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**A**: The purpose of defining different types of knowledge is to efficiently extract the underlying representation learned by the teacher model from the large-scale data. If we consider a network as a mapping function of input distribution to output, then different knowledge types help to approximate such a function. ...
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**A**: The proof can be found in Appendix A**B**: More results on aliasing for composition with smooth functions can be found in [Ber+06]**C**: The aliasing error is quite substantial, but since all energy in the theorem above is confined in highest possible harmonics, in practice one can expect to have milder discrep...
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**A**: proposed to distill the logits (before sotfmax layer) from teacher to student by minimizing the KL divergence, where a temperature factor is applied to soften the logits.**B**: Specifically, Hinton et al**C**: The seminal work [19] introduced the idea of knowledge distillation
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**A**: However, feature grouping is not always clear. The data might have hundreds of features or come from where the meaning of features is unclear**B**: Finally, we apply the CLIQUE subspace clustering algorithm [2] to the auto-mpg dataset to identify interesting subspaces. The resulting ENS-t-SNE embedding shows pa...
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**A**: The key to ETC is balancing exploitation and exploration along the representation learning process**B**: To this end, we construct a confidence set of embeddings upon identifying and estimating the Bellman operator, which further allows efficient exploration via optimistic planning. It is worth mentioning that s...
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**A**: See, e.g., Antos et al**B**: (2007); Munos and Szepesvári (2008a); Chen and Jiang (2019) and the references therein.**C**: 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 t...
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**A**: Mou2020linear further showed the asymptotic covariance of constant-stepsize SGD with Ployak-Ruppert averaging. Liang2019Statistical designed a moment-adjusted SGD method and provided non-asymptotic results that characterize the statistical distribution as the batch size of each step tends to infinity. Chen2020St...
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**A**: The rest of the paper is organized as follows**B**: In Appendix A known results on the continuous LBB condition are recalled and commented. Appendix B contains helpful relations used throughout the paper.**C**: In Section 2 the technique of T𝑇Titalic_T-coercivity is discussed, which provides important auxiliar...
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**A**: We also experimented with different families of wavelet coefficients, such as Daubechies, Coiflet, and Symlet series and observed that Haar wavelet was faster and gave more accurate test results than the others**B**: We used lifting scheme [82] to create learnable wavelet coefficients and observed a decline in p...
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**A**: The matrix B1subscript𝐵1B_{1}italic_B start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT of rows**B**: The order matrix of ΣΣ\Sigmaroman_Σ is A1subscript𝐴1A_{1}italic_A start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT below**C**: P3:=x1′+x3assignsubscript𝑃3superscriptsubscript𝑥1′subscript𝑥3P_{3}:=x_{1}^{\prime}+x_{3}italic_P s...
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**A**: While early attempts for solving math word problems exist feigenbaum1963computers; bobrow1964natural; charniak1969computer, research considering the specific link between formal mathematics and natural language at the discourse-level can be traced back to zinn1999understanding, who analysed formal proofs from t...
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**A**: One may think of species belonging to trophic chains with different connectivity patterns. **B**: The two networks share block 1111 (for instance basal species) but the remaining nodes of each network cannot be considered as equivalent in terms of connectivity**C**: Finally, let us consider two networks with pa...
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**A**: Figure 5: Performance of FactorNets for individual rotation learning**B**: (right) Distributions of absolute percentage errors (in %) of all data points in the dataset. **C**: (left) Predictions of rotation angle vs. the ground truth (normalized to [−1,1]11[-1,1][ - 1 , 1 ]) in test set
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**A**: Unlike recent supervised variants of infoNCE (Khosla et al., , 2020; Assran et al., , 2020; Zhong et al., , 2021) which can only leverage explicit (strong) supervision (e.g in form of labeled data), puNCE is also able to leverage implicit (weak) supervision from the unlabeled data**B**: The main idea is to use t...
