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**A**: [19] propose an original teacher-student architecture that uses the logits of the teacher model as the knowledge. Since then, some KD methods regard knowledge as final responses to input samples [3, 31, 58], some regard knowledge as features extracted from different layers of neural networks [24, 23, 41], and so...
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**A**: This is, indeed, true, but as shown in [De ̵+22] both FNO and DeepONet produce Runge-like oscillations when applied to data with discontinuities, so with current versions of these operators non-smooth data is out of question**B**: Bands are fixed by the choice of architecture and training data. Then, the natural...
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**A**: Earlier works only distill the knowledge from the final layer of neural networks, for example, the “logits” in image classification task [19, 1]**B**: This line of works encourage similar patterns to be elicited in the spatial dimensions [36, 50], and is constituted as state-of-the-art knowledge distillation app...
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**A**: In Figure 8 the first group is colored in red, the second group is colored in blue and the third group is colored in orange. We further partition the dataset into four groups based on the weights according to 25, 50 and 75 quantiles. In Figure 8 the datapoints corresponding to the first group are shown in diamon...
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Selection 1
**A**: (2016); Guo et al. (2016) analyze POMDPs where an arbitrary policy can conduct efficient exploration. Similarly, Cayci et al. (2022) consider POMDPs with a finite concentrability coefficient (Munos, 2003; Chen and Jiang, 2019), where the visitation density of an arbitrary policy is close to that of the optimal p...
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**A**: Without any coverage assumption on the offline data, the number of data needed to find a near-optimal policy can be exponentially large (Buckman et al., 2020; Zanette, 2021). To circumvent this problem, a few existing works study offline RL under a uniform coverage assumption, which requires the concentrability ...
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**A**: Without constraints, one can apply stochastic gradient descent (SGD) and its many variates, whose statistical properties (e.g., asymptotic normality) have been comprehensively studied from different aspects (Robbins1951stochastic; Kiefer1952Stochastic; Polyak1992Acceleration; Ruppert1988Efficient). However, unli...
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**A**: Another open problem is the analysis of isoparametric generalized Taylor-Hood families in 2D and 3D to cope with curved boundaries. Perturbation arguments similar to those used in [6], [7] for isogeometric generalized Taylor-Hood families seem to be a promising approach for this open problem.**B**: The present ...
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**A**: Table 1 shows that WaveMix is the current SOTA for Cityscapes dataset in terms of single scale inference mIoU among models pre-trained using only ImageNet-1k dataset. Higher mIoU reported by other models [1] belong to multi-scale inference**B**: Performance of WaveMix on Cityscapes validation set along with the ...
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**A**: So, for h=1ℎ1h=1italic_h = 1 we have an expression Ξ1=H^1⁢(Z):=H~1⁢(Z)subscriptΞ1subscript^𝐻1𝑍assignsubscript~𝐻1𝑍\Xi_{1}=\hat{H}_{1}(Z):=\tilde{H}_{1}(Z)roman_Ξ start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT = over^ start_ARG italic_H end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ( italic_Z ) := over~ start_ARG i...
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**A**: Approaches that don’t pre-train or fine-tune transformers for specific linguistic relations instead explicitly represent relations using graphs li2020graph; zhang2020graph; zhang2022hgen. We propose the development of targeted pre-training objectives accounting for important aspects of mathematical rabe2020mathe...
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**A**: In the 7777 blocks structure, the species of block 1111 (represented on 4444 of the 6666 networks) prey on species from all other blocks with the exception of block 7777**B**: The basal species are separated between blocks 6666 and 7777 depending on whether or not they are preyed on by species from the first two...
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**A**: (left) Predictions of rotation angle vs. the ground truth (normalized to [−1,1]11[-1,1][ - 1 , 1 ]) in test set**B**: Figure 5: Performance of FactorNets for individual rotation learning**C**: (right) Distributions of absolute percentage errors (in %) of all data points in the dataset.
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**A**: Training data contains samples from both the classes and a set of unlabeled samples**B**: We further evaluate puNCE in the binary semi-supervised setting**C**: In particular, we perform experiments when only 1%, 5% and 10% of the data is available (Figure 5.2). It is important to note that, unlike PU Learning se...
