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**A**: [58] decouple the KLD into two uncorrelated losses and combine them by weighted summation.**B**: [19] use Kullback-Leibler Divergence (KLD) between the softened logits of teacher and student models as the loss to align the output distribution, and Zhao et al**C**: Response-based KD methods [19, 58, 3] have the n...
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**A**: It is described in Section 4**B**: However, it is possible to decrease aliasing error even when FNO is used for interpolation. One simply needs to train (or fine-tune) on a sufficiently fine grid. The decrease of aliasing error in this scenario is illustrated in the left plot of Figure 2a.**C**: Our solution to...
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**A**: Validating the anchor-point distillation. Then, we give more insight concerning the proposed objectives’ functionality through sensitivity analysis**B**: In terms of the anchor-point distillation, this work utilizes average pooling to extract the anchor in a local area from the original feature, forming the asso...
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**A**: In Fig. 4, we compare MPSE embedding of Palmer’s Penguins dataset to ENS-t-SNE (Fig. ENS-t-SNE: Embedding Neighborhoods Simultaneously t-SNE) using the same variables**B**: In the first view (Fig. 4(b)), blue and orange points are mixed, and in the second view (Fig. 4(c)), squared and circled shapes are mixed**...
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**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**: The first line of research studies offline RL in standard MDPs without any partial observability**B**: Table 1: We compare with most related representative works in closely related lines of research**C**: The second line of research studies online RL in POMDPs where the actions are specified by history-dependent...
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**A**: Toulis2017Asymptotic designed an implicit SGD method and showed the asymptotics of averaged implicit SGD iterates. Li2018Statistical designed an inference procedure for constant-stepsize SGD by averaging the iterates with recurrent burn-in periods**B**: Mou2020linear further showed the asymptotic covariance of c...
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**A**: The rest of the paper is organized as follows**B**: In Section 2 the technique of T𝑇Titalic_T-coercivity is discussed, which provides important auxiliary results for Section 3, which is the main section of the paper and contains the analysis of the discrete inf-sup conditions**C**: In Appendix A known results ...
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**A**: As shown in Figure 1 (c), the design of the WaveMix block is such it that does not collapse the spatial resolution of the feature maps, unlike CNN blocks that use pooling operations [9]**B**: However, unlike pooling or strided convolutions, a 2D-DWT is lossless as it expands the number of channels by the same fa...
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**A**: We can obviously neglect the trivial rows of B′superscript𝐵′B^{\prime}italic_B start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT and the corresponding rows of J′superscript𝐽′J^{\prime}italic_J start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT that are rows of 00 elements**B**: O⁢(s3⁢n)𝑂superscript𝑠3𝑛O(s^{3}n)italic_O (...
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**A**: zhong2019structural claim that supporting query expansion of math synonyms will improve recall and note that Approach0 does not support wildcard queries, which they later provide basic support for zhong2020accelerating. Tangent-CFT also does not evaluate on wildcard queries, and the authors suggest extending the...
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**A**: The first one is to allow the distribution of the block memberships to vary between networks and even to allow some networks to not populate certain blocks**B**: This is particularly useful to model networks with different sampling efforts, since it has a direct impact on the density of ecological networks (Blüt...
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**A**: Figure 5: Performance of FactorNets for individual rotation learning**B**: (left) Predictions of rotation angle vs. the ground truth (normalized to [−1,1]11[-1,1][ - 1 , 1 ]) in test set**C**: (right) Distributions of absolute percentage errors (in %) of all data points in the dataset.
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**A**: In real settings when we do not have knowledge about the dataset exact π𝜋\piitalic_π cannot be computed and needs to be estimated - referred to as the Mixture proportion estimation (MPE) problem**B**: We refer the reader to  (Ramaswamy et al., , 2016; Garg et al., , 2021; Ivanov, , 2020) for a detailed discussi...
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**A**: In the tubular link prediction task, however, the layer independent and layer dependent NNTucks have a similar test-AUC for nearly all values of K𝐾Kitalic_K. In both link prediction tasks we observe: variation in test-AUC for different values of K𝐾Kitalic_K and C𝐶Citalic_C; the layer redundant NNTuck has a lo...
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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**: A crucial point to bear in mind with quantum computing is that the memory capacity**C**: Experiments below used the 11-qubit trapped ion quantum computer described ...