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**A**: The CP tensor decomposition (Carroll and Chang, 1970; Harshman, 1970) and the Tucker decomposition (Tucker, 1966), have been implemented for their use in analyzing multilayer networks. The CP decomposition, for example, is implemented to interpret a fourth-order tensor of multilayer network data in Schein et al...
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**A**: johri2021nearest , and where necessary, the larger IonQ Aria machine with a capacity of 32 physical and 20 algorithmic qubits (ionq2022aria, )**B**: Experiments below used the 11-qubit trapped ion quantum computer described by Johri et al**C**: A crucial point to bear in mind with quantum computing is that the m...
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**A**: Propositions 3333 and 4444 define neutral graphs which are neither homophilic nor heterophilic**B**: Proposition 3333 states that a uniformly random graph, which has no label preference on edges, is neutral thus has a homophily score of 0.50.50.50.5. Proposition 5555 considers edge density: for graphs with the s...
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**A**: Dotted and dashed lines illustrate risk trajectories under three different slight perturbations from the initialization. In Figure (b), the left plot illustrates the reduction in total risk over time. The dashed blue lines indicate when a new learner joins. The right plot shows the equilibrium-risk for a subset ...
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**A**: (2006, 2008) propose methods for regression based on both individual-level and aggregate-level statistics. Sun et al**B**: (2017) infer voting patterns using aggregate statistics. We are not aware of any works that attempt to estimate properties of existing classifiers from aggregate statistics alone. In particu...
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**A**: Only our approximate k𝑘kitalic_k-Motiflets identify all k=20𝑘20k=20italic_k = 20 repeats of the riff. **B**: When adding a small noise, blurred or too small motifs are reported**C**: From the competitors, none correctly identifies all occurrences, even when given optimal parameters
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**A**: Besides, we consider both additive and multiplicative communication noises in the process of the information exchange among nodes**B**: and mutually independent and it is required that the expectations of the regression matrices be known in [28]-[29].**C**: All these challenges make it difficult to analyze the c...
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**A**: The first approach injects error in the evaluations of the fixed-point operator, and the heuristics are used to dynamically adjust the magnitude of the injected error**B**: The second approach projects the least-squares problem in the Anderson mixing computation onto a subspace, and the heuristics are used to dy...
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**A**: The MoDe: Me and Mo de: Pro are powered by 200-watt motors**B**: They fold to fit on a train or in the boot of a car.With pedal assist, riders reach speeds of up to 15mph (25km/h)**C**: Transportation: Ford unveiled two prototype electric bikes at Mobile World Congress in Barcelona
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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**: The T1 and T2 relaxation times used by MRiLab were matrices of size 108×90×901089090108\times 90\times 90108 × 90 × 90 with values in the range 0s to 4.5s for T1 and 0s to 2.2s for T2. For each pair of {TE, TR}, we generated 24 different 2D axial MR slices of a 3D brain volume, so in total we obtained 4800 MR sl...
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**A**: The free boundary of the compact support moves outward with a finite speed, known as the property of finite speed propagation [71]**B**: As a consequence, numerical simulations of the PME are often difficult by using Eulerian methods, which may fail to capture the movement of the free boundary and suffer from nu...
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**A**: We study the properties of these two metrics. **B**: One of these distances is an ISM whereas the second is a sliced distance**C**: In this section, we make use of the structure of γ𝛾\gammaitalic_γ-sheaves to construct metrics which are efficiently computable for sublevel sets persistence modules by relying on ...
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**A**: Figure 3 illustrates how the F1 score for each variable ordering changes, as we vary the sample sizes for each of the 16 networks. For many networks, we see that variable ordering makes a large difference in learnt accuracy**B**: In the most extreme cases, such as Asia, Formed, Property, and Hailfinder, there i...
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**A**: Besides the distance of a divisor from a non-halting state, its distance from a recurrent state also plays a central role in our investigations, defined as**B**: A divisor f𝑓fitalic_f is called recurrent if there is a non-trivial chip-firing game starting from f𝑓fitalic_f that leads back to f𝑓fitalic_f**C**:...
