invariant predictor for defending multiple $\ell_p$ bounded adversarial perturbations. GBN consists of a multi-branch BN layer and a gated sub-network. Each BN branch in GBN is in charge of one perturbation type to ensure that the normalized output is aligned towards learning perturbation-invariant representation. Meanwhile, the gated sub-network is designed to separate inputs added with different perturbation types. We perform an extensive evaluation of our approach on commonly-used dataset including MNIST, CIFAR-10, and Tiny-ImageNet, and demonstrate that GBN outperforms previous defense proposals against multiple perturbation types (\ie, $\ell_1$, $\ell_2$, and $\ell_{\infty}$ perturbations) by large margins.

Memristors provide a tempting solution for weighted synapse connections in neuromorphic computing due to their size and non-volatile nature. However, memristors are unreliable in the commonly used voltage-pulse-based programming approaches and require precisely shaped pulses to avoid programming failure. In this paper, we demonstrate a current-limiting-based solution that provides a more predictable analog memory behavior when reading and writing memristive synapses. With our proposed design READ current can be optimized by about 19x compared to the 1T1R design. Moreover, our proposed design saves about 9x energy compared to the 1T1R design. Our 3T1R design also shows promising write operation which is less affected by the process variation in MOSFETs and the inherent stochastic behavior of memristors. Memristors used for testing are hafnium oxide based and were fabricated in a 65nm hybrid CMOS-memristor process. The proposed design also shows linear characteristics between the voltage applied and the resulting resistance for the writing operation. The simulation and measured data show similar patterns with respect to voltage pulse-based programming and current compliance-based programming. We further observed the impact of this behavior on neuromorphic-specific applications such as a spiking neural network

The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling MAX $k$-SAT problems, specifically for $k=3$ and $k=4$. The novel $4$-SAT QAOA circuit construction we present uses measurement based uncomputation, followed by classical feed forward conditional operations. The QAOA circuit parameters for $3$-SAT are optimized via exact classical (noise-free) simulation, using HPC resources to simulate up to $20$ rounds on $10$ qubits. In order to explore the limits of current NISQ devices we execute these optimized QAOA circuits for random $3$-SAT test instances with clause-to-variable ratio $4$ on four trapped ion quantum computers: Quantinuum H1-1 (20 qubits), IonQ Harmony (11 qubits), IonQ Aria 1 (25 qubits), and IonQ Forte (30 qubits). The QAOA circuits that are executed include $n=10$ up to $p=20$, and $n=22$ for $p=1$ and $p=2$. The high round circuits use upwards of 9,000 individual gate instructions, making these some of the largest QAOA circuits executed on NISQ devices. Our main finding is that current NISQ devices perform best at low round counts (i.e., $p = 1,\ldots, 5$) and then -- as expected due to noise -- gradually start returning satisfiability truth assignments that are no better than randomly picked solutions as the number of QAOA rounds are further increased.

For a given function $F$ from $\mathbb F_{p^n}$ to itself, determining whether there exists a function which is CCZ-equivalent but EA-inequivalent to $F$ is a very important and interesting problem. For example, K\"olsch \cite{KOL21} showed that there is no function which is CCZ-equivalent but EA-inequivalent to the inverse function. On the other hand, for the cases of Gold function $F(x)=x^{2^i+1}$ and $F(x)=x^3+{\rm Tr}(x^9)$ over $\mathbb F_{2^n}$, Budaghyan, Carlet and Pott (respectively, Budaghyan, Carlet and Leander) \cite{BCP06, BCL09FFTA} found functions which are CCZ-equivalent but EA-inequivalent to $F$. In this paper, when a given function $F$ has a component function which has a linear structure, we present functions which are CCZ-equivalent to $F$, and if suitable conditions are satisfied, the constructed functions are shown to be EA-inequivalent to $F$. As a consequence, for every quadratic function $F$ on $\mathbb F_{2^n}$ ($n\geq 4$) with nonlinearity $>0$ and differential uniformity $\leq 2^{n-3}$, we explicitly construct functions which are CCZ-equivalent but EA-inequivalent to $F$. Also for every non-planar quadratic function on $\mathbb F_{p^n}$ $(p>2, n\geq 4)$ with $|\mathcal W_F|\leq p^{n-1}$ and differential uniformity $\leq p^{n-3}$, we explicitly construct functions which are CCZ-equivalent but EA-inequivalent to $F$.

