context stringlengths 250 5.57k | A stringlengths 250 4.17k | B stringlengths 250 3.69k | C stringlengths 250 8.2k | D stringlengths 250 4.12k | label stringclasses 4
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This already suffices to implement the standard Newton iteration, i.e., to
approximate (1) by Δx=−f(x)/f′(x)Δ𝑥𝑓𝑥superscript𝑓′𝑥\Delta x=-f(x)/f^{\prime}(x)roman_Δ italic_x = - italic_f ( italic_x ) / italic_f start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ). | Rnm′′/Rnm′superscriptsuperscriptsubscript𝑅𝑛𝑚′′superscriptsuperscriptsubscript𝑅𝑛𝑚′{R_{n}^{m}}^{\prime\prime}/{R_{n}^{m}}^{\prime}italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT / italic_R start_POSTSUBSCRIPT it... | Division of (29) through Rnm′(x)superscriptsuperscriptsubscript𝑅𝑛𝑚′𝑥{R_{n}^{m}}^{\prime}(x)italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x ) yields
| Rnm′(x)superscriptsuperscriptsubscript𝑅𝑛𝑚′𝑥\displaystyle{R_{n}^{m}}^{\prime}(x)italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT ( italic_x )
≅\displaystyle\cong≅ | Rnm′′(x)superscriptsuperscriptsubscript𝑅𝑛𝑚′′𝑥\displaystyle{R_{n}^{m}}^{\prime\prime}(x)italic_R start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_m end_POSTSUPERSCRIPT start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT ( italic_x )
≅\displaystyle\cong≅ | B |
The case where d𝑑ditalic_d is even is very similar, but requires a few changes that would complicate the pseudocode.
So, for the clarity of our exposition, we analyse the case d𝑑ditalic_d odd here and then explain the differences for the case d𝑑ditalic_d even in the next subsection. |
The key idea is to transform the diagonal matrix with the help of row and column operations into the identity matrix in a way similar to an algorithm to compute the elementary divisors of an integer matrix, as described for example in [23, Chapter 7, Section 3]. Note that row and column operations are effected by left... | So twice the quantity (17) is contributed to the maximum length of an MSLP for Algorithm 3.
In addition, we must also include the cost of the initial computation of T1subscript𝑇1T_{1}italic_T start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT given by Lemma 4.2, namely 5f−15𝑓15f-15 italic_f - 1 instructions, and then two addit... |
For the purposes of determining the cost of Taylor’s algorithm in terms of matrix operations, namely determining the length of an MSLP for the algorithm, we assume that the field elements −gicgrc−1subscript𝑔𝑖𝑐superscriptsubscript𝑔𝑟𝑐1-g_{ic}g_{rc}^{-1}- italic_g start_POSTSUBSCRIPT italic_i italic_c end_POSTSU... | To aid the exposition and analysis, Algorithm 3 refers to several subroutines, namely Algorithms 4–7. In an implementation the code for the Algorithms 4–7 would be inserted into Algorithm 3 in the lines where they are called. We present them as subroutines here to improve the readability of Algorithm 3. However, we ass... | D |
where Ω⊂ℝdΩsuperscriptℝ𝑑\Omega\subset\mathbb{R}^{d}roman_Ω ⊂ blackboard_R start_POSTSUPERSCRIPT italic_d end_POSTSUPERSCRIPT with d=2𝑑2d=2italic_d = 2 or 3333 for simplicity, and is an open bounded domain with polyhedral boundary ∂ΩΩ\partial\Omega∂ roman_Ω, the symmetric tensor 𝒜∈[L∞(Ω)]symd×d𝒜superscriptsubscrip... | In [MR2718268] is shown that the number of eigenvalues that are very large is related to the number of connected sub-regions on τ¯∪τ¯′¯𝜏superscript¯𝜏′\bar{\tau}\cup{\bar{\tau}}^{\prime}over¯ start_ARG italic_τ end_ARG ∪ over¯ start_ARG italic_τ end_ARG start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT with large coefficien... | It is hard to approximate such problem in its full generality using numerical methods, in particular because of the low regularity of the solution and its multiscale behavior. Most convergent proofs either assume extra regularity or special properties of the coefficients [AHPV, MR3050916, MR2306414, MR1286212, babuos85... |
As in many multiscale methods previously considered, our starting point is the decomposition of the solution space into fine and coarse spaces that are adapted to the problem of interest. The exact definition of some basis functions requires solving global problems, but, based on decaying properties, only local comput... | One difficulty that hinders the development of efficient methods is the presence of high-contrast coefficients [MR3800035, MR2684351, MR2753343, MR3704855, MR3225627, MR2861254]. When LOD or VMS methods are considered, high-contrast coefficients might slow down the exponential decay of the solutions, making the method ... | B |
Similarly, from a P𝑃Pitalic_P-stable triangle A′B′C′superscript𝐴′superscript𝐵′superscript𝐶′A^{\prime}B^{\prime}C^{\prime}italic_A start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_B start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT italic_C start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT, we can also construct △ABC△𝐴�... | Alg-A computes at most n𝑛nitalic_n candidate triangles (proof is trivial and omitted) whereas Alg-CM computes at most 5n5𝑛5n5 italic_n triangles (proved in [8]) and so as Alg-K.
(by experiment, Alg-CM and Alg-K have to compute roughly 4.66n4.66𝑛4.66n4.66 italic_n candidate triangles.) | Our algorithm given in section 4 (denoted by Alg-One) is different from Alg-DS.
First, step 1 of Alg-One sets the initial value of (r,s,t)𝑟𝑠𝑡(r,s,t)( italic_r , italic_s , italic_t ) differently from the initial value (1,2,3)123(1,2,3)( 1 , 2 , 3 ) used by Alg-DS. |
Our experiment shows that the running time of Alg-A is roughly one eighth of the running time of Alg-K, or one tenth of the running time of Alg-CM. (Moreover, the number of iterations required by Alg-CM and Alg-K is roughly 4.67 times that of Alg-A.) | Comparing the description of the main part of Alg-A (the 7 lines in Algorithm 1) with that of Alg-CM (pages 9–10 of [8]),
Alg-A is conceptually simpler. Alg-CM is claimed “involved” by its authors as it contains complicated subroutines for handling many subcases. | C |
Widely spreading rumors can be harmful to the government, markets and society and reduce the usefulness of social media channel such as Twitter by affecting the reliability of their content.
Therefore, effective method for detecting rumors on Twitter are crucial and rumors should be detected as early as possible before... | Widely spreading rumors can be harmful to the government, markets and society and reduce the usefulness of social media channel such as Twitter by affecting the reliability of their content.
Therefore, effective method for detecting rumors on Twitter are crucial and rumors should be detected as early as possible before... | The city police had to warn the population to refrain from spreading related news on Twitter as it was getting out of control: “Rumors are wildfires that are difficult to put out and traditional news sources or official channels, such as police departments, subsequently struggle to communicate verified information to t... |
We observe that at certain points in time, the volume of rumor-related tweets (for sub-events) in the event stream surges. This can lead to false positives for techniques that model events as the aggregation of all tweet contents; that is undesired at critical moments. We trade-off this by debunking at single tweet le... | at an early stage. Our fully automatic, cascading rumor detection method follows
the idea on focusing on early rumor signals on text contents; which is the most reliable source before the rumors widely spread. Specifically, we learn a more complex representation of single tweets using Convolutional Neural Networks, tha... | B |
\left(\sqrt{\frac{\log\log t}{\log t}}\right)∥ divide start_ARG bold_w ( italic_t ) end_ARG start_ARG ∥ bold_w ( italic_t ) ∥ end_ARG - divide start_ARG over^ start_ARG bold_w end_ARG end_ARG start_ARG ∥ over^ start_ARG bold_w end_ARG ∥ end_ARG ∥ = italic_O ( square-root start_ARG divide start_ARG roman_log roman_log i... | In some non-degenerate cases, we can further characterize the asymptotic behavior of 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ). To do so, we need to refer to the KKT conditions (eq. 6)
of the SVM problem (eq. 4) and the associated |
where the residual 𝝆k(t)subscript𝝆𝑘𝑡\boldsymbol{\rho}_{k}(t)bold_italic_ρ start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ( italic_t ) is bounded and 𝐰^ksubscript^𝐰𝑘\hat{\mathbf{w}}_{k}over^ start_ARG bold_w end_ARG start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT is the solution of the K-class SVM: | The follow-up paper (Gunasekar et al., 2018) studied this same problem with exponential loss instead of squared loss. Under additional assumptions on the asymptotic convergence of update directions and gradient directions, they were able to relate the direction of gradient descent iterates on the factorized parameteriz... | where 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ) has a bounded norm for almost all datasets, while in zero measure case 𝝆(t)𝝆𝑡\boldsymbol{\rho}\left(t\right)bold_italic_ρ ( italic_t ) contains additional O(loglog(t))𝑂𝑡O(\log\log(t))italic_O ( roman_log roman_log ( italic_t ) ) componen... | A |
We observe that at certain points in time, the volume of rumor-related tweets (for sub-events) in the event stream surges. This can lead to false positives for techniques that model events as the aggregation of all tweet contents; that is undesired at critical moments. We trade-off this by debunking at single tweet le... |
In this work, we present a deep analysis on the feature variants over 48 hours for the rumor detection task. The results show that the low-level hidden representation of tweets feature is at least the second best features over time. We also derive explanations on the low performance of supposed-to-be-strong high-level... |
We investigate how the performance of different types of low and high-level features changes over time (during the spreading of rumors); improving the understanding of feature impact and model design for rumor detection at different points in time. | the idea on focusing on early rumor signals on text contents; which is the most reliable source before the rumors widely spread. Specifically, we learn a more complex representation of single tweets using Convolutional Neural Networks, that could capture more hidden meaningful signal than only enquiries to debunk rumor... | The performance of user features is similar with the Twitter features, they are both quite stable from the first hour to the last hour. As shown in Table 9, the best feature over 48 hours of the user feature group is UserTweetsPerDays and it is the best feature overall in the first 4 hours, but its rank decreases with ... | A |
Results. The baseline and the best results of our 1stsuperscript1𝑠𝑡1^{st}1 start_POSTSUPERSCRIPT italic_s italic_t end_POSTSUPERSCRIPT stage event-type classification is shown in Table 3-top. The accuracy for basic majority vote is high for imbalanced classes, yet it is lower at weighted F1. Our learned model achie... | RQ3. We demonstrate the results of single models and our ensemble model in Table 4. As also witnessed in RQ2, SVMall𝑆𝑉subscript𝑀𝑎𝑙𝑙SVM_{all}italic_S italic_V italic_M start_POSTSUBSCRIPT italic_a italic_l italic_l end_POSTSUBSCRIPT, will all features, gives a rather stable performance for both NDCG and Recall... | For this part, we first focus on evaluating the performance of single L2R models that are learned from the pre-selected time (before, during and after) and types (Breaking and Anticipate) set of entity-bearing queries. This allows us to evaluate the feature performance i.e., salience and timeliness, with time and type ... | Multi-Criteria Learning. Our task is to minimize the global relevance loss function, which evaluates the overall training error, instead of assuming the independent loss function, that does not consider the correlation and overlap between models. We adapted the L2R RankSVM [12]. The goal of RankSVM is learning a linear... | We further investigate the identification of event time, that is learned on top of the event-type classification. For the gold labels, we gather from the studied times with regards to the event times that is previously mentioned. We compare the result of the cascaded model with non-cascaded logistic regression. The res... | D |
RL [Sutton and Barto, 1998] has been successfully applied to a variety of domains,
from Monte Carlo tree search [Bai et al., 2013] and hyperparameter tuning for complex optimization in science, engineering and machine learning problems [Kandasamy et al., 2018; Urteaga et al., 2023], | The techniques used in these success stories are grounded on statistical advances on sequential decision processes and multi-armed bandits.