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**A**: Conversely, we use and define the terms of layer dependence, independence, and redundance in specific ways, as defined either by a model or by a statistical test. These terms all specify what type of interdependence is present in a multilayer network. **B**: The vocabulary around assessing interdependence amongs...
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**A**: A crucial point to bear in mind with quantum computing is that the memory capacity**B**: johri2021nearest , and where necessary, the larger IonQ Aria machine with a capacity of 32 physical and 20 algorithmic qubits (ionq2022aria, )**C**: Experiments below used the 11-qubit trapped ion quantum computer described ...
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**A**: As homophily and performance are correlated, in the restructuring process, number of edges are chosen based on homophily level on the validation set**B**: As shown in Equation 5, we chose 48000480004800048000 edges for Chameleon and 26000260002600026000 edges for Squirrel, each corresponds to the first peak of ...
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**A**: In short, this work analyzes natural dynamics with consequences for the distribution of subpopulations amongst independent learners; whether or not the consequences are desirable depend on the specific application considered. **B**: In others, where proportional representation of groups across learners, models, ...
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**A**: This could be the case, for instance, if it is known that a fairness-preserving procedure (e.g., Hardt et al., 2016; Woodworth et al., 2017) was used to generate the classifier**B**: More generally, the fact that the classifier is fair may be disclosed to the public even if the classifier itself or its predictio...
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**A**: In this section we discuss the quality of the discovered motif sets**B**: We assume that a method finds a motif set if the reported motifs overlap with the ground truth.**C**: The purpose is to compare methods not only by the size and extent of found motifs as in the previous section, but also to consider wheth...
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**A**: [38] investigated a consensus plus innovation based decentralized linear regression algorithm over random networks with random regression matrices**B**: They proved that if the regression matrices and communication graphs satisfy the stochastic spatio-temporal persistence of excitation condition, properly choosi...
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**A**: The notation MM is used to refer to the Matrix Market Collection, and SS for the SuiteSparse Matrix Collection. **B**: In Table 1, we report the matrices and their most significant properties**C**: The sources used to retrieve the matrices are specified in Table 1 as well
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**A**: All the aforementioned methods assume the existence of a training dataset, where each summary is associated with a particular topic**B**: Thus, we adopt the approach of [5] to compile and release a topic-oriented dataset. **C**: However, currently there are no existing large-scale training datasets for abstracti...
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**A**: We start from the following definitions. A standard cell is a pattern that represents the 2D/3D abstraction of the qubits and the gates that form a sub-circuit (e.g**B**: the Clifford+T decomposition of the Toffoli gate). Tiling is the procedure by which circuits are designed in a manner that is compatible with ...
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**A**: In contrast, recent works employ advanced platforms such as MRiLab [7] and Brainweb [13], which rely on biophysical models that use complex non-linearities to estimate MR images in different parameters. MRiLab is an MR image simulator equipped with the generalized multi-pool exchange model for accurate MRI simul...
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**A**: These numerical schemes are directly constructed based on a prescribed continuous energy-dissipation law for the system, without the need for the underlying PDE**B**: The incorporation of mesh-free neural network discretization opens up exciting possibilities for tackling high-dimensional gradient flows arising ...
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**A**: Next, we recall the notion of graded-barcodes for constructible sheaves on ℝℝ\mathbb{R}blackboard_R and how we can compute the convolution distance between two such sheaves from their graded-barcode, thanks to the derived isometry theorem [1]. We end the section by providing a purely sheaf-theoretic formulation ...
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**A**: In optimal ordering, the variables are ordered so that they are consistent with the topological ordering of the nodes in the reference graph**B**: We compare the sensitivity of the F1 score relative to the default alphabetic ordering and two other orderings which we term “optimal” and “worst”**C**: This optimal ...
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**A**: For multigraphs with a constant number of vertices, Manjunath [17] gave a polynomial time algorithm that computes the rank of a divisor. Furthermore, by a corollary of the Riemann-Roch theorem, the rank can be computed in polynomial time for divisors of degree greater than 2⁢g−22𝑔22g-22 italic_g - 2, where g𝑔g...
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**A**: For the CIFAR10/100 dataset, we employ the MS-ResNet architecture, as detailed in Ref. [52], to validate the effectiveness of the TCJA on deep residual neural networks**B**: The TCJA module is integrated at the bottom of each MS-ResNet block.**C**: Specifically, we utilize the standard MS-ResNet-18 architecture...