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**A**: Solving the above objective requires iterating over all possible combinations of eigenvectors, which is infeasible in general**B**: It also requires performing expensive eigendecomposition with O⁢(N3)𝑂superscript𝑁3O(N^{3})italic_O ( italic_N start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT ) time complexity**C**: I...
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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**: It can be seen that indeed, in some cases (#Exp I,II,IV) the minimal unfairness is close to zero although the true unfairness is not, demonstrating the first phenomenon discussed above. Nonetheless, note that in the other experiments, the ratio between the true unfairness and the lower bound is non-trivial, rang...
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**A**: It contains 3.0003.0003.0003.000 measurements at 128⁢H⁢z128𝐻𝑧128Hz128 italic_H italic_z, equal to 23⁢s23𝑠~{}23s23 italic_s**B**: ECG Heartbeats contains a patient’s (ID 71717171) heartbeat from the LTAF database (Petrutiu et al., 2007)**C**: The heartbeat rate is 60606060 to 80808080 bpm. Known motifs are a c...
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**A**: In reality, many learning tasks process very large datasets, and thus decentralized parallel processing of data by communicating and computing units in the network is necessary, see e.g**B**: [23]-[24] and references therein**C**: Besides, if the data contains sensitive private information (e.g. medical and soc...
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**A**: On the other hand, AA also introduces the overhead of solving the least-squares problem (5) at each iteration. This computation overhead is outweighed by the benefit from fewer iterations when solving problems in which evaluating the operator G𝐺Gitalic_G incurs the dominant cost**B**: However, there are many pr...
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**A**: Our main objective was to gauge how well STAS is correlated with human judgments. We asked participants to evaluate how relevant is the generated summary with respect to the given topic. The human evaluation was presented as a multiple-choice question with 10 answers (1 to 10)**B**: In order to validate the reli...
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**A**: However, this is intractable when billions or trillions of transistors are considered**B**: Therefore, while full-custom design permits full optimization to meet design specifications, it is neither computationally nor economically viable for large system designs.**C**: The naive “full-custom” approach for opti...
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**A**: The results can be seen in Figures 6 and 6 for both models. The evaluation metrics on this test-set can be found in Table 2. **B**: We used this tool to generate test scans in 5 different parameter settings**C**: Brainweb is a simulated brain database that contains a set of realistic MRI data volumes produced by...
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**A**: Numerical simulation of phase-field type models is often challenging. To capture the dynamics of the evolution of the thin diffuse interface, the mesh size should be much smaller than ϵitalic-ϵ\epsilonitalic_ϵ, the width of the diffuse interface**B**: Traditional numerical methods often use an adaptive or moving...
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**A**: In particular, we show that increasing the number of parameters of two filtrations of topological spaces can only increase the interleaving/convolution distance between their associated persistence modules/sheaves**B**: On our way, we prove several results and provide examples that may be of independent interest...
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**A**: TABU is a variant of HC and is, as one might expect, sensitive to variable ordering, but the mean F1 change of 0.278 is considerably less than that of 0.412 for HC**B**: This may be because Tabu undoes some of the incorrect arbitrarily orientated arcs as it escapes local maxima towards the end of the learning pr...
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**A**: From the positive side, Luo [16] introduced the notion of rank-determining sets of metric graphs, and verified the existence of finite rank-determining sets constructively. Hladký, Král, and Norine [13] confirmed a conjecture of Baker [2] relating the ranks of a divisor on a graph and on a tropical curve, and p...
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**A**: For the CIFAR10-DVS dataset, we adopt the VGG11-like architecture introduced in TET [36]**B**: To maintain the same training settings as [36] for TCJA-TET-SNN, we use the triangle surrogate function, eliminate the last LIF layer, and replace the SMSE loss with TET loss. For TCJA-SNN, the TCJA module is added bef...
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**A**: Given**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_POSTSUPERSCRIPT**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**: Subsequently, Heuristic 2 further reduces the remaining search space by an additional 34%percent3434\%34 %, and Heuristic 3 contributes an additional reduction of 65%percent6565\%65 % to the remaining search space.**B**: To evaluate the efficacy of the pruning heuristics introduced in Section  5.2, we conduct e...
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**A**: Neither the European Union nor the granting authority can be held responsible for them.**B**: This work received funding from Ford Inc., and from the European Union (ERC, Bayes-RL, Project Number 101041250)**C**: Views and opinions expressed are however those of the author(s) only and do not necessarily reflect...