The MAB crystallizes the fundamental trade-off between exploration and exploitation in sequential decision making. | we propagate forward the sequential random measure pM(θt,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡𝑎subscriptℋ:1𝑡p_{M}(\theta_{t,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t , italic_a end_POSTSUBSCRIPT | caligraphic_H start_POSTSUBSCRIPT 1 : ... | SMC weights are updated based on the likelihood of the observed rewards:
wt,a(m)∝pa(yt|xt,θt,a(m))proportional-tosuperscriptsubscript𝑤𝑡𝑎𝑚subscript𝑝𝑎conditionalsubscript𝑦𝑡subscript𝑥𝑡superscriptsubscript𝜃𝑡𝑎𝑚w_{t,a}^{(m)}\propto p_{a}(y_{t}|x_{t},\theta_{t,a}^{(m)})italic_w start_POSTSUBSCRIPT italic_t , it... | the fundamental operation in the proposed SMC-based MAB Algorithm 1
is to sequentially update the random measure pM(θt,a|ℋ1:t)subscript𝑝𝑀conditionalsubscript𝜃𝑡𝑎subscriptℋ:1𝑡p_{M}(\theta_{t,a}|\mathcal{H}_{1:t})italic_p start_POSTSUBSCRIPT italic_M end_POSTSUBSCRIPT ( italic_θ start_POSTSUBSCRIPT italic_t , itali... | A |
For time delays between carb entries and the next glucose measurements we distinguish cases where glucose was measured at most 30 minutes before logging the meal, to account for cases where multiple measurements are made for one meal – in such cases it might not make sense to predict the glucose directly after the meal... | These are also the patients who log glucose most often, 5 to 7 times per day on average compared to 2-4 times for the other patients.
For patients with 3-4 measurements per day (patients 8, 10, 11, 14, and 17) at least a part of the glucose measuremtents after the meals is within this range, while patient 12 has only t... | For time delays between carb entries and the next glucose measurements we distinguish cases where glucose was measured at most 30 minutes before logging the meal, to account for cases where multiple measurements are made for one meal – in such cases it might not make sense to predict the glucose directly after the meal... | Likewise, the daily number of measurements taken for carbohydrate intake, blood glucose level and insulin units vary across the patients.
The median number of carbohydrate log entries vary between 2 per day for patient 10 and 5 per day for patient 14. | Median number of blood glucose measurements per day varies between 2 and 7. Similarly, insulin is used on average between 3 and 6 times per day.
In terms of physical activity, we measure the 10 minute intervals with at least 10 steps tracked by the google fit app. | A |
Various measures are used in the literature and by benchmarks to evaluate the performance of fixation models. In practice, results are typically reported for all of them to include different notions about saliency and allow a fair comparison of model predictions Kümmerer et al. (2018); Riche et al. (2013). A set of nin... | Later attempts addressed that shortcoming by taking advantage of classification architectures pre-trained on the ImageNet database Deng et al. (2009). This choice was motivated by the finding that features extracted from CNNs generalize well to other visual tasks Donahue et al. (2014). Consequently, DeepGaze I Kümmerer... |
In this work, we adopted KLD as an objective function and produced fixation density maps as output from our proposed network. This training setup is particularly sensitive to false negative predictions and thus the appropriate choice for applications aimed at salient target detection Bylinskii et al. (2018). Defining ... | A prerequisite for the successful application of deep learning techniques is a wealth of annotated data. Fortunately, the growing interest in developing and evaluating fixation models has lead to the release of large-scale eye tracking datasets such as MIT1003 Judd et al. (2009), CAT2000 Borji and Itti (2015), DUT-OMRO... | To assess the predictive performance for eye tracking measurements, the MIT saliency benchmark Bylinskii et al. (2015) is commonly used to compare model results on two test datasets with respect to prior work. Final scores can then be submitted on a public leaderboard to allow fair model ranking on eight evaluation met... | B |
We observe that the reduction from MinCutwidth to MinLoc from Section 4.1 combined with the reduction from MinLoc to MinPathwidth from Section 5.2 gives a reduction from MinCutwidth to MinPathwidth. Moreover, this reduction is approximation preserving; thus, it carries over approximations for MinPathwidth (e. g., [21,... | Pathwidth and cutwidth are classical graph parameters that play an important role for graph algorithms, independent from our application for computing the locality number. Therefore, it is the main purpose of this section to translate the reduction from MinCutwidth to MinPathwidth that takes MinLoc as an intermediate s... | In the following, we obtain an approximation algorithm for the locality number by reducing it to the problem of computing the pathwidth of a graph. To this end, we first describe another way of how a word can be represented by a graph. Recall that the reduction to cutwidth from Section 4 also transforms words into grap... | One of the main results of this section is a reduction from the problem of computing the locality number of a word α𝛼\alphaitalic_α to the probem of computing the pathwidth of a graph. This reduction, however, does not technically provide a reduction from the decision problem Loc to Pathwidth, since the constructed gr... |
We observe that the reduction from MinCutwidth to MinLoc from Section 4.1 combined with the reduction from MinLoc to MinPathwidth from Section 5.2 gives a reduction from MinCutwidth to MinPathwidth. Moreover, this reduction is approximation preserving; thus, it carries over approximations for MinPathwidth (e. g., [21,... | A |
Another three models were trained using the signals as 1D.
The first model was a FNN with dropout, the second a three layer 1D CNN and the third a 2D CNN same as the first but trained with a stacked version of the signal (also trained with data augmentation). | Gotlibovych et al.[117] trained an one layer CNN network followed by a LSTM using 180h of PPG wearable data to detect AF.
Use of the LSTM layer allows the network to learn variable-length correlations in contrast with the fixed length of the convolutional layer. | An one hidden layer network was used for the initial testing of all voxels to obtain a small number of candidates, followed by a more accurate classification with a deep network.
The learned image features are further combined with Haar wavelet features to increase the detection accuracy. | Experiments by the authors showed that the three layer 1D CNN created better and more stable results.
In[101] the authors trained a network with an one convolutional layer with dropout followed by two RNNs to identify stress using short-term ECG data. | Another three models were trained using the signals as 1D.
The first model was a FNN with dropout, the second a three layer 1D CNN and the third a 2D CNN same as the first but trained with a stacked version of the signal (also trained with data augmentation). | C |
Figure 3: Comparison with Rainbow and PPO. Each bar illustrates the number of interactions with environment required by Rainbow (left) or PPO (right) to achieve the same score as our method (SimPLe). The red line indicates the 100100100100K interactions threshold which is used by the our method. | We evaluate our method on 26262626 games selected on the basis of being solvable with existing state-of-the-art model-free deep RL algorithms222Specifically, for the final evaluation we selected games which achieved non-random results using our method or the Rainbow algorithm using 100100100100K interactions., which in... | In our empirical evaluation, we find that SimPLe is significantly more sample-efficient than a highly tuned version of the state-of-the-art Rainbow algorithm (Hessel et al., 2018) on almost all games. In particular, in low data regime of 100100100100k samples, on more than half of the games, our method achieves a score... |
The primary evaluation in our experiments studies the sample efficiency of SimPLe, in comparison with state-of-the-art model-free deep RL methods in the literature. To that end, we compare with Rainbow (Hessel et al., 2018; Castro et al., 2018), which represents the state-of-the-art Q-learning method for Atari games, ... |
Figure 3: Comparison with Rainbow and PPO. Each bar illustrates the number of interactions with environment required by Rainbow (left) or PPO (right) to achieve the same score as our method (SimPLe). The red line indicates the 100100100100K interactions threshold which is used by the our method. | C |
Zhang et al. [11] trained an ensemble of CNNs containing two to ten layers using STFT features extracted from EEG band frequencies for mental workload classification.
Giri et al. [12] extracted statistical and information measures from frequency domain to train an 1D CNN with two layers to identify ischemic stroke. | The names of the classes are depicted at the right along with the predictions for this example signal.
The image between m𝑚mitalic_m and bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT depicts the output of the one layer CNN Signal2Image module, while the ‘signal as image’ and spectrogram h... | Figure 1: High level overview of a feed-forward pass of the combined methods.
xisubscript𝑥𝑖x_{i}italic_x start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT is the input, m𝑚mitalic_m is the Signal2Image module, bdsubscript𝑏𝑑b_{d}italic_b start_POSTSUBSCRIPT italic_d end_POSTSUBSCRIPT is the 1D or 2D architecture ‘base ... | The spectrogram S2I results are in contrary with the expectation that the interpretable time-frequency representation would help in finding good features for classification.
We hypothesize that the spectrogram S2I was hindered by its lack of non-trainable parameters. | For the purposes of this paper and for easier future reference we define the term Signal2Image module (S2I) as any module placed after the raw signal input and before a ‘base model’ which is usually an established architecture for imaging problems.