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**A**: Ω=(0,12)2Ωsuperscript0122\Omega=\bigl{(}0,\frac{1}{2}\bigr{)}^{2}roman_Ω = ( 0 , divide start_ARG 1 end_ARG start_ARG 2 end_ARG ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT**B**: Given**C**: Since all four corners of ΩΩ\Omegaroman_Ω are π/2𝜋2\pi/2italic_π / 2, we have μ=(1,1,1,1)𝜇1111\mu=(1,1,1,1)italic_μ = (...
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**A**: The inexecutability due to these reasons cannot be identified by static analysis and can only be determined by executions. All such inexecutable functions are filtered out.**B**: An action candidate may not be executable due to various reasons: (1) the function is disabled by the owner or admin; (2) internal fun...
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**A**: Further, our approach can exploit low dimensional structure of the task distribution, when such exists, to obtain improved bounds. Finally, we showed that our approach can be “plugged-in” the VariBAD algorithm to improve generalization. **B**: Using KDE for density estimation, we obtain state-of-the-art PAC boun...
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**A**: For example, given diarrhea and nausea as queries, we not only can find their corresponding anchors 腹瀉 (diarrhea) and 噁心 (nausea), but also 拉肚子 (liquid bowel movements) as well as 想吐 (want to vomit), respectively. **B**: Case 1: Non-anchor words close to the anchors**C**: Even though only anchors involve in dete...
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**A**: The pre-trained ViT model was pulled from the timm python library**B**: For saliency analysis, the absolute values of the gradients of prediction probabilities with respect to input pixels were calculated using the backward() method of pytorch during a backward pass.**C**: Training and inference using ViT was i...
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**A**: FuSeBMC’s main new features can be summarised as follows: **B**: This journal paper explains the latest developments to the FuSeBMC fuzzer**C**: The work presented here substantially extends our previous published conference papers (Alshmrany et al., 2020, 2021, 2022)
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**A**: As in [17], “q𝑞qitalic_q-bit precision” means the machine epsilon (or relative accuracy of the floating-point numbers we compute with) is 21−qsuperscript21𝑞2^{1-q}2 start_POSTSUPERSCRIPT 1 - italic_q end_POSTSUPERSCRIPT**B**: For example, the widely-used double-precision arithmetic has 53-bit precision and a m...
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**A**: Sample2 uses imbalanced positive and negative samples. Specifically, sample2 randomly removes 20% of L𝐿Litalic_L links as the missing links. In the training step, the positive set is composed of 80% of the removed links (16% of L𝐿Litalic_L links), and the negative set is composed of 80% of all nonexistent link...
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**A**: We measure the transfer learning accuracy on multiple downstream datasets and report the average accuracy [37]**B**: We follow [12] to use a set of vision datasets including Cars [39], CIFAR-10 [40], CIFAR-100 [40], CUB [68], Flowers [54], Food [9], and Pets [55]‡‡‡Pets uses CC BY-SA 4.0 license; Cars and Image...
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**A**: Then we denote |A|=(|ai⁢j|)𝐴subscript𝑎𝑖𝑗|A|=(|a_{ij}|)| italic_A | = ( | italic_a start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT | )**B**: Let A=(ai⁢j)𝐴subscript𝑎𝑖𝑗A=(a_{ij})italic_A = ( italic_a start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT ) and N={1,2,…,n}𝑁12…𝑛N=\{1,2,\ldots,n\}it...
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**A**: The travelling salesman problem is the classic hard problem of this type, the Eulerian cycle problem is a polynomial-time solvable example. We note that the order and adjacency types were, also under these names, already described in [ES15, p. 68]. Due to the different nature of these types of problems, it appea...
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**A**: In the present paper, we also consider such a Riemannian metric on a simpler structured bounded open convex feasible set, in order to focus on multilevel representation and accelerated first-order optimization that copes with large problem sizes**B**: To this end, we employ information geometry in order to desi...
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**A**: As monotonicity constraints abound, there are specialized statistical methods aimed at fitting and modeling monotonic functions such as Isotonic Regression [2, 25, 26] as well as many other works related to monotone approximation [10, 20, 46]**B**: Neural networks are no exception: Several works are devoted to t...