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**A**: In spatial-wise, data flows between layers as ANN. The TCJA module operates by initially compressing information along both temporal and spatial dimensions, then apply TLA and CLA to establish the relationship in both temporal and channel dimensions and blend them by CCF layer.**B**: Figure 4: The Framework of ...
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**A**: 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 = ( 1 , 1 , 1 , 1 )**B**: 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_POSTSUPERSC...
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**A**: The external threat to validity mainly lies in the subjects used in our study**B**: We mitigate this risk by using diverse and reputable data sources, including academic papers (Qin et al., 2021; Cao et al., 2021) and an industrial database (SlowMist, 2023). **C**: The flash loan attacks we study might not be re...
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**A**: Interestingly, our bounds have a linear dependence on the horizon, compared to the exponential dependence in [33], but have an exponential dependence on the dimension of the prior distribution, corresponding to the exponential dependence on dimensionality of KDE. We argue, however, that in many practical cases t...
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**A**: We then discuss implications, limitations, and future directions in Section V. Finally, we draw a conclusion in Section VI.**B**: The rest of the paper is structured as follows: Section II reviews related works in monolingual ATR methods and cross-lingual ATR methods**C**: Section III illustrates our proposed c...
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**A**: As a specific instance, the Att-BLSTM classifier predicted that the story titled “AI predicts protein structures” is about Science and Technology and we implemented TERP to generate the optimal explanation behind this prediction as shown in Fig**B**: 5**C**: We see that the most influential keywords are ’species...
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**A**: BAP has useful analysis and verification techniques. BAP relies on an intermediate language (IL) in its analysis. Also, SymbexNet (Song et al., 2014) and SymNet (Sasnauskas et al., 2012) are for verification of network protocols implementation. Avgerinos, Thanassis, et al. (Avgerinos et al., 2014) presented an a...
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**A**: We emphasize that high-precision computations are required only for the computation of fractional integration matrices and not for the solution of the resulting linear systems**B**: Our pseudo-stabilization technique discussed in Appendix A is essential to the scalability of the JFP method and thus also for its...
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**A**: An index for a topological feature is designed to quantify the expression of this feature**B**: For entities that do not hold the feature at all, they should have the same and the lowest value. If an entity that does not hold the feature has a higher index value than that does hold the feature, the index must b...
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**A**: However, on-device training on tiny edge devices is extremely challenging and fundamentally different from cloud training**B**: Such a small memory budget is hardly enough for the inference of deep learning models [47, 46, 7, 11, 43, 24, 44, 60], let alone the training, which requires extra computation for the ...
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**A**: 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\}italic_N = { 1 , 2 , … , italic_n }**B**: A=(ai⁢j)𝐴subscript𝑎𝑖𝑗A=(a_{ij})italic_A = ( italic_a start_POSTSUBSCRIPT italic_i italic_j end_POSTSUBSCRIPT...
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**A**: From the definitions of the different mutation operators, it is clear that they have different probabilities to create an offspring identical to the parent**B**: For all experiments, we report the runtime in terms of the number of fitness evaluations until the optimum is found**C**: Since this will have an influ...
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**A**: We used PyLops222https://github.com/PyLops/pylops, the linear operator library for Python, for performing bilinear interpolation and its transpose operation**B**: where B⁢I⁢(v)𝐵𝐼𝑣BI(v)italic_B italic_I ( italic_v ) is the standard bilinear interpolation operator**C**: Consequently, the grid transfer operator...
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**A**: It turns out, that up to the dependence on d𝑑ditalic_d, the size of our network is essentially optimal. We now prove Lemma 4.**B**: One may wonder whether this can be improved**C**: The network we’ve constructed in Theorem 21 uses (d+2)⁢n𝑑2𝑛(d+2)n( italic_d + 2 ) italic_n neurons to interpolate a monotone da...