An important property of a S2I is whether it consists of trainable para... | D |
In the realm of mobile robotics research, the motion control of terrestrial robots across varied terrains is a complex endeavor. To enhance locomotion efficacy and elevate mobility, hybrid robots have been actively developed in the past decade [1]. These robots astutely choose the most suitable locomotion mode from a s... | There are two primary technical challenges in the wheel/track-legged robotics area [2]. First, there’s a need to ensure accurate motion control within both rolling and walking locomotion modes [5] and effectively handle the transitions between them [6]. Second, it’s essential to develop decision-making frameworks that ... | This paper presents a novel methodology for achieving autonomous locomotion mode transitions in quadruped wheel/track-legged hybrid robots, taking into account both internal states of the robot and external environmental conditions. Our emphasis is on the “articulated wheel/track robot” [15], where the wheels or tracks... |
In the literature review, Gorilla [2] is able to switch between bipedal and quadrupedal walking locomotion modes autonomously using criteria developed based on motion efficiency and stability margin. WorkPartner [8] demonstrated its capability to seamlessly transition between two locomotion modes: rolling and rolking.... | This section describes the primary locomotion modes, rolling and walking locomotion of our hybrid track-legged robot named Cricket shown in Fig. 2. It also introduces two proposed gaits designed specifically for step negotiation in quadrupedal wheel/track-legged robots.
| A |
In other words, the algorithm designer can hedge against untrusted advice, by a small sacrifice in the trusted performance. Thus we can interpret r𝑟ritalic_r as the “risk” for trusting the advice: the smaller the r𝑟ritalic_r, the bigger the risk.
Likewise, for the list update problem, our (r,f(r))𝑟𝑓𝑟(r,f(r))( ita... | We introduced a new model in the study of online algorithms with advice, in which the online algorithm can leverage information about the request sequence that is not necessarily foolproof. Motivated by advances in learning-online algorithms, we studied tradeoffs between the trusted and untrusted competitive ratio, as ... | As argued in detail in [9], there are compelling reasons to study the advice complexity of online computation.
Lower bounds establish strict limitations on the power of any online algorithm; there are strong connections between randomized online algorithms and online algorithms with advice (see, e.g., [27]); online alg... |
All the above results pertain to deterministic online algorithms. In Section 6, we study the power of randomization in online computation with untrusted advice. First, we show that the randomized algorithm of Purohit et al. [29] for the ski rental problem Pareto-dominates any deterministic algorithm, even when the lat... | We begin in Section 2 with a simple, yet illustrative online problem as a case study, namely the ski rental problem.
Here, we give a Pareto-optimal algorithm with only one bit of advice. We also show that this algorithm is Pareto-optimal even in the space of all (deterministic) algorithms with advice of any size. | C |
Note that this algorithm can be massively parallelized since it naturally follows the Big Data programming model MapReduce [Dean & Ghemawat, 2008], giving the framework the capability of effectively processing very large volumes of data.
In Algorithm 2 is shown the training process described earlier. Note that the line... | It is worth mentioning that with this simple mechanism it would be fairly straightforward to justify when needed, the reasons of the classification by using the values of confidence vectors in the hierarchy, as will be illustrated with a visual example at the end of Section 5.
Additionally, the classification is also i... | This brief subsection describes the training process, which is trivial. Only a dictionary of term-frequency pairs is needed for each category.
Then, during training, dictionaries are updated as new documents are processed —i.e. unseen terms are added and frequencies of already seen terms are updated. | Note that with this simple training method there is no need neither to store all documents nor to re-train from scratch every time a new training document is added, making the training incremental101010Even new categories could be dynamically added.. Additionally, there is no need to compute the document-term matrix be... | Otherwise, it can be omitted since, during classification, gv𝑔𝑣gvitalic_g italic_v can be dynamically computed based on the frequencies stored in the dictionaries.
It is worth mentioning that this algorithm could be easily parallelized by following the MapReduce model as well —for instance, all training documents co... | D |
}(\frac{1}{\sqrt{KT}})divide start_ARG 1 end_ARG start_ARG italic_T end_ARG ∑ start_POSTSUBSCRIPT italic_t ∈ [ italic_T ] end_POSTSUBSCRIPT blackboard_E ∥ ∇ italic_F ( bold_w start_POSTSUBSCRIPT italic_t end_POSTSUBSCRIPT ) ∥ start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ≤ caligraphic_O ( divide start_ARG 1 end_ARG start... |
In this paper, we propose a novel method, called global momentum compression (GMC), for sparse communication in distributed learning. To the best of our knowledge, this is the first work that introduces global momentum for sparse communication in DMSGD. Furthermore, to enhance the convergence performance when using mo... | DEF-A achieves its best performance when λ=0.3𝜆0.3\lambda=0.3italic_λ = 0.3. In comparison, GMC+ outperforms DEF-A across different λ𝜆\lambdaitalic_λ values and shows a preference for a larger λ𝜆\lambdaitalic_λ (e.g., 0.5).
In the following experiments, we set λ𝜆\lambdaitalic_λ as 0.3 for DEF-A and 0.5 for GMC+. λ=... | Due to the larger compressed error introduced by RBGS compared with top-s𝑠sitalic_s when selecting the same number of components of the original vector to communicate, vanilla error feedback methods usually fail to converge. Xu and Huang (2022) propose DEF-A to solve the convergence problem by using detached error fee... | Note that the convergence guarantee of DEF-A and its momentum variant for non-convex problems is lacking in (Xu and Huang, 2022). We provide the convergence analysis for GMC+, which can be seen as a global momentum variant of DEF-A. We eliminate the assumption of ring-allreduce compatibility from (Xu and Huang, 2022) a... | D |
The sparser an activation function is the more it compresses, sometimes at the expense of reconstruction error.
However, by visual inspection of Fig. 5 one could confirm that the learned kernels of the SAN with sparser activation maps (Extrema-Pool indices and Extrema) correspond to the reoccurring patterns in the data... | Figure 3: Inverse compression ratio (CR−1𝐶superscript𝑅1CR^{-1}italic_C italic_R start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT) vs. normalized reconstruction loss (ℒ~~ℒ\tilde{\mathcal{L}}over~ start_ARG caligraphic_L end_ARG) for the 15151515 datasets of Physionet for various kernel sizes.
The five inner plots with t... | The sparser an activation function is the more it compresses, sometimes at the expense of reconstruction error.
However, by visual inspection of Fig. 5 one could confirm that the learned kernels of the SAN with sparser activation maps (Extrema-Pool indices and Extrema) correspond to the reoccurring patterns in the data... | These results suggest that reconstruction error by itself is not a sufficient metric for decomposing data in interpretable components.
Trying to solely achieve lower reconstruction error (such as the case for the Identity activation function) produces noisy learned kernels, while using the combined measure of reconstru... | Comparing the differences of φ¯¯𝜑\bar{\varphi}over¯ start_ARG italic_φ end_ARG between the Identity, the ReLU and the rest sparse activation functions in Fig. 4LABEL:sub@subfig:flithos_m we notice that the latter produce a minimum region in which we observe interpretable kernels.
| C |
\end{split}start_ROW start_CELL roman_Δ = end_CELL start_CELL italic_A italic_E divide start_ARG roman_Δ italic_P end_ARG start_ARG ∑ italic_C start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ⋅ italic_P start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ⋅ ( italic_P start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT + roman_Δ italic_P ) end_A... | The process of SPBLLA let UAVs free from message exchange. Therefore, there is no waste of energy or time consumption between two iterations, which significantly improves learning efficiency. All UAVs are altering strategies with a certain probability of ω𝜔\omegaitalic_ω, which is determined by τ𝜏\tauitalic_τ and m𝑚... |
Figure 7: Effect of dynamic degree index τ𝜏\tauitalic_τ on SPBLLA (2×1052superscript1052\times 10^{5}2 × 10 start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT iterations). The result is the same as PBLLA, which illustrates that algorithm does not affect convergence states. |
In this part, we investigate the influence of environment dynamic on the network states. With different scenarios’ dynamic degree τ∈(0,∞)𝜏0\tau\in(0,\infty)italic_τ ∈ ( 0 , ∞ ), PBLLA and SPBLLA will converge to the maximizer of goal function with different altering strategy probability. Fig. 6 presents the influence... | Figure 8: Effect of dynamic degree index τ𝜏\tauitalic_τ on SPBLLA (2×1052superscript1052\times 10^{5}2 × 10 start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT iterations). The result is the same as PBLLA, which illustrates that algorithm does not affect convergence states.
| B |
\nabla\cdot\mathbf{v}\end{array}\right)under¯ start_ARG bold_italic_π end_ARG = - italic_μ ( start_ARRAY start_ROW start_CELL 2 divide start_ARG ∂ italic_v start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT end_ARG start_ARG ∂ italic_r end_ARG - divide start_ARG 2 end_ARG start_ARG 3 end_ARG ∇ ⋅ bold_v end_CELL start_CELL ... | Π¯rsubscript¯Π𝑟\displaystyle\overline{\Pi}_{r}over¯ start_ARG roman_Π end_ARG start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT
=[−2Dr¯^∗(μ^r^(Dr^¯∗v¯r))−Dz¯^∗(μ^r^(Dr^¯∗v¯z+Dz^¯∗v¯r))]/r¯absentdelimited-[]absent2^¯𝐷𝑟^𝜇^𝑟¯^𝐷𝑟subscript¯𝑣𝑟absent^¯𝐷𝑧^𝜇^𝑟¯^𝐷𝑟subscript¯𝑣𝑧¯^𝐷𝑧subscript¯𝑣𝑟¯𝑟\displ... | Q¯πsubscript¯𝑄𝜋\displaystyle\overline{Q}_{\pi}over¯ start_ARG italic_Q end_ARG start_POSTSUBSCRIPT italic_π end_POSTSUBSCRIPT
=W¯^∗[μ^{2(Dr^¯∗v¯r)2+2(Dz^¯∗v¯z)2+(r^(∇^¯ω¯))2\displaystyle=\widehat{\overline{W}}*\biggl{[}\widehat{\mathbf{\mu}}\,\,\biggl% | =[−2Dz¯^∗(μ^r^(Dz^¯∗v¯z))−Dr¯^∗(μ^r^(Dr^¯∗v¯z+Dz^¯∗v¯r))]/r¯absentdelimited-[]absent2^¯𝐷𝑧^𝜇^𝑟¯^𝐷𝑧subscript¯𝑣𝑧absent^¯𝐷𝑟^𝜇^𝑟¯^𝐷𝑟subscript¯𝑣𝑧¯^𝐷𝑧subscript¯𝑣𝑟¯𝑟\displaystyle=\biggl{[}\underset{}{-2\widehat{\overline{Dz}}*\left(\widehat{%
\mathbf{\mu}}\,\,\widehat{r}\,\,\left(\overline{\wideh... | ∇^¯U¯¯^∇¯𝑈\displaystyle\overline{\widehat{\nabla}}\,\,\overline{U}over¯ start_ARG over^ start_ARG ∇ end_ARG end_ARG over¯ start_ARG italic_U end_ARG
=(Dr^¯∗U¯)𝐫^+(Dz^¯∗U¯)𝐳^absent¯^𝐷𝑟¯𝑈^𝐫¯^𝐷𝑧¯𝑈^𝐳\displaystyle=\left(\overline{\widehat{Dr}}*\overline{U}\right)\hat{\mathbf{r}% | A |
Let r𝑟ritalic_r be the relation on 𝒞Rsubscript𝒞𝑅\mathcal{C}_{R}caligraphic_C start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT given to the left of Figure 12.