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**A**: MedHelp is a popular English OHC consisting of various communities for consumers to discuss diseases**B**: We extracted 520,659 discussion threads from 106 different communities in MedHelp**C**: To gather Chinese contents, we collected three Chinese healthcare Q&A websites, including eDoctor222http://taiwanedoc...
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**A**: ViTs operate by segmenting input images into smaller patches, treating each patch as a token similar to words in NLP**B**: These patches are then embedded (patch-embeddings) and passed to the transformer layers conducting self-attention and feedforward operations**C**: Such a design allows ViTs to capture long-r...
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**A**: One of the challenges in software testing is assigning a quality measure to test-cases such that higher-quality test-cases detect more bugs than low-quality test-cases (Ivanković et al., 2019)**B**: These quality measures are called test adequacy criteria, and code coverage is the commonly used test adequacy cri...
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**A**: The subsequent results in this section will inform the second algorithm. **B**: The following result gives the action of ℐμsuperscriptℐ𝜇\mathcal{I}^{\mu}caligraphic_I start_POSTSUPERSCRIPT italic_μ end_POSTSUPERSCRIPT on the JFP basis and is the foundation of the first algorithm to be presented in the following...
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**A**: S11). The same capability applies to different setups, supporting the universality of the conclusion drawn.**B**: S9) and sample2 (Fig. S10 and Fig**C**: To make sure our results are not affected by different setups, we perform a robustness check by repeating the measurement in the main text using sample1 (Fig....
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**A**: The numbers are for updating the last two blocks of MCUNet-5FPS [47] model. **B**: QAS helps to bridge the accuracy gap without memory overhead (slightly higher due to randomness)**C**: Table 1: Updating real quantized graphs (int8) for the fine-tuning is difficult: the accuracy falls behind the floating-point c...
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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**: We hope that our general way to translate bit-string benchmarks into permutation-based benchmarks eases the future development of the mathematical analysis of permutation-based evolutionary algorithms, a subfield where, different from bit-string representations, many fundamental questions have not yet been studi...
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**A**: To Oana Curtef (University of Würzburg) we are indebted for her observation concerning line search. SM, SP and MZ gratefully acknowledge the generous and invaluable support of the Klaus Tschira Foundation.**B**: We thank Jan Plier (Heidelberg University) for simulation code that efficiently evaluates our objecti...
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**A**: We thank Arkadev Chattopadhyay for helpful feedback and Todd Millstein for discussing [42] with us which led us to think about monotone neural networks**B**: We are grateful to David Kim for implementing our construction of a monotone neural network and testing it over several monotone data sets**C**: Finally, ...
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**A**: Using DG methods, the inter-element continuity constraint of conforming FE methods is dropped and concatenations of arbitrary local polynomials with support in only one element can be used as test and trial functions. This property resembles the finite volume (FV) approach, in which the solution per element is a...
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**A**: The Collaborative Learning Model.   Most study for BAI has been done in the centralized model, in which just one agent pulls the set of arms sequentially**B**: The learning proceeds in rounds.**C**: (TZZ19, ; KZZ20, ) studied BAI in the collaborative learning (CL) model, where there are K𝐾Kitalic_K agents, who ...
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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**: In this paper, we proposed a new randomized fixed-precision algorithm for fast computation of tensor SVD (t-SVD). Unlike the existing randomized low tubal rank approximation methods, the proposed algorithm finds an optimal tubal rank and the corresponding low tubal rank approximation automatically given a data t...
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**A**: Thus, irrelevant features will be ignored**B**: PCTs (and decision trees in general) are robust to irrelevant features since the learning algorithm chooses only the most informative features when building (supervised) trees**C**: However, in semi-supervised PCTs this feature may be compromised, since the evaluat...
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**A**: fuse the information by processing RGB and depth at the early stage to extract a deeper relation on each pixel. Meanwhile, DeepIPC fuses the information by performing BEV semantic mapping to get the advantage of perceiving from a different perspective. **B**: Huang et al**C**: Together with AIM-MT [27], we deplo...
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**A**: Since every independent set intersects each of the clique-bags in at most one vertex, dynamic programming still computes maximum weight independent sets in such graphs in polynomial time even if the bags could be arbitrarily large.**B**: However, it is not always the size of a bag that matters**C**: For example...
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**A**: We first leverage the RDP guarantee for the Gaussian mechanism mironov2017renyi to analyze the privacy cost for one communication round under local output perturbation**B**: Proof Sketch. We derive the privacy guarantee using Rényi Differential Privacy (RDP) mironov2017renyi as a bridge**C**: Then we use RDP C...