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**A**: This paper tries to bridge this theoretical gap. It is structured as follows**B**: Notations and preliminaries are introduced in Section 2. Section 3 describes randomly shifted lattice rules, and Section 4 gives a brief overview over the analysis of conforming FE methods**C**: DG in the QMC framework is presente...
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**A**: It follows the successive elimination approach, and can be seen as a generalization of the algorithm for the heterogeneous CL setting in (KZ23, ) to the entire time-round tradeoff curve. **B**: Our algorithm is non-adaptive**C**: In this section, we present a CL algorithm that gives Theorem 2
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**A**: As a result, our theory provides a direct globalization strategy for works that employ quasi-Newton direction with only local convergence guarantees. For instance, it globalizes the recent work [45] which studies smooth and strongly convex finite sum problems, and proposes an incremental quasi-Newton method with...
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**A**: This will be our future work and we are planning to use it to develop fast tensor completion algorithms similar to the strategy done in [52]. A detailed theoretical analysis of the proposed algorithm needs to be investigated. This is also our future work. **B**: Simulations on synthetic and real-world data-sets ...
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**A**: Second, we established a parameter that allows varying degrees of supervision in the trees (i.e., how much the descriptive attributes influence the evaluation of the splits). In this way we can build supervised, semi-supervised, or unsupervised trees, dictated by the demands of the specific dataset we are dealin...
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**A**: On the other hand, Huang et al.’s [34] approach to early-stage fusion of RGB and depth data offers a novel perspective on multi-modal integration, yet it may face challenges in disentangling conflicting features. Our DeepIPC model seeks to balance these aspects, utilizing BEV mapping for enhanced spatial awarene...
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**A**: We reduce from the 3333-Coloring problem**B**: Equivalently,**C**: Recall that the task of 3333-Coloring is to decide whether a graph G𝐺Gitalic_G admits a proper 3333-coloring, that is, its vertices can be colored by three colors in such a way that adjacent vertices receive distinct colors
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**A**: Long-tail datasets are characterized by a significant imbalance, where minority classes have far fewer samples than majority ones**B**: This horizontal imbalance is distinct from the challenges addressed by VFL, where the same sample (whether it belongs to a majority or minority class) is vertically split across...
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**A**: The static graph neural network models can be then applied to these snapshots [58, 59, 60, 61, 62, 63].**B**: Based on the properties of dynamic graphs, current dynamic graph neural networks can be roughly divided into two categories [54, 55, 56, 57]: discrete-time based methods and continuous-time based methods...
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**A**: degrees from University of Science and Technology of China in 2013 and 2018, respectively. He is currently a Research Scientist with Watrix Technology Limited Co**B**: Xu Liu received the B.E. and Ph.D**C**: Ltd. His research interests include gait recognition, object detection and image segmentation.
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**A**: The dialogue policy module makes a dialogue decision given the current state (Zhang et al., 2019)**B**: Since handcrafted rules are non-extensible and resource-consuming (Zhao et al., 2021), deep reinforcement learning (DRL) has become a mainstream method for training dialogue policies (Wu et al., 2019; Wang et...
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**A**: Then, a Transformer-based Encoder-Decoder structure [33] is proposed for the Intention-Conditioned Variational Auto-Encoder (I-CVAE) in Section 3.3, inspired by [24]. Fig. 2 shows the overview of the proposed framework, that represents how the structure is extracted from the observed past and used to condition t...
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**A**: This experiment investigates the scalability of COUTA compared to its competing methods. Time efficiency w.r.t**B**: both time series length T𝑇Titalic_T and dimensionality D𝐷Ditalic_D are recorded. As for the scalability test w.r.t**C**: dimensionality, a group of seven time-series datasets with a fixed lengt...
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**A**: Although there are works in D2T that incorporate this aspect (Gong et al., 2020a), the two research niches are often disparate**B**: Numeracy for Data-to-text Generation: The NLP niche of building LLMs capable of quantitative reasoning (often referred to as Math-AI or Math-NLP) has garnered significant interest ...