Node classification is the task of predicting the labels of unlabeled nodes in a graph. State-of-the-art methods based on graph neural networks achieve excellent performance when all labels are available during training. But in real-life, models are often applied on data with new classes, which can lead to massive misclassification and thus significantly degrade performance. Hence, developing open-set classification methods is crucial to determine if a given sample belongs to a known class. Existing methods for open-set node classification generally use transductive learning with part or all of the features of real unseen class nodes to help with open-set classification. In this paper, we propose a novel generative open-set node classification method, i.e. $\mathcal{G}^2Pxy$, which follows a stricter inductive learning setting where no information about unknown classes is available during training and validation. Two kinds of proxy unknown nodes, inter-class unknown proxies and external unknown proxies are generated via mixup to efficiently anticipate the distribution of novel classes. Using the generated proxies, a closed-set classifier can be transformed into an open-set one, by augmenting it with an extra proxy classifier. Under the constraints of both cross entropy loss and complement entropy loss, $\mathcal{G}^2Pxy$ achieves superior effectiveness for unknown class detection and known class classification, which is validated by experiments on benchmark graph datasets. Moreover, $\mathcal{G}^2Pxy$ does not have specific requirement on the GNN architecture and shows good generalizations.

Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.

Understanding logical entailments derived by a description logic reasoner is not always straight-forward for ontology users. For this reason, various methods for explaining entailments using justifications and proofs have been developed and implemented as plug-ins for the ontology editor Prot\'eg\'e. However, when the user expects a missing consequence to hold, it is equally important to explain why it does not follow from the ontology. In this paper, we describe a new version of $\rm E{\scriptsize VEE}$, a Prot\'eg\'e plugin that now also provides explanations for missing consequences, via existing and new techniques based on abduction and counterexamples.

Knapsack is one of the most fundamental problems in theoretical computer science. In the $(1 - \epsilon)$-approximation setting, although there is a fine-grained lower bound of $(n + 1 / \epsilon) ^ {2 - o(1)}$ based on the $(\min, +)$-convolution hypothesis ([K{\"u}nnemann, Paturi and Stefan Schneider, ICALP 2017] and [Cygan, Mucha, Wegrzycki and Wlodarczyk, 2017]), the best algorithm is randomized and runs in $\tilde O(n + (1 / \epsilon) ^ {11/5})$ time [Deng, Jin and Mao, SODA 2023], and it remains an important open problem whether an algorithm with a running time that matches the lower bound (up to a sub-polynomial factor) exists. We answer the problem positively by showing a deterministic $(1 - \epsilon)$-approximation scheme for knapsack that runs in $\tilde O(n + (1 / \epsilon) ^ {2})$ time. We first extend a known lemma in a recursive way to reduce the problem to $n \epsilon$-additve approximation for $n$ items. Then we give a simple efficient geometry-based algorithm for the reduced problem.

Aerial-to-ground image synthesis is an emerging and challenging problem that aims to synthesize a ground image from an aerial image. Due to the highly different layout and object representation between the aerial and ground images, existing approaches usually fail to transfer the components of the aerial scene into the ground scene. In this paper, we propose a novel framework to explore the challenges by imposing enhanced structural alignment and semantic awareness. We introduce a novel semantic-attentive feature transformation module that allows to reconstruct the complex geographic structures by aligning the aerial feature to the ground layout. Furthermore, we propose semantic-aware loss functions by leveraging a pre-trained segmentation network. The network is enforced to synthesize realistic objects across various classes by separately calculating losses for different classes and balancing them. Extensive experiments including comparisons with previous methods and ablation studies show the effectiveness of the proposed framework both qualitatively and quantitatively.