Its abstract lattice ℒrsubscriptℒ𝑟\mathcal{L}_{r}caligraphic_L start_POSTSUBSCRIPT italic_r end_POSTSUBSCRIPT is represented to the right. | For convenience we give in Table 7 the list of all possible realities
along with the abstract tuples which will be interpreted as counter-examples to A→B𝐴→𝐵A\operatorname{\rightarrow}Bitalic_A → italic_B or B→A𝐵→𝐴B\operatorname{\rightarrow}Aitalic_B → italic_A. | The tuples t1subscript𝑡1t_{1}italic_t start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT, t4subscript𝑡4t_{4}italic_t start_POSTSUBSCRIPT 4 end_POSTSUBSCRIPT represent a counter-example to BC→A𝐵𝐶→𝐴BC\operatorname{\rightarrow}Aitalic_B italic_C → italic_A for g1subscript𝑔1g_{1}italic_g start_POSTSUBSCRIPT 1 end_POSTSUBSCRI... | If no confusion is possible, the subscript R𝑅Ritalic_R will be omitted, i.e., we will use
≤,∧,∨\leq,\operatorname{\land},\operatorname{\lor}≤ , ∧ , ∨ instead of ≤R,∧R,∨Rsubscript𝑅subscript𝑅subscript𝑅\leq_{R},\operatorname{\land}_{R},\operatorname{\lor}_{R}≤ start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT , ∧ start_P... | First, remark that both A→B𝐴→𝐵A\operatorname{\rightarrow}Bitalic_A → italic_B and B→A𝐵→𝐴B\operatorname{\rightarrow}Aitalic_B → italic_A are possible.
Indeed, if we set g=⟨b,a⟩𝑔𝑏𝑎g=\langle b,a\rangleitalic_g = ⟨ italic_b , italic_a ⟩ or g=⟨a,1⟩𝑔𝑎1g=\langle a,1\rangleitalic_g = ⟨ italic_a , 1 ⟩, then r⊧gA→... | A |
The sources of DQN variance are Approximation Gradient Error(AGE)[23] and Target Approximation Error(TAE)[24]. In Approximation Gradient Error, the error in gradient direction estimation of the cost function leads to inaccurate and extremely different predictions on the learning trajectory through different episodes b... |
To evaluate the Dropout-DQN, we employ the standard reinforcement learning (RL) methodology, where the performance of the agent is assessed at the conclusion of the training epochs. Thus we ran ten consecutive learning trails and averaged them. We have evaluated Dropout-DQN algorithm on CARTPOLE problem from the Class... |
The results in Figure 3 show that using DQN with different Dropout methods result in better-preforming policies and less variability as the reduced standard deviation between the variants indicate to. In table 1, Wilcoxon Sign-Ranked test was used to analyze the effect of Variance before applying Dropout (DQN) and aft... | To that end, we ran Dropout-DQN and DQN on one of the classic control environments to express the effect of Dropout on Variance and the learned policies quality. For the Overestimation phenomena, we ran Dropout-DQN and DQN on a Gridworld environment to express the effect of Dropout because in such environment the optim... |
Reinforcement Learning (RL) is a learning paradigm that solves the problem of learning through interaction with environments, this is a totally different approach from the other learning paradigms that have been studied in the field of Machine Learning namely the supervised learning and the unsupervised learning. Rein... | C |
Weakly supervised segmentation using image-level labels versus a few images with segmentation annotations. Most new weakly supervised localization methods apply attention maps or region proposals in a multiple instance learning formulations. While attention maps can be noisy, leading to erroneously highlighted regions... |
While most deep segmentation models for medical image analysis rely on only clinical images for their predictions, there is often multi-modal patient data in the form of other imaging modalities as well as patient metadata that can provide valuable information, which most deep segmentation models do not use. Therefore... | Deep learning has had a tremendous impact on various fields in science. The focus of the current study is on one of the most critical areas of computer vision: medical image analysis (or medical computer vision), particularly deep learning-based approaches for medical image segmentation. Segmentation is an important pr... |
We provide comprehensive coverage of research contributions in the field of semantic segmentation of natural and medical images. In terms of medical imaging modalities, we cover the literature pertaining to both 2D (RGB and grayscale) as well as volumetric medical images. |
Because of the large number of imaging modalities, the significant signal noise present in imaging modalities such as PET and ultrasound, and the limited amount of medical imaging data mainly because of high acquisition cost compounded by legal, ethical, and privacy issues, it is difficult to develop universal solutio... | A |
The best case is the bipartite graph, where the MAXCUT is known and it cuts all the graph edges.
The partition 𝐳𝐳{\mathbf{z}}bold_z found by our spectral algorithm on bipartite graphs is optimal, i.e., γ(𝐳)=MAXCUT/|ℰ|=1𝛾𝐳MAXCUTℰ1\gamma({\mathbf{z}})=\texttt{\small{MAXCUT}}{}/|\mathcal{E}|=1italic_γ ( bold_z ) = M... | From Fig. 9(b) we notice that the graphs 𝐀(1)superscript𝐀1{\mathbf{A}}^{(1)}bold_A start_POSTSUPERSCRIPT ( 1 ) end_POSTSUPERSCRIPT and 𝐀(2)superscript𝐀2{\mathbf{A}}^{(2)}bold_A start_POSTSUPERSCRIPT ( 2 ) end_POSTSUPERSCRIPT in GRACLUS have additional nodes that are disconnected.
As discussed in Sect. V, these are ... | In graphs that are close to be bipartite or, in general, that have a very sparse and regular connectivity, a large percentage of edges can be cut if the nodes are partitioned correctly.
Indeed, for these graphs the MAXCUT is usually large and is closer to the upper-bound in (11). | We recall that in those cases the MAXCUT is unknown and the gaps between the lower bound (0.5) and the upper bound (λmaxs/2subscriptsuperscript𝜆𝑠max2\lambda^{s}_{\text{max}}/2italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT / 2) can be arbitrarily large.
| We recall that in those cases the MAXCUT is unknown and the gaps between the lower bound (0.5) and the upper bound (λmaxs/2subscriptsuperscript𝜆𝑠max2\lambda^{s}_{\text{max}}/2italic_λ start_POSTSUPERSCRIPT italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT max end_POSTSUBSCRIPT / 2) can be arbitrarily large.
| B |
First, we analyze the performance of state-of-the-art methods for mapping random forests into neural networks and neural random forest imitation. The results are shown in Figure 4 for different numbers of training examples per class.
For each method, the average number of parameters of the generated networks across all... | The proposed method for generating labeled data from random forests by analyzing the decision boundaries enables training neural networks that imitate the random forests.
For instance, in the case of 5555 training examples per class, a two-hidden-layer network with 16161616 neurons in both layers already achieves the s... | Here, we additionally include decision trees, support vector machines, random forests, and neural networks in the comparison. The evaluation is performed on all nine datasets, and results for different numbers of training examples are shown (increasing from left to right). The overall performance of each method is summ... | NRFI with and without the original data is shown for different network architectures. The smallest architecture has 2222 neurons in both hidden layers and the largest 128128128128. For NRFI (gen-ori), we can see that a network with 16161616 neurons in both hidden layers (NN-16-16) is already sufficient to learn the dec... | NRFI introduces imitation instead of direct mapping. In the following, a network architecture with 32323232 neurons in both hidden layers is selected.
The previous analysis has shown that this architecture is capable of imitating the random forests (see Figure 4 for details) across all datasets and different numbers of... | C |
Theoretically, we establish the sample efficiency of OPPO in an episodic setting of Markov decision processes (MDPs) with full-information feedback, where the transition dynamics are linear in features (Yang and Wang, 2019b, a; Jin et al., 2019; Ayoub et al., 2020; Zhou et al., 2020). In particular, we allow the trans... |
We study the sample efficiency of policy-based reinforcement learning in the episodic setting of linear MDPs with full-information feedback. We proposed an optimistic variant of the proximal policy optimization algorithm, dubbed as OPPO, which incorporates the principle of “optimism in the face of uncertainty” into po... | Our work is based on the aforementioned line of recent work (Fazel et al., 2018; Yang et al., 2019a; Abbasi-Yadkori et al., 2019a, b; Bhandari and Russo, 2019; Liu et al., 2019; Agarwal et al., 2019; Wang et al., 2019) on the computational efficiency of policy optimization, which covers PG, NPG, TRPO, PPO, and AC. In p... | Moreover, we prove that, even when the reward functions are adversarially chosen across the episodes, OPPO attains the same regret in terms of competing with the globally optimal policy in hindsight (Cesa-Bianchi and Lugosi, 2006; Bubeck and Cesa-Bianchi, 2012). In comparison, existing algorithms based on value iterati... |
Broadly speaking, our work is related to a vast body of work on value-based reinforcement learning in tabular (Jaksch et al., 2010; Osband et al., 2014; Osband and Van Roy, 2016; Azar et al., 2017; Dann et al., 2017; Strehl et al., 2006; Jin et al., 2018) and linear settings (Yang and Wang, 2019b, a; Jin et al., 2019;... | C |
For instance, the prior p(𝐖)𝑝𝐖p(\mathbf{W})italic_p ( bold_W ) allows us to incorporate information about properties, such as sparsity, that we expect to be present in the DNN.