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**A**: Dashed lines indicate the distances between the noisy sample and other samples in a clean subset with girl-chair**B**: wKNN replaces the noisy predicate in with a soft label, assigning a score of 0.25 to the new label sitting on and a score of 0.75 to the old label in.**C**: Figure 6: The illustration of NSC
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**A**: Besides mining attacks, researchers also proposed other incentive-based attacks. For example, based on the assumption that miners are inclined to choose the most profitable mining strategy to work, Michael et al. [mirkin2020bdos] propose the Blockchain Denial of Service (BDoS) attack**B**: Instead of getting a h...
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**A**: Figure 7: Learning rate warmup gradually reduces the preconditioned sharpness during optimization. Left: The evolution of the preconditioned sharpness for a 6L-6L encoder-decoder Pre-LN transformer trained on the WMT En=>De task at η=.001𝜂.001\eta=.001italic_η = .001 with a linear warmup period of 40000 steps*...
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**A**: As mentioned above, the stochastic embedding methods belong to the second category of manifold learning methods we consider here, i.e., based on divergence optimization**B**: Instead, the target mapping ξ𝜉\xiitalic_ξ is parametrized based on neural networks that perform nonlinear dimensionality reduction. The ...
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**A**: This method of subdomain growth has the flaw that the final subdomain assignation is impacted by the order in which the elements are considered**B**: The robustness of the algorithm can be assessed by randomly permuting the list of elements before the subdomain assignation**C**: In 200 samples, 93% of nodes are ...
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**A**: Dataset. We verify the performance of the model on a simulated dataset provided by [24]**B**: The training set includes a variety of networks sized from 25 to 50 network nodes, while the test and validation set are sized from 50 to 300 network nodes. The larger network brings the following attribute changes: **...
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**A**: In contrast, as a special case of the low-rank model, linear MDPs have a similar form of structures but with an extra assumption that the linear representation is known a priori (Du et al., 2019b; Yang & Wang, 2019; Jin et al., 2020; Xie et al., 2020; Ayoub et al., 2020; Cai et al., 2020; Yang & Wang, 2020; Chen...
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**A**: The decoupling approach was developed for importance sampling in MV-SDEs (dos Reis et al., 2023; Ben Rached et al., 2023), where the idea is to approximate the MV-SDE law empirically as in (4), use the approximation as input to define a decoupled MV-SDE and apply a change of measure to it**B**: First, we introdu...
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**A**: An illustrative example of a challenging environment is the spacecraft being erroneously directed to a tighter orbit than would be recommended 181818It is improbable that the autonomous system’s executive will adopt an approach tailored to each of the myriad potential situations a spacecraft may encounter in the...
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**A**: This project was started during a visit of MW to MIT, supported by an Amazon Research Award**B**: Part of this work was done while MW visited the Simons Institute for the Theory of Computing in Berkeley, CA, supported by a Simons-Berkeley Research Fellowship**C**: SS acknowledges support from an NSF-CAREER award...
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**A**: Similarly, the second highest ranked hole aligns with points from the next largest triangle. **B**: Despite the lack of a signal using traditional methods, both the persistence and the centrality functions, viewed as rankings, reveal some patterns**C**: Mirroring the previous bootstrap sample, the highest ranked...
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**A**: Remark. In our multi-task learning framework, using the independent BN can effectively mitigate the interference of different domains, as shown in Eq. 4**B**: In addition, in our method, most of the modules are shared for all domains, which can sufficiently exploit all samples to reduce the third item in Eq. 4. ...
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**A**: al**B**: Similarly, TinyTL introduces extra residual blocks to MobileNet [23, 6] for memory efficient on-device learning. Guo et**C**: [17] proposes re-composing a ResNet with depth-wise and point-wise convolutions, and re-training only the depth-wise part during fine-tuning.
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**A**: Regularization technique is widely used in online convex optimization problems [40]**B**: Online learning methods enable model updates incrementally from sequential data, offering greater efficiency and scalability than traditional batch learning**C**: Online Mirror Descent, an extension of Mirror Descent [41], ...
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**A**: WB would like to thank Dustin Steinhauer for an introduction to the Fisher information matrix many years ago**B**: CRJ’s work was partially supported by the Intel Graphics and Visualization Institutes of XeLLENCE, the National Institutes of Health under award R24 GM136986, the Department of Energy under grant nu...