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**A**: As shown in Fig. 2, we construct the environment**B**: Note that, since sampling which of neighbors to update is discrete, we could not optimize it through stochastic gradient descent based methods [42, 82]**C**: More importantly, the process of deciding whether neighbor nodes should be updated or retained can b...
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**A**: He is currently a Research Scientist with Watrix Technology Limited Co. Ltd. His research interests include pattern recognition, computer vision and machine learning.**B**: Chunshui Cao received the B.E. and Ph.D. degrees from University of Science and Technology of China in 2013 and 2018, respectively**C**: Du...
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**A**: DPAV utilizes the partial average between the predicted maximal action value and the predicted minimal action value to estimate the ground truth maximum action value, where the weights are dynamically adaptive and problem-dependent**B**: The rationale here is that DPAV  learns the optimal trade-off between the p...
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**A**: On the one hand, researchers aimed at simplifying the problem by modelling future as a deterministic function based on the observed video, regardless of future uncertainty [2, 22]**B**: Existing literature [1, 2, 20, 21, 22, 26, 28] can be classified into two categories in terms of how to deal with the future**C...
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**A**: 5 presents a base time series sub-sequence 𝒔𝒔\bm{s}bold_italic_s and corresponding native anomaly examples generated via these six data perturbation operations within ΩΩ\Omegaroman_Ω.**B**: Fig**C**: These six perturbation functions can simulate abnormal behaviors in time series data
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**A**: Figure 1**B**: Illustration of D2T: Narration of time-series data (COVID19 progression in the United Kingdom at the top, the Carbon-Monoxide emissions in the state of Kansas, United States at the bottom) with the LLM-based framework T3superscript𝑇3T^{3}italic_T start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT (T-Cu...
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**A**: 43.6% on metric Mean under PredCls over Motifs). This proves that our improvements to the NSC module do make the model more robust to all predicates compared to the original NICE-v1. 3) NICEST achieves the highest performance on the Mean metric across the three tasks (e.g., 45.3% on Mean under PredCls over Motif...
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**A**: Previous work has shown that malicious miners can launch attacks by not following the standard mining process, e.g., hiding or discarding mined blocks, releasing a block to cause a fork [torres2021frontrunner, wu2020survive, wang2021securing, tsabary2021mad]**B**: This kind of attack is generally referred to as ...
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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**: The PostLN Transformer training fails late in the warmmup period. **C**: Figure 7:...
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**A**: J.R. acknowledges funding from the Polish Science Foundation (START), the National Science Center in Poland (Sonata 2021/43/D/ST4/00920, ‘‘Statistical Learning of Slow Collective Variables from Atomistic Simulations’’), and the Ministry of Science and Higher Education in Poland**B**: acknowledge the support of ...
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**A**: Such small vessel trees can be modeled in a variety of ways. It is natural to ask which region of the ventricle is perfused by a given coronary artery**B**: There are many methods by which the ventricle can be divided. However, as we have access to the rich coronary vascular data set, we construct a physiologica...
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**A**: Graph Convolutional Networks (GCN) is a known feature-extraction technique for non-Euclidean spaces [9]**B**: GCNs are capable of learning the graph structure by aggregating each node’s embedding with its neighbors**C**: In the conventional architecture, GCN is proven to be capable of incorporating node and edg...
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**A**: The ι𝜄\iotaitalic_ι-CCE can be found efficiently by the method developed in Xie et al**B**: An ι𝜄\iotaitalic_ι-CCE may not have mutually independent marginals since the two players take actions in a correlated way**C**: (2020) for arbitrary ι>0𝜄0\iota>0italic_ι > 0.
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**A**: As a proof of concept, we numerically solve the 1D (d=1𝑑1d=1italic_d = 1) control PDE arising from the Kuramoto model (5) using finite differences and extend the solution to the entire domain using linear interpolation**B**: Using such a method to solve (14) in higher dimensions (d≫1much-greater-than𝑑1d\gg 1i...
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**A**: Overall, this work contributes to the ongoing collective efforts aimed at demonstrating the feasibility of autonomous asteroid exploration, challenging the cautious and conservative approach inherited from current ground-in-the-loop missions**B**: The results highlight the potential for rapid autonomous explorat...