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**A**: In the case of conforming finite element discretizations for the elliptic PDE problem, it is enough to analyze the parametric regularity of the continuous problem**B**: Below, we briefly recap the main parametric regularity results for the affine and uniform as well as the lognormal model.**C**: The parametric ...
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**A**: If the time budget is small, then the number of heavy arms must be small. Consequently, the probability that the set of heavy arms contain the best arm is also small, because all arms are almost equally uncertain at the beginning of each round. In other words, the set of heavy arms would be an almost random subs...
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**A**: To attain a superlinear convergence rate, the IQN method [45] has integrated quasi-Newton directions with incremental updates, albeit with only local convergence guarantees**B**: It is noteworthy that the aforementioned algorithms are applicable in (strongly) convex cases. However, within the nonconvex nonsmooth...
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**A**: Simulations on synthetic and real-world data-sets confirmed that the proposed algorithm is efficient and applicable. This algorithm can be generalized to higher order tensors according to the paper [46]**B**: In this paper, we proposed a new randomized fixed-precision algorithm for fast computation of tensor SVD...
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**A**: However, in semi-supervised PCTs this feature may be compromised, since the evaluation of the splits depends on both target and descriptive attributes. To deal with this issue, we propose feature-weighted SSL-PCTs. **B**: Thus, irrelevant features will be ignored**C**: PCTs (and decision trees in general) are ro...
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**A**: With a better perception, the model can leverage useful information which results in better drivability. Second, driving in the low light condition is harder than in the normal condition, especially for DeepIPC and AIM-MT which only rely on RGB images at the early perception stage**B**: Meanwhile, Huang et al.’s...
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**A**: The main property of such graphs is that they enjoy the bounded local treewidth property. In other words, any planar graph of a small diameter has a small treewidth**B**: A natural research direction is to extend such methods to intersection graphs of geometric objects [24, 34]. However, even for very “simple” o...
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**A**: In addition, nowadays multimodal data has been ubiquitous, while usually, each client is only able to collect one or a few data modalities due to resource limitations. Therefore, VFL provides an effective way to allow such clients to train a model leveraging information from different data modalities jointly.**B...
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**A**: In this subsection, we perform ablation study to verify the effectiveness of our two components: 1) time-aware attentional aggregating module which consists of one aggregate process for calculating the interaction message and one information propagation process for calculating the intermediate embeddings, as sh...
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**A**: Yongzhen Huang received the B.E. degree from Huazhong University of Science and Technology in 2006, and the Ph.D**B**: degree from Institute of Automation, Chinese Academy of Sciences in 2011. He is currently an Associate Professor with School of Artificial Intelligence, Beijing Normal University, and works in ...
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**A**: Although the time complexity of ensemble models can be reduced by parallel computing, but that increases the space complexity**B**: So, the overall computational complexity is still high and resource consuming. **C**: Combining the results of Figure 3 and Table 2, DPAV DQN achieves better or comparable performan...
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**A**: Then, we define an out-of-context error as predicting a verb or a noun which is unseen in a given intention. For instance, if the model predicts the action ‘drive bike’ in a video where the human intention is ‘washing a dog’, we claim that the model has an out-of-context error**B**: To determine the observed cla...
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**A**: 9 presents the execution time of COUTA and its ten competing state-of-the-art methods on time series datasets with various sizes**B**: Fig**C**: Note that this experiment excludes three general anomaly detectors (i.e., OCSVM, ECOD, and GOAD) that are not originally designed for time series data. COUTA has good s...
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**A**: Graph-to-text translation is not only central to D2T as its application carries over to numerous NLG fields such as question answering (He et al., 2017; Duan et al., 2017), summarization (Fan et al., 2019), and dialogue generation (Liu et al., 2018a; Moon et al., 2019). Further, the D2T frameworks for graph-to-...