In Section 3.1.3, we review weight quantization approaches based on the Bayesian paradigm, and in Section 3.2.3, we review pruning approach... | We presented an overview of the vast literature of the highly active research area concerned with resource efficiency of DNN inference.
We have identified three major directions of research, namely (i) network quantization, (ii) network pruning, and (iii) approaches that target efficiency at the structural level. | In this section, we provide a comprehensive overview of methods that enhance the efficiency of DNNs regarding memory footprint, computation time, and energy requirements.
We have identified three different major approaches that aim to reduce the computational complexity of DNNs, i.e., (i) weight and activation quantiza... | Sparse attention mechanisms and approximations have been proposed to address this issue and improve the efficiency of transformers for longer sequences.
We refer to the work of Tay et al. (2022) which provides an overview of various transformer-based architectures that focus on efficiency, reduced memory-footprint and ... | This paper is dedicated to giving an extensive overview of the current directions of research of these approaches, all of which are concerned with reducing the model size and/or improving inference efficiency while at the same time maintaining accuracy levels close to state-of-the-art models.
We have identified three m... | B |
Take any embedding of 𝕊1superscript𝕊1\mathbb{S}^{1}blackboard_S start_POSTSUPERSCRIPT 1 end_POSTSUPERSCRIPT into ℝ4superscriptℝ4\mathbb{R}^{4}blackboard_R start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT and let ϵ>0italic-ϵ0\epsilon>0italic_ϵ > 0 be small. Consider the boundary Cϵsubscript𝐶italic-ϵC_{\epsilon}italic_C st... | Given a closed connected n𝑛nitalic_n-dimensional metric manifold M𝑀Mitalic_M and a field 𝔽𝔽\mathbb{F}blackboard_F, we define the strong filling radius sFillRad(M;𝔽)sFillRad𝑀𝔽\mathrm{sFillRad}(M;\mathbb{F})roman_sFillRad ( italic_M ; blackboard_F ) as half the length of the largest interval in the n𝑛nitalic_n-t... |
In this section, we recall the notions of spread and filling radius, as well as their relationship. In particular, we prove a number of statements about the filling radius of a closed connected manifold. Moreover, we consider a generalization of the filling radius and also define a strong notion of filling radius whic... | The reader familiar with concepts from applied algebraic topology will have noticed that the definition of strong filling radius of an n𝑛nitalic_n-dimensional metric manifold coincides with (one half of) the maximal persistence of its associated Vietoris-Rips persistence module. In fact, for each nonnegative integer k... | By invoking the relationship between the Vietoris-Rips persistent homology and the strong filling radius, one can verify that the strong filling radii of two n𝑛nitalic_n-dimensional metric manifolds M𝑀Mitalic_M and N𝑁Nitalic_N are close if these two manifolds are similar in the Gromov-Hausdorff distance sense.
| D |
A tick indicates that the tool has the corresponding features/capabilities, while a tick in parentheses means the tool offers implicit support (i.e., it could be done manually, in an ad hoc manner, but is not explicitly supported).
The table does not include works that do not contain a concrete visualization tool as th... |
VisCoDeR [22] supports the comparison between multiple projections generated by different DR techniques and parameter settings, similarly to our initial parameter exploration, using a scatterplot view with an on-top heatmap visualization for evaluating the quality of these projections. In contrast to t-viSNE, it does ... | After choosing a projection, users will proceed with the visual analysis using all the functionalities described in the next sections. However, the hyper-parameter exploration does not necessarily stop here. The top 6 representatives (according to a user-selected quality measure) are still shown at the top of the main ... | After the analysis, we decided on GEP mainly because it has a good overlap of functionalities with t-viSNE, is well-known, available online, and works correctly with user-provided data. VisCoDeR [22], for example, also provides an overlap of features, but the focus of the tool and the tasks it supports—the comparison o... | we present t-viSNE, a tool designed to support the interactive exploration of t-SNE projections (an extension to our previous poster abstract [17]). In contrast to other, more general approaches, t-viSNE was designed with the specific problems related to the investigation of t-SNE projections in mind, bringing to light... | A |
The second taxonomy classifies the reviewed algorithms based exclusively on their behavior, i.e., how they generate new candidate solutions for the function to be optimized. Our aim is to group together algorithms with similar behavior, without considering its inspirational metaphor.
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Another criterion to group SI based algorithms is the specific behavior of the animal that captured the attention of researchers and inspired the algorithm. This second criterion is also reflected in Tables 3-6, classifying each algorithm as belonging to one of the following behavioral patterns: | We believe that this dual criterion can be very useful for researchers. The first one helps classify the different proposals by their origin of inspiration, whereas the second one provides valuable information about their algorithmic similarities and differences. This double classification allows researchers to identif... |
Considering the classifications obtained in our study, we have critically examined the reviewed literature classification in the different taxonomies proposed in this work. The goal is to analyze if there is a relationship between the algorithms classified in the same category in one taxonomy and their classification ... | Comparing the two taxonomies to each other and the algorithms falling into each of their categories, it can be observed that there is not a strong relationship between them. Interestingly, this unveils that features characterizing one algorithm are loosely associated with its inspirational model. For instance, algorith... | B |
However, the existing methods are limited to graph type data while no graph is provided for general data clustering. Since a large proportion of clustering methods are based on the graph, it is reasonable to consider how to employ GCN to promote the performance of graph-based clustering methods.
In this paper, we propo... | Classical clustering models work poorly on large scale datasets. Instead, DEC and SpectralNet work better on the large scale datasets. Although GAE-based models (GAE, MGAE, and GALA) achieve impressive results on graph type datasets, they fail on the general datasets, which is probably caused by the fact that the graph... | However, the existing methods are limited to graph type data while no graph is provided for general data clustering. Since a large proportion of clustering methods are based on the graph, it is reasonable to consider how to employ GCN to promote the performance of graph-based clustering methods.
In this paper, we propo... |
Figure 1: Framework of AdaGAE. k0subscript𝑘0k_{0}italic_k start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT is the initial sparsity. First, we construct a sparse graph via the generative model defined in Eq. (7). The learned graph is employed to apply the GAE designed for the weighted graphs. After training the GAE, we update ... | (1) Via extending the generative graph models into general type data, GAE is naturally employed as the basic representation learning model and weighted graphs can be further applied to GAE as well. The connectivity distributions given by the generative perspective also inspires us to devise a novel architecture for dec... | D |
Path Maximum Transmission Unit Discovery (PMTUD) determines the MTU size on the network path between two IP hosts. The process starts by setting the Don’t Fragment (DF) bit in IP headers. Any router along the path whose MTU is smaller than the packet will drop the packet, and send back an ICMP Fragmentation Needed / P... | Methodology. The core idea of the Path MTU Discovery (PMTUD) based tool is to send the ICMP Packet too Big (PTB) message from a spoofed source IP address, belonging to the tested network, and in the 8 bytes payload of the ICMP to insert the real IP address belonging to the prober. If the network does not enforce ingres... | Methodology. We send a DNS request to the tested network from a spoofed IP address belonging to the tested network. If the network does not enforce ingress filtering, the request will arrive at the DNS resolver on that network. A query from a spoofed source IP address will cause the response to be sent to the IP addres... |
Methodology. We use services that assign globally incremental IPID values. The idea is that globally incremental IPID [RFC6864] (Touch, 2013) values leak traffic volume arriving at the service and can be measured by any Internet host. Given a server with a globally incremental IPID on the tested network, we sample the... |
Path Maximum Transmission Unit Discovery (PMTUD) determines the MTU size on the network path between two IP hosts. The process starts by setting the Don’t Fragment (DF) bit in IP headers. Any router along the path whose MTU is smaller than the packet will drop the packet, and send back an ICMP Fragmentation Needed / P... | A |
For each batch T𝑇Titalic_T from 3 through 10, the batches 1,2,…,T−112…𝑇11,2,\ldots,T-11 , 2 , … , italic_T - 1 were used to train skill NN and context+skill NN models for 30 random initializations of the starting weights. The accuracy was measured classifying examples from batch T𝑇Titalic_T (Fig. 3A, Table 1, Skill... |
The purpose of this study was to demonstrate that explicit representation of context can allow a classification system to adapt to sensor drift. Several gas classifier models were placed in a setting with progressive sensor drift and were evaluated on samples from future contexts. This task reflects the practical goal... |
Second, skill NN and context+skill NN models were compared. The context-based network extracts features from preceding batches in sequence in order to model how the sensors drift over time. When added to the feedforward NN representation, such contextual information resulted in improved ability to compensate for senso... | An alternative approach is to emulate adaptation in natural sensor systems. The system expects and automatically adapts to sensor drift, and is thus able to maintain its accuracy for a long time. In this manner, the lifetime of sensor systems can be extended without recalibration.
| While natural systems cope with changing environments and embodiments well, they form a serious challenge for artificial systems. For instance, to stay reliable over time, gas sensing systems must be continuously recalibrated to stay accurate in a changing physical environment. Drawing motivation from nature, this pape... | A |
Let ti+∈𝒯+subscriptsuperscript𝑡𝑖superscript𝒯t^{+}_{i}\in\mathcal{T}^{+}italic_t start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ∈ caligraphic_T start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT, and let q1subscript𝑞1q_{1}italic_q start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT be a poi... | Case (ii): p∈P[st+(i−1)−5k2+1,st(i)−5k2]𝑝𝑃𝑠superscript𝑡𝑖15superscript𝑘21normal-st𝑖5superscript𝑘2p\in P[st^{+}\mkern-2.0mu(i-1)-5k^{2}+1,\mathrm{st}(i)-5k^{2}]italic_p ∈ italic_P [ italic_s italic_t start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT ( italic_i - 1 ) - 5 italic_k start_POSTSUPERSCRIPT 2 end_POSTSU... | A(3)[i,q1,q2]:={The length of the shortest path from q1 to q2 that visits all points in P[1,st(i)], such that the neighbour of q2 is a point in P[1,st(i)−5k2].assignsuperscript𝐴3𝑖subscript𝑞1subscript𝑞2casesThe length of the shortest path from q1 to q2 that visits all points in P[1,st(i)], such that the neig... | st}(i)]$, such that the neighbour of $q_{2}$ is a point in $P[1,\mathrm{st}(i)%
-5k^{2}]$.}\end{cases}italic_A start_POSTSUPERSCRIPT ( 3 ) end_POSTSUPERSCRIPT [ italic_i , italic_q start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , italic_q start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT ] := { start_ROW start_CELL The length of the sh... | Not shown is the property that the neighbour of q2subscript𝑞2q_{2}italic_q start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT is a point in P[1,st(i)−5k2]𝑃1st𝑖5superscript𝑘2P[1,\mathrm{st}(i)-5k^{2}]italic_P [ 1 , roman_st ( italic_i ) - 5 italic_k start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ].