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**A**: While an interesting feature, the promise of being able to connect labeling to specific times and places in order to see patterns was more useful in the case of already connected manuscripts**B**: For each selection of manuscripts, a visual sidebar allowed us to see inventory numbers, total number of images per...
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**A**: Liang Ding received Ph.D**B**: from the University of Sydney**C**: He works on deep learning for NLP, including language model pretraining, language understanding, generation, and translation. He published over 40 research papers in NLP/AI, including ACL, EMNLP, ICLR, and ICML. He was the area (session) chair ...
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**A**: The conflict caught the attention of existing defacers, who performed many attacks against other countries but not Russia and Ukraine until just after the invasion, suggesting their choice of targets was influenced**B**: Defacement Motives**C**: We also found some ‘new faces’ e.g., the second most active deface...
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**A**: Nonetheless, there are instances within the Road Sign dataset where HET does not perform optimally at lower k𝑘kitalic_k values but recovers effectiveness at higher k𝑘kitalic_ks**B**: When dissecting performance relative to the datasets, HET exhibits robust results for ImageNet, CIFAR10, and X-Ray**C**: This co...
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**A**: An alternative is to allow the data embedding itself to be parametrized and then train the embedding. Such strategies have been shown to improve generalization of the kernel-based quantum model [75, 69]. We note that this is an additional process to train and select an appropriate embedding before implementing ...
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**A**: Section 4 describes in detail the implementation all the proposed recognition approaches. In Section 5, the performance and the evaluation metrics of the different methods is assessed. We conclude with a summary of our finding and make proposals for further work. **B**: Following an introduction, Section 2 gives...
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**A**: II00\displaystyle 011\displaystyle 11Uncertainty Score (GCJ)Norm.Imit.Obf. IObf**B**: II00\displaystyle 011\displaystyle 11Uncertainty Score (GH)Abuhamad et al.Caliskan et al.Original Figure 4. Anonymization performance (uncertainty score) in the**C**: Norm.Imit.Obf. IObf
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**A**: To make a valid comparison, we use the off-shelf dataset miniImageNet (100 classes) as the large train set for ProtoNet, and use the train set in CoOp for the few-shot reference set for it**B**: We train ProtoNet on miniImageNet with 400 epochs and 8-way k𝑘kitalic_k-shot (k=1,2,4,8,16𝑘124816k=1,2,4,8,16italic_...
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**A**: This study uncovers pronounced disparities in label distributions between Africa and other regions 333For a thorough comparison of distributions, refer to Figures 24 and 27 in Koh et al**B**: (2021).. These distinctions encompass a notable decrease in recreational facilities and a marked rise in single-unit resi...
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**A**: Let 𝒲𝒲\mathcal{W}caligraphic_W denote the graph of 𝒱𝒱\mathcal{V}caligraphic_V, which is defined by **B**: We now verify that 𝒱𝒱\mathcal{V}caligraphic_V is upper-semicontinuous**C**: To this end, it suffices to prove that the graph of 𝒱𝒱\mathcal{V}caligraphic_V is closed; c.f. [MR0755330, Ch. 1, Corollary...
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Selection 4
**A**: As discussed before, if the sum of the columns of A𝐴Aitalic_A is less or equal than 1, the assignment is univalent, i.e**B**: Regarding the assignment matrix A𝐴Aitalic_A, we can use the very same structure to describe a preallocation**C**: each channel is assigned to maximum one tenant. In the process of preal...
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Selection 2
**A**: We investigate the computational complexity of all the comparative baselines, TCVAE and its variant w/o CCNF**B**: With the multivariate setting and all the methods’ current finest implementation, we perform a statistical comparison of the time costs and parameter volumes on Traffic in Table VI**C**: From the ex...
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Selection 3
**A**: Recently, there is growing interest in including a physics-based prior into neural networks**B**: Refs**C**: 16, 17, 18 introduce concepts from Lagrangian or Hamiltonian mechanics into neural networks, allowing them to learn and respect conservation laws for deterministic dynamical systems. These dynamical prior...
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Selection 2
**A**: We will present an overview of the different types of models, their implications, and their limitations. This does not constitute an exhaustive list of all the mathematical models associated with these MRs, but rather an introductory presentation for common models used in trajectory planning. Readers familiar wi...