In this study, we propose using an over-the-air computation (OAC) scheme for the federated k-means clustering algorithm to reduce the per-round communication latency when it is implemented over a wireless network. The OAC scheme relies on an encoder exploiting the representation of a number in a balanced number system and computes the sum of the updates for the federated k-means via signal superposition property of wireless multiple-access channels non-coherently to eliminate the need for precise phase and time synchronization. Also, a reinitialization method for ineffectively used centroids is proposed to improve the performance of the proposed method for heterogeneous data distribution. For a customer-location clustering scenario, we demonstrate the performance of the proposed algorithm and compare it with the standard k-means clustering. Our results show that the proposed approach performs similarly to the standard k-means while reducing communication latency.

There has been extensive evidence demonstrating that deep neural networks are vulnerable to adversarial examples, which motivates the development of defenses against adversarial attacks. Existing adversarial defenses typically improve model robustness against individual specific perturbation types (\eg, $\ell_{\infty}$-norm bounded adversarial examples). However, adversaries are likely to generate multiple types of perturbations in practice (\eg, $\ell_1$, $\ell_2$, and $\ell_{\infty}$ perturbations). Some recent methods improve model robustness against adversarial attacks in multiple $\ell_p$ balls, but their performance against each perturbation type is still far from satisfactory. In this paper, we observe that different $\ell_p$ bounded adversarial perturbations induce different statistical properties that can be separated and characterized by the statistics of Batch Normalization (BN). We thus propose Gated Batch Normalization (GBN) to adversarially train a perturbation-invariant predictor for defending multiple $\ell_p$ bounded adversarial perturbations. GBN consists of a multi-branch BN layer and a gated sub-network. Each BN branch in GBN is in charge of one perturbation type to ensure that the normalized output is aligned towards learning perturbation-invariant representation. Meanwhile, the gated sub-network is designed to separate inputs added with different perturbation types. We perform an extensive evaluation of our approach on commonly-used dataset including MNIST, CIFAR-10, and Tiny-ImageNet, and demonstrate that GBN outperforms previous defense proposals against multiple perturbation types (\ie, $\ell_1$, $\ell_2$, and $\ell_{\infty}$ perturbations) by large margins.

Memristors provide a tempting solution for weighted synapse connections in neuromorphic computing due to their size and non-volatile nature. However, memristors are unreliable in the commonly used voltage-pulse-based programming approaches and require precisely shaped pulses to avoid programming failure. In this paper, we demonstrate a current-limiting-based solution that provides a more predictable analog memory behavior when reading and writing memristive synapses. With our proposed design READ current can be optimized by about 19x compared to the 1T1R design. Moreover, our proposed design saves about 9x energy compared to the 1T1R design. Our 3T1R design also shows promising write operation which is less affected by the process variation in MOSFETs and the inherent stochastic behavior of memristors. Memristors used for testing are hafnium oxide based and were fabricated in a 65nm hybrid CMOS-memristor process. The proposed design also shows linear characteristics between the voltage applied and the resulting resistance for the writing operation. The simulation and measured data show similar patterns with respect to voltage pulse-based programming and current compliance-based programming. We further observed the impact of this behavior on neuromorphic-specific applications such as a spiking neural network

The Quantum Alternating Operator Ansatz (QAOA) is a hybrid classical-quantum algorithm that aims to sample the optimal solution(s) of discrete combinatorial optimization problems. We present optimized QAOA circuit constructions for sampling MAX $k$-SAT problems, specifically for $k=3$ and $k=4$. The novel $4$-SAT QAOA circuit construction we present uses measurement based uncomputation, followed by classical feed forward conditional operations. The QAOA circuit parameters for $3$-SAT are optimized via exact classical (noise-free) simulation, using HPC resources to simulate up to $20$ rounds on $10$ qubits. In order to explore the limits of current NISQ devices we execute these optimized QAOA circuits for random $3$-SAT test instances with clause-to-variable ratio $4$ on four trapped ion quantum computers: Quantinuum H1-1 (20 qubits), IonQ Harmony (11 qubits), IonQ Aria 1 (25 qubits), and IonQ Forte (30 qubits). The QAOA circuits that are executed include $n=10$ up to $p=20$, and $n=22$ for $p=1$ and $p=2$. The high round circuits use upwards of 9,000 individual gate instructions, making these some of the largest QAOA circuits executed on NISQ devices. Our main finding is that current NISQ devices perform best at low round counts (i.e., $p = 1,\ldots, 5$) and then -- as expected due to noise -- gradually start returning satisfiability truth assignments that are no better than randomly picked solutions as the number of QAOA rounds are further increased.