| B |
There are quite a few results on free (and related) products of self-similar or automaton groups (again see [15] for an overview) but many of them present the product as a subgroup of an automaton/self-similar group and, thus, loose the self-similarity property. An exception here is a line of research based on the Bel... |
There are quite a few results on free (and related) products of self-similar or automaton groups (again see [15] for an overview) but many of them present the product as a subgroup of an automaton/self-similar group and, thus, loose the self-similarity property. An exception here is a line of research based on the Bel... | While our main result significantly relaxes the hypothesis for showing that the free product of self-similar semigroups (or automaton semigroups) is self-similar (an automaton semigroup), it does not settle the underlying question whether these semigroup classes are closed under free product. It is possible that there ... | from one to the other, then their free product S⋆T⋆𝑆𝑇S\star Titalic_S ⋆ italic_T is an automaton semigroup (8). This is again a strict generalization of [19, Theorem 3.0.1] (even if we only consider complete automata).
Third, we show this result in the more general setting of self-similar semigroups111Note that the c... | However, there do not seem to be constructions for presenting arbitrary free products of self-similar groups in a self-similar way. For semigroups, on the other hand, such results do exist. In fact, the free product of two automaton semigroups S𝑆Sitalic_S and T𝑇Titalic_T is always at least
very close to being an auto... | D |
Here, we study these methods. We find that their improved accuracy does not actually emerge from proper visual grounding, but from regularization effects, where the model forgets the linguistic priors in the train set, thereby performing better on the test set. To support these claims, we first show that it is possible... | It is also interesting to note that the drop in training accuracy is lower with this regularization scheme as compared to the state-of-the-art methods. Of course, if any model was actually visually grounded, then we would expect it to improve performances on both train and test sets. We do not observe such behavior in ... |
Based on these observations, we hypothesize that controlled degradation on the train set allows models to forget the training priors to improve test accuracy. To test this hypothesis, we introduce a simple regularization scheme that zeros out the ground truth answers, thereby always penalizing the model, whether the p... |
The usage of visual cues and sensitivities in existing methods is superfluous because the results indicate that performance improves through degradation of training accuracy. We hypothesize that simple regularization that does not rely on cues or sensitivities can also achieve large performance gains for VQA-CP. To te... | Here, we study these methods. We find that their improved accuracy does not actually emerge from proper visual grounding, but from regularization effects, where the model forgets the linguistic priors in the train set, thereby performing better on the test set. To support these claims, we first show that it is possible... | B |
For the question answering task, we leveraged the PrivacyQA corpus (Ravichander et al., 2019). PrivacyQA consists of 1,750 questions about the contents of privacy policies from 35 privacy documents. While crowdworkers were asked to come up with privacy related questions based on public information about an application... |
In order to address the requirement of a language model for the privacy domain, we created PrivBERT. BERT is a contextualized word representation model that is pretrained using bidirectional transformers (Devlin et al., 2019). It was pretrained on the masked language modelling and the next sentence prediction tasks an... | Modern robust language models, such as transformer-based architectures, benefit from increasingly large training sets. These models can be used on downstream tasks (Devlin et al., 2019) to improve performance. Results have shown that in-domain fine tuning of such pre-trained language models have produced a significant ... |
Table 3 shows the results for the answer sentence selection task comparing the performance between BERT and PrivBERT. Results from BERT are as reported by Ravichander et al. (2019). PrivBERT achieves state of the art results improving on the results of BERT by about 6%. PrivBERT therefore has been shown to achieve sta... | Table 2 shows the results for the data practice classification task comparing the performance between RoBERTa, PrivBERT and Polisis (Harkous et al., 2018), a CNN based classification model. We report reproduced results for Polisis since the original paper takes into account both the presence and absence of a label whil... | C |
Following our design goals and derived analytical tasks, we implemented StackGenVis, an interactive VA system that allows users to build powerful stacking ensembles from scratch. Our system consists of six main interactive visualization panels (see StackGenVis: Alignment of Data, Algorithms, and Models for Stacking En... | and (v) we track the history of the previously stored stacking ensembles in StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(b) and compare their performances against the active stacking ensemble—the one not yet stored in the history—in StackGenVis: Alignme... | (ii) in the next algorithm exploration phase, we compare and choose specific ML algorithms for the ensemble and then proceed with their particular instantiations, i.e., the models;
(iii) during the data wrangling phase, we manipulate the instances and features with two different views for each of them; (iv) model explo... | Predictions’ Space.
The goal of the predictions’ space visualization (StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics(f)) is to show an overview of the performance of all models of the current stack for different instances. | The model exploration phase is perhaps the most important step on the way to build a good ensemble. It focuses on comparing and exploring different models both individually and in groups. Due to the page limits, we now assume that we selected the most performant models, removed the remaining from the stack, and reached... | B |
We thus have 3333 cases, depending on the value of the tuple
(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))𝑝𝑣delimited-[]010𝑝𝑣delimited-[]323𝑝𝑣delimited-[]313𝑝𝑣delimited-[]003(p(v,[010]),p(v,[323]),p(v,[313]),p(v,[003]))( italic_p ( italic_v , [ 010 ] ) , italic_p ( italic_v , [ 323 ] ) , italic_p ( italic_v... | {0¯,1¯,2¯,3¯,[013],[010],[323],[313],[112],[003],[113]}.¯0¯1¯2¯3delimited-[]013delimited-[]010delimited-[]323delimited-[]313delimited-[]112delimited-[]003delimited-[]113\{\overline{0},\overline{1},\overline{2},\overline{3},[013],[010],[323],[313],%
[112],[003],[113]\}.{ over¯ start_ARG 0 end_ARG , over¯ start_ARG 1 end... | Then, by using the adjacency of (v,[013])𝑣delimited-[]013(v,[013])( italic_v , [ 013 ] ) with each of
(v,[010])𝑣delimited-[]010(v,[010])( italic_v , [ 010 ] ), (v,[323])𝑣delimited-[]323(v,[323])( italic_v , [ 323 ] ), and (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), we can confirm that | p(v,[013])=p(v,[313])=p(v,[113])=1𝑝𝑣delimited-[]013𝑝𝑣delimited-[]313𝑝𝑣delimited-[]1131p(v,[013])=p(v,[313])=p(v,[113])=1italic_p ( italic_v , [ 013 ] ) = italic_p ( italic_v , [ 313 ] ) = italic_p ( italic_v , [ 113 ] ) = 1.
Similarly, when f=[112]𝑓delimited-[]112f=[112]italic_f = [ 112 ], | By using the pairwise adjacency of (v,[112])𝑣delimited-[]112(v,[112])( italic_v , [ 112 ] ), (v,[003])𝑣delimited-[]003(v,[003])( italic_v , [ 003 ] ), and
(v,[113])𝑣delimited-[]113(v,[113])( italic_v , [ 113 ] ), we can confirm that in the 3333 cases, these | D |
For both BLEU and C Score, Jac Score is around 1 in each cluster, which means the persona descriptions are not similar. The dialogue quantity also seems similar among different clusters. So we can conclude that data quantity and task profile does not have a major impact on the fine-tuning process.
| Data Quantity. In Persona, we evaluate Transformer/CNN, Transformer/CNN-F and MAML on 3 data quantity settings: 50/100/120-shot (each task has 50, 100, 120 utterances on average). In Weibo, FewRel and Amazon, the settings are 500/1000/1500-shot, 3/4/5-shot and 3/4/5-shot respectively (Table 2).
When the data quantity i... |
To answer RQ1, we compare the changing trend of the general language model and the task-specific adaptation ability during the training of MAML to find whether there is a trade-off problem. (Figure 1) We select the trained parameter initialization at different MAML training epochs and evaluate them directly on the met... | Task similarity. In Persona and Weibo, each task is a set of dialogues for one user, so tasks are different from each other. We shuffle the samples and randomly divide tasks to construct the setting that tasks are similar to each other. For a fair comparison, each task on this setting also has 120 and 1200 utterances o... | To answer RQ3, we conduct experiments on different data quantity and task similarity settings. We compare two baselines with MAML :
Transformer/CNN, which pre-trains the base model (Transformer/CNN) on the meta-training set and evaluates directly on the meta-testing set, and Transformer/CNN-F, which fine-tunes Transfor... | D |
In addition, the AOAs and AODs should be tracked in the highly dynamic UAV mmWave network.