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**A**: To our knowledge, this is the first work that analyzes the computation of Brascamp–Lieb constants via Thompson geometry. We note that a similar Finslerian lens can be employed to understand other Picard iterations arising from problem (1.3)**B**: Our analysis leverages the Thompson part metric on the manifold of...
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**A**: The centrality plots suggest the presence of a relatively important signal within the point cloud data**B**: This is evidenced by the large difference in the maximum centrality value for the highest ranked hole compared to the others**C**: Notably, this hole coincides with the one previously identified using th...
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**A**: FixMatch is a significant simplification of existing SSL methods (DBLP:conf/nips/SohnBCZZRCKL20, ). It first generates pseudo-labels using the model’s predictions on weakly-augmented unlabeled images**B**: Despite its simplicity, FixMatch achieves state-of-the-art performance across a variety of standard semi-su...
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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**: Therefore, we look at the difference between the loss function values with adaptive weights versus any fixed weights after B𝐵Bitalic_B batches (where ΘΘ\Thetaroman_Θ and λ⁢(t)𝜆𝑡\lambda(t)italic_λ ( italic_t ) are estimated on this batch)**B**: We are interested in the stability of the algorithm with adaptive ...
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**A**: In a large number of practical applications, one regularizes inverse problems by adding a penalty term to the misfit function for the purpose of penalizing undesirable aspects of the recovered function**B**: For example, in our definition of the source identification problem in Section 4.1 (see also equation (19...
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**A**: In addition, including other types of relationships outside of parent-child relationships, such as synonyms, could be of interest. Furthermore, including more means to show the data distribution could help in the process of creating the label hierarchy.**B**: To further include object localization tasks, an addi...
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**A**: Table XIII: Results (%) of cross-task prompt transfer on BERT-base**B**: Notably, positive transfers are in green and “Avg.” denotes the average performance of all target tasks. Numbers in the subscript indicate relative improvements of PanDa compared to the vanilla PoT. **C**: The red-colored row shows the re...
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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**: We also found some ‘new faces’ e.g., the second most active defacer targeting Russia after t...
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**A**: Our observations reveal a consistent trend across all datasets and architecture combinations: HET closely tracks the upperbound line, which represents the theoretical maximum transferability**B**: As k𝑘kitalic_k increases, HET maintains commendable performance, deviating by at most approximately 20**C**: Parti...
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**A**: As a result, as shown in Fig. 6, global measurements do not lead to the exponential concentration of the fidelity kernel for low depth ansatze**B**: For example, the MNIST classification task does not satisfy the assumptions of Proposition 3**C**: This demonstrates that the structure of the training data matters...
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**A**: Data augmentation methods such as random cropping, random rotation, colour jittering, horizontal flipping are performed to the all data. After data augmentation, the total number of each class of RGB video data and video combined bounding box data is 2420 and 432 respectively**B**: The data used for the first a...
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**A**: 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**: II00\displaystyle 011\displaystyle 11Uncertainty Score (GCJ)Norm.Imit.Obf. IObf
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**A**: In (a)-(d), we assume there are 2 classes per task and shared prompt contexts are in the same color.**B**: Figure 1: A conceptual comparison of different prompt tuning methods**C**: (a) class-agnostic CoOp, (b) class-specified CoOp, (c) hard prompt sharing for CoOp, (d) our soft prompt sharing, (e) average perf...
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**A**: (2021).. These distinctions encompass a notable decrease in recreational facilities and a marked rise in single-unit residential properties. **B**: Label distribution shifts can also be corroborated through analysis on the WILDS benchmark dataset, which investigates shifts in distributions within untamed and unr...
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**A**: Our second main contribution is to propose and study a monotone Finite Element Method (FEM) for approximating weak solutions to the MFG PDI (4). In this context, monotonicity of the FEM refers to the presence of a discrete maximum principle**B**: There is a wide range of approaches to constructing monotone FEMs;...
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Selection 3
**A**: We also have to note that the scenarios were defined in order to provide challenging allocation tasks for the algorithms (utility values are bound from above by 6/12/20 respectively), to be able to compare the efficiency of different methods and parameter sets in non-trivial tasks (if there is no resource scarci...
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Selection 2
**A**: The cases of different distribution frequencies often exist in some scenarios. We will consider the dynamics to improve our model in the future. Second, we will explore its application in other real distribution-drift scenarios, such as research hot spots, stock trend forecasting, and product demand analysis.**B...