For a given function $F$ from $\mathbb F_{p^n}$ to itself, determining whether there exists a function which is CCZ-equivalent but EA-inequivalent to $F$ is a very important and interesting problem. For example, K\"olsch \cite{KOL21} showed that there is no function which is CCZ-equivalent but EA-inequivalent to the inverse function. On the other hand, for the cases of Gold function $F(x)=x^{2^i+1}$ and $F(x)=x^3+{\rm Tr}(x^9)$ over $\mathbb F_{2^n}$, Budaghyan, Carlet and Pott (respectively, Budaghyan, Carlet and Leander) \cite{BCP06, BCL09FFTA} found functions which are CCZ-equivalent but EA-inequivalent to $F$. In this paper, when a given function $F$ has a component function which has a linear structure, we present functions which are CCZ-equivalent to $F$, and if suitable conditions are satisfied, the constructed functions are shown to be EA-inequivalent to $F$. As a consequence, for every quadratic function $F$ on $\mathbb F_{2^n}$ ($n\geq 4$) with nonlinearity $>0$ and differential uniformity $\leq 2^{n-3}$, we explicitly construct functions which are CCZ-equivalent but EA-inequivalent to $F$. Also for every non-planar quadratic function on $\mathbb F_{p^n}$ $(p>2, n\geq 4)$ with $|\mathcal W_F|\leq p^{n-1}$ and differential uniformity $\leq p^{n-3}$, we explicitly construct functions which are CCZ-equivalent but EA-inequivalent to $F$.

Node classification is the task of predicting the labels of unlabeled nodes in a graph. State-of-the-art methods based on graph neural networks achieve excellent performance when all labels are available during training. But in real-life, models are often applied on data with new classes, which can lead to massive misclassification and thus significantly degrade performance. Hence, developing open-set classification methods is crucial to determine if a given sample belongs to a known class. Existing methods for open-set node classification generally use transductive learning with part or all of the features of real unseen class nodes to help with open-set classification. In this paper, we propose a novel generative open-set node classification method, i.e. $\mathcal{G}^2Pxy$, which follows a stricter inductive learning setting where no information about unknown classes is available during training and validation. Two kinds of proxy unknown nodes, inter-class unknown proxies and external unknown proxies are generated via mixup to efficiently anticipate the distribution of novel classes. Using the generated proxies, a closed-set classifier can be transformed into an open-set one, by augmenting it with an extra proxy classifier. Under the constraints of both cross entropy loss and complement entropy loss, $\mathcal{G}^2Pxy$ achieves superior effectiveness for unknown class detection and known class classification, which is validated by experiments on benchmark graph datasets. Moreover, $\mathcal{G}^2Pxy$ does not have specific requirement on the GNN architecture and shows good generalizations.

Graph convolution networks (GCN) are increasingly popular in many applications, yet remain notoriously hard to train over large graph datasets. They need to compute node representations recursively from their neighbors. Current GCN training algorithms suffer from either high computational costs that grow exponentially with the number of layers, or high memory usage for loading the entire graph and node embeddings. In this paper, we propose a novel efficient layer-wise training framework for GCN (L-GCN), that disentangles feature aggregation and feature transformation during training, hence greatly reducing time and memory complexities. We present theoretical analysis for L-GCN under the graph isomorphism framework, that L-GCN leads to as powerful GCNs as the more costly conventional training algorithm does, under mild conditions. We further propose L^2-GCN, which learns a controller for each layer that can automatically adjust the training epochs per layer in L-GCN. Experiments show that L-GCN is faster than state-of-the-arts by at least an order of magnitude, with a consistent of memory usage not dependent on dataset size, while maintaining comparable prediction performance. With the learned controller, L^2-GCN can further cut the training time in half. Our codes are available at //github.com/Shen-Lab/L2-GCN.