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Selection 3
**A**: The assumptions are also sufficiently broad to apply for most mixtures but they can presumably be weakened further**B**: For a given mixture model, Proposition 4 is relatively easy to apply because the mapping from standard parameterization to natural parameters is usually known and known to be invertible.**C**:...
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Selection 4
**A**: This section is devoted to the proofs of Theorem 2, Theorem 4, and Theorem 3**B**: We then move on to prove Theorem 4 and Theorem 3 in Section 4.2.**C**: We begin in Section 4.1 by analysing the problem of counting k𝑘kitalic_k-matchings in somewhere dense host graphs, and proving Theorem 2; this is the most te...
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Selection 1
**A**: And bias-free uniform data can be used to guide the model to learn unbiased embedding, forcing the model to discard item popularity [43]. However, obtaining such uniform data needs to randomly expose items to users, which may hurt user experience and the data is usually of a small scale which makes the learning ...
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Selection 2
**A**: To further demonstrate the effectiveness of our method, we also conduct the intra-dataset experiment on the SCID dataset**B**: It is worth noting that both GraphIQA and VCRNet are retrained on large-scale IQA datasets [84, 85] and ImageNet [86]. As such, it is not surprising that they demonstrate inferior perfor...
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Selection 2
**A**: To conclude, there is a correspondence between edge-wise homophily measures and classification evaluation measures**B**: Adjusted homophily corresponds to both Cohen’s Kappa and Matthews coefficient**C**: In terms of the satisfied properties, adjusted homophily dominates all other measures derived from this corr...
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Selection 2
**A**: As demonstrated in the next section, these hypotheses are satisfied for a number of interesting examples besides the qubit systems treated in Section 3. **B**: In this section, we generalize the main results from the previous section to the general von Neumann algebraic setting**C**: Apart from technical challen...
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Selection 2
**A**: Moreover, we report the performance of different operations conducted in CPA-Boot. As depicted in Fig. 6, the main overhead of CPA-Boot stems from asymmetric cryptography used for certificate validation, packet encryption and decryption, and key exchange.**B**: Table 5 quantifies the experimental performance666...
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Selection 1
**A**: Several motivating examples are provided in this subsection**B**: The first is adopted from [Lanzon and Bhowmick, 2023], which provides a class of negative imaginary systems characterised by an LTI auxiliary system and a dynamic supply rate**C**: The example is paraphrased in terms of Definition 2.
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Selection 1
**A**: Bai et al. [14] analyzes a probability for a trajectory to reach a target set, which is a subset of a safe set. Nejati et al. [15] develop a compositional approach for constructing CBFs for stochastic hybrid systems, which forms an excellent theory in terms of applications because they use numerical methods such...
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Selection 4
**A**: This difference is more distinct in the test with examples without a necessary relation between them**B**: The results of both tests show that the use of PoLMDP policies allows an IRL agent to learn the underlying reward function and the teacher’s intentions faster than using a standard optimal policy**C**: In t...
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Selection 3
**A**: Random variables are in capital case (e.g**B**: X𝑋Xitalic_X), and their realization are in lower case (e.g**C**: x𝑥xitalic_x). All random variables take values in some alphabets that are in calligraphic letters (e.g. 𝒳𝒳\mathcal{X}caligraphic_X). We shall restrict our attention to finite alphabets only.
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Selection 2
**A**: This paper aims at answering the above questions**B**: Note that a large admittance (or equivalently, a small impedance) indicates that the converter’s behavior is closer to a voltage source. To make a fair comparison, we consider the scenario where both GFL control and GFM control aim at regulating the AC volta...
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Selection 4
**A**: However, the trend itself may be of interest, and modeling it together with the dependence structure can be preferable. The former can be estimated by smoothing the data, using methods such as Kernel Smoothing [26], Locally Weighted Scatterplot Smoothing (Lowess), or Smoothing Splines, to name just a few**B**: T...
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Selection 1
**A**: Datasets. For the empirical analysis, we test on the standard OSR datasets as described in Protocol A of Sec**B**: The unknown class can be constituted by a diverse set of semantic classes, but is regarded as a single chunk. The known classes must have no semantic overlap with the unknown class. **C**: 6.1. Each...
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Selection 3