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**A**: Hyperparameter of NSC. The hyperparameter of NSC is the K𝐾Kitalic_K in wKNN**B**: From the results, we can observe that the SGG performance is robust to different K𝐾Kitalic_K. To better make a trade-off of different metrics, we set K𝐾Kitalic_K to 3.**C**: We investigated K={1,3,5}𝐾135K=\{1,3,5\}italic_K = {...
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**A**: Attackers can decide among PSM, honest or selfish mining based on profitability**B**: The reward of honest and selfish mining is given in Section 6 for comparisons. We show the optimal mining strategy for the attacker in Section 8.**C**: In the following, we illustrate the reward of PSM
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**A**: Right: Same as left, but with a PostLN Transformer. In both cases the preconditioned curvature closely tracks the 38/η38𝜂38/\eta38 / italic_η bound during warmup, however there is a noticeable gap at the smaller batch size**B**: Figure 7: Learning rate warmup gradually reduces the preconditioned sharpness duri...
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**A**: In Fig. 4, we can see the lower-lying free-energy basins in the reweighted stochastic embeddings are captured by both mrse and stke**B**: Specifically, mrse captures more states below a threshold of 25 kJ/mol in comparison to the embedding rendered by stke, in which the rest of the states is placed over 25 kJ/mo...
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**A**: With the analysis described above, it is possible to generate coronary arterial networks that adhere to given conditions. These networks have terminal segments which should reasonably give rise to a small vessel tree**B**: There are many methods by which the ventricle can be divided. However, as we have access t...
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**A**: Only few papers have considered to extrapolate their proposed model on a larger network [5], something which, this far, has been considered infeasible in real-world scenarios. Moreover, successful extrapolation would require introducing task-specific non-linearity (i.e., queuing theory and network calculus in th...
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**A**: We further theoretically prove that our algorithms recover the true representations and simultaneously achieve sample efficiency in learning the optimal policy and Nash equilibrium in MDPs and MGs respectively. We also provide empirical studies to demonstrate the efficacy of the UCB-based contrastive learning me...
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**A**: Using such a method to solve (14) in higher dimensions (d≫1much-greater-than𝑑1d\gg 1italic_d ≫ 1) is computationally expensive due to the curse of dimensionality**B**: In such cases, model reduction techniques (Hartmann et al., 2016, 2015) or solving the minimization problem (1) using stochastic gradient method...
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**A**: Current missions have a conservative and cautious operational profile, often taking months of surveying and slowly approaching the target to constrain the uncertainties to very low levels before the primary goal of the mission [48, 54]**B**: In addition to these benefits, and more importantly, an autonomous and ...
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**A**: This project was started during a visit of MW to MIT, supported by an Amazon Research Award**B**: SS acknowledges support from an NSF-CAREER award (1846088). **C**: 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 Researc...
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**A**: We introduced novel centrality measures that leverage both persistence and merge dynamics of homology classes**B**: These measures aim to capture a more comprehensive picture of the topological structure within point cloud data compared to traditional summaries**C**: The algorithm for computing the merge dynamic...
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**A**: 1) In the third term, when m𝑚mitalic_m is a larger value, the total value is smaller, which indicates that we should use the available samples to train the model. In other words, most modules in the designed model should be shared for all domains or tasks**B**: 2) The last term is the distribution discrepancy b...
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**A**: As shown in Tab**B**: 5, depth-wise separable convolution introduces the minimal parameter budget while achieving the best results. Apart from 4 adapting variants proposed in this work, we also explore other design choices used in previous works**C**: We experiment on spatial down-sampling of feature maps [7].
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**A**: We also propose an online learning strategy that balances the priorities between changepoints detection, model fitting, and PDEs discovery. For future works, we plan to extend our research to more complex scenarios, including PDEs with parameters that are arbitrary functions of the time domain. Additionally, we ...