To this end, in Section IV we will further propose a novel predictive AOA/AOD tracking scheme in conjunction with tracking error treatment to address the high mobility challenge, then we integrate these operations into the codebo... |
The specialized codebook design of the DRE-covered CCA for multi-UAV mobile mmWave communications. Under the guidance of the proposed framework, a novel hierarchical codebook is designed to encompass both the subarray patterns and beam patterns. The newly proposed CA codebook can fully exploit the potentials of the DR... |
The rest of this paper is as follows. In Section II, the system model is introduced. In Section III, the CCA codebook design and the codebook-based joint subarray partition and AWV selection algorithms are proposed. Next, the TE-aware codebook-based beam tracking with 3D beamwidth control is further proposed in Sectio... | After the discussion on the characteristics of CCA, in this subsection, we continue to explain the specialized codebook design for the DRE-covered CCA. Revisiting Theorem 1 and Theorem 3, the size and position of the activated CCA subarray are related to the azimuth angle; meanwhile, the beamwidth is determined by the ... |
In this section, we characterize the CCA from several relevent aspects in III-A and design a specialized hierarchical codebook for the DRE-covered CCA in III-B, wherein the subarray activation/partitioning patterns (in terms of subarray location and size) are carefully integrated with the angular domain beam patterns ... | D |
We start in this section by giving proofs only for the 1111-color case, without the completeness requirement. While this case does not directly correspond to any formula used in the proof of Theorem 3.7 (since matrices (4) have 2 rows even when there are no binary predicates), this case gives the flavor of the argument... | To conclude this section, we stress that although the 1111-color case contains many of the key ideas, the multi-color case requires a finer
analysis to deal with the “big enough” case, and also may benefit from a reduction that allows one to restrict | We start in this section by giving proofs only for the 1111-color case, without the completeness requirement. While this case does not directly correspond to any formula used in the proof of Theorem 3.7 (since matrices (4) have 2 rows even when there are no binary predicates), this case gives the flavor of the argument... | This will be bootstrapped to the multi-color case in later sections. Note that the 1111-color case with the completeness requirement is not very interesting, and also not useful for the general case: completeness states that every node on
the left must be connected, via the unique edge relation, to every node on the ri... | The requirement that M¯|N¯conditional¯𝑀¯𝑁\bar{M}|\bar{N}over¯ start_ARG italic_M end_ARG | over¯ start_ARG italic_N end_ARG is extra big enough ensures that we have enough edges to perform the edge swapping.
This completes the proof for case 2 when the assumptions (a1) and (a2) hold. | C |
Let the initial distribution ρ0subscript𝜌0\rho_{0}italic_ρ start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT be the standard Gaussian distribution N(0,ID)𝑁0subscript𝐼𝐷N(0,I_{D})italic_N ( 0 , italic_I start_POSTSUBSCRIPT italic_D end_POSTSUBSCRIPT ). Under certain regularity conditions, ρ^⌊t/ϵ⌋(m)superscriptsubscript^𝜌𝑡it... | Szepesvári, 2018; Dalal et al., 2018; Srikant and Ying, 2019) settings. See Dann et al. (2014) for a detailed survey. Also, when the value function approximator is linear, Melo et al. (2008); Zou et al. (2019); Chen et al. (2019b) study the convergence of Q-learning. When the value function approximator is nonlinear, T... | The proof of Proposition 3.1 is based on the propagation of chaos (Sznitman, 1991; Mei et al., 2018, 2019).
In contrast to Mei et al. (2018, 2019), the PDE in (3.4) can not be cast as a gradient flow, since there does not exist a corresponding energy functional. Thus, their analysis is not directly applicable to our se... | Meanwhile, our analysis is related to the recent breakthrough in the mean-field analysis of stochastic gradient descent (SGD) for the supervised learning of an overparameterized two-layer neural network (Chizat and Bach, 2018b; Mei et al., 2018, 2019; Javanmard et al., 2019; Wei et al., 2019; Fang et al., 2019a, b; Che... | The key to our analysis is a mean-field perspective, which allows us to associate the evolution of a finite-dimensional parameter with its limiting counterpart over an infinite-dimensional Wasserstein space (Villani, 2003, 2008; Ambrosio et al., 2008; Ambrosio and Gigli, 2013). Specifically, by exploiting the permutati... | B |
Table 5 shows that: 1) Sharing parameters for the computation (Equation 6) of the depth-wise LSTM hidden state significantly hampers performance, which is consistent with our conjecture. 2) Sharing parameters for the computation of gates (Equations 2, 3, 4) leads to slightly higher BLEU with fewer parameters introduce... | It is a common problem that increasing the depth does not always lead to better performance, whether with residual connections Li et al. (2022b) or other previous studies on deep Transformers Bapna et al. (2018); Wang et al. (2019); Li et al. (2022a), and the use of wider models is the usual method of choice for furthe... |
We implemented our approach based on the Neutron implementation of the Transformer Xu and Liu (2019). To show the effects of depth-wise LSTMs on the 6-layer Transformer, we first conducted experiments on the WMT 14 English to German and English to French news translation tasks to compare with the Transformer baseline ... |
Our approach with the Transformer base setting brings about more improvements on the English-German task than that on the English-French task. We conjecture that maybe because the performance on the English-French task using a large dataset (∼similar-to\sim∼36363636M sentence pairs) may rely more on the capacity of th... |
We examine whether depth-wise LSTM has the ability to ensure the convergence of deep Transformers and measure performance on the WMT 14 English to German task and the WMT 15 Czech to English task following Bapna et al. (2018); Xu et al. (2020a), and compare our approach with the pre-norm Transformer in which residual ... | D |
A∈⟦φ⟧XA\in\llbracket\varphi\rrbracket_{X}italic_A ∈ ⟦ italic_φ ⟧ start_POSTSUBSCRIPT italic_X end_POSTSUBSCRIPT and B𝐵Bitalic_B is a σσ\upsigmaroman_σ-structure in X𝑋Xitalic_X such
that A≤B𝐴𝐵A\leq Bitalic_A ≤ italic_B, then B∈⟦φ⟧XB\in\llbracket\varphi\rrbracket_{X}italic_B ∈ ⟦ italic_φ ⟧ start_POSTSUBSCRIPT italic_... | (a1,…,an)∈𝐑Asubscript𝑎1…subscript𝑎𝑛superscript𝐑𝐴(a_{1},\dots,a_{n})\in\mathbf{R}^{\!A}( italic_a start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_a start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ) ∈ bold_R start_POSTSUPERSCRIPT italic_A end_POSTSUPERSCRIPT, (f(a1),…,f(an))∈𝐑B𝑓subscript𝑎1…𝑓subscript𝑎𝑛s... | and such that (a1,…,an)∈𝐑f(A)⇔A⊧ρR(a1,…,an)iffsubscript𝑎1…subscript𝑎𝑛superscript𝐑𝑓𝐴models𝐴subscript𝜌𝑅subscript𝑎1…subscript𝑎𝑛(a_{1},\dots,a_{n})\in\mathbf{R}^{\!f(A)}\iff A\models\rho_{R}(a_{1},\dots,a_{%
n})( italic_a start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_a start_POSTSUBSCRIPT italic_n end... | by |fi(A)|≜|A|≜subscript𝑓𝑖𝐴𝐴|f_{i}(A)|\triangleq|A|| italic_f start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT ( italic_A ) | ≜ | italic_A | and (a1,…,an)∈𝐑fi(A)subscript𝑎1…subscript𝑎𝑛superscript𝐑subscript𝑓𝑖𝐴(a_{1},\dots,a_{n})\in\mathbf{R}^{\!f_{i}(A)}( italic_a start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … ... | (a1,…,an)∈|A|nsubscript𝑎1…subscript𝑎𝑛superscript𝐴𝑛(a_{1},\dots,a_{n})\in|A|^{n}( italic_a start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT , … , italic_a start_POSTSUBSCRIPT italic_n end_POSTSUBSCRIPT ) ∈ | italic_A | start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT, (f(a1),…,f(an))∈𝐑B𝑓subscript𝑎1…𝑓subscript𝑎𝑛sup... | A |
IMAGES captured by wide-angle camera usually suffer from a strong distortion, which influences the important scene perception tasks such as the object detection and recognition [1, 2, 3], semantic segmentation [4, 5], and image denoising [6, 7]. The distortion rectification tries to recover the real geometric attribut... | In particular, we redesign the whole pipeline of deep distortion rectification and present an intermediate representation based on the distortion parameters. The comparison of the previous methods and the proposed approach is illustrated in Fig. 1. Our key insight is that distortion rectification can be cast as a probl... | Accurately estimating the distortion parameters derived from a specific camera, is a crucial step in distortion rectification. However, two main limitations that make the distortion parameters learning challenging. (i) The distortion parameters are not observable and hard to learn from a single distorted image, such as... |
In contrast to the long history of traditional distortion rectification, learning methods began to study distortion rectification in the last few years. Rong et al. [8] quantized the values of the distortion parameter to 401 categories based on the one-parameter camera model [22] and then trained a network to classify... | Previous learning methods directly regress the distortion parameters from a distorted image. However, such an implicit and heterogeneous representation confuses the distortion learning of neural networks and causes the insufficient distortion perception. To bridge the gap between image feature and calibration objective... | B |
The momentum coefficient is set as 0.9 and the weight decay is set as 0.001. The initial learning rate is selected from {0.001,0.01,0.1}0.0010.010.1\{0.001,0.01,0.1\}{ 0.001 , 0.01 , 0.1 } according to the performance on the validation set. We do not adopt any learning rate decay or warm-up strategies.
The model is tra... | Figure 2 shows the learning curves of the five methods. We can observe that in the small-batch training, SNGM and other large-batch training methods achieve similar performance in terms of training loss and test accuracy as MSGD.
In large-batch training, SNGM achieves better training loss and test accuracy than the fou... | Hence, with the same number of gradient computations, SNGM can adopt a larger batch size than MSGD to converge to the ϵitalic-ϵ\epsilonitalic_ϵ-stationary point.