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Selection 2
**A**: b. Recovering the latent representation from the sequential dSprites images. The left column represents the latent space learned from SDE-VAE. The right column represents the latent representation learned from DynAE.**B**: Figure 6: Comparison of the results on dSprites dataset obtained from SDE-VAE and DynAE w...
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Selection 1
**A**: If they are the same ([139, 7]), we have a closed trajectory**B**: If the initial and final positions differ (see [12, 138]), we have an open trajectory**C**: We find closed trajectories in repetitive tasks, such as a multirotor UAV operating as a data ferry [7], an MR doing periodic data collection from sensor ...
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Selection 2
**A**: (Eqn. 1)**B**: First, we will require a more specific notation for the parameterization of the generative model, however. **C**: Such models will be sufficient to communicate the concepts the proof relies on but generalizations will be discussed in Secs. 5 and 6
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Selection 3
**A**: We then move on to prove Theorem 4 and Theorem 3 in Section 4.2.**B**: 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**C**: This section is devoted to the proofs of Theorem 2, Theorem 4, a...
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Selection 3
**A**: Next, we will introduce the definition and the quantitative calculation of two kinds of fairness.**B**: However, they only focus on the accuracy regarding one kind of user behavior, ignoring the relations between multiple user behaviors and the unfairness caused by popularity bias. Different from MACR [12] and P...
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Selection 2
**A**: Subsequently, we increase the feature dimension from 512 to 1792, and the performance improvement is only evidenced in the SCID →→\rightarrow→ SIQAD setting, accompanied by an increase in model complexity. A significant performance drop can be observed when the dimension is increased to 2048, revealing a larger ...
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Selection 2
**A**: To further characterize the datasets and distinguish different sorts of heterophily, we propose a new measure called label informativeness. **B**: Based on this framework, we suggest using adjusted homophily to measure whether similar nodes tend to be connected**C**: In summary, we propose a theoretical framewor...
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Selection 2
**A**: It is hence legitimate to ask whether, in return, such Talagrand-type inequalities imply hypercontractivity. This question was answered in the positive in the classical, continuous setting in [BH99, Proposition 1], and later on for discrete spaces in [Vö16]. It would be interesting to consider the similar proble...
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Selection 3
**A**: Existing research efforts focus on firmware integrity and provide no countermeasures against hardware supply-chain attacks in multiprocessor secure boot**B**: In fact, defending against this new hardware attack surface is challenging: It is difficult to examine all steps through the global supply chain from man...
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Selection 4
**A**: It mimics [van der Schaft, 2017, Prop. 3.2.16] and establishes asymptotic stability for an open-loop system through dissipativity.**B**: In this subsection, we establish feedback asymptotic stability via dissipativity with dynamic supply rates**C**: The following technical lemma is needed in the proof of Theorem...
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Selection 2
**A**: For a stochastic system, a subset of the state space is generally hard to be (almost sure) invariance because the diffusion coefficient is required to be zero at the boundary of the subset111The detail is discussed in[18], which aims to make the state of a stochastic system converge to the origin with probabilit...
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Selection 1
**A**: Habibian and Losey [9] developed a framework for legible allocation of subtasks in teams composed by robots and humans. MacNally et al**B**: More recently, several works have extended the notion of legibility to domains other than robotic motion. The focus on improving the transparency and explainability of mach...
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Selection 4
**A**: 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.**B**: Random variables are in capital case (e.g**C**: X𝑋Xitalic_X), and their realization are in lower case (e.g
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Selection 4
**A**: Furthermore, the analysis in  [9] only considers one type of GFM control (i.e., VSM) and directly approximates a VSM as an ideal voltage source (without deriving the equivalent impedance as will be done in this paper). Such an approach might not apply to other GFM methods once they have weaker voltage source beh...
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Selection 1
**A**: A grid search was conducted to find**B**: The order p=4𝑝4p=4italic_p = 4 for a VAR model is a common choice in the analysis of quarterly macroeconomic series, for example, [14], [15] and [10]. The first model we fitted was DeepVARwT(4)**C**: The number of input t𝑡titalic_t functions and the hidden state size w...
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Selection 1
**A**: We develop an effective OSR method based on our theoretical finding given in Fig. 2**B**: Then, we integrate the loss term with other regularizers that enhance the separation of the unknown via the Jacobian norm difference. Finally, for the unknown class detection in the inference stage, we utilize the sample-w...
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Selection 4