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**A**: The relevant question to ask is whether this mesh is better suited to the task than any other potential mesh**B**: As a consequence, it is difficult to answer the question through comparison of convergence rates of different methods, for example.**C**: Answering this question is notoriously difficult in inverse...
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**A**: Additionally, more robust general connections between divergent image collections should allow greater retrieval and discoverability in the cultural heritage sector between varied vocabularies or even across multilingual metadata schemas (Angjeli & Isaac, 2008; Gehrke et al., 2015). This can even be used as a st...
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**A**: Additionally, we show that our PanDa consistently improves over vanilla PoT by 2.3% average score across all tasks and models, and makes the prompt-tuning achieve competitive and even better performance than full-parameter model-tuning in various PLM scales scenarios.**B**: Large-scale experiments are conducted ...
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**A**: A flow of packets is considered to be an attack if any sensor observes at least five packets for the same victim IP or IP prefix, and the attack is deemed to last from the first packet until the last packet preceding 15 minutes without further packets. In 2022, the median number of honeypots contributing data wa...
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**A**: The average transferability of a sample when ranking its potential perturbations for the CIFAR10 and ImageNet datasets over 100 trials**B**: Table 3**C**: Columns represent the various ranking methods, and rows indicate the combination of victim and surrogate model architectures, ensuring that F0subscript𝐹0F_{0...
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**A**: We refer the reader to Appendix F of Ref. [29] for more details.**B**: As sketched in Fig. 5(a), each individual image (i.e., an input data point) is dimensionally reduced to a real-valued vector of length n𝑛nitalic_n using principle component analysis**C**: We choose to focus on the binary classification task...
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**A**: Action recognition models can extract spatio-temporal information efficiently, however, require huge computational power**B**: [7] proposed SlowFast, an efficient network with two pathways, i.e., a slow pathway to learn static semantic information and a fast pathway focusing on learning temporal cues. Each pathw...
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**A**: II00\displaystyle 011\displaystyle 11Uncertainty Score (GH)Abuhamad et al.Caliskan et al.Original Figure 6. Anonymization performance (uncertainty score) in the**B**: II00\displaystyle 011\displaystyle 11Uncertainty Score (GCJ)Norm.Imit.Obf. IObf**C**: Norm.Imit.Obf. IObf
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**A**: Therefore, it is necessary to investigate if introducing multi-task learning to prompt tuning of VLMs is feasible and effective.**B**: Vision-language models (VLMs) are recently adapted to few-shot image recognition tasks by optimizing prompt context**C**: However, existing works of prompt tuning target on sing...
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**A**: (2018); Yang et al. (2020); Wang et al. (2020); Li et al. (2021); Wang et al. (2022b); Zhao et al. (2021)**B**: These invariant representations are typically obtained by applying appropriate linear or nonlinear transformations to the input data. The central challenge in these methods lies in enforcing the invari...
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**A**: The proof of uniqueness of weak solutions of (9) uses the Comparison Principle of elliptic operators (see Section 4)**B**: In order to preserve this approach on the discrete level, we consider here approximations by a monotone finite element method that satisfies a discrete maximum principle (see, e.g., [ciarlet...
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**A**: In recent years, a number of elegant and efficient channel auction algorithms are developed for dynamic channel assignments and important challenges such as strategy proofness and computational complexity are studied [11]. Low-complexity matching-based channel assignment algorithms are developed to find stable ...
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Selection 4
**A**: Due to the non-stationarity of the real-world environment, distributional drift has been an essential issue in time series data. However, few existing methods focus on the distributional drift of time series**B**: Some methods [30, 31, 32, 29, 33, 34, 35] strategically cater to future data via adapting their mod...
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Selection 2
**A**: There are a variety of additional avenues for such a dynamics-based approach. Through both theoretical analysis and numerical experiments, our results further support the previous findings that constraining the latent dynamics is enough to uniquely identify the latent representation up to an isometry 30, 31**B**...