Empirical results on deep learning further verify that SNGM can achieve better test accuracy than MSGD and other state-of-the-art large-batch training methods... | Table 6 shows the test perplexity of the three methods with different batch sizes. We can observe that for small batch size, SNGM achieves test perplexity comparable to that of MSGD, and for large batch size, SNGM is better than MSGD. Similar to the results of image classification, SNGM outperforms LARS for different b... | showed that existing SGD methods with a large batch size will lead to a drop in the generalization accuracy of deep learning models. Figure 1
shows a comparison of training loss and test accuracy between MSGD with a small batch size and MSGD with a large batch size. We can find that large-batch training indeed | B |
The other three results are based on a reduction to a single-stage, deterministic robust outliers problem described in Section 4; namely, convert any ρ𝜌\rhoitalic_ρ-approximation algorithm for the robust outlier problem into a (ρ+2)𝜌2(\rho+2)( italic_ρ + 2 )-approximation algorithm for the corresponding two-stage sto... | The other three results are based on a reduction to a single-stage, deterministic robust outliers problem described in Section 4; namely, convert any ρ𝜌\rhoitalic_ρ-approximation algorithm for the robust outlier problem into a (ρ+2)𝜌2(\rho+2)( italic_ρ + 2 )-approximation algorithm for the corresponding two-stage sto... | We now describe a generic method of transforming a given 𝒫𝒫\mathcal{P}caligraphic_P-Poly problem into a single-stage deterministic robust outlier problem. This will give us a 5-approximation algorithm for homogeneous 2S-MuSup and 2S-MatSup instances nearly for free; in the next section, we also use it obtain our 11-a... |
In this section we tackle the simplest problem setting, designing an efficiently-generalizable 3333-approximation algorithm for homogeneous 2S-Sup-Poly. To begin, we are given a list of scenarios Q𝑄Qitalic_Q together with their probabilities pAsubscript𝑝𝐴p_{A}italic_p start_POSTSUBSCRIPT italic_A end_POSTSUBSCRIPT,... |
We follow up with 3333-approximations for the homogeneous robust outlier MatSup and MuSup problems, which are slight variations on algorithms of [6] (specifically, our approach in Section 4.1 is a variation on their solve-or-cut methods). In Section 5, we describe a 9-approximation algorithm for an inhomogeneous MatSu... | D |
The ways to deal with the convex cost functions with bounded or Lipschitz continuous (sub)gradients employ the boundness or Lipschitz continuity of the (sub)gradients, respectively ([4], [7], [13]-[17]).
In [13], the gradients of local cost functions satisfy Lipschitz continuity, in which, the key step of analyzing the... | That is, the mean square error at the next time can be controlled by that at the
previous time and the consensus error. However, this can not be obtained for the case with the linearly growing subgradients. Also, different from [15], the subgradients are not required to be bounded and the inequality (28) in [15] does n... | As a result, the existing methods are no longer applicable. In fact, the inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditional mean square error, which leads the nonegative supermartingale converg... | I. The local cost functions in this paper are not required to be differentiable and the subgradients only satisfy the linear growth condition.
The inner product of the subgradients and the error between local optimizers’ states and the global optimal solution inevitably exists in the recursive inequality of the conditi... | (Lemma 3.1).
To this end, we estimate the upper bound of the mean square increasing rate of the local optimizers’ states at first (Lemma 3.2). Then we substitute this upper bound into the Lyapunov function difference inequality of the consensus error, and obtain the estimated convergence rate of mean square consensus (... | A |
This experiment measures the information loss of MuCo. Note that, the mechanism of MuCo is much more different from that of generalization. Thus, for the sake of fairness, we compare the information loss of MuCo and Mondrian when they provide the same level of protections. Then, the experiment measures the effectivene... |
We observe that the results of MuCo are much better than that of Mondrian and Anatomy. The primary reason is that MuCo retains the most distributions of the original QI values and the results of queries are specific records rather than groups. Consequently, the accuracy of query answering of MuCo is much better and mo... |
Results from Figure 10 show that the increase of l𝑙litalic_l lowers the information loss but raises the relative error rate. It is mainly because the number of tuples in each group increases with the growth of l𝑙litalic_l. On the one hand, in random output tables, the probabilities that tuples have to cover on the Q... |
Observing from Figure 7(a), the information loss of MuCo increases with the decrease of parameter δ𝛿\deltaitalic_δ. According to Corollary 3.2, each QI value in the released table corresponds to more records with the reduction of δ𝛿\deltaitalic_δ, causing that more records have to be involved for covering on the QI ... |
This experiment measures the information loss of MuCo. Note that, the mechanism of MuCo is much more different from that of generalization. Thus, for the sake of fairness, we compare the information loss of MuCo and Mondrian when they provide the same level of protections. Then, the experiment measures the effectivene... | C |
In this section, we introduce our practice on three competitive segmentation methods including HTC, SOLOv2 and PointRend. We show step-by-step modifications adopted on PointRend, which achieves better performance and outputs much smoother instance boundaries than other methods.
| Bells and Whistles. MaskRCNN-ResNet50 is used as baseline and it achieves 53.2 mAP. For PointRend, we follow the same setting as Kirillov et al. (2020) except for extracting both coarse and fine-grained features from the P2-P5 levels of FPN, rather than only P2 described in the paper. Surprisingly, PointRend yields 62.... | HTC is known as a competitive method for COCO and OpenImage. By enlarging the RoI size of both box and mask branches to 12 and 32 respectively for all three stages, we gain roughly 4 mAP improvement against the default settings in original paper. Mask scoring head Huang et al. (2019) adopted on the third stage gains an... |
Due to limited mask representation of HTC, we move on to SOLOv2, which utilizes much larger mask to segment objects. It builds an efficient yet simple instance segmentation framework, outperforming other segmentation methods like TensorMask Chen et al. (2019c), CondInst Tian et al. (2020) and BlendMask Chen et al. (20... | Deep learning has achieved great success in recent years Fan et al. (2019); Zhu et al. (2019); Luo et al. (2021, 2023); Chen et al. (2021). Recently, many modern instance segmentation approaches demonstrate outstanding performance on COCO and LVIS, such as HTC Chen et al. (2019a), SOLOv2 Wang et al. (2020), and PointRe... | B |
For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| For the significance of this conjecture we refer to the original paper [FK], and to Kalai’s blog [K] (embedded in Tao’s blog) which reports on all significant results concerning the conjecture. [KKLMS] establishes a weaker version of the conjecture. Its introduction is also a good source of information on the problem.
| We denote by εi:{−1,1}n→{−1,1}:subscript𝜀𝑖→superscript11𝑛11\varepsilon_{i}:\{-1,1\}^{n}\to\{-1,1\}italic_ε start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT : { - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT → { - 1 , 1 } the projection onto the i𝑖iitalic_i-s coordinate: εi(δ1,…,δn)=δisubscript𝜀𝑖subsc... |
Here we give an embarrassingly simple presentation of an example of such a function (although it can be shown to be a version of the example in the previous version of this note). As was written in the previous version, an anonymous referee of version 1 wrote that the theorem was known to experts but not published. Ma... |
In version 1 of this note, which can still be found on the ArXiv, we showed that the analogous version of the conjecture for complex functions on {−1,1}nsuperscript11𝑛\{-1,1\}^{n}{ - 1 , 1 } start_POSTSUPERSCRIPT italic_n end_POSTSUPERSCRIPT which have modulus 1111 fails. This solves a question raised by Gady Kozma s... | D |
In this section, we describe our proposed algorithm LSVI-UCB-Restart, and discuss how to tune the hyper-parameters for cases when local variation is known or unknown. For both cases, we present their respective regret bounds. Detailed proofs are deferred to Appendix B. Note that our algorithms are all designed for inh... |
After showing the action-value function estimate is the optimistic upper bound of the optimal action-value function, we can derive the dynamic regret bound within one epoch via recursive regret decomposition. The dynamic regret within one epoch for Algorithm 1 with the knowledge of B𝜽,ℰsubscript𝐵𝜽ℰB_{\bm{\theta},\m... |
In practice, the transition function ℙℙ\mathbb{P}blackboard_P is unknown, and the state space might be so large that it is impossible for the learner to fully explore all states. If we parametrize the action-value function in a linear form as ⟨ϕ(⋅,⋅),𝒘⟩bold-italic-ϕ⋅⋅𝒘\langle\bm{\phi}(\cdot,\cdot),\bm{w}\rangle⟨ bo... |
Our proposed algorithm LSVI-UCB-Restart has two key ingredients: least-squares value iteration with upper confidence bound to properly handle the exploration-exploitation trade-off (Jin et al., 2020), and restart strategy to adapt to the unknown nonstationarity. Our algorithm is summarized in Algorithm 1. From a high-... |
In this paper, we studied nonstationary RL with time-varying reward and transition functions. We focused on the class of nonstationary linear MDPs such that linear function approximation is sufficient to realize any value function. We first incorporated the epoch start strategy into LSVI-UCB algorithm (Jin et al., 202... | C |
Fake news is news articles that are “either wholly false or containing deliberately misleading elements incorporated within its content or context” (Bakir and McStay, 2018). The presence of fake news has become more prolific on the Internet due to the ease of production and dissemination of information online (Shu et a... | Singapore is a city-state with an open economy and diverse population that shapes it to be an attractive and vulnerable target for fake news campaigns (Lim, 2019). As a measure against fake news, the Protection from Online Falsehoods and Manipulation Act (POFMA) was passed on May 8, 2019, to empower the Singapore Gover... |
In general, respondents possess a competent level of digital literacy skills with a majority exercising good news sharing practices. They actively verify news before sharing by checking with multiple sources found through the search engine and with authoritative information found in government communication platforms,... | While fake news is not a new phenomenon, the 2016 US presidential election brought the issue to immediate global attention with the discovery that fake news campaigns on social media had been made to influence the election (Allcott and Gentzkow, 2017). The creation and dissemination of fake news is motivated by politic... | Fake news is news articles that are “either wholly false or containing deliberately misleading elements incorporated within its content or context” (Bakir and McStay, 2018). The presence of fake news has become more prolific on the Internet due to the ease of production and dissemination of information online (Shu et a... | A |
We conduct experiments to investigate the performance gain concerning entity degrees. Typically, an entity with a higher degree indicates that it has more neighboring entities. Consequently, the computation of attention scores to aggregate these neighbors becomes crucial.
|
We conduct experiments to explore the impact of the numbers of unseen entities on the performance in open-world entity alignment. We present the results on the ZH-EN datasets in Figure 6. Clearly, the performance gain achieved by leveraging our method significantly increases when there are more unseen entities. For ex... | Figure 4 shows the experimental results. decentRL outperforms both GAT and AliNet across all metrics. While its performance slightly decreases compared to conventional datasets, the other methods experience even greater performance drops in this context. AliNet also outperforms GAT, as it combines GCN and GAT to aggreg... |
The results on the ZH-EN dataset are depicted in Figure 7. For entities with only a few neighbors, the advantage of leveraging DAN is not significant. However, as the degree increases, incorporating DAN yields more performance gain. This upward trend halts until the degree exceeds 20. Overall, DAN exhibits significant... | Table 4 presents the results of conventional entity alignment. decentRL achieves state-of-the-art performance, surpassing all others in Hits@1 and MRR. AliNet [39], a hybrid method combining GCN and GAT, performs better than the methods solely based on GAT or GCN on many metrics. Nonetheless, across most metrics and da... | C |
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