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Selection 3
**A**: These UAVs can control its position and orientation independently, as opposed to underactuated multirotor UAVs which are the focus of most of the current research in CaTP nowadays**B**: This new capability introduced by omnidirectional UAVs can be exploited in creative ways to develop new techniques such as maki...
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Selection 1
**A**: Theorem 1 can also remains relevant for standard Gaussian mixtures. For instance, the result of Theorem 1 may help in analyzing their convergence properties (e.g. Xu and Jordan, 1996; Dwivedi et al., 2018).**B**: The main challenge is usually the parameterization criterion but also the generative model first has...
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Selection 3
**A**: 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 technical part**B**: This section is devoted to the proofs of Theorem 2, Theorem 4, and Theorem 3**C**: We then move on to prove Theorem 4 and Theorem 3 in ...
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Selection 4
**A**: Instead of blindly erasing the impact of popularity, this work takes the initial step to consider the effect of item quality and solve the unfairness problems caused by popularity bias in multi-behavior recommendation**B**: In the future, there are many research directions for further exploration: 1) the analys...
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Selection 3
**A**: In particular, the two types of features extracted from images of the SIQAD dataset are visualized. From the figure, we can observe: 1) The distortion-aware features of the reference images are clustered into one group as their distortions are the same though the images contain different contents**B**: In our me...
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Selection 2
**A**: For this, we formalize some desirable properties of a reasonable homophily measure and check which measures satisfy which properties. One essential property is called constant baseline and, informally speaking, it requires a measure to be not biased towards particular numbers of classes or their size balance**B*...
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Selection 1
**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 4
**A**: We measure the number of executed instructions rather than CPU cycles of the boot process, as FVP is not cycle-accurate and each instruction takes equally one cycle to execute (fvp-cycle, )**B**: To this end, we enable PMU (short for performance monitor unit (pmu, )) monitoring by setting a PMU control register ...
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Selection 4
**A**: In this subsection, we establish feedback asymptotic stability via dissipativity with dynamic supply rates**B**: It mimics [van der Schaft, 2017, Prop. 3.2.16] and establishes asymptotic stability for an open-loop system through dissipativity.**C**: The following technical lemma is needed in the proof of Theorem...
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Selection 1
**A**: Then, we suggest a new stochastic ZCBF for calculating a probability that a trajectory achieves a designed subset of a safe set before leaving the safe set. Our stochastic ZCBF satisfies an inequality, which differs from the previous results in [9, 10, 11, 12, 13, 14, 15] because the inequality directly includes...
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Selection 1
**A**: Then, using either a policy generated by PoLMDP or the optimal policy, we obtained, for each initial position, ten trajectories of 20 steps each between that initial position and each of the possible goals**B**: With all the trajectories generated, we then took each trajectory and sequentially gave more examples...
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Selection 3
**A**: X𝑋Xitalic_X), and their realization are in lower case (e.g**B**: Random variables are in capital 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 3
**A**: A larger gSCR indicates a larger stability margin.**B**: When all the wind farms in Fig. 4 adopt GFL control and have homogeneous dynamics, the multi-wind-farm system is (small signal) stable if and only if gSCR>CgSCRgSCRCgSCR{\rm gSCR}>{\rm CgSCR}roman_gSCR > roman_CgSCR**C**: Here CgSCRCgSCR{\rm CgSCR}roman_Cg...
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Selection 4
**A**: Fig. 9 shows three annual temperature anomaly series from distinct regions: the Northern Hemisphere, the Southern Hemisphere and the Tropics from 1850 to 2021, which are described in detail in [19]**B**: The data are temperature anomalies relative to a reference period of 1961-1990 [19]. Each series consists of ...
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Selection 1
**A**: 7**B**: A significant attribute of our methodology lies in the employment of our margin-based loss, m-OvR, which not only optimizes intra-class compactness but also ensures inter-class separation by circumventing inter-class collapse, as detailed in Prop**C**: This aspect renders our work as an improvement over...
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Selection 2